Data Analysis for Risk Management – Economics, Finance and Business
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Jajuga, Krzysztof (Ed.); Dziechciarz, Józef (Ed.) Book Data Analysis for Risk Management – Economics, Finance and Business Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Jajuga, Krzysztof (Ed.); Dziechciarz, Józef (Ed.) (2024) : Data Analysis for Risk Management – Economics, Finance and Business, ISBN 9783725814169, MDPI - Multidisciplinary Digital Publishing Institute, Basel, https://doi.org/10.3390/books978-3-7258-1415-2 This Version is available at: https://hdl.handle.net/10419/312693 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/
mdpi.com/journal/risks Special Issue Reprint Data Analysis for Risk Management - Economics, Finance and Business Edited by Krzysztof Jajuga and Józef Dziechciarz
Data Analysis for Risk Management—Economics, Finance and Business
Data Analysis for Risk Management—Economics, Finance and Business Editors Krzysztof Jajuga J´ozef Dziechciarz Basel •Beijing •Wuhan •Barcelona •Belgrade •Novi Sad •Cluj •Manchester
Editors Krzysztof Jajuga Department of Financial Investments and Risk Management Wroclaw University of Economics and Business Wroclaw Poland J´ ozef Dziechciarz Department of Econometrics and Operations Research Wroclaw University of Economics and Business Wroclaw Poland Editorial Office MDPI St. Alban-Anlage 66 4052 Basel, Switzerland This is a reprint of articles from the Special Issue published online in the open access journal Risks (ISSN 2227-9091) (available at: https://www.mdpi.com/journal/risks/special issues/Data Analysis for Risk Management). For citation purposes, cite each article independently as indicated on the article page online and as indicated below: Lastname, Firstname, Firstname Lastname, and Firstname Lastname. Article Title. Journal Name Year, Volume Number, Page Range. ISBN 978-3-7258-1416-9 (Hbk) ISBN 978-3-7258-1415-2 (PDF) doi.org/10.3390/books978-3-7258-1415-2 © 2024 by the authors. Articles in this book are Open Access and distributed under the Creative Commons Attribution (CC BY) license. The book as a whole is distributed by MDPI under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs (CC BY-NC-ND) license.
Contents About the Editors ..............................................vii Preface .................................................... ix Krzysztof Jajuga Data Analysis for Risk Management—Economics, Finance and Business: New Developments and Challenges Reprinted from: Risks 2023,11, 70, doi:10.3390/risks11040070 ..................... 1 Joanna G´orka and Katarzyna Kuziak Volatility Modeling and Dependence Structure of ESG and Conventional Investments Reprinted from: Risks 2022,10, 20, doi:10.3390/risks10010020 ..................... 6 Victor Shevchuk and Roman Kopych Exchange Rate Volatility, Currency Misalignment, and Risk of Recession in the Central and Eastern European Countries Reprinted from: Risks 2021,9, 82, doi:10.3390/risks9050082 ...................... 31 Ewa Dziwok and Marta A. Kara´s Systemic Illiquidity Noise-Based Measure—A Solution for Systemic Liquidity Monitoring in Frontier and Emerging Markets Reprinted from: Risks 2021,9, 124, doi:10.3390/risks9070124 ..................... 50 Orlando Rivera-Escobar, John Willmer Escobar and Diego Fernando Manotas Measurement of Systemic Risk in the Colombian Banking Sector Reprinted from: Risks 2022,10, 22, doi:10.3390/risks10010022 ..................... 79 Aneta Ptak-Chmielewska and Paweł Kopciuszewski New Definition of Default—Recalibration of Credit Risk Models Using Bayesian Approach Reprinted from: Risks 2022,10, 16, doi:10.3390/risks10010016 .....................106 Tomasz Berent and Radosław Rejman Bankruptcy Prediction with a Doubly Stochastic Poisson Forward Intensity Model and Low-Quality Data Reprinted from: Risks 2021,9, 217, doi:10.3390/risks9120217 .....................122 Aldona Fraczkiewicz-Wronka, Tomasz Ingram, Karolina Szymaniec-Mlicka and Piotr Tworek Risk Management and Financial Stability in the Polish Public Hospitals: The Moderating Effect of the Stakeholders’ Engagement in the Decision-Making Reprinted from: Risks 2021,9, 87, doi:10.3390/risks9050087 ......................146 Yaser Ahmad Arabyat, Ahmad Ali AlZubi, Dyala M. Aldebei and Samerra’a Ziad Al-oqaily An Efficient Method for Pricing Analysis Based on Neural Networks Reprinted from: Risks 2022,10, 151, doi:10.3390/risks10080151 ....................169 Gero Szepannek An Overview on the Landscape of R Packages for Open Source Scorecard Modelling Reprinted from: Risks 2022,10, 67, doi:10.3390/risks10030067 .....................183 Adam ´ Sliwi´nski, Joanna Dropia and Norbert Duczkowski Risk Factors Affecting Bancassurance Development in Poland Reprinted from: Risks 2021,9, 130, doi:10.3390/risks9070130 .....................216 v
Bła˙ zej Kocha´nski Which Curve Fits Best: Fitting ROC Curve Models to Empirical Credit-Scoring Data Reprinted from: Risks 2022,10, 184, doi:10.3390/risks10100184 ....................235 vi
About the Editors Krzysztof Jajuga Krzysztof Jajuga is president of CFA Society Poland and a full professor of finance at Wroclaw University of Economics and Business, Poland. He holds master’s, doctoral, and habilitation degree from Wroclaw University of Economics and Business, was awarded the title of titular professor by President of Poland, has an honorary doctorate from Cracow University of Economics and University WSB, and has an honorary professorship from Warsaw University of Technology, University of Warmia and Mazury in Olsztyn. He is president-elect of International Federation of Classification Societies. He carries out research and has published numerous papers and monographs in the area of financial markets, risk management, household finance, multivariate statistics, and quantitative methods in economic sciences. He is editor in chief of Argumenta Oeconomica (JCR journal). He collaborates with many financial institutions and enterprises. J´ozef Dziechciarz J´ ozef Dziechciarz is a professor at Wroclaw University of Economics and Business and is a member of the Committee of Statistics and Econometrics of the Polish Academy of Sciences. His research is in the area of econometric models. vii
Risks 2023,11,70 The paper by Shevchuk and Kopych (2021) considers risk management at the macro level. The authors estimate the exchange rate volatility using the EGARCH (1,1) model and its impact on the business cycle fluctuations in four Central and Eastern European countries. The main findings of the paper are the impact of the components of the Index of Economic Freedom, inflation and crisis on exchange rate volatility. This volume also contains two papers where the risk management is studied at the micro level. The paper by Fr ˛aczkiewicz-Wronka et al. (2021) considers the relationship between risk management and the financial stability of public hospitals in Poland. This was empirically studied using data from more than 100 hospitals. The results show that risk management practices are positively related to financial stability and that the hospitals with well-developed risk management practices are better prepared to keep their financial stability at the required level. The other paper in this group, by ´ Sliwi´nski et al. (2022), aims to identify the risk factors affecting bancassurance development in Poland. The group of risk factors contained the factors directly related to the insurance product and those resulting from the specificity of the bancassurance channel. The study was conducted on the basis of data on the gross premiums written in Poland in the years 2004–2019. 3. Conclusions The importance of risk management methodology has grown significantly in the past thirty years. In the first section, the main challenges to be faced by risk managers are indicated. To conclude, the most important risks that should be managed on all levels are: - Climate and environmental risk; - Cyber risk; - Media (and social media) risk—many media go viral by providing fake news, and unfortunately the recipients of this news use it to make decisions; - Technology risk (non-transparent and non-professional computer algorithms). All the mentioned risks have an impact on the economy and financial sector, and therefore education and data analysis methodology play a crucial role. Acknowledgments: The author and his co-editor are grateful to the MDPI Publisher for the invitation to act as guest editors of this Special Issue and are indebted to the editorial staff of “Risks” for their kind co-operation, patience and committed engagement. Conflicts of Interest: The author declares no conflict of interest. References Arabyat, Yaser Ahmad, Ahmad Ali AlZubi, Dyala M. Aldebei, and Samerra’a Ziad Al-oqaily. 2022. An Efficient Method for Pricing Analysis Based on Neural Networks. Risks 10: 151. [CrossRef] Berent, Tomasz, and Radosław Rejman. 2021. Bankruptcy Prediction with a Doubly Stochastic Poisson Forward Intensity Model and Low-Quality Data. Risks 9: 217. [CrossRef] Dziwok, Ewa, and Marta A. Kara´s. 2021. Systemic Illiquidity Noise-Based Measure—A Solution for Systemic Liquidity Monitoring in Frontier and Emerging Markets. Risks 9: 124. [CrossRef] Fr ˛aczkiewicz-Wronka, Aldona Kinga, Tomasz Ingram, Karolina Barbara Szymaniec-Mlicka, and Piotr Tworek. 2021. Risk Management and Financial Stability in the Polish Public Hospitals: The Moderating Effect of the Stakeholders’ Engagement in the Decision- Making. Risks 9: 87. [CrossRef] Górka, Joanna, and Katarzyna Kuziak. 2022. Volatility Modeling and Dependence Structure of ESG and Conventional Investments. Risks 10: 20. [CrossRef] Kochanski, Bła˙ zej. 2022. Which Curve Fits Best: Fitting ROC Curve Models to Empirical Credit-Scoring Data. Risks 10: 184. [CrossRef] Ptak-Chmielewska, Aneta, and Paweł Kopciuszewski. 2022. New Definition of Default—Recalibration of Credit Risk Models Using Bayesian Approach. Risks 10: 16. [CrossRef] Rivera-Escobar, Orlando, John Willmer Escobar, and Diego Fernando Manotas. 2022. Measurement of Systemic Risk in the Colombian Banking Sector. Risks 10: 22. [CrossRef] Shevchuk, Victor, and Roman Kopych. 2021. Exchange Rate Volatility, Currency Misalignment, and Risk of Recession in the Central and Eastern European Countries. Risks 9: 82. [CrossRef] 4
Risks 2023,11,70 ´ Sliwi´nski, Adam, Joanna Dropia, and Norbert Duczkowski. 2022. Risk Factors Affecting Bancassurance Development in Poland. Risks 9: 130. [CrossRef] Szepannek, Gero. 2022. An Overview on the Landscape of R Packages for Open Source Scorecard Modelling. Risks 10: 67. [CrossRef] Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. 5
Citation: Górka, Joanna, and Katarzyna Kuziak. 2022. Volatility Modeling and Dependence Structure of ESG and Conventional Investments. Risks 10: 20. https:// doi.org/10.3390/risks10010020 Academic Editor: Wing-Keung Wong Received: 14 December 2021 Accepted: 6 January 2022 Published: 12 January 2022 Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). risks Article Volatility Modeling and Dependence Structure of ESG and Conventional Investments Joanna Górka 1and Katarzyna Kuziak 2,* 1Department of Econometrics and Statistics, Nicolaus Copernicus University in Torun, 87-100 Toru´n, Poland; [email protected] 2 Department of Financial Investments and Risk Management, Wroclaw University of Economics and Business, 53-345 Wrocław, Poland *Correspondence: [email protected]oc.pl Abstract: The question of whether environmental, social, and governance investments outperform or underperform other conventional financial investments has been debated in the literature. In this study, we compare the volatility of rates of return of selected ESG indices and conventional ones and investigate dependence between them. Analysis of tail dependence is important to evaluate the diversification benefits between conventional investments and ESG investments, which is necessary in constructing optimal portfolios. It allows investors to diversify the risk of the portfolio and positively impact the environment by investing in environmentally friendly companies. Examples of institutions that are paying attention to ESG issues are banks, which are increasingly including products that support sustainability goals in their offers. This analysis could be also important for policymakers. The European Banking Authority (EBA) has admitted that ESG factors can contribute to risk. Therefore, it is important to model and quantify it. The conditional volatility models from the GARCH family and tail-dependence coefficients from the copula-based approach are applied. The analysis period covered 2007 until 2019. The period of the COVID-19 pandemic has not been analyzed due to the relatively short time series regarding data requirements from models’ perspective. Results of the research confirm the higher dependence of extreme values in the crisis period (e.g., tail-dependence values in 2009–2014 range from 0.4820/0.4933 to 0.7039/0.6083, and from 0.5002/0.5369 to 0.7296/0.6623), and low dependence of extreme values in stabilization periods (e.g., tail-dependence values in 2017–2019 range from 0.1650 until 0.6283/0.4832, and from 0.1357 until 0.6586/0.5002). Diversification benefits vary in time, and there is a need to separately analyze crisis and stabilization periods. Keywords: ESG; risk management; volatility; GARCH; copula; tail dependence 1. Introduction The pandemic has highlighted social and global inequality and spiked interests in environmental, social, and governance (ESG) investing. ESG assets reached $35.3 trillion in 2020 from around $30.7 trillion in 2018, reaching a third of current total global assets under management, according to the Global Sustainable Investment Association (http: //www.gsi-alliance.org/, accessed on 18 November 2021). According to the 2020 Trends Report, investors are considering ESG factors across USD 17 trillion of professionally managed assets, a 42% increase since 2018. Such continued growth is expected over the long term, too. Since 1995, the value of US sustainable investment assets (USD 639 billion) has increased more than 25-fold (USD 16.6 trillion in 2020), at a compound annual growth rate of 14% (US SIF 2020). A few terms are used interchangeably to describe environmental, social, and governance investments, e.g., socially responsible investing (SRI), responsible investing, sustainable investing, and impact investing. In this paper, we understand ESG investing in terms of the ESG factors, which enhance traditional financial analysis, making it more complete. Risks 2022,10, 20. https://doi.org/10.3390/risks10010020 https://www.mdpi.com/journal/risks 6
Risks 2022,10,20 There are some ESG factors that are helpful in the evaluation of investment performance. Investments with high ESG scores can increase rates of return, while those with poor ESG scores may inhibit these rates. One may find energy consumption, pollution, climate change, waste production, natural resource preservation (deforestation, carbon emission reduction), and animal welfare among the environmental factors. The social factors include human rights, child and forced labor, community engagement, health and safety, stakeholder relations and employee relations, customer success, data hygiene, and security. The governance factors contain the following: quality of management, board independence, conflict of interest, executive compensation, hiring and onboarding best practices, transparency, and disclosure. In this paper, we use the term ESG to refer to these indices, which include the companies that disclose these factors. Morgan Stanley’s research on nearly 11,000 mutual funds between 2004 and 2018 indicates there is no financial trade-off in returns of sustainable funds compared to traditional ones. Moreover, sustainable funds showed lower downside risk. The number of ESG focused funds has been growing, since 2004 by 144% (Morgan Stanley, Institute for Sustainable Investing, Sustainable Reality. Analyzing Risk and Returns of Sustainable Funds, 2019. www.morganstanley.com, accessed on 18 November 2021). A growing number of investors not only focus on the profitability of investment strategies but also look for their social value. ESG investing fulfills this goal. ESG looks at the company’s environmental, social, and governance practices, as well as traditional ones. ESG investors believe that investments in companies employing ESG practices may have a material impact on their investments’ profitability and risk. Moreover, they accept a lower return in the short term and even slightly higher risk because of the additional future value of their investment. Considering ESG benefits in investing for economic value is not a new concept. The report “Who Cares, Wins—Connecting Financial Markets to a Changing World”, which provided guidelines for companies to incorporate ESG into their operations, was published in 2004. The first ESG index, the Domini 400 Social Index (now known as the MSCI KLD 400 Social Index), was launched in May 1990. Since then, the ESG indices have evolved to meet investors’ unique needs in investing. ESG equity indices are used as benchmarks for ESG investment, as the underlying assets of passive ESG investment tools (such as exchange-traded funds), and as related riskmanagement tools (ESG index futures). ESG equity indices are usually constructed based on parent equity indices incorporating ESG investment styles. The construction process may comprise screening out the companies with negative ESG impacts and including the companies with positive ESG impacts by adjusting their relative weights. Therefore, the risk-return performances of these indices may be different from those of their parent indices with traditional investment strategies (HKEX 2020). Making investment decisions, including portfolio construction, requires knowledge of volatility and dependence between financial time series. Determination of the dependence structure is essential for portfolio management, and the misinterpretation of the strength of this dependence can lead to wrong investment decisions. Pearson’s linear correlation coefficient is the most common and widely used correlation measure. Because of its linearity, it is a tool appropriate only for measuring the dependence between variables of elliptic distributions. In situations where empirical data are characterized by, for example, asymmetric and non-elliptic distributions, with high kurtosis or skewness, the use of linear correlation coefficient is not advisable. In such instances, copula functions are better tools for investigating the dependence structure between the time series (Messaoud and Aloui 2015). The objective of the paper is to evaluate the attractiveness of ESG investments as a potential diversifier for conventional investments. In this study, we examine the following hypothesis: Hypothesis 1 (H1). ESG investments outperform conventional investments in terms of risk. 7
Risks 2022,10,20 Hypothesis 2 (H2). Asymptotic dependence increases during the crisis on the market (declines of stock market indices), stabilizing during the non-crisis periods. There are many ESG indices; in this paper, we select five ESG indices (see Table A1 for details). Conventional stock indices are represented by the Dow Jones Industry Average (DJI) and the S&P 500 (GSPC). Because little is known about the dependence structure between ESG and conventional investments, the contribution of this paper is to fill this research gap. The pioneering character of this research—application of tail dependence to ESG investments, is highly contributing both to the knowledge of the field as well as to the practice of assets selection in portfolio construction. The paper also contributes to improving the understanding of volatility and the (tail) dependence structure between ESG and conventional investments. By quantifying the overall and lower tail risk between these two assets, we indicate that these dependencies exist, can be quantified, and are not negligible, especially in times of crisis. The research results confirm the higher dependence of extreme values in the crisis period (declines of indices); however, this is also due to increased volatility during this period. The paper is structured as follows: the introduction, literature review, research methodology, data description, empirical results, discussion, conclusions, and references. Literature Review Managi et al. (2012) report no statistical difference in means and volatilities generated from the SRI indices and conventional indices in neither of the studied regions (the US, the UK, and Japan). Furthermore, they found strong comovements between the two indices in both regimes (bear and bull). In contrast, Ortas et al. (2014) found that in the period of the global financial crisis of 2008, social and responsible investment strategies were less risky in comparison to conventional investments. There is no consensus in the literature as to whether ESG investments are characterized by very high returns and very low risks compared to conventional ones. Weber and Ang (2016) analyzed the performance of an emerging market SRI index concerning its financial performance compared to conventional indices. Their results indicate that the SRI index outperformed in terms of mean return the majority of the conventional emerging market portfolios. Similarly, Verheyden et al. (2016) found that both global and developed-markets portfolios (a 10% best-in-class ESG screening approach) show higher returns, lower (tail) risk, and no significant reduction of diversification potential. On the other hand, Giese and Lee (2019) reported no clear consensus on whether ESG criteria have enhanced risk-adjusted returns. The empirical findings in the report on ESG indices performance (HKEX 2020), indicate that many ESG indices tended to have similar, if not better, risk-return performances then their parent indices. This implies that investment in ESG indices may provide equally good or even better returns while pursuing an ethics-focused investment strategy. Ouchen (2021) empirically verified whether the series of returns of an ESG index was less volatile than that of a conventional stock index. He concluded that the ESG index was relatively less turbulent than the stock index. Jain et al. (2019) reported there is no significant difference in the performance between sustainable indices and conventional indices. Plastun et al. (2022) investigated returns on ESG and conventional indices. They showed no significant differences between ESG and conventional indices. The types of price effects detected by them were the same for the cases of ESG and conventional indices (but their power was different in some cases). Charles et al. (2016) compared the risk-adjusted performance between ESG and conventional indices, as well as within the ESG indices, examining it based on standard and tail risk measures. They showed that the ESG screens for equities lead neither to a significant outperformance nor an underperformance compared to the benchmarks. They 8
Risks 2022,10,20 also indicated that the weights used to construct these indices (sustainability-score weights vs. market cap-weights) seemed to impact their risk and performance. Apergis et al. (2015) employed a standard cointegration methodology and a novel time-varying quantile cointegration approach to investigate whether the US Dow Jones Sustainability Index and its conventional parent index are integrated. The results confirmed the presence of an asymmetric long-run relationship between these indices that is not detected by the standard methodology of cointegration. Classical Markowitz portfolio theory does not consider the role currently played by the ESG investments on the market. It applies risk and return as single criteria, assuming that investors are rational and seek the highest return at the lowest level of risk, and their utility functions are convex (Markowitz 1952). Incorporating the ESG-based factor into the portfolio selection problem, Pedersen et al. (2021) proposed a hypothesis that explained how the increasingly widespread adoption of ESG affected portfolio choice and equilibrium asset prices. In the case of dependency modeling for classical portfolio theory, linear correlation coefficients were used (assuming elliptic distributions of returns). The problem appears because the returns are not correlated strongly when they are around zero; however, the correlation increases in the tails. Then an appropriate tool for dependency modeling is the copula function (Sklar 1959). Empirical research indicates that stock returns also display an asymmetric dependence in growing and declining markets, i.e., this dependence may be stronger in bearish markets than in bullish markets and tends to increase in the periods of violent fluctuations of prices (Ang and Bekaert 2002; Jondeau 2016; Longin and Solnik 2001). Because of the detected asymptotic dependence of random variables in tails (Patton 2006), the authors apply copula functions. This approach allows investigating the dependence in variance and in tails, which is not possible using standard dependence measures. While more than 2000 empirical studies have been conducted analyzing the ESG factors and financial performance, still little is known about the dependence structure and the associated risks (Friede 2019). This is especially important as ESG scores are often related to investment risk (Bax et al. 2021). Due to the imperfections of financial time series (they are not normally distributed) and correlation coefficients (which measure linear relationship and are constant in time), we applied GARCH family models and copula functions accompanied with some heavy-tailed marginal distributions. 2. Data and Methods 2.1. Research Methodology The ability to forecast volatility of assets is vital for portfolio selection and asset management, as well as for the pricing of primary and derivative assets (Engle and Ng 1993). Early studies point to volatility clustering, leptokurtosis, and the leverage effect in stock-returns time series (Mandelbrot 1963) and (Fama and Fama 1965). The additional features of financial time series observed across different financial assets (stocks, stock indices, exchange rates) are as follows: stationarity, fat tails, asymmetry, aggregational Gaussianity, quasi-long-range dependence, and seasonality (e.g., Rydberg 2000; Taylor 1986 ). In the GARCH model, the variance is influenced by the square of the lagged innovation. However in the equity returns the leverage effect (higher impact of negative shocks on volatility) is observed, the simple GARCH model fails to describe it. GARCH (1,1) with a generalized residuals distribution can capture more volatility assessment than other models. On the other hand, the impact of asymmetry on stock market volatility and return analysis is beyond the descriptive power of the asymmetric GARCH models, which could capture more details. There are several limitations to GARCH models. The most important one is the inability to capture the asymmetric performance. For that reason, EGARCH, GJR-GARCH, and APGARCH models were proposed. Furthermore, the asymmetric GARCH models can 9
Risks 2022,10,20 measure the effect of positive or negative shocks on stock market returns and volatility incompletely, and the GARCH (1,1) comparatively fails to accomplish this. The GJR-GARCH model performs better in the face of asymmetry, producing a predictable conditional variance during the period of high volatility. In addition, among the asymmetric GARCH models, the performance of the EGARCH model appeared to be superior. Based on the properties of the studied time series: volatility clustering, leptokurtosis, asymmetry, leverage effects, mean-reversion, and stationarity—we apply the following models from the GARCH family: GARCH, EGARCH, GJR-GARCH, APGARCH, and AVGARCH in the study. We selected the GARCH model using the Akaike (AIC) and Bayesian (BIC) information criteria. Tables A2–A5 present only the results of estimation for the best-fitted models according to these criteria (with the minimum criteria values). Base ARMA(p,q) model is as follows (Box and Jenkins 1983; Brockwell and Davis 1991 ): rt=φ1rt−1+...+φprt−p+εt−θ1εt−1−...−θqεt−q where εt∼i.i.d.(0, ht). The autoregressive conditional heteroskedasticity (ARCH) models were introduced by Engle (1982) and their generalization, the GARCH models, by Bollerslev (1986). The standard GARCH(q,p) model (Bollerslev 1986) may be written as: ht=ω+ q ∑ i=1 αiε2 t−i+ p ∑ i=1 βiht−i where ht is the conditional variance, ω the intercept, and ε2 t the residuals from the ARMA model. Some researchers pointed out limitations of the GARCH model. The most important one is that GARCH cannot capture asymmetric performance. Later, for improving this problem, EGARCH, GJR-GARCH, and APGARCH were proposed. The exponential GARCH (EGARCH) is designed to model the logarithm of the variance rather than the level, and this model accounts for an asymmetric response to a shock. The exponential GARCH model of Nelson (1991) is defined as: ln ht=ω+ q ∑ i=1 (αizt−i+γi(|zt−i|−E|zt−i|)) + p ∑ i=1 βiln ht−i where the coefficient αi captures the sign effect and γi the size effect. E|zt−i| is the expected value of the absolute standardized innovation zt. The Glosten–Jagannathan–Runkle GARCH (GJR-GARCH) as GARCH model captures features of financial time series like leptokurtic returns and volatility clustering.However, the GJR-GARCH model of Glosten et al. (1993) models positive and negative shocks on the conditional variance asymmetrically by the use of the indicator function I: ht=ω+ q ∑ i=1αiε2 t−i+γiIt−iε2 t−i+ p ∑ i=1 βiht−i where γi now represents the ’leverage’ term. The indicator function I takes on value of 1 for ε≤0 and zero otherwise. The asymmetric power ARCH (APARCH) model of Ding et al. (1993) allows for both leverage and the Taylor effect, named after Taylor (1986) who observed that the sample autocorrelation of absolute returns was usually larger than that of squared returns: htδ=ω+∑q i=1αi(|εt−i|−γiεt−i)δ+∑p i=1βiht−iδ, 10
Risks 2022,10,20 where δ∈R+ , being a Box–Cox transformation of √ht , and γi the coefficient in the leverage term. The absolute value GARCH (AVGARCH) model of Taylor (1986) and Schwert (1990): ht=ω+∑q i=1αiht−i(|zt−i−η2i|−η1i(zt−i−η2i)) +∑p i=1βiht−i, where η1iand η2iare rotations and shifts parameters respectively. This paper examines the structure of interdependence between ESG and conventional indices. In order to achieve this goal, we fit different theoretical distributions to the series of returns. Then, we assumed the best-fitted distribution describing the process of returns as a marginal distribution applied for our copula estimation. We used the two-stage maximum likelihood method to estimate the parameters of the considered two-dimensional copulas. In addition to testing the goodness of fit of alternative copulas, we also verified a set of hypotheses relating to the correlation matrix. The concept of copula, was first introduced by Sklar (1959). The theoretical background for copulas is provided by Sklar’s theorem. There exists a copula Csuch that: ∀x1∈X1|i|x2∈X2F(x1,x2)=C(F1(x1),F2(x2)) where F is two-dimensional joint distribution with the marginal distributions F1 , F2 of random variables (X1,X2).IfF1,F2are continuous, the copula Cis unique: C(u1,u2)=FF−1 1(u1),F−1 2(u2) where (u1,u2)∈[0,1],F−1 i(u)=inf{x;Fi(x)≥u}for i=1,2. The proof is provided by, e.g., Nelsen (2006). One may use a wide range of parametric copula families to capture the different structures of dependence (e.g., Gaussian, Archimedean). In the paper, we applied the following copulas: Student’s t, Joe–Clayton (a combination of the Joe copula and the Clayton copula), Gumbel–Clayton (a combination of the Clayton copula and the Gumbel copula), and survival. The Gaussian copula does not capture tail dependence, Student’s t-copula has symmetric tail dependence in both lower and upper tails, and the Clayton and Gumbel copulas have only lower and upper tail dependence, respectively. Survival copulas correspond to rotation by 180 degrees. For two dimensions following copulas are defined as (Patton 2006): (1) Gaussian/normal (N) copula CN(u1,u2;)=NΦ−1(u1),Φ−1(u2) where Nis the normal joint distribution and Φ−1 is the quantile of the univariate normal distribution; (2) Student’s t/t (t) copula Ct(u1,u2;ν,ρ)=tν,ρt−1 ν(u1),t−1 ν(u2) where ρ∈[−1,1] , tν,ρ is the joint Student’s t distribution and t−1 ν is the univariate Student’s t distribution with νdegrees of freedom; (3) Clayton–Gumbel (BB1) copula C{BB1}(u1,u2;θ,δ)=1+u−θ 1−1δ+u−θ 2−1δ1 δ−1 θ where θ≥0, δ≥1; 11
Risks 2022,10,20 (4) Joe–Clayton (BB7) copula C{BB7}(u1,u2;θ,δ)=1−1−1−uθ 1−δ+1−uθ 2−δ−1−1 δ1 θ where θ≥0, δ≥1, u1=1−u1,u2=1−u2. Survival copula is the copula of (1 − u 1 ) and (1 − u 2 ) instead of u 1 and u 2 , respectively. Its function can measure the asymmetric dependence on the opposite side of the distribution as compared to the original function. Our focus was on the extreme downside market risk, so we investigated the lower tail dependence in detail. The tail-dependence coefficients (Patton 2006) are: •Lower tail-dependence coefficient: λL=lim u→0+P(X2≤F−1 2(u)|X1≤F−1 1(u))= lim u→0+ C(u,u) u •Upper tail-dependence coefficient: λU=lim u→1−P(X2>F−1 2(u)|X1F−1 1(u))= lim u→1− 1−2u+C(u,u) 1−u in the case that the limit exists, λL , |λU∈[0,1] and ( λL= 0 ∨λU= 0), dependence is present. The bivariate normal distribution is tail independent, the bivariate Student’s t-distribution exhibits the same upper and lower tail dependence, the bivariate Joe–Clayton and Gumbel–Clayton distributions have both lower and upper tail dependence. The concept of tail dependence is embedded within the copula theory. Instead of Pearson’s correlation coefficient in the copula theory, we use the Kendall’s τ coefficient (Nelsen 2006; Patton 2006). For each pair, the Kendall’s τ is estimated and the p-values of the independence test based on the Kendall’s τwere determined in the study. In this paper, we used functions from the VineCopula library in R (Stoeber et al. 2018). We made the following assumptions during the estimation process: we took 39 copulas into consideration, we applied the Maximum Likelihood Estimation (MLE) method, and we used the AIC selection criterion to select the best-fitted copula. To measure the discrepancy between a hypothesized model and the empirical model, we used the goodness-of-fit (GoF) statistics based on the Kendall’s process as proposed by Wang and Wells (2000). For computation of p-values, the parametric bootstrap described by Genest et al. (2006) was used. 2.2. Data Description In the study, we used five selected ESG indices (presented in Table A1) and two stock indices—Dow Jones Industry and the S&P 500. Daily logarithmic rates of return for them were calculated, as a difference between logarithms of two consecutive closing prices multiplied by 100 (they can be interpreted as percentage changes). The data set was retrieved from the Thomson Reuters database. In Table 1, Table 4, Table 7 and Table 10 descriptive statistics for rates of return of selected indices were given. The period of analysis covered 3 July 2007 until 31 December 2019. We considered, based on important market events (e.g., global financial crisis, debt crisis in the EU, fall in oil prices) and data requirements from the models’ perspectives, the following four subperiods: 1. 3 July 2007–30 January 2009 (388 observations)—the global financial crisis period; 2. 2 December 2009–30 July 2014 (1140 observations)—the period of debt crisis in the EU; 3. 3 June 2014–31 January 2017 (633 observations)—the Russian financial crises, fall in oil prices; 4. 3 January 2017–31 December 2019 (746 observations)—stabilization period. 12
Risks 2022,10,20 3. Results 3.1. General Remarks In order to identify the processes of the series of daily rates of return of the ESG indices and conventional indices (S&P 500, DJI) during the period between 3 July 2007 and 31 December 2019 (excluding the COVID-19 pandemic), it is essential to conduct graphical, statistical, and econometric examinations of these time series to check for their stationarity and the presence of the ARCH effect. We conduct such analysis for four subperiods. The graphic examination of values of all indices shows that they are not stationary, but their daily rates of return are stationary (see Figures 1, 3, 5 and 7). We applied unit root tests, i.e., the Augmented Dickey–Fuller, Phillips–Perron, and KPSS to confirm stationarity. At the same time, the distribution of the returns has tails, which are heavier than the tails of the normal distribution. To confirm this, we used the Jarque–Bera test and Q-Q plots. Generally, the daily returns for both types of indices exhibit no significant autocorrelation, supporting the hypothesis that the returns are uncorrelated across time. To confirm this, we applied the Ljung–Box test. Finally, we checked whether the rates of return are characterized by the ARCH effect using the McLeoda and Li test. The null hypothesis is that the rates of return do not have the ARCH effect, while the alternative hypothesis is that they have the ARCH effect. In all subperiods, the ARCH effect was detected in the returns. In the case of the standardized innovations from the ARMA-GARCH models, at the assumed 5% level of significance, the p-values for the Engle test are greater than 0.05 (see Tables A3–A5), which means that the null hypothesis was not rejected, i.e., the ARCH effect is not present in the innovations. Hence, the models are free from conditional heteroskedasticity in almost all cases (only in the first period for three indices the ARCH effect is present—Table A2). To verify the autocorrelation in the innovations, we used the Ljung–Box test. The null hypothesis that the innovations are independently distributed was not rejected in all the cases (see Tables A2–A5). It means that the models have been well-chosen and fitted. Finally, the persistence parameters are close to one, which is high (see Tables A2–A5), meaning that the variance moves slowly through time. We employ not only normally distributed innovations, but also the Student’s t-distributions, the generalized error distribution (GED) and a skewed version of both. The reason for considering distributions other than normal is that a GARCH model with conditional normal errors has fatter tails than the normal distribution, and for many financial time series the standardized innovations still appear to be leptokurtic. Therefore, assuming a leptokurtic unconditional distribution for the innovations seems more appropriate. Because the market returns are not normally distributed, the Gaussian copula would not capture tail dependence. Therefore, we fitted the Student’s t-copula and the combination of Clayton and Gumbel copulas. At a 1% significance level for the chosen copulas, we cannot reject the null hypothesis (GoF test), i.e., our copulas are the true copulas. Due to the observed nonnormality in the returns distribution, we measured the dependence by using Kendall’s τ coefficient. All results for the Kendall’s τ coefficient are statistically significant. In the first two subperiods, dependencies were higher than in the next two subperiods (see Table 2, Table 3, Table 5, Table 6, Table 8, Table 9, Table 11 and Table 12). To quantify the degree of tail dependence in each pair, the Kendall’s τ is estimated and the p-values of the independence test based on the Kendall’s τ are determined (see Figure 2 and Tables 2 and 3). The results indicate the existence of positive, significant dependence. We analyzed the dependence for 10 pairs of indices, namely S&P and ESG—5 pairs and DJI and ESG—5 pairs. Dependence between S&P and DJI exhibited lower tail dependence in three subperiods; only in the 2008 global financial crisis was the tail dependence symmetric. In the first and last subperiod, ESG and conventional investments showed lower and symmetric tail dependence—in the first subperiod for 5 pairs in the lower tail, for 5 pairs symmetric; in the third subperiod for 3 pairs in the lower tail and for 7 pairs symmetric. In the second period, ESG and conventional investments exhibited lower and upper tail 13
Risks 2022,10,20 Figure 6. Kendall’s τand copulas, 3 June 2014–31 January 2017. Table 8. Dependence structure for the GSPC and ESG indices, 3 June 2014–31 January 2017. GSPC and ... DJI A1SGI SXWESGP SEESGSEP SGESGSEP TRESGQ1 Copula Clayton–Gumbel t t t t Clayton–Gumbel Par 1.0439 0.9777 0.5900 0.4638 0.5336 0.7395 Par2 4.2304 2.5661 3.8015 4.0842 4.0282 1.5687 Beta 0.8388 0.5237 λL0.8547 0.8521 0.3184 0.2296 0.2709 0.5502 λU0.8220 0.8521 0.3184 0.2296 0.2709 0.4444 logLik 963.82 1075.43 161.66 98.89 129.49 282.82 AIC −1923.64 −2146.7 −319.32 −193.79 −254.97 −561.64 Indep. (p-value) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 GoF test 0.0287 2.3726 2.9012 6.674 2.6074 0.0385 p-value 0.285 0.365 0.245 0.03 0.23 0.7 Indep.—testing for independence for pairs of variables (H0:τ=0). Table 9. Dependence structure for DJI and ESG indices, 3 June 2014–31 January 2017. DJI and ... A1SGI SXWESGP SEESGSEP SGESGSEP TRESGQ1 Copula Clayton–Gumbel t t t Clayton–Gumbel Par 1.1266 0.5777 0.4481 0.5130 0.7433 Par2 3.5402 4.0794 4.1390 4.1347 1.5194 Beta 0.8126 0.5093 λL0.8405 0.2954 0.2190 0.2535 0.5413 λU0.7837 0.2954 0.2190 0.2535 0.4219 logLik 868.61 153.33 93.46 120.53 267.18 AIC −1733.22 −302.65 −182.93 −237.06 −530.36 Indep. (p-value) 0.0000 0.0000 0.0000 0.0000 0.0000 GoF test 0.0248 2.8387 7.2067 5.637 0.0421 p-value 0.625 0.265 0.025 0.075 0.675 Indep.—testing for independence for pairs of variables (H0:τ=0). 3.5. The Stabilization Period (4 January 2017–31 December 2019) In the stabilization period, all indices are not normally distributed (mostly low kurtosis comparing to previous periods, but higher than for normal distribution, negative asymmetry, as confirmed by the Jarque–Bera test) with positive means and similar standard deviations for S&P 500, DJI, and A1SGI. In the case of standard deviation for other ESG indices, large differences were observed—low for SGESGSEP and high for SEESGSEP (Table 10). In the whole period, two subperiods characterized by high volatility (visible 20
Risks 2022,10,20 volatility clustering in beginning of 2018 and the beginning of 2019—Figure 7) were observed for S&P 500, DJI, and A1SGI. For other ESG indices not only these clusters were observed (high volatility was during the whole of 2018 and the first half of 2019). Volatility of three indices, namely S&P 500, DJI, and A1SGI, was modeled by AVGARCH (innovations with skewed Student’s t and skewed GED distributions). There is no consensus in the modeling volatility of the ESG indices. There were applied GJR-GARCH and EGARCH (innovations with Student’s t and skewed normal distributions). From Table A5, we can see that all the parameters have very small p-values, which shows their statistical significance. Persistence ranges from 0.9581 to 0.9564 for S&P 500 and DJI, and from 0.9169 to 0.9628 for the ESG indices. Table 10. Descriptive statistics, 4 January 2017–31 December 2019. GSPC DJI A1SGI SXWESGP SEESGSEP SGESGSEP TRESGQ1 Minimum −4.184 −4.714 −4.169 −2.765 −3.297 −2.515 −3.333 Maximum 5.693 5.996 5.563 2.687 3.831 2.477 2.555 1. Quartile −0.225 −0.266 −0.251 −0.368 −0.436 −0.369 −0.344 3. Quartile 0.451 0.443 0.449 0.454 0.459 0.412 0.448 Mean 0.049 0.049 0.049 0.030 0.011 0.015 0.035 Median 0.069 0.075 0.066 0.046 0.025 0.030 0.049 SE Mean 0.030 0.031 0.029 0.025 0.027 0.023 0.025 LCL Mean −0.009 −0.011 −0.009 −0.019 −0.042 −0.031 −0.014 UCL Mean 0.108 0.109 0.106 0.078 0.065 0.061 0.084 Variance 0.663 0.702 0.648 0.450 0.554 0.407 0.465 Stdev 0.815 0.838 0.805 0.671 0.744 0.638 0.682 Skewness −0.502 −0.508 −0.485 −0.273 −0.131 −0.237 −0.420 Kurtosis (−3) 6.620 7.227 6.444 1.214 2.059 1.374 1.696 Figure 7. The rates of return, 4 January 2017–31 December 2019. 21
Risks 2022,10,20 The highest values of Kendall’s τ (see Figure 8) are between indices of the same type (S&P 500 and DJI, and SEESGSEP and SGESGSEP). High dependence is observed between S&P 500 and A1SGI and between DJI and A1SGI, low dependence between S&P 500 and SEESGSEP, and between DJI and SEESGSEP. For example, for the GSPC–SEESGSEP relationship—the observed copula has the lowest dependency—depends by 16.50% on the upper tail and 16.50% on the lower tail (the same dependency). The pair GSPC–A1SGI has a dependency of 88.22% on the lower tail, and of 85.32% on the upper tail. It means the interaction has a greater effect in the lower tail. This interaction was also observed in the pairs DJI–A1SGI, DJI–TRESGQ1, DJI–SXWESGP, and GSPC–TRESGQ1. Figure 8. Kendall’s τand copulas, 4 January 2017–31 December 2019. The dependences between the S&P 500 and ESG indices and between the DJI and ESG indices were modeled by the Clayton–Gumbel, t, and Joe–Clayton copula (see Tables 11 and 12) . Dependences between S&P 500 and SEESGSEP, and between S&P 500 and SGESGSEP compared to DJI were modeled by using the t copula. In the other cases, we used other copulas. For example, the GSPC-TRESGQ1 relationship is modeled by the Clayton–Gumbel copula, and DJI–SGESGSEP by the Survival Joe–Clayton copula. Table 11. Dependence structure for the GSPC and ESG indices, 4 January 2017–31 December 2019. GSPC and ... DJI A1SGI SXWESGP SEESGSEP SGESGSEP TRESGQ1 Copula Joe–Clayton Clayton–Gumbel t t t Clayton–Gumbel Par 3.9223 1.0932 0.6060 0.4171 0.4443 0.8964 Par2 5.3912 5.0599 4.9383 5.0582 4.9680 1.6639 Beta 0.7145 0.8672 0.5745 λL0.8794 0.8822 0.2733 0.1650 0.1807 0.6283 λU0.8067 0.8532 0.2733 0.1650 0.1807 0.4832 logLik 847.98 1231.71 175.35 80.16 91.18 391.80 AIC −1691.97 −2459.43 −346.69 −156.33 −178.37 −779.59 Indep. (p-value) 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 GoF test 0.0167 0.0438 2.4133 0.2038 0.2798 0.1366 p-value 0.96 0.02 0.274 0.926 0.882 0.012 Indep.—testing for independence for pairs of variables (H0:τ=0). 22
Risks 2022,10,20 Table 12. Dependence structure for the DJI and ESG indices, 4 January 2017–31 December 2019. DJI and ... A1SGI SXWESGP SEESGSEP SGESGSEP TRESGQ1 Copula Joe–Clayton Survival Clayton–Gumbel tt Survival Joe–Clayton Par 3.8520 0.2404 0.4205 0.4489 2.3596 Par2 5.2688 1.4921 5.9725 5.4041 1.0007 Beta 0.7115 0.3935 0.5121 λL0.8767 0.4087 0.1357 0.1665 0.6586 λU0.8028 0.1448 0.1357 0.1665 0.5002 logLik 839.08 167.21 80.10 92.97 353.55 AIC −1674.17 −330.42 −156.20 −181.93 −703.09 Indep. (p-value) 0.0000 0.0000 0.0000 0.0000 0.0000 GoF test 0.0297 0.0558 1.8649 1.0997 0.0733 p-value 0.685 0.485 0.43 0.525 0.3 Indep.—testing for independence for pairs of variables (H0:τ=0). 4. Discussion Our study does not confirm the outperformance of the ESG indices compared to conventional ones in terms of risk in the considered subperiods. However, generalization of the results is limited by the selection of a market index as a proxy of an investment portfolio. Other empirical studies demonstrate a strong correlation between the lower risk related to sustainability and better financial performance (Whelan et al. 2021). During the 2008 global financial crisis Fernández et al. (2019) found that German green mutual funds had risk-adjusted returns slightly better than their peers (in the noncrisis period, they were equal to conventional funds but better than the SRI funds). Similarly, ESG stock indices performed better and recovered faster after the 2008 global financial crisis (Wu et al. 2017) . Other results confirm these findings, as in economic downturns, the high-rated mutual funds outperformed the low-rated funds, based on the Sharpe ratio (Das et al. 2018a, 2018b; Khajenouri and Schmidt 2020). In line are research by Abate et al. (2021) that mutual funds investing in high ESG stocks perform better than investing in low ESG score stocks. Gil-Bazo et al. (2010) confirm that SRI funds perform better than their conventional counterparts. In the study we evaluate whether conventional stock portfolios, including ESG companies, can effectively decrease portfolio risk, especially in times of financial distress on the market. Generally, we observe in all subperiods almost-weak to high lower-tail dependence between the ESG and conventional indices. Our findings indicate that there is low or symmetric tail dependence between ESG and conventional indices, meaning that if the ESG index decreases, the conventional one will also decrease accordingly. In the two first subperiods (economic downturn periods) lower tail dependence coefficients are higher comparing to the next two periods (‘stabilization’ periods). We conclude that dependencies exist, can be quantified, and are not negligible, especially in times of crisis. In risk management of an asset portfolio, we are interested whether the decline of one (or more) assets may influence the behavior of the other assets in a portfolio. Especially, the occurrence of simultaneous extreme events on the market implies that risk diversification breaks down just when it is crucial. In case of extreme events, classical dependence analysis (e.g., linear correlation) fails, a copula approach is used. Some researchers argue that considering ESG practices when creating an equity portfolio (selecting companies with high ESG scores) can act as protection against left-tail risk; therefore, reducing ex-ante expectations of a left-tail event (Shafer and Szado 2020; De and Clayman 2015; Djoutsa Wamba et al. 2020 ). The measurement of the tail dependence between ESG and conventional investment based on the copula approach, allows to monitor extreme risks between them. Understanding dependencies and risks is important for setting up adequate risk management as well as construction portfolios—ESG-diversified and resilient to crises. Bax et al. (2021) use the R-vine copula ESG risk model. They estimate all the conditional dependencies among 23
Risks 2022,10,20 assets as well as specify their interactions as modeled by different copulas families, but they also introduce three ESG risk measures that capture ESG risk, market risk conditionally on the ESG class, as well as an idiosyncratic risk component. 5. Conclusions As interest in ESG investments grows, it is crucial to better understand the various risks and return tradeoffs between ESG and conventional stocks and the dependence structures between them. We used GARCH family models to estimate conditional volatilities and the copula approach, in particular the (tail) dependence structure between ESG and conventional investments to quantify the overall and lower tail risk between these two investments. Hypothesis 1, that ESG investments outperform conventional ones in terms of risk was negatively verified—there are indices that underperform the conventional indices in selected subperiods. Hypothesis 2, that asymptotic dependence increases during the crisis on the market (declines of stock market indices), and it stabilizes during non-crisis periods was positively verified. The findings indicate that there is no significant difference in daily returns of ESG indices and conventional ones. The parameters are significant among all the estimations and comparisons, showing that GARCH family models may appropriately model the ESG and conventional index data. In most subperiods, the data for the ESG and conventional indices were negatively skewed. The EGARCH models this type of behavior, but in this study, also AVGARCH model was applied. Surprisingly, GJR-GARCH was not often used. We found relations between the selected ESG indices. A1GSI is related in construction to S&P 500, while three other ESG indices—SXWESGP, SEESGSEP, and SGESGSEP are related to each other. These relations were visible in similar behavior of the rates of return. Volatility clustering observed at S&P 500, DJI, and A1SGI was different from that in other ESG indices (but the scale of these differences depends on the subperiod). In the first subperiod, one cluster was observed for all the indices (there is no difference visible). In the second and third subperiod, two clusters were found for all indices, but the difference between these two groups of indices was present. The most visible differences were observed in the last subperiod. Only in the second period, results of model estimation are consistent for all the indices (ARMA-EGARCH models with innovations sged and sstd). We cannot confirm that the volatility of conventional indices should be modeled using different models than the volatility of the ESG—this depends on the time period and the market events. There are periods when volatility of all the indices may be modeled by using the same models, when there is a difference between the modeling of conventional and ESG indices, and when there is a difference between the modeling of ESG indices. The characteristics of the time series indicated the need to apply to the dependence analysis copula approach. To capture tail dependence, Student’s t-copula and the combination of the Clayton and Gumbel copulas were fitted best in this study. The choice of an appropriate copula function is crucial. Two features are important regarding the copula selection. The general structure of the chosen copula should coincide with the dependence structure of the real data. If the data show tail dependence than we must apply a copula which comprises tail dependence. In the periods of economic downturn (declines of stock market indices), the dependencies measured by Kendell’s tau coefficients were higher than in the less turbulent periods. The lower tail dependence and symmetric dependence between ESG and conventional investments were detected. High values of low tail-dependence coefficients were observed in the economic downturn periods; low in stabilization periods. This signifies higher dependence of extreme values in the economic downturn periods and low dependence of extreme values in stabilization periods. We conclude that when selecting the right model, the preliminary analysis of data is necessary, and the selection of the volatility model should be carried out for subperiods 24
Risks 2022,10,20 regarding different market-event characteristics. Results show, as in cases of systemic risk, that analysis of volatility and dependence structure should be carried out separately—in the periods of economic downturn and in less turbulent times. To extend this research for the future, a more detailed analysis, including ESG and non- ESG companies from different markets (developed and developing) would be beneficial. In addition, application of a time-varying model (time-varying copula) would give insights into dependence structure. Author Contributions: Conceptualization, K.K.; methodology, K.K. and J.G.; software, J.G.; formal analysis, K.K. and J.G.; investigation, K.K. and J.G.; data curation, J.G.; writing—original draft preparation, K.K. and J.G.; writing—review and editing, K.K. and J.G.; visualization, K.K. and J.G.; supervision, K.K.; funding acquisition, K.K. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Wroclaw University of Economics and Business. Conflicts of Interest: The authors declare no conflict of interest. Appendix A Table A1. Description of ESG indices. Name Ticker Description Market STOXX GLOBAL ESG LEADERS Index .SXWESGP The index offers a representation of the leading global companies in terms of environmental, Social, and governance criteria, based on ESG indicators provided by Sustainalytics Global STOXX Europe ESG Leaders Select 30 Price EUR Index .SEESGSEP The index captures the performance of stocks with low volatility and high dividends from the STOXX Global ESG Leaders Index. Europe STOXX Global ESG Leaders Select 50 Price EUR Index .SGESGSEP The index captures the performance of stocks with low volatility and high dividends from the STOXX Global ESG Leaders Index. The component selection process first excludes all stocks whose 3- or 12-month historical volatilities are the highest. Among the remaining stocks, the 50 stocks with the highest 12-month historical dividend yields are selected to be included in the index. Global Refinitiv IX Global ESG Equal Weighted Price Only .TRESGQ1 The index is a benchmark for investors seeking companies that actively invest in and promote ESG values and principles. The index tracks the price return and net total return of publicly traded equities across the world that display relatively high ESG. The constituents’ universe is derived from Refinitiv Global Developed Index (the parent index). Global Dow Jones Sustainability North America Composite Index .A1SGI The index comprises North American sustainability leaders as identified by S&P Global through the Corporate Sustainability Assessment (CSA). It represents the top 20% of the largest 600 North American companies in the S&P Global BMI based on long-term ESG criteria. North America Source: own elaboration based on particular indices’ websites. 25
Risks 2022,10,20 Appendix B Table A2. Family ARMA-GARCH models, 3 July 2007–30 January 2009. GSPC DJI A1SGI SXWESGP SEESGSEP SGESGSEP TRESGQ1 Model APARCH EGARCH GJR GARCH AVGARCH AVGARCH AVGARCH AVGARCH Distribution norm sstd norm norm norm norm norm φ1−1.8549 −1.8857 −1.8615 −0.2658 0.0000 0.0000 0.0000 0.0000 φ2−0.9319 −0.9614 −0.8876 −1.0050 0.0000 0.0000 0.0000 0.0000 θ11.7806 1.8063 1.6787 0.2702 0.1156 0.0000 0.0000 0.0000 0.0000 0.0167 θ20.6639 0.7189 0.3917 1.0118 −0.0562 0.0000 0.0000 0.0000 0.0000 0.0285 θ3−0.2059 −0.1801 −0.3394 0.0000 0.0000 0.0000 ω0.0512 0.0001 0.0555 0.0370 0.0454 0.0382 0.0312 0.0000 0.9834 0.0000 0.0000 0.0000 0.0000 0.0000 α10.0000 −0.1579 0.0000 0.0926 0.1398 0.1164 0.0753 1.0000 0.0000 1.0000 0.0000 0.0000 0.0000 0.0000 α20.1068 0.0000 β10.8751 0.9818 0.8774 0.8314 0.7855 0.8196 0.8354 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 γ1−0.4094 0.1037 0.1778 0.9532 0.0000 0.0001 γ21.0000 0.0000 η11 0.4877 0.4084 0.5056 0.6569 0.0000 0.0000 0.0000 0.0000 η21 0.8895 0.7126 0.6472 0.9940 0.0000 0.0000 0.0000 0.0000 δ1.0751 0.0000 skew 0.8852 0.0000 shape 11.4791 0.0642 Akaike 3.8296 3.7112 3.6759 3.7624 3.6824 3.6065 3.5371 Bayes 3.9521 3.8235 3.7678 3.8135 3.7743 3.6576 3.6085 Ljung–Box test 4.4482 6.3567 9.9787 6.9881 5.9840 6.6419 7.7529 0.9249 0.7845 0.4424 0.7266 0.8166 0.7588 0.6530 Engle Arch test 8.6312 15.2820 12.3802 21.5479 16.7602 30.0986 24.3912 0.7341 0.2264 0.4156 0.0429 0.1588 0.0027 0.0180 Persistence 0.9654 0.9818 0.9663 0.9730 0.9649 0.9693 0.9721 Note: the first row indicates the estimate parameters (or test statistics) and the second row—the p-value of the Student’s t-test (or appropriate test); Ljung–Box and Engle ARCH tests were calculated for standardized innovations. 26
Risks 2022,10,20 Table A3. ARMA-EGARCH models, 2 December 2009–30 July 2014. GSPC DJI A1SGI SXWESGP SEESGSEP SGESGSEP TRESGQ1 Distribution sged sged sstd sstd sged sstd sstd φ1−0.5969 −0.2909 0.0773 0.0000 0.0000 0.0000 θ10.5690 0.2501 0.0000 0.0000 ω−0.0042 −0.0162 −0.0081 0.0027 0.0023 −0.0017 0.0024 0.4793 0.0005 0.1138 0.1199 0.2122 0.6040 0.3074 α1−0.3983 −0.3570 −0.3832 −0.1023 −0.0918 −0.1150 −0.1117 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 α20.1515 0.1371 0.1687 0.0000 0.0049 0.0000 β10.9410 0.9411 0.9594 0.9910 0.9867 0.9816 0.9867 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 γ1−0.1456 −0.0852 −0.1791 0.0668 0.0672 0.1182 0.0808 0.0323 0.0003 0.0126 0.0000 0.0000 0.0002 0.0019 γ20.2681 0.2472 0.2805 0.0001 0.0003 0.0001 skew 0.8098 0.8356 0.7841 0.8657 0.8563 0.8689 0.8251 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 shape 1.3919 1.4247 7.7845 8.1811 1.5014 8.8081 6.7950 0.0000 0.0000 0.0000 0.0000 0.0000 0.0001 0.0000 Akaike 2.4940 2.3325 2.3731 2.9187 2.8993 2.5299 2.6496 Bayes 2.5382 2.3767 2.4084 2.9496 2.9258 2.5564 2.6762 Ljung–Box test 7.6686 4.6382 6.8038 5.5808 4.8186 6.0897 7.1695 0.6612 0.9140 0.7438 0.8492 0.9030 0.8077 0.7094 Engle ARCH test 7.8238 6.3159 7.2004 8.4786 13.9807 17.9072 10.1396 0.7987 0.8993 0.8441 0.7467 0.3019 0.1185 0.6037 Persistence 0.9410 0.9411 0.9594 0.9910 0.9867 0.9816 0.9867 Note: the first row indicates the estimate parameters (or test statistics) and the second row—the p-value of the Student’s t-test (or appropriate test); Ljung–Box and Engle ARCH tests were calculated for standardized innovations. Table A4. Family GARCH models, 3 June 2014–31 January 2017. GSPC DJI A1SGI SXWESGP SEESGSEP SGESGSEP TRESGQ1 Model AVGARCH AVGARCH AVGARCH EGARCH EGARCH GARCH AVGARCH Distribution sstd sstd sstd std std std std ω0.0361 0.0285 0.0302 −0.0215 −0.0147 0.0723 0.0326 0.0000 0.0000 0.0000 0.0560 0.2977 0.0052 0.0007 α10.2033 0.2302 0.2782 −0.1276 −0.1335 0.1981 0.1807 0.0000 0.0000 0.0000 0.0001 0.0007 0.0000 0.0000 β10.6804 0.7186 0.7042 0.9419 0.8972 0.7133 0.7933 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 γ10.2418 0.2775 0.0002 0.0003 η11 0.1086 −0.1145 −0.2498 −0.1651 0.1826 0.0000 0.0000 0.0450 η21 1.1870 1.1419 1.1495 0.9274 0.0000 0.0000 0.0000 0.0000 27
Risks 2022,10,20 Table A4. Cont. GSPC DJI A1SGI SXWESGP SEESGSEP SGESGSEP TRESGQ1 Model AVGARCH AVGARCH AVGARCH EGARCH EGARCH GARCH AVGARCH skew 0.8196 0.8599 0.8440 0.0000 0.0000 0.0000 shape 11.2696 7.7111 11.4148 10.6788 8.5965 9.6351 7.6282 0.0084 0.0001 0.0037 0.0022 0.0003 0.0018 0.0001 Akaike 2.1554 2.1590 2.1985 2.5601 2.7756 2.4024 2.3052 Bayes 2.2029 2.2065 2.2460 2.5940 2.8096 2.4296 2.3458 Ljung–Box test 15.6265 12.3524 13.1544 11.6801 7.0749 13.3207 11.0541 0.1108 0.2622 0.2152 0.3070 0.7184 0.2063 0.3533 Engle ARCH test 5.3622 4.8535 8.7917 9.6174 9.4367 12.2077 12.4372 0.9448 0.9627 0.7206 0.6495 0.6653 0.4291 0.4112 Persistence 0.9655 0.9749 0.9716 0.9419 0.8972 0.9114 0.9668 Note: the first row indicates the estimate parameters (or test statistics) and the second row—the p-value of the Student’s t-test (or appropriate test); Ljung–Box and Engle ARCH tests were calculated for standardized innovations. Table A5. Family ARMA-GARCH models, 4 January 2017–31 December 2019. GSPC DJI A1SGI SXWESGP SEESGSEP SGESGSEP TRESGQ1 Model AVGARCH AVGARCH AVGARCH EGARCH EGARCH GJR GARCH EGARCH Distribution sged sstd sged std std std snorm θ10.0766 0.0462 ω0.0392 0.0406 0.0338 −0.0707 −0.0417 0.0208 −0.0443 0.0000 0.0000 0.0000 0.0141 0.0407 0.0207 0.0021 α10.1456 0.1065 0.1321 −0.1286 −0.0982 0.0067 −0.1526 0.0000 0.0000 0.0000 0.0000 0.0036 0.7335 0.0000 β10.7806 0.8708 0.7995 0.9169 0.9394 0.8845 0.9402 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 γ10.1402 0.1375 0.1149 0.1793 0.0077 0.0009 0.0078 0.0000 η11 0.5809 1.0000 0.4573 0.0000 0.0001 0.0000 η21 0.5806 0.0786 0.6727 0.0000 0.0695 0.0000 skew 0.8846 0.8334 0.8564 0.8620 0.0000 0.0000 0.0000 0.0000 shape 1.2853 4.6528 1.3843 14.0514 8.7823 12.4842 0.0000 0.0000 0.0000 0.0145 0.0002 0.0122 Akaike 1.8836 1.9762 1.9035 1.9509 2.1482 1.8526 1.9036 Bayes 1.9269 2.0195 1.9468 1.9880 2.1791 1.8835 1.9345 Ljung–Box test 8.6446 7.6484 9.9759 9.0690 12.1615 9.3624 10.8849 0.5661 0.6631 0.4426 0.5256 0.2744 0.4981 0.3666 Engle ARCH test 9.3952 12.5922 10.9797 10.0092 20.3661 14.3953 8.8700 0.6689 0.3994 0.5307 0.6151 0.0605 0.2762 0.7140 Persistence 0.9581 0.9564 0.9628 0.9169 0.9394 0.9487 0.9402 Note: the first row indicates the estimate parameters (or test statistics) and the second row—the p-value of the Student’s t-test (or appropriate test); Ljung–Box and Engle ARCH tests were calculated for standardized innovations. 28
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Risks 2021,9,82 countries in order to decrease real exchange rate volatility (Caporale et al. 2011). However, the balance sheet effect implies that it may be optimal for monetary authorities to diminish exchange rate variation in order to decrease the cost of servicing and rolling-over foreigncurrency debt (Georgiadis and Zhu 2019). 3. Data and Methods 3.1. Data For the purpose of this study, we use data for the Czech Republic, Hungary, Poland, and Romania over the period of 2000–2019. All these countries follow free or managed floating exchange rate policies which makes it highly relevant for the study of a nominal exchange rate volatility. Quarterly series of the real gross domestic product (index, 2010 = 100 ), nominal and real effective exchange rates (index, 2010 = 100), as well as on the central bank reference rate (%), money aggregate M3 (in local currency), and the budget balance (% of GDP) are obtained from the IMF’s International Financial Statistics database (www.data.imf.org, accessed on 8 February 2021). As measures of institutional quality, the Index of Economic Freedom from the Heritage Foundation is used (www.heritage.org/index/dowload, accessed on 8 February 2021). The cyclical components of real output, yc t (%), as well of the currency misalignment, rerc t (%), were calculated as a percentage deviation of the current values from the Hodrick- Prescott filtered trend. The use of a nominal effective exchange rate, e t , is preferred in studies of the exchange rate variability because the RER variability incorporates price fluctuations, which represent another type of uncertainty for private agents (Barguellil et al. 2018). Other studies implement alternative measures of the currency misalignment. For example, Rodrik (2008) and Ribero et al. (2020) define RER misalignment as a difference between exchange rate adjusted for PPP conversion factors, ln(RERt)=ln(Et/(PPPt) , and the RER obtained from a regression on the log the GDP per capita: ln( RERt)=γ0+γ1ln(Yt)+εt . Table 1 shows the descriptive statistics of the main variables that are investigated in our study. Romania is characterized by the largest cyclical peak of its output fluctuations at almost 10%, with the deepest trough at − 4.3% as well. The cyclical components of real output reveal less instability in the Czech Republic and Hungary. The business cycle is much smoother in Poland, probably due to a very flat slowdown in 2009. However, Poland reveals the highest level of the currency misalignment, followed by Romania, Hungary, and the Czech Republic. Outcomes are similar for the NEER in first differences. As suggested by the Jarque-Bera statistics, all NEERs show evidence of non-normality. It is not surprising as the NEER is determined by random changes in bilateral exchange rates, including countries with high-risk currencies. Except for Romania, cyclical components of output are normally distributed. Figure 1 visualizes developments in the cyclical components of output and currency misalignment for the CEE countries. Business cycles of the Czech Republic, Hungary, and Poland seem to be quite synchronized, with cyclical output developments in Romania being somewhat different in terms of timing and amplitude. All countries experienced a boom in 2007–2008 followed by a remarkable slowdown in 2009–2010 (except Poland). After a period of anemic growth in 2013–2016, output dynamics have accelerated, though to a lesser extent in Romania. Currency misalignments had been more substantial in the 2000s, especially for the Polish zloty and the Romanian lei. On the eve of the world financial crisis there had been a remarkable appreciation of the CEE currencies in 2007–2008, with a steep reverse to follow in 2009. As recently, NEERs have been fluctuating approximately ±5% all around the equilibrium trend. 36
Risks 2021,9,82 Table 1. Descriptive statistics. Country Mean Max Min STD Jarque-Bera Gross domestic product (yct) Czech Republic 0.094 5.059 −2.701 1.965 4.345 Hungary 0.148 4.292 −3.474 1.768 2.269 Poland 0.065 3.961 −2.572 1.379 4.105 Romania −0.091 9.998 −4.259 2.538 140.88 *** Nominal effective exchange rate, in first differences (Δet) Czech Republic −0.005 0.061 −0.053 0.021 4.809 * Hungary 0.010 0.128 −0.057 0.032 53.833 *** Poland −0.001 0.151 −0.071 0.037 94.879 *** Romania 0.010 0.105 −0.067 0.030 7.437 ** Real exchange rate misalignment (rerct) Czech Republic 0.038 5.673 −9.636 3.201 8.508 ** Hungary −0.092 10.409 −9.257 3.528 6.794 ** Poland −0.231 14.860 −14.292 5.321 8.987 ** Romania 0.035 10.373 −11.296 4.196 0.968 Notes: ***, **, * denote rejection of the null hypothesis at 1%, 5%, and 10% respectively. (a) the cyclical components of output (yct) (b) currency misalignment (rerct) -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 Czech Republic Hungary Poland Romania -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 6 8 10 12 14 16 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 Czech Republic Hungary Poland Romania Figure 1. Business cycle and currency misalignment, 2000–2019 (in %). Source: own calculations based on data from IMF International Financial Statistics (www.data.imf.org, accessed on 8 February 2021). The Augmented Dickey-Fuller (ADF) stationarity test indicates that both cyclical components of output and currency misalignment variables are stationary in levels at the 5% significance level (Table 2). As expected, the NEERs are stationary in first differences. Similar to Borys et al. (2008), to measure the quality of domestic institutions and the progress of market reforms we use the Heritage Foundation database. Besides the composite Index of Economic Freedom (heritage t ), we consider nine sub-indices, namely business freedom (1), trade freedom (2), investment freedom (3), financial freedom (4), property rights (5), fiscal health (6), judicial effectiveness (7), labor freedom (8), and monetary freedom (9), ranging from 0 to 10 points. The importance of institutions used to be considered in the context of long-term growth, but it seems to be of the same role in managing short-term output fluctuations. As mentioned by Boar (2010), the key to the macroeconomic success of an emerging economy is not the initial choice of the exchange rate regime but rather the health of the fundamental institutions. 37
Risks 2021,9,82 Table 2. Unit root test. The Czech Republic Hungary Poland Romania Level ΔLevel ΔLevel ΔLevel Δ yct−2.428 ** −7.545 *** −2.696 *** −6.970 *** −3.642 *** −11.849 *** −2.945 *** −8.156 *** et−1.837 * −5.811 *** 1.066 −8.114 *** −0.323 −7.392 *** 1.532 −5.340 *** rerct−4.330 *** −6.986 *** −6.038 *** −7.856 *** −4.553 *** −7.492 *** −3.354 *** −7.577 *** Notes: ***, **, * denote rejection of the null hypothesis at 1%, 5%, and 10% respectively; Δis for first differences. 3.2. The Model of Exchange Rate Volatility The merit of the GARCH model stems from its ability to differentiate and recognize information that generates the exchange rate in a random process. The GARCH model is a robust model that is capable of dealing with the volatility associated with financial data characterized by skewed distribution and the problem of heteroscedasticity. In addition, the GARCH model allows for the differentiation and recognition of information that generates the exchange rate in a random process (Azid et al. 2005). Alternative measures of volatility such as the standard deviation and the coefficient of variation do not take into account the exchange rate uncertainty, which represents the unobserved fraction of exchange rate fluctuations (Barguellil et al. 2018). In the baseline model, the quarterly exchange rate volatility is specified as follows: Δet=Eet|Ωt−1+εt,εt/Ωt−1≈N(0,σt), (5) lnσ2 t=ω+α|εt−1| σ2 t−1−2 σt+γεt−1 σ2 t−1 +βlnσ2 t−1+δ1Δcpit+δ2CRISISt+ξt,(6) where et is the nominal effective exchange rate, Ωt−1 is the information set available at time t− 1, εt is the stochastic factor, and Δ is the operator of first differences. The expected value of exchange rate Eet|Ωt−1is modelled as ARMA(p,q) process. For the purpose of our study, ARMA(2,2) model is used. In line with Corsetti et al. (2017), the interest rate differential between foreign and domestic rates, as well as the lagged terms of trade, are included as explanatory variables too. Foreign interest rate, r∗ t ,is proxied by the 6-month LIBOR. As a measure of the domestic interest rate, rt , the money market rate is used for Poland and the lending rate is used for other CEE countries. The price index of domestically produced goods, pH,t , is proxied by the producer prices, with consumer prices in Germany being used as a measure of foreign prices, p∗ t. A one-period ahead forecast variance, σt , is a function of the mean ( ω ), the ARCH term ( α ), the EGARCH term ( β ), and three explanatory variables. A high value of α means significant impact of stochastic shocks, with a high value of β reflecting persistence in exchange rate volatility. The sum of both coefficients ( α and β ) indicates the speed of convergence of the forecast of the conditional volatility to a steady state (Koˇcenda and Valachy 2006). Asymmetry in the standardized shocks to lnσ2 t exists if γ= 0, why leverage exists if γ< 0 and γ<α<−γ (McAleer and Hafner 2014). Similar to Schnabl (2009), we used the consumer price index (CPI) as a proxy for macroeconomic stability. A country-specific dummy CRISIS t is supposed to control for asymmetric shocks. In the extended model, we test the link between exchange rate volatility and institutional features, as measured by the composite Index of Economic Freedom (heritage t ) and its sub-indices. As data on the Index of Economic Freedom are provided on the annual basis, we used procedure of the Holt-Winters exponential smoothing in order to obtain time series in the quarterly window. 3.3. The Model of Business Cycle A general representation for the cyclical components of real output model is given as follows: yct=a1yct+a2yeuroct+a3rerct+a4evark t+a5Δheritt+a6heritt+a7tradet+a8EUt+υt, (7) 38
Risks 2021,9,82 where yeuroct is the cyclical component of real output in the Eurozone (%), evark t are alternative measures of exchange rate volatility (k = 1, 2), heritt is the composite index of economic freedom as provided by the Heritage Foundation, tradet is the trade balance (% of GDP), EUt is the dummy for entering the European Union, and υt is the stochastic factor. Our regression model incorporates both exchange rate volatility around a constant level and the currency misalignment interpreted as a percentage deviation of the observed RER from the Hodrick-Prescott trend. Other explanatory variables include the Eurozone business cycle, the composite Index of Economic Freedom, the trade balance and the dummy for EU accession. The trade balance accounts for external factors that can affect the cyclical components of real output. A dummy for the EU accession is included as an explanatory variable that accounts for effects of economic integration of the CEE countries. Similar to the country-specific cyclical components of real output, business cycle for the Eurozone is obtained with the Hodrick-Prescott filter. As suggested by De Haan et al. (2006), a measure of economic freedom is used both in levels and first differences. It is demonstrated that such a specification explains significantly more of the variation in economic growth. While most of empirical studies confirm a positive relationship between all areas of economic freedom and economic growth, for example Doucouliagos and Ulubasoglu (2006) or Emara and Reyes (2020), it is not straightforward whether more of economic freedom is helpful to the same extent in stabilizing cyclical fluctuations of economy. Bjørnskov (2016) finds that crisis risk and duration are not affected by economic freedom, but it has an effect on the peak-to-trough GDP ratios and recovery times of crises. Two measures of volatility are employed, as presented above. Conditional variance from the baseline model, evar1 t , accounts for domestic consumer prices and crisis developments as external factors. On the other hand, conditional variance from the extended model, evar2 t , reflects impact of the Index of Economic Freedom across its nine sub-indices. In the extended model, we add the budget balance, budget t (% of GDP), and two measures of monetary policy, i.e., excess money supply, moneyc t (%), and the central bank reference rate, rcb t (%), to the list of explanatory variables. Excess money supply is calculated as a difference between money aggregate M3 and its trend obtained with the Hodrick-Prescott filter. While the use of the central bank reference rate reflects a standard monetary policy tool under a floating exchange rate regime, the excess money supply can control for attempts by the central bank to sterilize capital flows. 4. Results and Discussion 4.1. Determinants of Exchange Rate Volatility As the Jarque-Bera test implies non-normal error distribution for Δ e t ,weuse EGARCH(1,1) models with the asymmetric Student’s t-distribution. Estimates of the baseline model are presented in Table 3. Among determinants of the mean exchange rate, the interest rate differential is associated with depreciation for three out of four countries, being in line with the logic of Equation (3). However, the relationship for Romania is just the opposite. As for the lagged terms-of-trade, there is no evidence of a direct link between higher domestic prices and depreciation. For the Czech Republic, Poland, and Romania, there is an inverse relationship between both variables. Contrary to predictions of Corsetti et al. (2017), deflation abroad does not lead to depreciation of the exchange rate. The ARCH term ( α ) indicates that impact of “surprises” from previous periods is the strongest in the Czech Republic and Poland (higher than one α implies that shocks to exchange rate can destabilize its volatility), with a much weaker effect in Hungary and Romania. Based on the value of the EGARCH term ( β ), persistence of exchange rate volatility is observed at the statistically significant level in the Czech Republic only. As indicated by the sum of α and β , the speed of convergence of the forecast of the conditional volatility to a steady state is very slow in the Czech Republic and Poland. The standardized shocks to lnσ2 t are symmetrical in Poland, as the value of γ is not statistically different from zero. For the Czech Republic and Romania, the negative value of γ implies that 39
Risks 2021,9,82 negative news affects the exchange rate volatility more heavily than positive news. It is just the opposite in Hungary. No preconditions for leverage are met in any country. Table 3. Univariate EGARCH results (baseline model). The Czech Republic Hungary Poland Romania A. Mean equation results r∗ t−rt0.002 *** 0.001 *** 0.005 *** −0.001 *** pH,t−1−p∗ t−1−0.003 *** 0.008 −0.298 *** −0.007 *** B. Variance equation results ω−6.175 *** −6.687 ** −7.961 *** −6.671 ** α1.198 *** 0.660 * 1.172 *** 0.635 *** γ−0.380 * 0.491 ** −0.230 −0.316 ** β0.350 *** 0.212 0.060 0.298 Δcpit−60.059 *** −11.957 −13.118 14.232 ** CRISISt1.647 *** 2.309 ** 3.017 *** 1.010 ** Obs 80 80 80 80 AIC −5.222 −4.497 −4.203 −4.648 Notes: ***, **, * represent statistical significance at 1%, 5%, and 10%, respectively. Among the control variables, inflation contributes to exchange rate volatility in the Czech Republic and Romania, though with opposite signs. There is no difference between all four CEE countries in that crisis developments are associated with higher exchange rate volatility. In the extended model (Table 4), a statistically significant direct relationship between the lagged terms-of-trade and mean exchange rate emerges in Hungary. The ARCH effect somewhat decreases in Poland and Romania, with the opposite outcome observed in the Czech Republic and Hungary. As suggested by the value of β , there are no changes to the assessment of persistence in exchange rate volatility in the Czech Republic. However, exchange rate variability becomes more persistent in Hungary. Considering the sum of ARCH and EGARCH coefficients, a control for institutional features implies a significantly slower speed of convergence of the forecast of the conditional volatility to a steady state in Hungary. For other countries, changes are rather marginal. Asymmetry of the standardized shocks to lnσ2 t is confirmed for Hungary and Romania, while the negative coefficient of γ becomes insignificant for the Czech Republic. Among other changes, inflation becomes a factor behind lower exchange rate volatility in Hungary. Except the Czech Republic, the coefficient of CRISIStbecomes significantly lower for other countries. As suggested by the estimated coefficients on sub-indices of economic freedom, in a more liberal environment exchange rate volatility becomes lower. The only exception is Hungary, where monetary freedom brings about a higher exchange rate volatility. On the whole, the effects of economic freedom on exchange rate volatility are country specific. Property rights guarantees decrease exchange rate volatility in Romania. Fiscal health exerts the same effect on volatility in Hungary. Success in anticorruption activities contributes to a lower exchange rate volatility the Czech Republic and Poland. In the extended model, inflation becomes a volatility-decreasing factor in Poland, with a positive coefficient on libortchanging sign. No changes in the effects of crisis developments are observed. Figure 2 plots the evolution of quarterly exchange rate volatility by country, with the conditional variation obtained by fitting the baseline and extended EGARCH(1,1) models in green and black colors, respectively. For all countries, periods of low volatility are followed by periods of high volatility which could be associated with periods of global financial crisis of 2008–2009 and/or domestic financial turmoil (the Czech Republic in 2001–2002, Hungary in 2012–2013, Romania in 2004–2005). Differences between two measures of exchange rate volatility seem to be quite small in the Czech Republic and Hungary, while being more pronounced in Poland and Romania. After controlling for the institutional features, volatility becomes somewhat smaller. Except Romania, the exchange rate volatility 40
Risks 2021,9,82 rose from the beginning of 2007, with a peak during the world financial crisis of 2008–2009. Volatility then subsided in the majority of CEE countries, except Hungary in 2012–2013. For Romania, there is an increase in volatility around 2005 that is followed by a smaller jump in 2008–2009. Table 4. Univariate EGARCH results (extended model). The Czech Republic Hungary Poland Romania A. Mean equation results r∗ t−rt0.002 *** 0.002 *** 0.005 *** −0.001 *** pH,t−1−p∗ t−1−0.016 *** 0.009 *** −0.174 ** −0.006 *** B. Variance equation results ω−3.859 *** −1.989 −5.156 *** −5.692 *** α1.132 *** 0.735 *** 1.068 *** 0.575 ** γ−0.310 0.461 *** −0.148 −0.218 * β0.328 ** 0.405 ** −0.002 0.198 Δcpit−68.857 *** −38.708 ** −43.191 15.671 *** CRISISt1.832 *** 1.571 *** 2.965 ** 0.584 * herit5 t———−0.036 ** herit6 t—−0.104 *** — — herit7 t−0.052 ** — −0.067 *** — herit9 t— 0.059 ** — — Obs 80 80 80 80 AIC −5.215 −4.528 −4.160 −4.640 Notes: ***, **, * represent statistical significance at 1%, 5%, and 10%, respectively. (a) the Czech Republic (b) Hungary (c) Poland (d) Romania 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 0 0.0005 0.001 0.0015 0.002 0.0025 0.003 0.0035 0.004 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018 2019 Figure 2. Conditional variance from EGARCH(1,1) Model. 41
Risks 2021,9,82 To summarize, volatility patterns of the CEE countries seem to be similar in respect to both ARCH and EGARCH effects, especially after controlling for the institutional features. However, there are differences in asymmetry of volatility shocks and effects of control variables. In that respect, our results do not reject that volatility in the CEE economies has country-specific features (Koˇcenda and Valachy 2006). 4.2. Determinants of the Business Cycle We estimate Equation (3) with the general method of moments (GMM) estimator. Comparing with OLS or IV estimators, the GMM method is preferred for better dealing with problems of simultaneity bias, reverse causality, and omitted variable bias, as well as for obtaining estimates of dummy coefficients (Caporale et al. 2011). Table 5 presents the results for the baseline model of cyclical components of real output. Table 5. Regression results for cyclical components of output (baseline model). The Czech Republic Hungary Poland Romania (1) (2) (1) (2) (1) (2) (1) (2) yct−10.360 *** 0.357 *** 0.640 *** 0.638 *** 0.418 *** 0.430 *** 0.680 *** 0.669 *** yeuroct0.860 *** 0.866 *** 0.318 *** 0.324 *** 0.563 *** 0.524 *** 0.398 ** 0.388 ** evar1 t53.257 *** — −91.930 *** — 30.180 — −229.22 — evar2 t— 72.001 *** — −135.27 *** — 13.939 — −167.33 rerct— — 0.023 0.023 0.073 *** 0.080 *** — — rerct−10.034 0.035 — — — — 0.008 0.014 Δheritt7.773 7.901 −4.697 −3.577 0.967 1.165 7.909 8.169 heritt−0.196 *** −0.199 *** −0.091 * −0.084 * −0.088 * −0.092 * −0.174 −0.203 tradet−1−0.068 * −0.067 −0.077 *** −0.082 *** −0.039 −0.054 * −0.076 −0.076 EUt1.145 *** 1.149 *** 0.967 *** 0.985 *** 0.285 0.385 * 0.356 0.463 Obs 80 80 80 80 80 80 80 80 Adj. R20.92 0.92 0.87 0.87 0.68 0.67 0.71 0.71 Notes: ***, **, * represent statistical significance at 1%, 5%, and 10%, respectively. Standard errors are corrected for autocorrelation and heteroscedasticity (Newey and West 1994). For all countries, coefficients on the lagged dependent variable are significant at the 1% level. Inertia of cyclical developments in output is stronger in Hungary and Romania. These two countries are characterized by the lowest correlation with the business cycle of the Eurozone as well. Correlation between national and European business cycles is the strongest in the Czech Republic. According to the estimates of the baseline model, exchange rate volatility is associated with the risk of recession only in Hungary. An opposite effect is obtained for the Czech Republic. Exchange rate volatility is neutral in respect to the cyclical output developments in Poland and Romania. Such findings can be considered as evidence in favor of the exchange rate disconnect. However, neutrality of output fluctuations in respect to exchange rate volatility does not mean the same lack of reaction to currency misalignment. Exchange rate undervaluation has favorable growth effects in Poland. Assuming that there is exchange rate depreciation in response to such real shock as an increase in the foreign interest rate (Tables 3 and 4), it helps to stabilize the economy. Under such architecture of the exchange rate effects, a switch to free or managed floating looks like a reasonable exchange rate policy. In a wider context, our results imply that the Czech Republic and especially Poland both benefit from exchange rate flexibility and thus may not be interested in joining the Eurozone. However, such benefits are visible for Hungary, as the exchange rate volatility seems to be destabilizing. Among numerous explanations of the inverse relationship between exchange rate volatility and output, several ones are worth attention in the case of Hungary, such as higher risk premium, greater uncertainty about export revenues, higher risk for domestic and foreign direct investment, and adverse effect of credit constraints on domestic investments. Additionally, it is not ruled out that in a country with relatively low levels of financial development (real) exchange rate uncertainty exacerbates the negative investment effects of domestic credit market constraints (Aghion et al. 2009) or reflect disincentives for firms in creating jobs (Belke and Setzer 2003). 42
Risks 2021,9,82 There is no evidence of any favorable stabilization effects of economic freedom. A negative effect is the strongest for the Czech Republic, followed by Poland and Hungary. For Romania, a negative coefficient of herit t is insignificant. It is likely that our findings reflect an excessive level of economic liberalization attained during the period of negotiations with the European Union on the terms of EU accession. While the level of economic freedom is negatively correlated with cyclical fluctuations in output, changes in the level of economic freedom are neutral in respect to yct. Trade deficit is still an important factor behind economic growth in Hungary, Romania, and Poland (to lesser extent). Our results mean that economic recovery depends more on imports, not exports. In this context, traditional supply-side trade channels, as capital accumulation, modernization of industrial structure, and technological and institutional progress, seem to be relevant. As can be seen in the example of the Czech Republic and Poland, statistical significance of the coefficient on trade t−1 depends on the choice of the exchange rate variability. The stimulating effect of the EU accession is the strongest in the Czech Republic, followed by Hungary. For Poland, the coefficient of EU t is much smaller and statistically significant at the 10% level only in specification with evar2 t . No evidence of any EU accession effects is found for Romania. After controlling for fiscal and monetary policies (Tables 6 and 7), there are no changes in the assessment of exchange rate effects for Poland and Romania. For the Czech Republic, effects of exchange rate volatility on yc t are confirmed but the same favorable effect of the RER undervaluation emerges in the specification with the money supply. Similar stimulating effect of the RER undervaluation is found for Hungary, although only in specification with evar1 t . It is confirmed that exchange rate volatility contributes to a recession in Hungary. A negative link between economic freedom (in levels) and business cycle is very robust for the Czech Republic, while the estimates for other countries are specification dependent. For Hungary, economic freedom becomes neutral in respect to cyclical developments in output in 3 out of 4 specifications. It is just the opposite for Romania, where a statistically significant negative link between herit t and yc t emerges in specifications with both moneyc t and rcb t . Additionally, Romania emerges as the only CEE country with a statistically significant positive effect of an increase in economic freedom (in first differences) on output. For Poland, a negative relationship between herit t and yc t disappears in specification with moneyct, while being strengthened in the specification with rcbt. An excessive money supply, moneyc t , helps to stabilize output in the Czech Republic and Poland. Assuming a link between the money supply and exchange rate volatility (Devereux and Engel 2002), it only strengthens the assumption of shock-absorbing properties of the floating exchange rate regimes for the Czech koruna and Polish zloty. Table 6. Regression results for cyclical components of output (extended model-I). The Czech Republic Hungary Poland Romania (1) (2) (1) (2) (1) (2) (1) (2) yct−10.240 *** 0.238 *** 0.645 *** 0.619 *** 0.327 *** 0.331 *** 0.670 *** 0.668 *** yeuroct0.936 *** 0.939 *** 0.333 ** 0.375 *** 0.521 *** 0.493 *** 0.406 *** 0.381 ** evar1 t38.360 ** — −97.045 *** — 11.991 — −442.11 — evar2 t— 50.948 * — −136.54 *** — −0.478 — −517.79 rerct— — 0.034 * 0.031 0.083 *** 0.084 *** — — rerct−10.048 ** 0.049 ** — — — — 0.057 0.058 Δheritt4.655 4.685 −4.926 −4.460 −4.622 −4.768 11.400 11.059 heritt−0.113 *** −0.116 *** −0.072 −0.088 −0.037 −0.029 −0.277 * −0.267 * tradet−1−0.129 ** −0.128 ** −0.072 ** −0.074 ** −0.066 * −0.078 * −0.117 ** −0.120 ** EUt1.255 *** 1.261 *** 0.836 *** 0.926 *** 0.316 0.350 0.892 * 0.890 * moneyct0.064 * 0.064 * 0.016 0.001 0.066 ** 0.071 ** 0.033 0.041 budgett−10.085 *** 0.086 *** −0.014 −0.021 0.087 0.103 0.160 ** 0.163 ** Obs 72 72 76 76 80 80 73 73 Adj. R20.93 0.93 0.87 0.87 0.69 0.70 0.74 0.74 Notes: ***, **, * represent statistical significance at 1%, 5%, and 10%, respectively. Standard errors are corrected for autocorrelation and heteroscedasticity (Newey and West 1994). 43
Risks 2021,9,82 Table 7. Regression results for cyclical components of output (extended model-II). The Czech Republic Hungary Poland Romania (1) (2) (1) (2) (1) (2) (1) (2) yct−10.304 *** 0.301 *** 0.498 *** 0.514 *** 0.307 *** 0.311 *** 0.668 *** 0.664 *** yeuroct0.830 *** 0.834 *** 0.404 *** 0.392 *** 0.517 *** 0.482 *** 0.437 *** 0.458 ** evar1 t46.973 *** — −59.862 *** — 31.262 * — −83.717 — evar2 t— 62.817 *** — −91.840 *** — 21.202 — −15.943 rerct— — 0.015 0.012 0.091 *** 0.097 *** — — rerct−10.022 0.022 — — — — 0.064 0.067 Δheritt3.453 3.605 4.835 5.042 −1.372 −0.556 14.565 * 14.923 * heritt−0.164 ** −0.168 ** 0.113 0.102 −0.254 ** −0.256 ** −0.419 ** −0.446 ** tradet−1−0.087 * −0.086 * −0.147 *** −0.144 *** — — −0.084 −0.081 EUt1.207 *** 1.212 *** 0.783 *** 0.828 *** 0.756 ** 0.802 ** 1.377 ** 1.466 ** rcbt0.056 0.058 −0.137 *** −0.129 *** 0.119 *** 0.129 *** 0.021 0.025 budgett−10.077 *** 0.077 *** −0.026 −0.027 0.085 0.102 0.149 ** 0.153 ** Obs 80 80 80 80 80 80 68 68 Adj. R20.92 0.92 0.89 0.90 0.70 0.70 0.73 0.73 Notes: ***, **, * represent statistical significance at 1%, 5%, and 10%, respectively. Standard errors are corrected for autocorrelation and heteroscedasticity (Newey and West 1994). An increase in the central bank reference rate acts in the expected countercyclical manner in Hungary, while counterintuitive proportional link between rcb t and yc t is observed in Poland. It is possible to hypothesize that such an outcome results from efforts by the central bank to avoid appreciation of the exchange rate. As a higher central bank rate can tap capital inflows, sterilization policies substitute a stronger currency with a higher excessive money supply that ultimately becomes responsible for an increase in output. For Romania, it is likely that the lack of sensitivity to the central bank policy rate is explained by the balance sheet effect, as argued by Georgiadis and Zhu (2019). For the Czech Republic and Romania, there is evidence of stabilization properties of the fiscal tightening. The so-called non-Keynesian effects of fiscal policy mean that in the case of recession it is necessary to improve the budget balance, not engage in rounds of fiscal stimuli, as has been the case in many industrial countries since the world financial crisis of 2008–2009. When the extended dataset is used (using both fiscal and monetary variables), there are several changes to the assessment of trade and EU accession output effects. A negative link between trade t−1 and yc t is confirmed for Hungary and it becomes more stable for the Czech Republic. As for Poland and Romania, a negative impact of the trade balance is observed in specifications with moneyc t , but the effect is lost in specifications with rcb t . A strong procyclical effect of entering the EU is confirmed for the Czech Republic and Hungary. For Poland, a stimulating effect of similar amplitude emerges in the specification with rcbt, although it is not observed in the specification with moneyct. 5. Robustness Check As suggested by Rodrik (2008), we use the measure of currency misalignment based on the RER adjusted for the level of output. This measure adjusts the relative price of tradables to nontradables for the fact that the relative prices of nontradables tend to rise in line with the higher level of output. Our estimates support the assumption of the RER appreciation for the Czech Republic, Hungary, and Romania (Table 8). However, no link between the level of output and RER is found for Poland. Table 8. Estimates of the RER adjusted for the level of output. The Czech Republic Hungary Poland Romania γ07.748 *** 5.965 *** 4.450 *** 6.002 *** γ1−0.663 *** −0.276 *** 0.043 −0.294 *** Obs 80 80 80 80 Adj. R20.69 0.12 0.01 0.43 Notes: *** represents statistical significance at 1%. 44
Risks 2021,9,82 Estimates of the determinants of cyclical components of output are presented in Tables 9 and 10. With the use of the measure of currency misalignment based on the RER adjusted for the level of output, rerpppc t , the architecture of main relationships between exchange rate developments and cyclical changes in output is confirmed. First, exchange rate volatility is a stabilizing factor in the Czech Republic, with an opposite effect in Hungary. For Romania, exchange rate volatility is neutral in respect to the business cycle. As for Poland, a possibility of stimulating effect is offered by specification with evar1 t and rcbt, but it is not confirmed by the estimates of other specifications. Table 9. Regression results for cyclical components of output (extended model-I). The Czech Republic Hungary Poland Romania (1) (2) (1) (2) (1) (2) (1) (2) yct−10.187 * 0.185 * 0.586 *** 0.596 *** 0.366 *** 0.373 *** 0.640 *** 0.638 *** yeuroct0.949 *** 0.951 *** 0.355 ** 0.356 *** 0.474 *** 0.427 *** 0.303 ** 0.278 * evar1 t37.831 * — −87.808 *** — 22.424 — −444.68 — evar2 t— 49.362 * — −129.40 *** — 5.169 — −498.50 rerpppct— — 0.027 * 0.024 0.063 *** 0.063 *** — — rerpppct−10.033 * 0.033 * — — — — 0.040 0.039 Δheritt8.567 8.618 −2.809 −2.327 −6.044 −6.607 11.398 10.853 heritt−0.184 *** −0.187 *** −0.161 ** −0.157 ** −0.140 −0.126 −0.389 ** −0.372 ** tradet−1−0.180 ** −0.179 ** −0.085 ** −0.085 ** −0.099 ** −0.115 *** −0.160 ** −0.159 ** EUt1.805 *** 1.813 *** 1.256 *** 1.244 *** 0.743 ** 0.783 ** 1.212 ** 1.179 ** moneyct0.075 ** 0.075 * 0.015 0.014 0.045 0.052 * 0.034 0.040 budgett−10.067 *** 0.067 *** −0.032 −0.035 0.069 0.093 0.162 ** 0.161 ** Obs 72 72 76 76 80 80 73 73 Adj. R20.92 0.92 0.87 0.88 0.67 0.65 0.73 0.73 Notes: ***, **, * represent statistical significance at 1%, 5%, and 10%, respectively. Standard errors are corrected for autocorrelation and heteroscedasticity (Newey and West 1994). Table 10. Regression results for cyclical components of output (extended model-II). The Czech Republic Hungary Poland Romania (1) (2) (1) (2) (1) (2) (1) (2) yct−10.279 *** 0.276 *** 0.505 *** 0.501 *** 0.345 *** 0.354 *** 0.654 *** 0.651 *** yeuroct0.833 *** 0.837 *** 0.410 *** 0.398 *** 0.484 *** 0.437 *** 0.373 ** 0.391 * evar1 t45.579 ** — −52.010 *** — 47.452 *** — −157.76 — evar2 t— 60.632 ** — −81.150 *** — 41.580 — −82.239 rerpppct——−0.014 −0.014 0.059 *** 0.062 *** — — rerpppct−10.007 0.007 — — — — 0.024 0.023 Δheritt5.425 5.609 5.398 5.479 −6.651 −6.475 14.545 * 14.455 * heritt−0.196 *** −0.201 *** 0.197 0.186 −0.306 ** −0.303 ** −0.488 ** −0.510 ** tradet−1−0.085 −0.084 −0.147 *** −0.144 *** — — −0.101 −0.094 EUt1.305 *** 1.311 *** 0.528 0.541 0.992 ** 1.024 ** 1.548 ** 1.618 ** rcbt0.089 0.091 −0.164 *** −0.156 *** 0.100 *** 0.108 *** 0.039 0.044 budgett−10.074 *** 0.074 *** −0.029 −0.030 0.040 0.061 0.130 * 0.132 * Obs 78 78 80 80 80 80 68 68 Adj. R20.92 0.92 0.89 0.90 0.67 0.65 0.74 0.74 Notes: ***, **, * represent statistical significance at 1%, 5%, and 10%, respectively. Standard errors are corrected for autocorrelation and heteroscedasticity (Newey and West 1994). Second, cyclical output effects of currency misalignment are quite similar. Regardless of specifications of regression model or indicators of currency misalignment used, it is confirmed that undervaluation of the Polish zloty has a stimulating effect on output. As argued by Rodrik (2008), such an outcome can be explained by the size of the tradable sector (especially industry); however, it is less convincing that undervaluation is aimed at compensating for the institutional weakness and the market failures (information and coordination externalities). Undervaluation of the Czech koruna brings about stabilization effects only in the specification with moneyc t . The case is similar with the Hungarian forint, but in this case a positive coefficient on rerpppctbecomes insignificant in the specification with evar2 t. Higher levels of economic freedom unambiguously destabilize output for the Czech Republic and Romania. However, changes in the level of economic freedom have an opposite effect in the latter, quite similar to the estimates with rerc t (Table 7). For Hungary, a negative link between herit t and yc t becomes statistically significant in the specification with moneyc t . Estimates for Poland do not reveal any differences in respect to output effects of economic freedom. 45
Risks 2021,9, 124 financial systems are elaborate networks, liquidity effects tend to be self-reinforcing, which creates a range of multiple equilibria with different liquidity characteristics (Buiter 2008). A shortage of liquidity has obvious negative consequences. However, benign cyclical conditions may mask liquidity risks (Bessembinder et al. 2011). Moreover, ample market liquidity driven by cyclical factors may promote excessive risk-taking (Clementi 2001). It may also lead financial institutions to build up unsustainable leverage, with negative consequences for financial stability (Geanakoplos 2010). Similarly, irrational overconfidence in highly liquid markets favors trading frenzies, amplifying asset price bubbles ( Scheinkman and Xiong 2003; Brunnermeier 2008 ). This situation appeared after the crisis in 2007–2009, when an increase of control, and lower rates moved the lending industry towards the nonbanking industry. Furthermore, the COVID-19 crisis revealed the scale of leverage in nonbanking investment (Duffie 2020; Vivar et al. 2020; Vassallo et al. 2020). This rapid growth of the nonbanking sector, however, has rendered traditional monetary policy tools, such as increasing the money supply to banks and accepting broader collateral, insufficient. 2.1. Systemic Illiquidity: Research and Existing Measures Multiple illiquidity-related effects lead to systemic risk amplification. Table 1 sums up the more prominent literature contributions focused on such liquidity effects and their impacts on systemic risk. We specify these effects by categorizing them in relation to phenomena typical for systemic risk and the financial system sector in which they occurred in the cited studies. We also indicate other sectors that may potentially be affected by the described effects. The empirical studies on the effects presented above are presented in the papers by Coval and Stafford (2007), Loutskina and Strahan (2009), Aragon and Strahan (2009), and Boyson et al. (2010). Among more recent papers, one may find the study by Banerjee and Mio (2014), who researched the empirical impacts of new liquidity regulation on the banking sector, using the UK as an example. The paper by Chan-Lau et al. (2009) and the IMF’s (2009) Global Financial Stability Review contained two network models of interbank exposures, allowing them to assess the network externalities of bank failures using institutional data. In a similar framework, Sapra (2008) found that mark-to-market accounting creates an illiquidity contagion, unlike historical cost accounting. Boss et al. (2004) and Gofman (2015) used network models based on empirical data from the interbank market to model contagion signal transmission in the banking sector. Table 1. The studies of illiquidity effects categorized by the focus and sector of the financial system. Systemic Risk Occurrence Liquidity Effects Primary Sector of Occurrence Other Sectors Possibly Affected by the Effect Authors Illiquidity exposure Correlated exposures to illiquidity, free-riding Banking sector Shadow banking Bhattacharya and Gale (1987) Maturity rat-race and excessive short-term debt 1 Brunnermeier and Oehmke (2013) Illiquidity contagion Fire sales and their effect on prices Financial assets markets Banking sector, shadow banking, investment funds, SIFIs Shleifer and Vishny (1992) Market incompleteness and effects of illiquidity on prices Allen and Gale (1994, 2000a, 2000b) Snowball effect, in which the loss spiral interacts with a margin spiral 1 Brunnermeier and Pedersen (2009) Market illiquidity contagion Cespa and Foucault (2014) 52
Risks 2021,9, 124 Table 1. Cont. Systemic Risk Occurrence Liquidity Effects Primary Sector of Occurrence Other Sectors Possibly Affected by the Effect Authors Illiquidity-driven crises Constraints to arbitrage adding to illiquidity Financial assets markets - Shleifer and Vishny (1997) Arbitrage affecting liquidity both ways Gromb and Vayanos (2002) Runs caused by mark-to-market accounting Banking sector, shadow banking, investment funds, SIFIs Cifuentes et al. (2005) Bank runs triggering illiquidity, which triggers further bank runs Banking sector Diamond and Rajan (2005) Leverage, illiquidity spirals, and financial frictions Brunnermeier et al. (2013) Brunnermeier and Sannikov (2014) Informationally driven market freezes Interbank market fragility due to fear of adverse selection Banking sector -Flannery (1996) Lack of information about the counterparty risk causes the banks to stop lending to each other upon large shocks Caballero and Simsek (2013) Interbank market freezes caused by information asymmetry Heider et al. (2015) Information asymmetry as a source of repo markets collapse Financial assets markets Banking sector, financial markets, shadow banking, investment funds, Acharya et al. (2011) Collateral value vs. its price Gorton and Ordonez (2014) The table categorizes papers investigating liquidity risk effects that are relevant for systemic risk. The reported effects are grouped into four types of systemic risk triggers and arranged according to financial system sector or segment. 1 A loss spiral occurs when the losses on a few assets induce the market participants to reduce their positions in many other assets. Then these sales depress market prices, prompting further losses; a margin spiral occurs when market participants apply higher margin requirements because of the reduced market liquidity. Both effects reinforce each other, increasing the pressure to sell more assets (Brunnermeier and Pedersen 2009). More recent publications related to systemic risk treat illiquidity as the necessary condition for fragility accumulation or for contagion. In relation to market freezes, Afonso et al. (2011) revealed how interbank loans in the US became more sensitive to borrower characteristics during the crisis. Still, they reported no evidence of liquidity hoarding, in contrast to the predictions in the theoretical model by Allen et al. (2009) and to the empirical findings from the interbank markets in the UK (Acharya and Merrouche 2013), and in the euro area (Gabrieli and Georg 2014). On a similar note, Morris and Shin (2012) analyzed toxic asset market freezes caused by the breakdown of common knowledge about maximum losses. In turn, banking panics have been empirically studied by Iyer and Peydro (2011) and Iyer and Puri (2012), among others. Finally, Schrimpf et al. (2020) pointed out the consequences of the leverage and margin spiral that amplified liquidity risk in the euro area during the COVID-19 crisis, which was also emphasized in the recent Financial Stability Review (ECB 2020). All mentioned phenomena have liquidity problems at their core. 53
Risks 2021,9, 124 2.2. Measures of Systemic Illiquidity—Overview We will now discuss and categorize the measures proposed by other authors to measure systemic liquidity. They form two vast sets: simple indicators and much more complex—often multifaceted—models. Indicators are structurally simple constructs built of a few readily observable variables that allow for straightforward interpretation. By virtue, they are most often related to a specific segment of the financial system; therefore, they are not cross-sectional. Among financial soundness indicators (FSIs), one may distinguish current and forward-looking indicators. The first group allows the analysis of the current developments in the financial system, while the second one allows inferences to be drawn about possible future outcomes (see: Berg and Pattillo 1999 or Kumar and Persaud 2001). Sometimes, the same indicator may serve both purposes if analyzed vis-à-vis its historical path (trend) or distribution (quantile). Nelson and Perli (2007, p. 350) state that the US Federal Reserve was using more than 100 different indicators at the time of their publication. They discussed, for instance, indicators of market liquidity, including bid–ask spreads and volumes (e.g., on bonds, bills, and various derivatives, such as swaps), credit default swap (CDS) spreads, and liquidity premiums (yield on less-liquid security minus yield on highly liquid (benchmark) security). Indicators used by others include interbank market rates, interbank market traffic, and the demand changes for central bank facilities (Afonso et al. 2011). In relation to the banking sector, there is the basic liquidity ratio (short-term resources vs. short-term liabilities) and other similar ratios, such as quick assets to assets or client deposit ratios (Gersl and Heˇrmánek 2007). The ECB uses a broad set of indicators to analyze financial soundness, such as the ratio of liquid assets to short-term liabilities (see, e.g., ECB 20). Finally, basic composite indicators are available for advanced financial markets. These include volatility indices, such as the VIX. A complete list of liquidity-focused indicators is very extensive. However, Jobst (2012) selected the indicators most useful from the systemic risk perspective (Table 2). Table 2. Liquidity risk indicators. Quantity-Based Indicators Price-Based Indicators Monetary liquidity Base money and broader monetary aggregates Policy and money-market interest rates Access to central bank liquidity facility (e.g., bidding volume) Monetary conditions indices Foreign exchange reserves Funding liquidity Bank liquidity ratios Unsecured interbank lending (Libor–OIS spreads) Secured interbank lending (repo rates) Bank net cash flow estimates Margins and haircuts on repo collateral FX swap basis Maturity mismatch measures Violation of arbitrage conditions (bond–CDS basis, covered interest rate parity) Commercial paper market volumes Spreads between assets with similar credit characteristics Qualitative surveys of funding conditions Market liquidity Transaction volumes Bid–ask spreads on selected global assets Qualitative fund manager surveys The table presents existing liquidity risk indicator types categorized in relation to the type of liquidity and the numerical base of the indicator. Indicators are limited to those used in systemic risk analysis. Source: Jobst (2012, p. 13). 54
Risks 2021,9, 124 The systemic risk perspective requires a broader view that goes beyond a set of individual indicators for individual institutions or markets and allows for a system-level analysis. For this reason, multiple complex measures focused on systemic liquidity have been developed in recent years (see Appendix B). These measures significantly differ in terms of the data requirements and the output they produce. Some models relate to the whole financial system, while others have a narrower focus. There are methods that use the data from a given market segment to capture the liquidity crisis in that same segment. Others use data from one segment to shed light on another one. Finally, there are cross-sectional proposals. For some of the overviewed measures, the link between the measurement method and liquidity is direct (e.g., SRL in Jobst 2014). For others, it is indirect and comes from the theoretical justification of a given measure, rather than from the data per se. 2.3. Measures of Systemic Illiquidity—Empirical Application Possibilities For any risk measure to be effective, the theoretical assumptions necessary for its use must be fulfilled. In this study, the systemic illiquidity measure must be in line with the fact that during the sample period, the Central and Eastern European financial systems were characterized by: • Developing (frontier or emerging) markets in terms of the structure (banking sector dominance, with traditional banking products), maturity (affecting data availability and historical data span), and depth (including the limited variety of markets, the size of the stock market, and the numbers and types of existing financial instruments); • Relatively well-developed economies in terms of the stability of prices (relatively low and stable inflation), currency, capital flows, and monetary policy targets and tools. Furthermore, timing is critical in systemic risk monitoring. An adequate liquidity risk measure should produce at least a daily frequency time series, because liquidity may evaporate very fast. For the same reason, the input data should also be minimally affected by lags—any data reporting and preprocessing time must be minimal. Finally, the data should also represent all financial institutions that are systemically important (SIFIs) in the given system. After analyzing almost 60 systemic risk measures found in the literature, we identified only 13 measures focused on liquidity-related turbulence, despite the unargued impact of illiquidity on systemic risk. These are the approaches proposed by Getmansky et al. (2004) ; Chan et al. (2006); Perotti and Suarez (2011); Khandani and Lo (2011); Severo (2012) ; Brunnermeier et al. (2014); Jobst (2014); Greenwood et al. (2015); Karkowska (2015); and Duarte and Eisenbach (2019). We analyzed all of them in terms of applicability to the studied CEE region. We describe this process below and illustrate it in Table 3 afterward. We also provide details about each of these measures in Table A1 (Appendix B). The first step of elimination involved the practical aspects, such as data availability and dependability. For each country in our study, we asked whether solid data required for the calculation of a given measure existed. Several approaches required the data from market segments that were not sufficiently developed in the CEE region. More specifically, they were based on data regarding instruments or indices that were not quoted regularly (or at all) in frontier markets. For emerging markets, even though the data existed, it was too scarce to draw solid conclusions about systemic liquidity. Given the factors discussed above, we eliminated the measures based on hedge fund data (Getmansky et al. 2004; Chan et al. 2006) and the method utilizing derivatives (Severo 2012). Another question that we asked regarded the facilitation of daily risk monitoring. Market liquidity can evaporate from the markets very fast. Thus, to be useful for systemic risk analysis, a liquidity measure must provide information on a daily basis. Unfortunately, the existing methods focused on the banking sector could not be used to obtain a daily time series. They included the liquidity risk charges proposal by Perotti and Suarez (2011) , Liquidity Mismatch Index (Brunnermeier et al. 2014), Jobst’s (2014) Systemic Risk-Adjusted Liquidity Model, the Cumulative Distance to Default by Karkowska (2015), and the measure of systemicness 55
Risks 2021,9, 124 by Greenwood et al. (2015) and its expansion by Duarte and Eisenbach (2019). They were incompatible with the goal of creating a daily systemic illiquidity monitoring tool, even though the institutional focus of these measures was proper for the frontier and emerging markets in which banks are the main providers of systemic liquidity. Frontier stock markets are shallow and the data are scarce, which significantly limits the potential of measures based solely on stock-market data to indicate system-wide liquidity in the CEE region. Therefore, in our empirical analysis, we could not use liquidityfocused measures such as the liquidity factor (Pastor and Stambaugh 2003), the contrarian strategy and price-impact liquidity measures (Khandani and Lo 2011), or the liquidity noise measure by Hu et al. (2013). In effect, we were unable to identify any ready-made daily frequency systemic illiquidity measure that could be successfully applied in frontier and emerging markets. Therefore, we developed a new measure to fill the existing gap. Table 3. Analysis of systemic illiquidity measures for applicability to CEE. Measure Authors Is the Application Possible? (Data Limitations) Is Contemporaneous Measurement Possible? (Issues of Lags and Frequency) Does it Facilitate Systemic Risk Analysis? (Coverage/Proxying the Whole Financial System) Liquidity factor Pastor and Stambaugh (2003) YES YES NO A set of interpretable parameters Getmansky et al. (2004) NO x x Broader hedge-fund-based systemic risk measures Chan et al. (2006) NO x x A system of liquidity risk charges (LRCs) Perotti and Suarez (2011) YES NO x Contrarian strategy liquidity measure (CSL) Khandani and Lo (2011) YES YES NO Price-impact liquidity measure (PIL) Khandani and Lo (2011) YES YES NO Systemic Liquidity Risk Index (SLRI) Severo (2012) NO x x Daily liquidity noise measure Hu et al. (2013) NO x x Liquidity Mismatch Index (LMI) Brunnermeier et al. (2014) YES NO x Systemic risk-adjusted liquidity (SRL) model Jobst (2014) YES NO x Systemicness Greenwood et al. (2015) NO x x Cumulative Distance to Default (CDD) Karkowska (2015) YES NO x Aggregate vulnerability (AV) and illiquidity concentration Duarte and Eisenbach (2019) NO x x The table presents the step-by-step process used to find a systemic liquidity risk measure by answering three questions (YES/NO). A negative answer to a given question eliminated the measure from further analysis (x). 56
Risks 2021,9, 124 3. Parametric Models and Their Potential in Systemic Liquidity Analysis Financial market participants find multiple applications for the estimated yield curve. The first application of the Nelson–Siegel–Svensson methodology took place in the late 1980s, when Nelson and Siegel (1987) described their fitting technique for the first time. They used the estimated yield curve to predict the price of a long-term US Treasury bond. However, the application possibilities were much broader, including modeling the demand functions, testing theories regarding the term structure of the interest rates, and graphic display for informative purposes. The forward rate, a solution to the differential equation that generates spot rates that are applicable as a forecast, was a main driver for the parsimonious models’ exploration and their future popularity. After the introduction of Svensson’s (1994, 1995, 1999) extension to the Nelson–Siegel model, in which forward rates are used to indicate market expectations of future interest rates, the model started to be widely used by central banks to estimate market expectations of future rates, as well as depreciation rates. The reports published by BIS (2005) and ECB (Nymand-Andersen 2018) indicated that the Nelson–Siegel–Svensson model had become the most popular tool used to estimate the term structure of interest rates and market expectations. Additionally, the relatively recent appearance of negative rates called for a revision of term-structure estimation models, rendering various modern approaches inapplicable. However, as Garcia and Carvalho (2019) noticed, despite the negative rates observed in 20 countries, the Nelson–Siegel–Svensson model maintains good prognostic features and seems to be a good option for monetary policy institutions and market players. Other common uses for the structural models include marking-to-market, interest-rate modeling, and portfolio risk-management methods (see, e.g., Martellini et al. 2003 and Choudhry 2018). Structural models are also utilized for the calculation of systemic risk buffers in the insurance sector. In particular, the latest solvency requirements for economic and regulatory capital purposes suggest using the Nelson–Siegel–Svensson model to determine the ultimate long-term forward rate (UFR) (EIOPA 2017). This change resulted from the study by Zigraiova and Jakubik (2017), which emphasized the benefits of the Nelson–Siegel methodology (EIOPA 2016). Furthermore, parametric models also have been used in liquidity risk measurement. A good example is the study by Hu et al. (2013), which used the Svensson model on hedge fund returns and currency-carry trade data to create a measure of dispersion (a so-called “noise measure”). They constructed the measure of market noise by calculating the root mean square error between the market and theoretical yields, and applied it as a liquidity risk factor in portfolio risk modeling. Noise in the Treasury market informs about liquidity in the broad market because the Treasury market has low intrinsic noise, high liquidity, and low credit risk; i.e., the noise becomes high when liquidity drops. This particular application shows the potential to use structural models in liquidity risk measurement. Our idea consists of applying the structural models to measure the liquidity risk of the financial system as a whole. In particular, we used the information about how market yields deviate from the theoretically expected yields (modeled in different ways) in response to market frictions. We postulate that this phenomenon results from the liquidity shortage that manifests in response to systemic events. The main two channels of risk transmission here are information asymmetry and behavioral effects. To obtain information about systemic liquidity in the banking-based financial systems (such as CEE), we applied the measure to the interbank market. Therefore, we used the interbank market data and the information embedded in the interest-rate-term structure. The term structure of interest rates has informational value for systemic risk analysis. It reacts to the expectations of the market participants, especially in the short term. It changes with changing expected risk premiums for liquidity and default risk, and it depends on risk-aversion characteristics and preferences of the market participants. It also reacts to central banks’ activities (as proven inter alia by Lucas 1978; Cox et al. 1981; Shiller and McCulloch 1990; and Mehra 1995). Therefore, it is an essential source of information about 57
Risks 2021,9, 124 the stability of the financial market, and in a broader sense, the financial system affected by this market. The money market is a component of the financial market of assets with a maturity not exceeding one year, and by definition, it is a wholesale market with its core in interbank transactions. The interest rate on loans in the developed interbank market is a reference system for determining fixed-asset prices, as well as for loan contracts in the entire economy. Therefore, a well-functioning interbank market plays a key role in the transmission of monetary policy and the redistribution of liquid assets (Schmitz 2011). Central banks are interested in constructing interbank market yields mainly because of the information about the forward rates embedded in them. In fact, many financial instruments’ parameters in the CEE region are based directly on the interbank rates (Interbank Offered Rates—“IBOR”). Successful monetary-policy transmission involves a linkage between the banks’ operating target and the interbank lending rate. Thus, the conditions in the interbank lending market have significant effects on monetary-policy transmission. The weakening of this link creates a significant challenge for central banks and is one of the factors that motivated the creation of extraordinary liquidity and credit facilities. The importance of the money market in maturity transformation was relatively small before 1980. However, in recent decades banks have increasingly replaced governmentguaranteed individual deposits with uninsured wholesale deposits from the interbank money market. For example, their value in the US had increased by 160% by the year 2000 (Feldman and Schmidt 2001). At the same time, the loans granted to other banks in many countries have had a growing share in assets. For instance, at the end of 2005, interbank loans accounted for 29% of Swiss and 25% of German banks’ assets (Upper 2007). By the end of 2006, the interbank assets exceeded their shares in five out of eight developed countries. In many European banks, interbank assets accounted for five times or more than the equity (Upper 2011). Moreover, during COVID-19, the balance sheets for the biggest central bank have increased by 50%, making interbank loans a potential contagion channel. Indeed, one of the most characteristic symptoms of the global financial crisis was the increase in interbank market tensions, which manifested through a decrease in the turnover and a sharp increase in interest rates and spreads. Explaining this mechanism, Lubi´nski (2013, p. 22) articulated that “the contribution of the interbank money market to the stability of the system boils down to facilitating banks’ liquidity management.” Banks’ resilience to liquidity shocks and their ability to lend to each other is crucial for macroeconomic stability. The tensions in the interbank market limit this ability. Nonetheless, interbank loans are generally not included in the macroprudential regulations against overexposure and concentration, especially when groups of banks are concerned. Due to high flows in currencies and derivatives, mutual exposure of financial institutions is treated as an element of the sector’s specificity, and the resulting exposure to direct contagion is considered its attribute (Blåvarg and Nimander 2002). In addition, due to the lack of appropriate regulation, information on interbank exposures is usually not available, and market participants only have an approximate idea of the actual scale of dependence. For this reason, they do not know which banks have claims against bankruptcy, which may lead to a general undermining of trust (Schoenmaker 1996). As uninsured money-market instruments are associated with higher risk, they react to changes more quickly. Thus, their interest rates are more variable than the interest on regular deposits (Mishkin 2007). This market is also most sensitive to the loss of confidence that accompanies turbulence. This is usually immediately reflected in widening spreads, lowering numbers of transactions, and the shortening of their maturity. The market may also be ineffective due to the asymmetry of information, its incompleteness, or the market power of some entities (especially SIFIs). During turbulence, solvent banks’ liquidity problems may lead to insolvency because such banks cannot obtain sufficient interbank loans, and they must sell long-term assets below their fundamental value. Regardless of the nature of the adverse stimulus, interbank loans may contribute to contagion through an associated flow of information and the linking of portfolios and 58
Risks 2021,9, 124 balance sheets. In the first case, the contagion results from passing information from more liquid markets or markets in which prices are previously disclosed to others. Based on unfavorable information about one institution, business entities draw conclusions about the threat to others (which may be correct or not) (Kiyotaki and Moore 2002). Additionally, unfavorable interpretation arises from the observation that individual institutions’ portfolios and balance sheets are connected, while assets and liabilities must be equal. There are several methods proposed by various authors that use the interbank market as a source of information about systemic risk. Among these, one may find the aforementioned paper by Hu et al. (2013), but also the network model proposed by Elsinger et al. (2006) or the PA–CA–BA measure developed by Drehmann and Tarashev (2011). Among the most interesting empirical studies of the interbank market in terms of systemic risk is the publication by Allen and Gale (2000a, 2000b), who found that the interbank market’s susceptibility to adverse liquidity shocks depends on its structure. 4. Empirical Application of the Systemic Illiquidity Noise-Based Measure In a preliminary phase of this research, we successfully applied the proposed Systemic Illiquidity Noise-based measure, SIN, to the Polish interbank market (Dziwok 2017). This small study showed that the Polish market is sufficiently sensitive to new information inflow to apply a “noise-type” liquidity measure based on parametric models. Using daily WIBOR data and applying the Nelson–Siegel–Svensson models to limited time horizons, Dziwok (2017, pp. 34–35) confirmed that the model was suitable for analyzing systemic liquidity. The measure detected increased illiquidity-driven volatility in the Polish financial system around the global financial crisis. Kara´s (2019) confirmed these results in a longer horizon study (for the years 2006–2018). This method is advantageous for contemporaneous liquidity measurement. For instance, the Basel III liquidity criteria (LCR and NSFR measures) are based on the asset– liability position of the banking sector, and therefore they are prone to a time lag, because the data needs to be gathered, recalculated, and delivered (published) before the measures can be calculated. SIN depicts the current condition of the interbank almost instantly. This makes it a better indicator of financial system liquidity for systemic risk analysis. 4.1. Methodology Let us assume that τ is the point in time when the curve is constructed. Then, the value of a zero-coupon instrument at maturity is equal to one: Pt(τ,t)= 1, where tis maturity and capital growth takes a continuous form. A spot rate could be described as the average of instantaneous forward rates: i(τ,t)=1 t−τt τfτ(s)ds. (1) The value of a zero-coupon instrument at the moment τ when the curve is constructed Pτ(τ,t) is equal to the discount factor δ(τ,t) and follows the formula (de La Grandville 2001): Pτ(τ,t)=δ(τ,t)=e−i(τ,t)·(t−τ)=e−t τfτ(s)ds. (2) In a special case, when the moment of the rate’s construction is τ = 0, and assuming that: Pτ(τ,t)=P0(0, t)≡P(t),δ(τ,t)=δ(0,t)≡δ(t),fτ(s)=f0(s)≡f(s), (3) we may simplify Formula (2) into the following form: P(t)=δ(t)=e−i(0,t)·t=e−t 0f(s)ds. (4) 59
Risks 2021,9, 124 As outlined above, we can model the yield curve by constructing a continuous function based on existing discrete market data, using the functional relationship between the discount factor, the spot rate, and the instantaneous forward rate (2). The existing interrelation among a discounting factor δ(t) , a spot rate i(0,t) , and an implied forward rate f(s) enables us to search for only one of them. When one rate is established, the level of the others is received through equation (James and Weber 2000). We divided the yield-curve construction process into several phases, including selecting the data, building the cash flow matrix, defining the theoretical price vector, and establishing the estimation criteria (to fit the curve to real data). Phase 1: data selection. For the moment τ= 0 a set of kzero-coupon assets with different maturities is chosen, for which the present values are Plfor l=1, 2,. . . ,k, while the face value equals 1. Phase 2: building of the cash-flow matrix. For the collected zero-coupon data, a diagonal cash-flow matrix C is constructed, for which the elements correspond to the payments. Phase 3: a vector of theoretical prices. A vector of theoretical prices Pl=Pll=1,2,...,k is described as the product of the cash-flow matrix and the estimators of discount factors (interrelated with parameters through Formula (4)): ⎡ ⎢ ⎢ ⎢ ⎣ P1 P2 . . . Pk ⎤ ⎥ ⎥ ⎥ ⎦=C·δ(t1),δ(t2),···,δ(tk)T(5) Phase 4: the fitting criteria. The parameters are found by minimizing the mean square error (MSE) between theoretical and market data. The measure could involve either prices or yields that allow the function Ψ(·)to be minimized, such as: Ψ(P)= k ∑ l=1Pl−Pl2→min, (6) or Ψ(Y)= k ∑ l=1il−il2→min. (7) One of the main reasons for the extensive use of the parametric model for yield-curve modeling is its plainness and a limited number of estimated parameters. The Nelson–Siegel– Svensson model shows the instantaneous forward rate as a function of six parameters, β0 , β1,β2,β3,υ1,υ2, such that: f(s)=β0+β1·e−s υ1+β2·s υ1·e−s υ1+β3·s υ2·e−s υ2(8) The spot rate i(0, t)received through Formula (1) has the following form: i(0,t)=β0+(β1+β2)1−e−t υ1 t υ1−β2·e−t υ1+β3·⎛ ⎝1−e−t υ2 t υ2−e−t υ2⎞ ⎠(9) Through the description of the discount factor δ(t)=e−i(0,t)·t (Formula (4)), the spot rate (Formula (9)), and the theoretical vector of prices (Formula (5)), the estimation process (Formula (6)) aims to find parameters that minimize the function Ψ(·) , which involves imposing a set of specified initial conditions during the estimation process on the parameter vector. For each point of the estimated curve, the error value (i.e., the noise) reflects the degree of deviation between the theoretical and the market rates, regardless of the length of the transaction. 60
Risks 2021,9, 124 In the final step, we introduce a modification. For short-term instruments, their prices are similar, despite the significant differences in yields. This relation results from the nonlinear relationship between the price and the yield to maturity, which shows that for short terms, the asset price goes to unity (face value) (Schich 1997). To maximize the potential of the error function Ψ(Y) to serve as a noise-based illiquidity measure, we gave higher weights to errors in the prices of instruments with a shorter maturity. To improve the quality of Ψ(P)in this way, we used the concept of duration (Fabozzi 2007). Correcting the price-error function via the inverse of the duration allows the quality of matching to be increased for instruments with shorter maturities. After this modification, the yield-curve estimation requires finding the parameters that minimize the following function: Ψ(P/D)= k ∑ l=1Pl−Pl Dl 2 →min (10) In such a form, the noise-based measure better signals these deviations from the theoretical curve that are informative of sudden changes in the interbank market systemic liquidity position. This characteristic makes SIN even more useful for systemic risk measurement. 4.2. Data and Empirical Results We applied the presented computational methodology to selected Central and Eastern European (CEE) countries, including Bulgaria, Croatia, Czechia, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, and Slovakia. We used interbank data in the form of the Interbank Offered Rates. Data span encompasses years 2006 to 2020. Typically, in the CEE region, one can build a term structure of the spot interest rates for the interbank market (interbank deposit rates, Treasury bonds, and bills) and forward interest rates (interest-rate-based derivatives). The interbank deposit market is characterized by the ease of conducting transactions, their growing volume in the studied period, and the domination of short-term maturities (between one day (overnight, O/N) and one year). However, these characteristics relate only to the “IBOR” reference rates in the region. In several countries, continuous data for derivatives (e.g., FRAs, swaps) do not exist. Hence, to keep the estimations comparable, we limited the data used in yield estimations to IBORs for all the sampled countries. Figures 1–10 present the results. Generally, we can say that in all the studied cases, the SIN measure signaled increased risk in two periods between 2007 and early 2010, as well as between late 2010 and 2013. This observation corresponds to the unfolding of the global financial crisis and the sovereign debt crisis in Europe, validating the sensitivity of the SIN measure to the clear-cut financially driven systemic crises in the study period. We also observed a period of increased liquidity risk in the euro area during the ongoing COVID-19 pandemic. We also observed for all the analyzed markets that following the global financial crisis, liquidity volatility and illiquidity risk gradually fell to comparatively low levels around 2015. At that time, the macroprudential regulations aimed at the elimination of systemic problems from the interbank market were also introduced. The fact that these tools were, to a point, successful is visible in Figures 1–10. Although the risk was not eliminated in total, the markets entered the economic crisis caused by the pandemic in a completely different state of liquidity than was the case for the global financial crisis and the public debt crisis. The markets were characterized by a high shock-absorption capacity this time around. The SIN measure indicated a set of characteristic differences between the studied countries. The differences corresponded to the scale of risk and the specific timing of it. The results also pointed to country-specific periods of higher risk, which seemed to be driven by local events. Below we discuss the results in more detail, separately for the emerging markets and for the frontier markets. In this study, we analyzed three markets that were classified as emerging during the study period, namely the Czech, Hungarian, and Polish markets. These markets differed 61
Risks 2021,9, 124 ȱ Figure 10. SIN measure for Slovakia between 2006 and 2020. 4.3. COVID-19 Pandemic In the postcrisis period and before the COVID-19 pandemic, when ample liquidity still remained in the financial system—a remnant of the quantitative easing and prolonging negative interest rates—systemic illiquidity risk was minimal. The results suggested that the scale of risk in the interbank market has gone down. Nevertheless, one cannot be certain that this change is a permanent one. In fact, one may also argue that the risk was not mitigated, but simply shifted to the shadow-banking sector (ECB 2020). The direction of the diffusion of the COVID-19 crisis varied from the systemic shocks observed before. Compared to the crisis in 2007–2010, when the shock originated in the financial sector and then spilled over to the real economy, the COVID-19 pandemic spread oppositely: first, the real economy was affected, then the spillover to the financial sector followed (BIS 2020). For less-developed countries of the EME region, the COVID-19 pandemic mainly caused shocks in capital flows that influenced currency exchange rates, causing the depreciation of local currencies (Financial Stability Board FSB). Central banks started to offer foreign-exchange operations to stabilize the exchange-rate volatility, and immediately announced liquidity support to protect the financial system against any disruptions (IOSC 2020) . In the CEE region, the central banks of Hungary, Poland, and Romania purchased government securities in secondary markets to restore their liquidity and strengthen the mechanism of monetary-policy transmission (Cantúet al. 2021, p. 15). Among other actions, the central banks implemented reserve policy changes to quickly free up liquidity and established nontargeted lending operations in the first months of the pandemic (Cantú et al. 2021, p. 11). The immediate intervention of the central banks, which supported the process of market running, enabled them to minimize negative consequences of the pandemic for the financial sector in the study period. This was depicted by the low levels of the SIN measure. In the euro area, the situation in the interbank market was quite different. “While the core of the financial system—including major banks and financial infrastructures—entered the crisis more resilient than in the run-up to the global financial crisis, the COVID-19 shock led to severe liquidity stress in the system” (BIS 2021, p. 3). Described liquidity shocks were recorded by the SIN measure (Figure 11). They were short and took place at the beginning of the COVID-19 pandemic. In March 2020, asset markets froze in many countries. The growing cash needs resulted in the widening of spreads on fixed-income instruments, the yields (mainly long-term) of which increased significantly (Schrimpf et al. 2020; Hördahl and Shim 2020). The situation was observed mainly in the developed markets in Europe—especially in the euro area, where the outflow from money market funds reflected sudden liquidity needs (IOSC 2020). Investors tried to move from the more-liquid, but also riskier, sector (various asset classes) into a less-sensitive one (sovereign bonds). 68
Risks 2021,9, 124 ȱ Figure 11. SIN measure for Estonia, Latvia, Lithuania, and Slovakia (euro area) between 2019 and 2020. To compare the scale of risk with previous years, see Appendix A. The situation stabilized very quickly (by the end of March in the euro market) thanks to the immediate and synchronized reaction of the central banks. ECB announced and implemented several supportive actions: the temporary capital and operational relief in reaction to coronavirus (12 March 2020), the temporary pandemic emergency purchase program (18 March 2020) and a package of collateral easing measures (7 April and 22 April 2020) (EBA 2020). Our results confirmed that for the time being, these measures alleviated systemic risk in the financial system. One should bear in mind that the illiquidity and the effects of the COVID-19 pandemic may be delayed in time because of the financial help from euro-area governments that basically poured liquidity directly into the system, a series of actions that in this respect resembles quantitative easing (see Christensen and Gillan 2014). It will thus certainly be interesting to see how the SIN measure behaves in the upcoming months and in a longer period of two or more years, when the economic downturn that started with the pandemic will put most of the strain on systemic risk. The longer-term effects of the help packages will most definitely be significant, and it is difficult to say with certainty what adverse effects will follow. Nonetheless, at least three facts are certain. Governments are running unprecedented deficits and public debt has been building up fast, also in the face of the locked-down economy. In the past, the public debt buildup resulted in the increase of systemic illiquidity risk, among other things. This time, the inflation effects are also uncertain, as the monetary policy interest-rate channel working through the interbank market is almost nonexistent, with historically low base rates across the region. Secondly, the issues of moral hazard are clear. The large-scale support measures introduced recently “may induce moral hazard, causing investors to underestimate market risk [and] infer that liquidity support will always be provided” (BIS 2021, p.18), which will cause systematic mispricing of the market liquidity risk. Thirdly, many central banks have had deteriorated balance sheets ever since the global financial crisis, which was the effect of the previous unprecedented activities to stabilize the financial system, such as direct quantitative easing and buying back bad collateral from the banking sector. Now, “The need to intervene in such a substantial way has meant that central banks had to take on material financial risk” (BIS 2021, p. 2). It is impossible to say how this will affect their stability in the longer run and what the exit strategy is at this point. From a global perspective, we are facing unprecedented uncertainty in any economic and financial aspect that exists. The effects of the current events are so unpredictable for one reason: namely, the entire global economy and the entire global financial sector is being affected by the same crisis at once. It is no longer the case of one market problem spilling over to the rest of the world—this time the shock is simultaneous everywhere. There are questions regarding whether the rescue measures will be able to outlast the pandemic until it subsides for good, and what will happen when the support measures start to be phased out. 69
Risks 2021,9, 124 5. Conclusions In the course of this paper, we discussed the role of liquidity and its imbalances in systemic risk materialization, and we overviewed the results of existing systemic illiquidityfocused theoretical and empirical research. This literature review showed how important liquidity measurement and monitoring are in systemic risk analysis. Next, we discussed the applicability of the existing methods of systemic liquidity measurement to the CEE region. We concluded that these methods were inapplicable to the frontier and emerging financial markets under our analysis, and therefore a new approach is necessary to measure systemic liquidity risk for the given set of countries. This conclusion also held for many other less-developed financial markets in the world that are characterized by the same specificity as the countries analyzed by us. In this way, we found an existing research gap in systemic liquidity analysis that relates to countries with frontier and emerging markets. To fill the gap, we developed a new approach to illiquidity risk measurement using the interbank market data and Nelson–Siegel–Svensson methodology. Our measure—the Systemic Illiquidity Noise (SIN)-based measure—was empirically applied to a selected set of 10 CEE countries. In this way, we obtained the results of systemic illiquidity analysis for seven frontier and three emerging financial markets, for which such analysis was impossible before. The empirical results displayed a successful application of the proposed method. The SIN measure proved to be sensitive to the global liquidity breakdown that took place during the global financial crisis and the European debt crisis. Similarly, the measure was reactive at times of locally important systemic events, such as runs on banks or periods of significant currency depreciation in different countries. Moreover, SIN facilitated identifying three divergent sets of countries with different systemic liquidity risk characteristics. The results also captured the impact of introducing the euro currency on systemic liquidity risk. For the example of the euro area, we also showed that the SIN measure reacted to a liquidity shock caused by the current pandemic. This was despite the fact that the financial sector was very liquid before the shock. In effect, we may conclude that the SIN measure was sensitive to systemic liquidity shocks of different origins and magnitudes, regardless of the prevailing levels of liquidity per se. There were at least two significant advantages to the methodology developed in the course of this study. First, the SIN measure allowed for contemporaneous monitoring of systemic liquidity at a minimal cost—using well-known models and easily accessible data. This is of potential high value to any frontier or emerging market regulator and supervisor, as such monitoring may be easily introduced and sustained, giving macroprudential bodies a better chance to react to future financial crises and to mitigate potential costs of such crises. Second, although the study encompassed only 10 selected countries, given their diversity and the stability of our results, there is a potential for the successful application of our method to other markets, as long as there is a continuous interbank market there. Although the Interbank Offered Rates were used in this study, other similar types of rates also would be feasible, regardless of their fixing methodology. Such a potential of broad application of our measure creates an opportunity for a better and increased understanding of systemic liquidity disturbances on an international scale, regardless of the level of financial market development in each specific country. Finally, this study is of pragmatic value not only to regulators, but also to other participants in the financial system, especially banks, because they may also use the SIN measure to monitor the systemic liquidity risk that affects them so significantly. Betterinformed regulators and financial market participants would be better-equipped to make better risk management decisions, which in the long run might add to lowering systemic risk in the financial system as a whole. Author Contributions: Conceptualization, M.A.K. and E.D.; Data curation, E.D.; Formal analysis, M.A.K. and E.D.; Funding acquisition, M.A.K.; Investigation, M.A.K. and E.D.; Methodology, M.A.K. 70
Risks 2021,9, 124 and E.D.; Project administration, M.A.K.; Software, E.D.; Validation, M.A.K. and E.D.; Visualization, E.D.; Writing—original draft, M.A.K. and E.D.; Writing—review & editing, M.A.K. and E.D. All authors have read and agreed to the published version of the manuscript. Funding: This research project was funded by the National Science Centre under Agreement UMO- 2018/29/N/HS4/02783. Conflicts of Interest: The authors declare no conflict of interest. Appendix A ȱ Figure A1. Systemic Illiquidity Noise-based measure calculated for the euro area. Appendix B Table A1. Measures focused on illiquidity applicable to systemic-scale analysis. Measurement Output Authors Short Description Liquidity factor Pastor and Stambaugh (2003) A measure of market liquidity computed as the equally weighted average of the liquidity measures of individual stocks, using daily data. Specifically, the liquidity measure for a stock is the ordinary least squares regressed function of quantities of the daily returns on this stock in a given month, its volume, and the value-weighted market return. The measure relies on the principle that order flow induces greater return reversals when liquidity is lower, viewing volume-related return reversals as arising from liquidity effects. A set of interpretable parameters Getmansky et al. (2004) The proposal to use autocorrelation of returns of hedge funds as a proxy of their liquidity; the first-, second-, and third-order autocorrelations for each hedge fund’s returns are computed using an econometric model of return smoothing coefficients and used as a proxy for quantifying illiquidity exposure—the less liquid the fund, the more serial correlation is observed. 71
Risks 2021,9, 124 Table A1. Cont. Measurement Output Authors Short Description Broader hedge-fund-based systemic risk measures Chan et al. (2006) A set of three measures quantifying the hedge funds’ impact on systemic risk by examining the risk/return profiles of hedge funds, using returns and sizes data, at the individual and aggregate levels in relation to the investment risk they bear: autocorrelation-based measure of illiquidity exposures, a liquidation probability-based measure, and the regime-switching-based model quantifying the aggregate distress level in the hedge fund sector. Five measures of contagion potential Billio et al. (2012) A structured approach to measure systemic risk with indicators based on illiquidity (quantified by autocorrelation) and correlation, using principal component analysis (indicating the degree of assets commonality), regimeswitching models, Granger causality tests (indicating the direction of propagation of systemic triggers), and network diagrams (visualizing the connectedness via directional networks), focused on detecting of interdependence between banks, brokers, insurers, and hedge funds, based on statistical relations among their market returns. This way, the authors quantify the potential contagion effects in the analyzed financial system. A system of liquidity risk charges (LRCs) Perotti and Suarez (2011) Pigouvian charges are calculated per unit of refinancing risk-weighted liabilities based on a vector of additional systemic factors (such as size and interconnectedness) in a given period. The weighting function is decreasing and smooth to avoid regulatory arbitrage, which could distort market rates. The model is aimed at making banks internalize negative systemic effects of fragile funding strategies , but the computed size of charges may be used as a tool for quantifying liquidity risk showing which institutions generate more risk for the financial system. Contrarian strategy liquidity measure (CSL) Khandani and Lo (2011) A proposal to apply mean-reversion equity market strategy (buying losers and selling winners over 5 to 60 min lagged returns) to proxy the market-making (i.e., liquidity-provisioning) profits and to obtain equity market liquidity measure by observing the performance of this trading strategy. The authors showed that when it does very well, there is less liquidity in the market, and vice versa. Price-impact liquidity measure (PIL) An inverse proxy of liquidity, in which liquidity is measured with a linear-regression estimate of the volume required to move the price of a security by one dollar; i.e., higher values of lambda imply lower liquidity and market depth. The aggregate measure of market liquidity (PIL) is computed as the daily cross-sectional average of the estimated price-impact coefficients. Systemic Liquidity Risk Index (SLRI) Severo (2012) The SLRI is calculated by integrating the deviations of the following basis spreads: covered interest parity, the on-the-run versus the off-the-run interest-rate spread on government bonds, and the interest-rate spread between the overnight index swap (OIS) and short-term government bonds and the CDS basis spread, to represent the degree of their comovement first component score from a principal component analysis (based on historical time-series data) is used. 72
Risks 2021,9, 124 Table A1. Cont. Measurement Output Authors Short Description Liquidity Mismatch Index (LMI) Brunnermeier et al. (2014) Measures the difference between the cash-equivalent future values of the assets and liabilities of a bank; it utilizes the cash-equivalent value, which is the product of the asset or liability current value, multiplied by the liquidity weight (positive for assets, negative for liabilities), which depends on an assumed stress scenario, Value-at-Liquidity-Risk, defined as the quantile of worst losses (e.g., 5%), and the Expected Liquidity Loss , which corresponds to the average of the liquidity losses beyond this threshold. The authors proposed to use LMI to identify the most systemically important financial institutions. Systemic risk-adjusted liquidity (SRL) model Jobst (2014) Estimates the probability and severity of joint liquidity events; i.e., instances of banks jointly breaching their Net Stable Funding Ratios. Estimation process: 1. The components of the NSFR are valued at market prices in order to generate a time-varying measure of funding risk relative to prudential liquidity standards. 2. Aggregate cash flow implications of changes to liquidity risk are modeled as a put option to estimate losses expected from insufficient stable funding. 3. Individually estimated liquidity risk net exposures are aggregated via a multivariate distribution to determine the probabilistic measure of joint liquidity shortfalls on a system-wide level. Systemicness Greenwood et al. (2015) A linear model of fire-sale-induced liquidity crises, computing banks’ equity shock exposures to system-wide deleveraging and to spillovers induced by individual banks; systemicness is a (quantity) measure of a bank’s contribution to financial sector fragility, proportional to its size,leverage, and connectedness (owning large and illiquid asset classes to which other banks are also highly exposed).The key assumption is that banks target a given level of leverage, and this implies asset sales when leverage grows beyond the target. It allows the measurement of how the distribution of banks’ leverage and risk exposures contributes to systemic risk. Cumulative Distance to Default (CDD) Karkowska (2015) The distance-to-default measure is a market-based measure of credit risk based on Merton’s model, in which the equity of a firm is modeled as a call option on the value of its assets. The exercise price is equal to the value of the liabilities (the firm defaults when its assets’ value falls below its debt face value). For implementation, the face value of debt is assumed to be equal to the sum of short-term liabilities and half the long-term liabilities from the balance-sheet data. The model is calibrated using the analyzed institution’s market value and its equity price volatility. Karkowska used this method to derive the DD value for each institution forming the studied banking system and aggregated the data to obtain a systemic risk measure equal to the total probability of default of all the studied institutions. 73
Risks 2021,9, 124 Table A1. Cont. Measurement Output Authors Short Description Aggregate vulnerability (AV) and illiquidity concentration Duarte and Eisenbach (2019) An extension of the systemicness measure that includes the panel analysis tracking vulnerabilities over time. It takes banks’ leverage, asset holdings, asset liquidation behavior, and the price impact of liquidating assets in the secondary market as given, and models banks’ responses to negative liquidity shocks (fire-sale spillovers); using information embedded in repo haircuts to account for changes in asset-specific liquidity and flow-of-funds data, it allows to measure aggregate liquidity, defined as the sum of all the second-round spillover losses (not the initial direct losses) as a share of the total equity capital in the system; the factors’ decomposition applied produces a new component of AV, namely illiquidity concentration. The authors showed that the measure Granger-causes most other systemic risk measures. The table presents all the complex measures applicable to systemic risk analysis focused on illiquidity considered in the study. For each method or measure, we provide a short description of the mechanism behind the measurement output. Notes 1Countries were classified according to the criteria of the S&P DJI’s Global Benchmark Index for the study period. 2Poland instigated the emergency mechanism to limit public debt in 2014, when the debt was at 56% of GDP. 3 In that period, several cases of monely laundering were reported in the CEE region, including ABLV bank (Latvia), Danske Bank (Estonia), Versobank (Estonia), and other smaller banks in the Baltics. References Acharya, Viral V., and Ouarda Merrouche. 2013. Precautionary Hoarding of Liquidity and Interbank Markets: Evidence from the Subprime Crisis. Review of Finance 17: 107–60. [CrossRef] Acharya, Viral V., Douglas Gale, and Tanju Yorulmazer. 2011. Rollover Risk and Market Freezes. The Journal of Finance 66: 1177–209. [CrossRef] Afonso, Gara, Anna Kovner, and Antoinette Schoar. 2011. Stressed, Not Frozen: The Federal Funds Market in the Financial Crisis. Staff Report 437. New York: Federal Reserve Bank. Allen, Franklin, and Douglas Gale. 1994. Limited Market Participation and Volatility of Asset Prices. The American Economic Review 84: 933–55. Allen, Franklin, and Douglas Gale. 2000a. Bubbles and Crises. The Economic Journal 110: 236–55. [CrossRef] Allen, Franklin, and Douglas Gale. 2000b. Financial Contagion. Journal of Political Economy 108: 1–33. [CrossRef] Allen, Franklin, Elena Carletti, and Douglas Gale. 2009. Interbank market liquidity and central bank intervention. Journal of Monetary Economics 56: 639–52. [CrossRef] Andrie¸s, Alin Marius, Simona Nistor, and Nicu Sprincean. 2018. The impact of central bank transparency on systemic risk—Evidence from Central and Eastern Europe. Research in International Business and Finance 51: 100921. [CrossRef] Aragon, George, and Philip Strahan. 2009. Hedge Funds as Liquidity Providers: Evidence from the Lehman Bankruptcy. Working Paper 15336. Cambridge: National Bureau of Economic Research. Balogh, Eva S. 2015. Ten Hungarian Banks Failed Within One Year. Hungarian Spectrum, March 4. Banerjee, Ryan N., and Hitoshi Mio. 2014. The Impact of Liquidity Regulation on Banks. BIS Working Papers 470. Basel: Bank for International Settlements. Bank for International Settlements (BIS). 2005. Zero-Coupon Yield Curves: Technical Documentation. BIS Paper No 25. Basel: Monetary and Economic Department, Bank for International Settlements. Bank for International Settlements (BIS). 2020. A Global Sudden Stop. Chapter 1 and Chapter 2, Annual Economic Report 2020. Basel: Bank for International Settlements. Bank for International Settlements (BIS). 2021. COVID-19 Support Measures. Extending, Amending and Ending. April 6. Available online: https://www.fsb.org/wp-content/uploads/P060421-2.pdf (accessed on 23 March 2021). Bank of Estonia (BE). 2007. Financial Stability Review 2/2007. Available online: https://www.eestipank.ee/en/publications/series/ financial-stability-review (accessed on 23 March 2021). Bank of Estonia (BE). 2011. Financial Stability Review 2/2011. Available online: https://www.eestipank.ee/en/publications/series/ financial-stability-review (accessed on 23 March 2021). 74
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Risks 2022,10,22 is relatively common to find associations between characteristics such as size, fund structure and business model of credit institutions, with channels through which systemic risk emerges under certain conditions. Bostandzic and Weiß (2018) proposed that the methodology was used to choose variables and link them with systemic risk measures to evaluate the explanatory power of the above characteristics on the risk measures implemented in this study. Among the works with a research proposal similar to that for this study are the contributions by Lin et al. (2018) and Bostandzic and Weiß (2018), which also use three measures of systemic risk, previously exposed, to determine the financial institutions with a more significant contribution to systemic risk and determine the underlying factors that were conducive to such contribution. However, the two studies mentioned above use geopolitically different samples. Lin et al. (2018) use a sample of Taiwanese financial institutions; within this configuration, factors such as size, leverage ratios and price/book value influence the contribution to systemic risk in a transversal dimension. Bostandzic and Weiß (2018) use a sample of North American and European banks, finding that, on average, European banks contribute more to global risk, mainly due to a riskier portfolio and greater interconnection with the system. As of the time of writing this manuscript, no similar studies were found in which the three risk measures were used to investigate the Colombian economy. Thus, this work presents the first approach to determine the overall performance of these systemic risk measures implemented for the Colombian banking sector. 3. Proposed Methodology The following provides a summary of the basic inputs for constructing the systemic risk measures CoVaR and MES. Value at Risk (VaR) and expected shortfall (ES) are considered standard risk measures in financial institutions. VaR allows estimating the maximum expected loss of a risky asset or portfolio in a defined time frame and under a confidence level α , given (1 −α ) corresponds to the probability of a loss greater than the established level. For the case presented here, α equals 95%. The representation of this concept is shown below: PrR<−VaR(1−α)=(1−α)(1) where Ris a random variable that represents the profit or loss of a given portfolio. ES is the expected shortcoming conditioned on the losses, being more significant than that of the VaR, that is: ES(1−α)=−ERR≤−VaR(1−α)(2) Indeed, the expected shortcomings are the average returns in the months in which the portfolio losses exceed the VaR limit. 3.1. CoVaR It is important to note that downside risk statistics such as VaR are customary to present the outcomes in positive values (i.e., − VaR) as in Equation (1) since it is implicitly understood that these refer to a loss. However, when addressing the CoVaR methodology, the definition of VaR presented in Equation (3) shows that it does not follow this convention, in the author’s own words: “In practice, the sign is often switched, a sign convention we will not follow” (Tobias and Brunnermeier 2011, p. 7). PXi≤VaRi (1−α)=(1−α)(3) where Xi corresponds to the loss of the bank i for which the VaRi (1−α) is defined. Considering the previous definition, Xi corresponds to the negative variation rates of the market value of the total assets of bank i, which are covered in the data and variables section. 84
Risks 2022,10,22 When performing the analysis of the risk measure of CoVaR, a confidence interval equal to 95% (α=95%) is assumed for both the calculation of CoVaR and VaR. This confidence interval is commonly used for the development of this methodology, unless otherwise specified. Following the interpretation of the CoVaR made by López-Espinosa et al. (2012), the CoVaR is defined as the maximum expected loss for a specific portfolio (in this case, a representative portfolio of the entire banking market) for a given confidence level and time horizon, conditional on the maximum expected loss on the part of one of the institutions that make up the portfolio (in this case, bank), at a specific level of trust and time horizon. According to Tobias and Brunnermeier (2016), CoVaRj|i (1−α) distinguishes the VaR (1−α) system jconditioned on VaR (1−α)of entity i, which is: PXj≤CoVaRj|i (1−α)Xi=VaRi (1−α)=(1−α)(4) where Xj is the variable of the institution for which CoVaRj|i (1−α) is defined. This value corresponds to the negative weighted variation rate of the market value of the total assets banking system for institution i . While Equation (3) describes the definition of VaR, Equation (4) has a conditioned event attached to the definition of VaR; this implicitly defines the CoVaR of the banking system conditioned on bank i being at a level of (1−α) % of VaR. To calculate the entity i to the systemic risk of the system j (banking system for this study), Tobias and Brunnermeier (2016) suggest the following equation: DCoVaRj|i (1−α),t=CoVaRj|Xi t=VaRi (1−α) (1−α),t−CoVaRj|Xi t=Median (1−α),t(5) Equation (5) presents the contribution of bank i to the systemic risk of the banking sector as the difference between the CoVaR of the system conditioned on bank i being at a level (1 −α )% of the VaR and the CoVaR of the system conditioned on bank i being in its “normal” state (its median). This methodology uses quantile regression to calculate CoVaR because of its simplicity and efficiency (Tobias and Brunnermeier 2016). After the presentation of the methodology, some considerations will be presented below when interpreting the results. We note the lack of a causal relationship within the measure because it does not distinguish whether the contribution to systemic risk is causal or derived by common factors. Although indeed, the authors do not explicitly address the issue of causality, they mitigate the presence of common factors with the use of state variables because these fulfill the function of capturing the risk variation, which is not directly related to the risk exposure of the banking system (Tobias and Brunnermeier 2016). The econometric details of this tool are exposed in Appendix B. The choice of CoVaR as a tool to characterize systemic risk has, for this study, three important considerations, according to López-Espinosa et al. (2012). The first consideration is related to the possibility of deleveraging due to greater exposure to market risk in an environment of financial stress. The second consideration is related to the possibility of monitoring the dynamics presented by the systemic contribution of a particular bank to the system. The third consideration is the adaptability of configurations to condition nonlinear patterns and other relevant effects that account for the contributions of large banks to the banking system. 3.2. MES MES arises from the following argumentative structure developed by Acharya et al. (2017). Banks must break down the losses of the entire company into contributions of individual groups or negotiation tables (investments); in this way, the return of bank R can be decomposed into the sum of the returns obtained in each investment ri as fol- 85
Risks 2022,10,22 lows: R=∑ i yiri , where yi is the investment share i in the portfolio. From the definition of ES, we have: ES(1−a)=−∑ i yiEriR≤−VaR(1−α)(6) From this equation, the sensitivity of the general risk to exposure yi to each investment iis given by: ∂ES(1−α) ∂yi =−EriR≤−VaR(1−α)≡MESi (1−α)(7) From the above equation, MESi is the marginal expected shortcoming of investment i and is interpreted as the risk taken by investment i and how this attaches risk to the general return for the bank. The previous measure is derived from the perspective of a single institution, and its investment instruments can be approximated to a system comprising different firms (banks). In this way, the ES of the banking system can be established by considering R as the aggregate return of the banking sector. Under this configuration, the MES corresponds to the partial derivative of the ES of the banking system concerning bank participation when the banking system is in an adverse scenario (Boucher et al. 2013). In this way, each bank’s contribution to system risk can be measured through its MES; the more significant the MES of a bank, the more outstanding the bank’s contribution to systemic banking risk. Finally, the construction of the MES methodology presents, in a reduced form, a measure of systemic risk that is a function of observable data and statistical techniques similar to the models (Acharya et al. 2017). 3.3. SRISK SRISK, proposed by Brownlees and Engle (2016), indicates a financial institution’s contribution to systemic risk; the methodology is defined as the expected capital deficit conditioned on a significant market decline. SRISK is a function of institution size, leverage and the expected loss in share price conditioned on the market decline. SRISK is derived from the stock market and accounting data to construct a measure based on market behavior and the size and degree of leverage of firms; its purpose is to measure the expected undercapitalization of a firm conditioned on a systemic event (Brownlees and Engle 2016). The variable of interest is capital deficit, which, according to Brownlees and Engle (2016) , is obtained taking into account the minimum capital reserve that the firm needs (for regulatory reasons) minus its market capitalization; in this way, the capital deficit of firm i in month tis given by CSit (capital shortfall), which corresponds to: CSi,t=kAi,t−Wi,t=k(Di,t+Wi,t)−Wi,t(8) where Wit is market capitalization, Dit is the book value of the debt, Ait is the value of the quasi asset and k is the prudential capital requirement. For this study, the prudential capital requirement of 8% was taken as a reference. If the capital deficit determined with Equation (8) is negative, the result is interpreted as excess capital, a result that would indicate an “appropriate” functioning of the institution; if capital deficit is positive, the institution is in a state in which its main activities are at risk. We assume that the systemic event corresponds to a sufficiently extreme scenario, understood as a decline in the market below threshold C during time horizon h to increase the utility of SRISK; the justification of the above lies in the model developed by Acharya et al. (2017), where the capital deficit of a firm generates negative externalities if it occurs when the system is truly at risk; for this, they denote a return of the multiperiod arithmetic market between the period t+ 1 and t+h as Rmt+1:t+h and the systemic event as {Rmt+1:t+h<C} . For this study, a horizon of 6 months and a threshold of 40% are considered. A representation of this concept is presented below: SRISKi,t=Et(CSi,t+hRm,t+1:t+h<C)=kEt(Di,t+hRm,t+1:t+h<C)−(1−k)Et(Wi,t+hRm,t+1:t+h<C)(9) 86
Risks 2022,10,22 In order to calculate expectations, the authors assume (as in this work) that in the case of a systemic event, the debt cannot be renegotiated; from the above, it is necessary to: Et(Di,t+hRm,t+1:t+h<C)=Dit (10) Based on the above mentioned: SRISKi,t=kDi,t−(1−k)Wi,t(1−LRMESi,t)=Wi,t[kLVGi,t+(1−k)LRMESi,t−1](11) where LVGit corresponds to the ratio of quasi-leverage (Dit +Wit)/Wit and LRMESit to expected long-term marginal losses. The arithmetic multiperiod expected return of the firm conditioned to a systemic event, is defined below: LRMESi,t=−Et(Ri,t+1:t+hRm,t+1:t+h<C)(12) where Rit+1:t+h is the multiperiod arithmetic return of the firm between periods t+ 1 and t+h . Based on the above, SRISK is a function of the size of the firm, its degree of leverage and the expected devaluation of stock conditioned on a fall in the market. In this way, SRISK is higher for firms that are larger, have the most leverage and have greater sensitivity to market movements (Brownlees and Engle 2016). For simplicity, the prudential ratio k (8%), the threshold C (40%) and the time horizon h (6 months) are implicit in the SRISK notation. Brownlees and Engle (2016) use the SRISK of institutions to build a systemic measure of financial stress; in this way, the total systemic risk in the financial system is measured by: SRISKt= N ∑ i=1 (SRISKi,t)+(13) where (SRISKit)+ denotes max(SRISKit,0) . SRISKt is interpreted as the approximate total amount of capital that the government should provide to rescue the financial system conditioned on the systemic event. Similarly, only the positive contributions of SRISK are considered, and the negative contributions are ignored because these correspond to capital surplus scenarios. In a crisis, it is unlikely that much of the excess capital will be mobilized into loans; therefore, it is not necessarily available to support the firms affected by the systemic event (Brownlees and Engle 2016). For example, Cáceres (2009) presents evidence for the Colombian case, where a substantial reduction in lending activity was observed during 2008, mainly caused by the supply side. These facts support the idea that the excess capital of banking entities during a financial crisis does not represent a risk environment for these institutions, at least in the short term, but that it does not tend to mitigate the spread and accentuation of the systemic event significantly. The methodology seems to be simple; however, within its structure, a relative complexity is evident when considering the LRMES approximation, although there are different specifications and estimation techniques to obtain it. The alternative proposed by the volatility laboratory (V-Lab) is used. The LRMES is constructed as follows: LRMESi,t=1−exp(log(1−h)xβi,t)(14) where: βi,t=ρi,t σi,t σm,t(15) Expressions (14) and (15) show that the LRMES is a function of the time horizon h , in this case, a threshold of six months for the market return to decrease by 40%, and the beta coefficient of the firm, constructed from the dynamic correlations (ρit) and conditional volatilities (σit , σmt ) of bank i and system variable m (V-Lab n.d.). This study utilized the EGARCH model developed by Nelson (1991) for variance and a standard DCC model developed by Engle (2002) for the correlations. For more details, please see Appendix C. 87
Risks 2022,10,22 The choice of the EGARCH model for estimating conditional volatilities is the result of multiple tests performed with different models of the GARCH family of models. Indeed, the EGARCH model presents the best behavior fit of volatilities on the series of the rate variations of the value in the market of the total assets of each bank i . The criteria used to determine the above were based on the minimization of information criteria such as Bayesian and Akaike. 4. Computational Results The sample for this study comprises banks present in the Colombian market and listed on the Colombian stock exchange. It is common to find similar studies that investigate the same topic of interest as this study, but they consider many financial institutions, including insurance companies, pension funds and stockbrokers. The difficulty of accessing these financial sector segments lies in the fact that many of them are not listed on the stock market, thus preventing the proper application of the methodologies described above. Thus, only commercial banks are considered; these banks tend to be classified as the most systemically important and the most impacted by a shock from the system. This fact is due to the specialty of its business and its activities and access to liquidity configuring its actions within the system (León et al. 2011). The sample consists of the following commercial banks: Banco de BogotáSA, Banco Popular SA, Banco de Occidente SA, Banco Comercial AV Villas SA, Banco Bilbao Vizcaya Argentaria SA and Bancolombia SA. Data were collected monthly from 2008 to 30 June 2017; stock prices, financial statements and the number of shares in circulation for the banks were collected. The information on stock prices and financial statements is in Colombian pesos and was obtained from the National Registry of Securities and Issuers—RNVE. The period for the analysis of systemic risk measures corresponds to the availability of the information required for this study. The three primary sources of information in this study present different frequencies in their publication: daily, monthly and quarterly, for the respective prices of shares, financial statements and annexes. This temporary mismatch requires analyzing each of the sources to determine the frequency of the result of the risk measures are presented, resulting in the choice of a monthly frequency that implies making “transformations” to the series that are not in that frequency. In the case of share prices, the monthly average of these was taken as a reference. Likewise, the number of outstanding shares, both ordinary and preferred, was transformed monthly by keeping them constant during the quarter following the cut-off date. For the construction of this study, it is essential to carry out the analysis of the systemic risk measures with a monthly frequency instead of daily or weekly, as tended to be applied in previous studies. In this way, there is a tendency to give greater prominence to movements in the stock market, considering the behavior of the rest of the information constant with a lower frequency than that of share prices. Based on the above, the monthly frequency of the financial statements was selected as the reference for constructing risk measures. This configuration allows the results of the development of the institution’s activities to be counteracted with the changes in their valuation in the stock markets. Lastly, the adoption of a monthly frequency reduced the presence of seasonal discontinuities that tend to be observed when implementing a weekly or daily frequency. The share of assets in the banking sector for the sample considered is shown in Figure 1. As of 31 January 2008, the banking sector had 16 institutions recognized as banking establishments; however, at the end of the study period (30 June 2017), a total of 26 banking establishments were registered, representing a growth of 62.5% in the number of establishments. 88
Risks 2022,10,22 Figure 1. Participation in the level of assets of the selected sample on the sector. Source: Owner. For the construction of the DCoVaR, in addition to the accounting and stock market information for the banks, information concerning state variables was required. It was decided to use the state variables cited in the academic literature that addresses the DCoVaR methodology. These variables are used under the argument that the interconnection between the global and local financial systems would allow these variables, coming from the US economy, to capture the temporal variation in the conditional moments of the returns of shares in large parts of the economies. Along with these, it was decided to attach the performance of relevant variables for the Colombian economy, such as the conditional volatilities of the exchange rate and indices of the Colombian stock market and the TES; for more information, see Appendix A. According to Arias et al. (2010), we have calculated the state variables with the use of principal components. This methodology allows us to avoid multicollinearity between variables and capture 80% of the volatility of the standardized variables. The results matrix of this methodology is incorporated into the quantile regressions to capture time variation in conditional moments of asset returns. Based on the above, when incorporating the state variables into Equations (4) and (5), they would be as follows: PXi≤VaRi (1−α),M=(1−α)(16) PXj≤CoVaRj|i (1−α),MXi=VaRi (1−α),M=(1−α)(17) where M represents the matrix that contributes to the model 80% of the volatilities presented by the state variables, and their effect within the quantile regression is interpreted as the effect they exert on the systemic risk of the banking sector in a specific quantile q , given the risk contributed by the banking institution. 4.1. Characteristics That Contribute to Systemic Risk To determine the characteristics of banks that contribute to systemic risk in the banking sector, the works of Bostandzic and Weiß (2018), Laeven et al. (2016), Laverde and Gutiérrez- Rueda (2012) and Lin et al. (2018) identify three characteristics that tend to generate the channels through which a bank becomes systemically important, i.e., the size of the 89
Risks 2022,10,22 institution, the fund structure of the institution and the business model of the institution. For more information, see Appendix A. Each of these characteristics is described below. • Size of the Institution: Evidence indicates that size is correlated with the complexity of the institution and the interconnection with the rest of the system (Bostandzic and Weiß 2018). Large institutions are generally less substitutable, a circumstance that tends to present a greater risk to the system’s integrity. The natural logarithm of an institution’s total assets is taken as a proxy for the above characteristics. • Fund Structure: For the structure of banks’ funds, the leverage behavior of the institution and the fragility and composition of the funds are used. To capture the leverage behavior of an institution, the leverage variable proposed by Acharya et al. (2017) , defined as the quasi-value in the market of the assets divided by the market capitalization of the institution under consideration, is used. The long-term financing indicator developed by the Financial Superintendence of Colombia and the ratio between deposits and total obligations are used to capture the structure and fragility of the funds. • Business Model: Three variables are used that can adequately characterize this characteristic in banks to determine the structure of the business model: income other than interest, the portfolio as a percentage of assets and the portfolio provision’s natural logarithm. 4.2. Market Value of Total Assets Tobias and Brunnermeier (2011) analyze the VaR and DCoVaR based on the growth rate of the market value of the total assets of each institution; based on these, the market value of total assets is related to the supply of credit to the real economy. For this, the following transformation is performed: Xi t= MEi tBAi t BEi t −MEi t−1BAi t−1 BEi t−1 MEi t−1BAi t−1 BEi t−1 =LEVi tMEi t−LEVi t−1MEi t−1 LEVi t−1MEi t−1 =MAi t−MAi t−1 MAi t−1 (18) where: BAi t=Corresponds to the book value of the total assets of bank iat time t. BEi t=Corresponds to the book value of the total shares of bank iat time t. MEi t= Corresponds to the market value of the total shares of bank i at time t . This variable considers both ordinary and preferred shares issued by the institution under consideration. LEVi t=BAi t BEi t = Corresponds to the ratio between total assets and the book value of the shares of bank iat time t. MAi t= Corresponds to the market value of the total financial assets of the bank i at time t . The above is conducted for each institution included in the analysis. To determine the systemic risk in the market, the authors consider the weighted average of the growth rate of total assets at market price for all financial institutions; in this way, the returns of the representative systemic portfolio for bank iare configured according to: XS,i t= n ∑ j=1,j=i ωj,tXj t(19) ωj,t=Wj tn ∑ j=1,j=i Wj t−1 and 0≤ωj,t≤1 (20) where Wj t is the variable used to perform the weighting. Based on the findings by López- Espinosa et al. (2012), the lagged value of the total assets of the institution under consideration is used. 90
Risks 2022,10,22 XS,i t corresponds to the global systemic portfolio for each institution; this is a weighted average of the returns for all banks except bank i . With the objective of generating results for three risk measures that are “comparable”, it was decided to use the previously established variables for the construction of the CoVaR, MES and SRISK. Finally, Table 1 presents the descriptive statistics of the variables presented in Equations (18) and (19). Table 1. Descriptive statistics of the market value growth rate of total assets and the system variable. Descriptive Statistics N Banks AV VILLAS BANCOLOMBIA BBVA BOGOTÁOCCIDENTE POPULAR Bank System Bank System Bank System Bank System Bank System Bank System Mín 113 − 0.428 − 0.336 − 0.514 − 0.178 − 0.302 − 0.236 − 0.142 − 0.212 − 0.095 − 0.314 − 0.197 − 0.267 1st Qu. 113 − 0.049 − 0.038 − 0.056 − 0.031 − 0.059 − 0.023 −0.02 − 0.023 − 0.016 − 0.029 − 0.027 − 0.033 Median 113 0.01 0.028 0.051 0.01 −0.01 0.017 0.006 0.022 0.002 0.026 0.003 0.024 Average 113 0.029 0.027 0.03 0.017 0.014 0.021 0.01 0.021 0.009 0.024 0.004 0.022 3rd Qu. 113 0.073 0.104 0.117 0.069 0.056 0.073 0.038 0.075 0.023 0.087 0.039 0.07 Max 113 1776 0.362 0.594 0.284 0.341 0.24 0.157 0.298 0.199 0.326 0.252 0.258 Source: Owner. Table 1 shows two variables of interest for each Bank. The first column labeled with the name of the “Bank” corresponds to the result of Equation (18) that represents the rate of change in the market value of the total assets of a particular bank. On the other hand, the columns identified as the “System” name correspond to Equation (19). The Table 1 also reports the respective values of minimum, first quartile, median, average, third quartile and maximum for each of the previous variables. The sample period is between 28 February 2008 and 31 June 2017, with 1356 data. 5. Discussion and Managerial Insights Tables 2 and 3 provide the EGARCH, DCC and quantile regression results for each bank and their respective proxy of the systemic variable. Likewise, the results of different tests performed to determine the suitability of the selected variables are presented. These tests include only the EGARCH model estimation that includes an ARMA model for the mean. The values in parentheses correspond to the standard error for the coefficients of the EGARCH model and the respective lags of the ARCH effects test. Finally, ***, **, * denote the significance of the coefficients, tests, or statistics at levels of 1, 5 and 10%, respectively. The behavior of the different risk measures was assessed to address the issue related to the realization of a systemic crisis in the Colombian banking sector; the results are presented in Table 4 and Figures 2–6. 91
Risks 2022,10,22 Table 2. ARMA and EGARCH results for the sample data. Specification AV VILLAS BANCOLOMBIA BBVA BOGOTÁOCCIDENTE POPULAR System Bank System Bank System Bank System Bank System Bank System Bank ARMA AR1 −0.034479 *** (0.000002) −0.246957 *** (0.000079) −0.049502 *** (0.000090 −0.214773 *** (0.000130) 0.302472 *** (0.000307) −1.07579 *** (0.000134) −1.026864 *** (0.001008) −0.404966 *** (0.000017) −0.103862 *** (0.000009) AR2 0.842407 *** (0.000113) 0.151093 *** (0.000241) −0.195470 *** (0.000173) 0.824432 *** (0.000828) −0.726260 *** (0.002171) −0.94786 *** (0.000556) −1.095858 *** (0.001594) −0.731353 *** (0.000040) AR3 0.041250 *** (0.000139) −0.144043 *** (0.000095) MA1 0.275944 *** (0.000001) 0.224597 *** (0.000269) 0.470256 *** (0.000408) −0.133322 *** (0.000054) 1.05083 *** (0.003667) −0.25046 *** (0.000009) 1.125084 *** (0.000669) 0.533917 *** (0.000044) −0.046343 *** (0.000009) MA2 −1.095661 *** (0.000231) −0.991695 *** (0.000063) 0.538468 *** (0.000342) 0.86165 *** (0.001624) 1.234945 *** (0.000874) 0.686710 *** (0.000009) −0.076016 *** (0.000005) MA3 −0.240641 *** (0.000104) −0.188052 *** (0.000150) 0.278034 *** (0.000166) 0.292615 *** (0.000109) 0.229717 *** (0.000012) −0.073302 *** (0.000001) MA4 0.355981 *** (0.000014) 0.264615 *** (0.000076) −0.447289 *** (0.001104) −0.184071 *** (0.000318) 0.051772 *** (0.000028) EGARCH ARCH1 0.799366 *** (0.000303) 0.012710 *** (0.000031) 0.246493 *** (0.000754) −0.576275 *** (0.000133) 0.605561 *** (0.000035) −0.069722 *** (0.000166) 0.33965 *** (0.001264) 0.44333 *** (0.000105) 0.537437 *** (0.000114) 0.422964 *** (0.001229) 0.011183 *** (0.000047) 0.149429 *** (0.000013) ARCH2 −0.579092 *** (0.000059) 0.323211 *** (0.000908) −0.384483 *** (0.001015) 0.140552 *** (0.000034) −0.789385 *** (0.000009) 0.132865 *** (0.000190) 0.154661 *** (0.000050) 0.157589 *** (0.000014) ARCH3 −0.451457 *** (0.000105) −0.853260 *** (0.000486) 0.702936 *** (0.000578) 0.219627 *** (0.000737) −0.104234 *** (0.000032) ARCH4 0.471059 *** (0.000138) −0.376674 *** (0.000009) GARCH1 0.644798 *** (0.000292) 0.726499 *** (0.000853) 0.997655 *** (0.009199) 0.036037 *** (0.000044) 0.540945 *** (0.000161) 0.961643 *** (0.003489) 0.35768 *** (0.001203) 0.41782 *** (0.000115) −0.042545 *** (0.000041) 0.815780 *** (0.000302) −0.125789 *** (0.000047) −0.227812 *** (0.000061) GARCH2 −0.107191 *** (0.000058) −0.022221 *** (0.000009) 0.534309 *** (0.000690) −0.490466 *** (0.000137) −0.21096 *** (0.000147) −0.77307 *** (0.000482) −0.328719 *** (0.000051) −1.000000 *** (0.000075) 0.973641 *** (0.001867) −0.009186 *** (0.000001) GARCH3 0.787467 *** (0.001844) 0.296964 *** (0.000203) 0.688145 *** (0.000609) 0.70607 *** (0.000028) 0.53256 *** (0.000298) 0.493064 *** (0.000072) 0.712506 *** (0.000023) 0.036081 *** (0.000036) 0.734146 *** (0.000337) GARCH4 −0.748643 *** (0.001662) −0.62262 *** (0.001066) −0.86264 *** (0.000495) 0.037023 *** (0.000091) −0.066404 *** (0.000157) −0.682825 *** (0.000912) −0.129795 *** (0.000016) GAMMA1 −0.885067 *** (0.000101) 0.996195 *** (0.000574) 0.115575 *** (0.000175) 0.632487 *** (0.000820) −0.420413 *** (0.000873) −0.246882 *** (0.001143) 1.15198 *** (0.032347) 1.21458 *** (0.000511) 0.721123 *** (0.000233) 0.930880 *** (0.000041) 1.589955 *** (0.001813) 0.459014 *** (0.000084) GAMMA2 0.029432 *** (0.000030) −0.943253 *** (0.000887) −0.331180 *** (0.001007) −1.079320 *** (0.000993) −0.417899 *** (0.000043) 1.408392 *** (0.000516) 0.076924 *** (0.000026) 1.140554 *** (0.000129) GAMMA3 1.135463 *** (0.000306) −0.448216 *** (0.000036) −1.413676 *** (0.000585) −0.140913 *** (0.000193) −0.888913 *** (0.001216) GAMMA4 −1.427526 *** (0.0000499 1.201497 *** (0.002484) Source: Owner. 92
Risks 2022,10,22 Table 3. Estimated results for the data sample. Specifications Banks AV VILLAS BANCOLOMBIA BBVA BOGOTÁOCCIDENTE POPULAR System Bank System Bank System Bank System Bank System Bank System Bank Statistic of Weighted ARCH LM Tests LAG 3.562 * (8) 3.006 * (6) 2.149 (5) 0.2935 (8) 0.3971 (7) 0.8164 (3) 0.1252 (6) 0.006104 (6) 2.378 (7) 0.05129 (6) 0.01764 (8) 0.004192 (7) LAG 5.027 (10) 4.306 (8) 2.688 (7) 1.3683 (10) 1.5182 (9) 0.9351 (5) 0.4744 (8) 0.108698 (8) 2.679 (9) 0.34029 (8) 1.50173 (10) 0.008476 (9) LAG 6.327 (12) 4.751 (10) 3.553 (9) 1.8888 (12) 2.8858 (11) 1.656 (7) 1.0434 (10) 0.211909 (10) 4.512 (11) 3.94416 (10) 1.72761 (12) 0.013002 (11) Statistic of Weighted Ljung-Box Test on Standardized Residuals LAG(1) 0.345 0.225 0.5031 0.01174 0.4766 0.3104 0.9113 0.6687 0.003 0.1306 0.7995 0.07855 LAG[2x(p+q)+ (p+q)−1] 9.145 1.497 1.1633 1.43577 9.1705 5.7734 5.6035 2.1882 7.931 6.9093 1.3296 3.1782 LAG[4x(p+q)+ (p+q)−1] 15.927 2.522 2.2855 3.18303 18.0695 15.5513 8.8423 3.8606 13.376 11.9768 2.4611 6.2216 t-value of Sign Bias Test Sign Bias 0.2625 1.92338 * 0.474 1.0172 1.1945 0.1973 1.0692 0.6155 0.4014 0.5628 0.7137 0.9539 −Sign Bias 0.3557 0.31216 0.01592 0.21837 0.1144 0.4438 0.4976 0.061 0.6078 0.152 0.783 0.2512 +Sign Bias 1.289 0.05067 0.24486 0.02748 1.1768 0.1897 1.6055 0.2599 0.6237 1.532 1.476 1.2071 Joint Effect 2.043 6.30388 * 0.33806 3.16204 2.0518 0.2438 3.2451 1.4817 1.0996 2.3709 3.0869 7.3373 * Statistic of Adjusted Pearson Goodness-of-Fit Test Group 20 25.23 24.52 24.52 23.11 16.73 10.01 13.9 14.61 18.86 13.55 17.44 19.92 Group 30 32.75 30.1 29.57 26.38 36.47 20.01 22.66 29.04 27.97 22.13 27.44 20.54 Group 40 42.4 48.77 40.27 31.78 36.73 27.53 28.95 30.37 45.23 33.19 37.44 36.73 Group 50 47.62 58.24 37.88 48.5 42.7 37 44.08 31.2 47.62 39.65 47.62 37.88 Dynamic Conditional Correlation (DCC) p1 0.051755 ** (0.025315) 0.039008 ** (0.015635) 0.086556 *** (0.004175) 0.25804 *** (0.059624) 0.000000 ** (0.000000) 0.063595 *** (0.021299) q1 0.486054 *** (0.185008) 0.860154** (0.380315) 0.461762 ** (0.214375) 0.37346 *** (0.131889) 0.902351 *** (0.115806) 0.553310 *** (0.165288) Normal distribution Yes Yes Yes Yes Yes Yes Quantile Regression (τ= 0.05) Intercept −0.13094 *** (0.01403) −0.103357 *** (0.009594) −0.10624 *** (0.01127) −0.10761 *** (0.01062) −0.13298 *** (0.01459) −0.10531 *** (0.01152) Beta −0.03467 (0.22383) 0.189388 *** (0.055078) 0.20543 ** (0.07904) 0.73401 *** (0.17231) 0.73588 *** (0.18341) −0.11914 (0.16436) 93
Risks 2022,10,22 6. Concluding Remarks This paper proposes a methodology for measuring systemic risk in the banking system. The methodology estimates three systemic risk measures widely referenced in academic papers after the subprime crisis, known as DCoVaR, MES and SRISK systemic risk index. These measures individually tend to capture characteristics of systemic risk events. Therefore, the combined use would better understand and identify the causes or triggers of systemic risk in the Colombian banking sector. The proposed methodology has been tested in the Colombian banking system to determine if this sector presented a systemic crisis between February 2008 and June 2017. Similarly, the banks’ characteristics would have to support the contribution to the sector’s systemic risk. We found evidence that a systemic event would not have materialized in the Colombian banking sector. The conclusion was provided by the SRISK systemic risk index results, which capture a particular bank’s undercapitalization in the face of the prolonged market downturn. The results showed that none of the banks considered presented a scenario of undercapitalization, implying that the economic losses imposed, mainly due to the subprime crisis, failed to endanger the stability of the Colombian banking system. Finally, the research results that seek to determine the explanatory power of the variables used as proxies of the characteristics identified as causing the systemic importance of an institution showed that these would not be explaining the behavior of the risk measures. This result would reinforce the conclusion of the absence of a systemic risk scenario in the Colombian banking sector and that the observed results in the risk averages were the product of the external impacts to which the sector was exposed. For methodological terms, it is essential to point out that the configuration of a monthly frequency for the analysis of systemic risk measures could be generating a Loss of explanatory power by the state variables evaluated for the DCoVaR modeling. On the other hand, we found that the mechanisms identified as drivers of systemic risk did not explain the behavior of the risk measures obtained in this work. The need to exhaustively evaluate the mechanisms by which both direct and indirect impacts, coming from the crisis suppresses, interact with the financial and regulatory systems of the Colombian economy by proposing a topic of interest to be developed. However, we consider that the preceding does not distort the results of the risk measurements implemented in this study, but rather, it is a reflection of the complexity that sustains this type of risk for both local and international financial systems. Determining that the presence of systemic risk in the Colombian banking sector was not configured during the sample does not imply that these results should be interpreted in a wrong way that leads to thinking that the Colombian banking sector is prepared to face any risk arising from the international context. On the contrary, the subprime crisis scenario reveals the growing dynamism of financial systems, which poses new challenges for the administration and management of risk both at the institutional level and for financial regulatory institutions and the central bank. For this reason, it is necessary to carry out the consolidation of joint work for the appropriate schematization to address the mechanisms that trigger instability within the national financial sector, in search of safeguarding not only its stability and solidity, but also the productive sector of the country that is today more exposed to the dynamics presented by the financial systems, mainly national. The results observed through the SRISK systemic risk index consistently respond to the events observed during and after the subprime crisis. In this way, this index is postulated with a tool that could be implemented to base or complement an early warning indicator for the Colombian economy, since its implementation in this research adequately captured the periods in which the sector was more affected by the events of greater relevance in the international context. 100
Risks 2022,10,22 Author Contributions: Conceptualization, O.R.-E. and J.W.E.; methodology, O.R.-E.; software, O.R.- E.; validation, O.R.-E., J.W.E. and D.F.M.; formal analysis, J.W.E.; investigation, O.R.-E.; resources, O.R.-E.; data curation, O.R.-E.; writing—original draft preparation, J.W.E.; writing—review and editing, J.W.E.; visualization, O.R.-E., supervision, J.W.E.; project administration, J.W.E. and D.F.M.; funding acquisition, D.F.M. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Conflicts of Interest: The authors declare no conflict of interest. Appendix A Variable Name Definition Data Source VIX VIX measures market expectation of near-term volatility conveyed by stock index option prices Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org (accessed on 27 January 2020) LIQSPR Short-term liquidity margin. Difference between three-month repo rate and three-month treasury bill rate. Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org (accessed on 27 January 2020) TBR3M Change in the three-month treasury bill rate. Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org (accessed on 27 January 2020) YIESPR Change in the slope of the returns curve. Spread between ten-year and three-month treasury bill rate. Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org (accessed on 27 January 2020) CRESPR Change in the credit spread between BAA-rated bonds and treasury bill rate (both with a maturity of ten years). Federal Reserve Bank of St. Louis, https://fred.stlouisfed.org (accessed on 27 January 2020) VOLTRM Conditional volatility of the representative foreign exchange rate returns of the Colombian foreign exchange market. Obtained from an ARMA-EGARCH (3.4–7.2) model. Own calculations with data obtained from the Banco de la república de Colombia. VOLCOLG Conditional volatility of the Colombia’s stock market index returns. Obtained from an ARMA-EGARCH (5.3–7.1) model. Own calculations with data obtained from the Banco de la república de Colombia. VOLTES Conditional volatility of the returns of Colombia’s treasury bills index (IDXTES). Obtained from an ARMA-EGARCH (3.4–6.3) model. Own calculations with data obtained from the Banco de la república de Colombia. Banks’ characteristics Total Assets Natural logarithm of the asset’s book value. Own calculations with data obtained from the managerial indicators published by the Superintendencia Financiera de Colombia. 101
Risks 2022,10,22 Variable Name Definition Data Source Leverage It corresponds to the quasi-market value of assets divided by the market value of equity, where the quasi-market value of assets is the book value of assets minus book value of equity + market value of equity (Acharya et al. 2017). Own calculations with data obtained from the managerial indicators published by the Superintendencia Financiera de Colombia. Operating income different from interests Operating income different from interest divided by total interest income. Own calculations with data obtained from the managerial indicators published by the Superintendencia Financiera de Colombia. Portfolio Participation of gross portfolio in total assets. This variable is calculated as the division of the gross portfolio by total assets. Own calculations with data obtained from the managerial indicators published by the Superintendencia Financiera de Colombia. Portfolio provision Natural logarithm of the portfolio provision. Own calculations with data obtained from the managerial indicators published by the Superintendencia Financiera de Colombia. Long-term financing index Indicator that captures the need to finance short-term debts with long-term resources (assets). It is obtained by dividing the subtraction of the obligations and short-term assets by the long-term assets. Own calculations with data obtained from the managerial indicators published by the Superintendencia Financiera de Colombia. Deposits Corresponds to the division of total deposits by total liabilities. Own calculations with data obtained from the managerial indicators published by the Superintendencia Financiera de Colombia. Source: Owner. Appendix B Quantile Regression The econometric tool used to capture the codependency between institutions and the system is the Quantile Regression. This is considered adequate according to Arias et al. (2010), since: This methodology provides a more extensive analysis than ordinary least squares because it estimates the relationship between random variables considering different quantiles. ( ... ) Furthermore, this is a methodology that can be easily estimated for a large number of independent variables (p. 4). This Regression method also approximates the different risk scenarios since it enables the evaluation of specific quantiles, thus capturing a large part of the states of nature captured by the sample used. A low quantile of the distribution is taken into account to estimate the CoVaR since it is in these small quantiles that financial stress episodes materialize; for this reason, the Regression by quantiles is convenient and applicable. In general, estimating a Regression by quantiles consists of minimizing the sum of the residuals, weighted asymmetrically by a function that depends on the analyzed quantile τ . 102
Risks 2022,10,22 That is, the τ Quantile Regression, where 0 <τ< 1. The above can be represented as a solution for the following expression: minβ∑ t ρτ(yt−f(xt,β)) (A1) where yt is the dependent variable, f(xt,β) represents a linear function of the parameters and variables used to explain the behavior of yt and ρτ represents the weight assigned to each observation, depending on the quantile τ analyzed. In the methodology proposed by Koenker and Bassett (1978), they propose the following representation for Equation (A1): minβ⎡ ⎣∑ t∈{t:yt≥f(xt,β)} τ|yt−f(xt,β)|+∑ t∈{t:yt<f(xt,β)} (1−τ)|yt−f(xt,β)|⎤ ⎦(A2) Appendix C Specifications for the Modeling of Variance and Conditioned Dynamic Correlations (DCC) The equation to capture the time variation of volatility follows the structure of the exponential GARCH model (EGACH) developed by Nelson (1991), which presents a solution to the problems associated with pessimistic estimates of the variance parameters. This specification makes it possible to capture the differential effect observed in shocks from both the “bad” and the “good” news on the behavior and magnitude of volatility, facts not captured by the standard ARCH/GARCH models because in these the conditional variance is not affected by the sign of the errors of past periods. The equation of the EGARCH model for the volatility dynamics follows the following structure: lnσ2 t=ω+ q ∑ i=1αi2 t−i+γi2 t−i−E(|t−i|)+ p ∑ i=1 βilnσ2 t−i(A3) From Equation (A3), we have that the shocks of positive returns (“Good news”) have αi+γi impacts on the volatility of the return, while a negative shock in the returns (“bad news”) has a shock of αi−γi on the volatility of the return. The DCC conditioned dynamic correlation model specification uses volatility-adjusted returns as follows: ∈it=rit σit ,∈mt=rmt σmt (A4) Cor∈it ∈mt =Rt=1ρit ρit 1=diag(Qit)−1 2diag(Qit)−1 2(A5) where Qit is also called the pseudo correlation matrix, in this way, the DCC model then specifies the dynamics of the Qit pseudo-correlation matrix as: Qit =(1−αci−βci)Si+αci∈it−1 ∈mt−1∈it−1 ∈mt−1+βciQit−1(A6) where Si is the matrix of unconditional correlations of the adjusted returns of the firm and the market, the model is estimated in two steps through the quasi maximum likelihood estimation. For more details on the estimation of this model, refer to Engle (2002). References Acharya, Viral V. 2009. A theory of systemic risk and design of prudential bank regulation. Journal of Financial Stability 5: 224–55. [CrossRef] Acharya, Viral V., Lasse H. Pedersen, Thomas Philippon, and Matthew Richardson. 2017. Measuring systemic risk. The Review of Financial Studies 30: 2–47. [CrossRef] 103
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Citation: Ptak-Chmielewska, Aneta, and Paweł Kopciuszewski. 2022. New Definition of Default— Recalibration of Credit Risk Models Using Bayesian Approach. Risks 10: 16. https://doi.org/10.3390/ risks10010016 Academic Editors: Krzysztof Jajuga and Józef Dziechciarz Received: 18 November 2021 Accepted: 6 January 2022 Published: 9 January 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). risks Article New Definition of Default—Recalibration of Credit Risk Models Using Bayesian Approach Aneta Ptak-Chmielewska 1,* and Paweł Kopciuszewski 2 1Institute of Statistics and Demography, Warsaw School of Economics, 02-554 Warsaw, Poland 2Faculty of Art, Technique and Communication, Vistula University of Warsaw, 02-787 Warsaw, Poland; [email protected] or [email protected] *Correspondence: [email protected].pl or [email protected]; Tel.: +48-501-71-23-71 Abstract: After the financial crisis, the European Banking Authority (EBA) has established tighter standards around the definition of default (Capital Requirements Regulation CRR Article 178, EBA/GL/2017/16) to increase the degree of comparability and consistency in credit risk measurement and capital frameworks across banks and financial institutions. Requirements of the new definition of default (DoD) concern how banks recognize credit defaults for prudential purposes and include quantitative impact analysis and new rules of materiality. In this approach, the number and timing of defaults affect the validity of currently used risk models and processes. The recommendation presented in this paper is to address current gaps by considering a Bayesian approach for PD recalibration based on insights derived from both simulated and empirical data (e.g., a priori and a posteriori distributions). A Bayesian approach was used in two steps: to calculate the Long Run Average (LRA) on both simulated and empirical data and for the final model calibration to the posterior LRA. The Bayesian approach result for the PD LRA was slightly lower than the one calculated based on classical logistic regression. It also decreased for the historically observed LRA that included the most recent empirical data. The Bayesian methodology was used to make the LRA more objective, but it also helps to better align the LRA not only with the empirical data but also with the most recent ones. Keywords: new definition of default; credit risk models; Bayesian approach 1. Introduction Following the financial crisis, EBA has established tighter standards around the definition of default (Capital Requirements Regulation—CRR Article 178, EBA/GL/2017/16) (EBA 2017) to achieve a higher comparability and consistency in models used for credit risk measurement and procedures and capital frameworks across banks and financial institutions. These requirements were supposed to be implemented by the end of 2020. The initial deadline for the implementation (for all banks using IRB approach) was the 1st of January 2021. These deadlines were under discussion with European Central Bank (ECB) by many banks, and now they are under further revision by ECB due to COVID—19 circumstances (EBA 2016b). Banks were allowed to choose either a one-step, or a two-step approach: • One-step approach—the introduction of the new definition of default (DoD) and recalibration of all relevant models in one step; • Two-step approach—first the introduction of the new DoD and then recalibration of relevant models. The two-step approach was introduced because ECB realized that one-step approach would most likely automatically trigger a material change of all models within a bank. The new DoD concern how banks recognize credit defaults for prudential purposes and also include quantitative impact analysis and new rules of materiality. In this approach, Risks 2022,10, 16. https://doi.org/10.3390/risks10010016 https://www.mdpi.com/journal/risks 106
Risks 2022,10,16 the number and timing of defaults determine whether existing models and processes are valid. Banks need to update their risk management practices and support pricing and accounting decisions related not only to the expected credit loss methodology (according to International Financial Reporting Standards—IFRS 9) (EU 2016) but also those related to capital requirements models (according to Internal Ratings Based Approach -IRB and Internal Capital Adequacy Assessment Process—ICAAP) (ICAAP 2018). These extensive and very detailed guidelines often challenge information technology (IT) infrastructure, processes, data engines and data analytics, commonly used model risk platforms, model implementation and execution and automated solutions (BCBS 2013) .In addition, these new standards have a significant impact on risk governance and management, frameworks and methodologies, data quality process assessments and reviews, as well as model recalibration needs and internal management policies and approval processes (Basel 2010, 2014). In recent research on the credit risk parameters modeling, different approaches incorporate small samples problem incorporation (Zi˛eba 2017), unbalanced samples or unresolved cases for LGD. Different techniques are proposed starting with traditional logistic or linear regression approach, two-stage modeling, ensemble models (Papouskova and Hajek 2019) , and new machine learning methods or non-parametric approach (Peláez Suárezetal. 2021). In the literature of the PD modeling mostly a frequentist approach is applied (Bellotti and Crook 2009 ; Crone and Finlay 2012; Lessmann et al. 2015; Wang et al. 2020), while only limited use of a Bayesian approach is present (Bijak and Matuszyk 2017; Bijak and Thomas 2015 ). Among the papers using a Bayesian approach, many use noninformative priors on the assumption of the likelihood normally asymptotically distributed with large data (Bijak and Thomas 2015). Some papers emphasize the importance of expert information and use that to gain informative priors (Jacobs and Kiefer 2010; Kiefer 2009) or use coefficient estimates of past data as priors for current data (Bijak and Matuszyk 2017). However, we find that effective use of informative priors is still a gap to be covered. The main contribution of this paper is to propose an approach to complement the scarce observational data post redefinition of DoD with simulated data. The Bayesian method was applied to anticipate this simulated and empirical data for a basic credit risk measure: probability of default (PD) re-calibration. Such example of Bayesian approach utilization in modeling and calibration of credit risk parameters is promising for trying to incorporate such approach in calibration of PD, using parameters estimated on empirical data for new DoD as prior information. For other parameters such as loss given default (LGD) and exposure of default (EAD) only a theoretical approach was proposed. The paper is organized as follows: Section 1 provides an overview of the main implications of regulatory requirements impacting banks from a risk management perspective, with a focus on credit risk models. In this section a literature review focused on Bayesian approach is presented. Section 2 describes current challenges from a modeling perspective and discusses a methodological proposal to address these gaps. Section 3 provides an empirical example of application on real data for retail customers. Final section contains concluding remarks and suggestions for future research. 2. Implications of the New Definition of Default—Literature Review This section provides a summary of the main changes implied by the new DoD and its impacts for credit risk modeling with specific emphasis for the institution under study in this article (one of European commercial banks). The literature review is limited to regulatory background and to Bayesian approach in research as the main focus of the paper. The regulation contains specific requirements addressing specific event identification and threshold calculations. As a high-level overview, the main directions of the introduced changes can be split into specific focus areas: Days Past Due (DpD) calculation, Unlikeliness to Pay Criteria (UTP), Return to Non-Default Status (probation period), and Other Significant Changes (EBA/GL/2017/16, EBA/RTS/2016/06) (EBA 2014, 2016a, 2016b, 2017, 2020). 107
Risks 2022,10,16 Materiality thresholds for days past due (DpD) includes not only absolute but also relative materiality thresholds for counting DpD until the event of default at 90 DpD (for retail exposures: 1% relative and 100 euros absolute, for non-retail exposures: 1% relative and 500 euros absolute). The amounts past due represent the sum of all amounts past due, including all fees, interests, and principal. For the relative threshold calculation, this amount is divided by the total on-balance and off-balance exposure. If the principal is not repaid when an interest only loan expires, counting DpD starts from that date despite the fact that the obligor continues to pay interest. Unlikeness to pay criteria (UTPs) will be recognized if the credit obligation gets a non-accrued status according to the accounting framework. Specific credit risk adjustments (SCRA) can be as follows: (i) sale of client’s credit obligation recognized as defaulted if economic loss exceeds 5%, (ii) distressed restructuring if the net present value of the obligation decreases by more than 1% the obligation is considered defaulted, (iii) bankruptcy, (iv) additional indications of UTP (including fraud, significant increase in obligor leverage, individual voluntary arrangements, significant delays in payment to other creditors, impaired credit history indicators, expecting worst status). A minimum probation period of three months is required for all defaults. The exemption stands for distressed restructurings where applies a 1-year minimum probation period. It is required to monitor the effectiveness of the cure policy on a regular basis, including also impact on cure rates and impact on multiple defaults. Indeed, to implement the new DoD it is important to consider the holistic view of all processes impacted. In this respect, the key aspect to consider is a robust control framework from a risk management perspective. This can be disentangled into aspects related to external data, application of the definition of default from a broader banking perspective and specific features linked to retail exposures. The implemented new definition of default (DoD), with above mentioned changes comparing to previous DoD, had a significant impact on existing rating systems and credit risk models. Along with days past due (DpD) calculations, changes to relative and absolute thresholds and default triggers were proposed. The implemented changes imposed changes to A-IRB models, their discriminatory power and calibration accuracy. As a consequence, some changes to IFRS 9 models will be required. All A-IRB models with material change must be recalibrated and redeveloped (ECB 2018) . This exercise will require recalibration and/or re-development and validation of all existing rating systems. This will be executed in the following steps: •Data sources for modeling acquisition; •Simulation of data according to the new definition of default; •Back-test of all A-IRB models: PD, LGD, EAD; •Recalibration of all models that showed material change during back-test; • Recalibration of all IFRS 9 models as a result of A-IRB models recalibration and redevelopment; • New Margin of Conservatism (MoC) calculation for existing models and the new DoD; •Assessment of Risk Weighted Assets (RWA) impact of this change; •Additional validation of rating systems. As a consequence of PD, LGD and EAD models re-calibration all IFRS 9 models based on IRB parameters should be re-calibrated. Lifetime adjustment for parameters PD and LGD could change due to different starting points. Finally, all changes require independent validation. In the case of multiple models and portfolios it will be a time and resources critical process in bigger financial institutions as the one under study in this article. The literature on new DoD is rather limited. We focused on available examples of incorporation of a Bayesian approach in credit risk parameters modeling, mostly for PD and LGD parameters. A methodology for credit default estimates applying Bayesian mixture models was presented in Simonian (2011). The author proposed robust models taking parameter uncertainty into account to generate a new model. In the context of credit 108
Risks 2022,10,16 risk parameters modeling, robust models are beneficial to practitioners when estimating default probabilities. Much less frequent are examples of Loss Given Default (LGD) estimations using a Bayesian approach. One of the examples is for LGD for unsecured retail loans as often found difficult to model. The typical is two-step approach, two separate regression models are estimated independently. This approach can be potentially problematic because it must be combined to make the final predictions about LGD. LGD can be than modeled using Bayesian methods (Bijak and Thomas 2015). In this approach only a single hierarchical model can be built instead of two separate models. It makes this a more appropriate approach. Authors used Bayesian methods, and alternatively the frequentist approach, and applied to the data on personal loans provided by a large UK bank. The posterior estimates of means of parameters that have been calculated using the Bayesian approach were very similar to the ones calculated in frequentist approach. An advantage of the Bayesian model was an individual predictive distribution of LGD for each loan. According to regulatory requirements applications of such distributions include also the downturn LGD calculations and the so called stressed LGD calculations. The lack of data is typical for a low default portfolio (LDP). Probability of default (PD) calibration in such situation is limited to add conservative add-ons that should cover the gap of information due to scarce default event data. As described in the article (Surzhko 2017) , a PD calibration framework proposes Bayesian inference. The main idea proposed is to calibrate prior using a “closest” available portfolio with reliable default statistics. Author proposed the form of the prior, criteria for a “closest” portfolio selection and application of the approach to real life data and artificial portfolios. The advantage of the approach proposed in the article is avoidance of the subjective level of conservatism assumption. The author also proposed an approach that could be used for stress-testing purposes. Bayesian informative prior selection method is also proposed for including additional information to credit risk modeling, specifically for PD, and to improve model performance (Wang et al. 2018). Authors used logistic regression to model the probability of default of mortgage loans; they applied the Bayesian approach with various priors and the frequentist approach for comparison. The authors proposed for the Bayesian informative prior selection method the coefficients in the PD model as time series variables. They built ARIMA models to prognose the coefficient values in future time periods and used these prognoses as Bayesian informative priors. According to their results the Bayesian models using this prior selection method outperformed in accuracy both approaches: frequentist models and Bayesian models with other priors. Based on U.S. mortgage loan data, the probability of default at account level using discrete time hazard analysis was analyzed (Wang et al. 2020). Authors employed the frequentist and Bayesian methods in estimation of the parameter, and also the default rate (DR) stress testing. By applying the Bayesian parameter posterior distribution to simulating the DR distribution, they reduced the estimation risk coming from usage of point estimates in stress testing. As estimation risk was addressed in this approach, they obtained more prudential forecasts of credit losses. The simulated DR distribution obtained using the Bayesian approach with the parameter posterior distribution had a standard deviation more than 10 times as large as the standard deviation from a frequentist approach with parameter mean estimates. The same observation was found for VaR (Value at Risk) estimates. Such examples of Bayesian approach utilization in modeling and calibration of credit risk parameters are promising for trying to incorporate such an approach in calibration of PD using parameters estimated on empirical data for new DoD as prior information. From this perspective this approach is unique in the research. 3. Proposed Recalibration and Re-Development Methods for Credit Risk Parameters The introduction of the new DoD entails backtesting of the old models built on the earlier version of DoD and taking appropriate remediation actions. The easiest way to fit a 109
Risks 2022,10,16 Table 2. Default rate and arrears amount. Year Count Default Rate Arrears Max [Thousand EUR] Arrears Average [Thousand EUR] 2008 6939 0.72% 10.59 6.36 2009 8973 0.57% 15.93 3.32 2010 7502 0.72% 14.29 2.64 2011 6889 1.32% 19.29 4.82 2012 7860 2.01% 19.21 4.19 2013 8993 2.62% 26.60 7.72 2014 9774 2.34% 32.68 7.00 2015 10,725 2.45% 28.64 8.52 2016 12,545 2.18% 22.42 6.40 2017 16,832 1.73% 36.84 20.93 2018 3290 1.52% 19.81 6.21 Simulated defaults were selected within the period 2008–2018 but empirical defaults were more relevant after 2019. The sample was split into two independent subsamples for simulated and empirical defaults. While the model was built on the whole sample, including both the simulated and empirical defaults, the recalibration was mainly performed on simulated data with the additional use of empirical defaults according to the Bayesian methodology. The process of recalibration includes the following steps: 1. Building the new PD model on the joint population for simulated and empirical defaults, i.e., a mixed population. The model is built with use of logistic regression; 2. Calculation of Long Run Average (LRA) on the simulated data. LRA is the average of default rates calculated within the given period of time; 3. Adjusting LRA through the Bayesian methodology, which combines both the simulated and empirical data. The role of empirical data is to adjust the LRA calculated on the simulated data; 4. Final recalibration of the PD parameter estimated in the 1st step at the facility level according to the posterior mean calculated at the step 3. The final step is also performed with Bayesian approach. Summarizing the above algorithm, the Bayesian approach was used both to find the posterior estimators and final recalibration of the model but was applied to two different models. The PD model was built on a population of around 15K observations and a default rate of 0.017424. The entire data set contained around 400 risk drivers that had been previously selected due to their business intuitiveness and high data quality. The model estimation procedure was based on logistic regression with a stepwise selection method assuming that the p-value for entering the variable into the model was 0.05 and the p-value for remaining in the data was 0.001. The final model was based on around 10 variables with the p-value for the test of significancy of the coefficient at the variable not higher than 0.004. The estimation procedure was performed in SAS. Ultimately, PD was explained by some transformations of the following variables: - Absolute breach in the past; - Relative breach in the past; - Maximum DpD in the past; - Amount of maximum arrears in the past; - Total obligations; - The age of the customer; - Account balance. The quality of the model measured with Area Under ROC Curve (AUC) is 0.9. The model was built on the reweighted population to increase the default rate. Both simulated and empirical data were included in the population, but the defaults were underrepresented 116
Risks 2022,10,16 by the reduction in the population of “good” customers. The abovementioned reasons require a recalibration process, but the latter require more sophisticated methods such as Bayesian approach. The next step after building the model was the choice of the calibration methodology. The starting point in this process was the calculation of Long Run Average of DR (LRA) on the simulated data, which was 0.017499, while the standard deviation of its estimator was 0.131123. An attempt was made to include empirical data that turned out to be too small to estimate risk parameters and the Bayesian methodology was used. The Bayesian approach can be considered as an improvement of LRA using empirical data that was initially calculated on the simulated data. In general, the PD calculated on simulated data is prior information, but the PD calculated on empirical data provides real information that is not biased by the simulation process. Nevertheless, the empirical population is too small to recalibrate the model. According to the Bayesian methodology, the following assumptions (6) and (7) were made and incorporated into the MCMC SAS procedure: PDsim ∼N(E(LRAsim),std(LRAsim)), (6) where: PDsim is a random variable normally distributed around E(LRAsim). E(LRA sim ) and std(LRA sim ) are the expected value of LRA and standard deviation of LRA, respectively, calculated on the simulated data. The above assumptions related to the distribution of PD sim is directly derived from the historical data. The distribution of the variable PD sim is considered as prior distribution. This is the case where prior distribution is more objective as it is based on historical data. We used many different prior distributions which are allowed by SAS MCMC procedure and the final posterior results were very similar which further proves robustness of the posterior estimators. The likelihood which is the distribution of the PD emp parameter on the empirical data is the binomial distribution with the number of trials that equals the number of observations n emp in the empirical data and the probability of success equals the PD sim calculated on the simulated data. Hence, the likelihood can be viewed as a conditional distribution of the PD parameter on empirical data given the PD sim calculated on the simulated data is defined as follows: PDempPDsim ∼Bnemp,PDsim, (7) where: PD emp is a random variable binomially distributed (Joseph 2021) with parameters nemp and PDsim. Based on the above two distributions of prior and likelihood, the characteristics of posterior density were calculated using the MCMC procedure and the following results for the posterior expected value and posterior standard deviation were obtained: PDsim|emp =E[PDsimPDemp]=0.0155 s[PDsimPDemp=0.0021 The obtained posterior mean PDsim|emp of 0.0155 is the new calibration purpose. The following table (see Table 3) summarizes all considered PD estimators obtained on the simulated data, empirical data, development data and the Bayesian calculation as a posterior mean. Table 3. PD estimator results. Simulated Data (Prior) Development Data Empirical Data Posterior 0.017499 0.017424 0.015198 0.0155 The final recalibration of the PD parameter was based on the new recalibration purpose using the logistic Bayesian model. The default flag shows binary distribution with the 117
Risks 2022,10,16 expected value that equals the unknown calibrated PD (PD cal ) depending on the simulated PD (PDsim) and two additional parameters aand bas follows: D∼Bin(f(PDsim,a,b)PDemp PDcal =f(PDsim,a,b)=f(a·lnPDsim 1−PDsim +b)(8) where fis the logistic function. Parameters aand bare hyperparameters normally distributed with the following mean and standard deviation: a∼N(1,σa) b∼NlnPDsim|emp 1−PDsim|emp −lnDRmod 1−DRmod ,σb(9) where DRmod = 0.017424 is the default rate on the modeled data set. The concept of the expected value for parameter bis that it should be positive when PDsim|emp is higher than DRmod but otherwise negative bearing in mind that this is an additive part to the log odds. The formula for b parameter is the main point in this Bayesian model to include the information about the posterior mean to which to calibrate the model. Both standard deviations σa and σb have standard deviation uniformly distributed over the interval (0,1). The upper value of the interval is based on previous experiments with data. An alternative approach to find estimators aand bis to use simple non-Bayesian regression logistic. The Bayesian approach is key in the previous step to find the posterior mean, but here it only serves as a consistent methodology and is not needed for finding the final recalibration formula. On the other hand, it can be easily extended by providing a greater external knowledge of the estimated parameters. Therefore, it can be taken as a pattern for the further calculations on other data, which is very flexible. Ultimately, posterior averages for aand bwere calculated, respectively (see Table 4). Table 4. Posterior parameters for the Bayesian approach. Parameter Mean STD 95% HPD Interval a0.88 0.0896 0.7229 1.0791 b−5.4135 0.2399 −5.8676 −4.9243 sigma_a 0.4013 0.298 0.00168 0.9242 sigma_b 0.9423 0.0535 0.8326 1 In order to obtain the final PD estimation formula, the logistic regression Equation (8) for the entire PD was applied. Additionally, the PD calibrated without the Bayesian method was calculated for comparison (see Table 5). It is worth mentioning that the simple logistic regression model based on the Equation (8) but without taking into account parameter distributions can be built with use of the following weights for all observations to adjust the mean default rate to posterior mean. In case of Bayesian approach weights were not needed as bparameter in the model plays the role of such adjustment. w=PDsim|emp 1−PDsim|emp ·1−DRmod DRmod (10) Table 5. Parameters calculated without the Bayesian approach. Parameter Mean STD 95% HPD Interval a1.1087 0.0192 1.0736 1.1498 b−5.9081 0.0512 −6.0129 −5.8132 118
Risks 2022,10,16 All PD’s distributions for the raw PD obtained from the model built on the reweighted sample, PD calibrated without the Bayesian methodology and PD using the Bayesian approach are presented below in Figure 6a,b. (a) (b) Figure 6. PD distribution: ( a ) Raw PD; ( b ) PD calibrated with and without the Bayesian approach. Source: own elaboration using SAS Enterprise Guide. Summarizing the classic approach to building the logistic regression model as the final calibration formula is possible only with introducing weights for observations; the Bayesian approach does not require weights but an appropriate definition of distributions for regression parameters. 5. Conclusions and Discussion Recent changes in economy caused by COVID pandemic (Batool et al. 2020) had an impact on sharing economy but also a significant impact on the banking sector. Recent changes in Industry 4.0 were also not neglectable for Banking 4.0 (Mehdiabadi et al. 2020). Significant regulatory changes imposed by regulatory authorities followed those changes. The regulatory requirements related to the change in the definition of default have significant impacts from a banking perspective, with the most material one on credit risk modeling. From a methodological point of view, all provisioning IFRS9 and capital IRB regulatory models need recalibration. At the same time, empirical evidence that is obtained when the new definition is applied to real portfolios is still being collected. In this context, the paper provides an overview of the main implications deriving from the regulation in different risk management areas (e.g., data, default definition, implementation, identification) and discusses a methodological proposal for IRB modeling recalibration to address the current challenges. The idea is to leverage the Bayesian approach for PD recalibration by retrieving information from both simulated and empirical data (e.g., a priory and a posteriori distributions). As discussed in the methodological section, this mathematical approach seems to be a promising solution to building a robust framework in the current phase and addressing the gaps. In our plans for future research, we foresee an empirical study to test how the proposed methodology can perform in different credit risk modeling contexts. Finally, we used the Bayesian approach in two steps: the first basic approach is to calculate the LRA on both simulated and empirical data. In addition, we used the same approach for the final model calibration to the posterior LRA. In summary, the Bayesian approach result for the PD LRA was slightly lower than the one calculated based on classical logistic regression (Figure 6). It also decreased for the historically observed LRA (Table 3) that included the most recent empirical data. The Bayesian methodology was used to make 119
Risks 2022,10,16 the LRA more objective, but it also helps to better align the LRA not only with the empirical data but also with the most recent ones. It allows us to consider the LRA as a random variable, where its variance tells us more about the significance of the point estimation. The greater the variance, the more empirical data need to be included in the calculation of the end value. When comparing the standard deviation of the LRA calculated on the simulated data, which is 0.131123 with the mean of 0.017499, there is still room to improve this estimator with less volatile data, such as empirical with the mean LRA of 0.0155 and much lower standard deviation of 0.00214. To sum up, it is a unique approach to statistical modeling that can combine different information, even expertise, not covered by historical data. Moreover, it can be applied to both LGD and EAD, but PD is preferred as the starting point. Promising results for PD were also obtained by (Wang et al. 2018) with ARIMA model results as prior for Bayesian approach confirming outperformance comparing to frequentist approach. From a practical point of view, using the Bayesian approach can significantly decrease the capital requirements, thus making savings for organization from managerial perspective. Close to the empirical values, the calculations of capital adequacy and provisions are as more precise, keeping of course regulatory requirements fulfilled. A weakness of the proposed approach, however mitigated, is due to normal distribution assumption. Some ideas for future research rely on further investigation of the Bayesian approach, but perhaps for small samples or other parameters as well. This approach seems also promising for IFRS 9 lifetime parameter estimation. Author Contributions: Conceptualization, A.P.-C. and P.K.; methodology, A.P.-C. and P.K.; software, P.K.; validation, A.P.-C.; formal analysis, P.K.; investigation, A.P.-C.; resources, A.P.-C.; data curation, P.K.; writing—original draft preparation, A.P.-C. and P.K.; writing—review and editing, A.P.-C.; visualization, P.K.; supervision, A.P.-C.; project administration, A.P.-C.; funding acquisition, A.P.-C. All authors have read and agreed to the published version of the manuscript. Funding: This research received no external funding. Data Availability Statement: Restrictions apply to the availability of these data. Data was obtained from 3rd Party and are not available. MDPI Research Data Policies. Conflicts of Interest: The authors declare no conflict of interest. References Basel. 2010. Basel III: A Global Regulatory Framework for More Resilient Banks and Banking Systems. Basel: Basel Committee on banking Supervision, Bank for International Settlements, December. Available online: https://www.bis.org/publ/bcbs189.pdf (accessed on 12 November 2021). Basel. 2014. Basel III: The Net Stable Funding Ratio. Basel: Basel Committee on banking Supervision, Bank for International Settlements, October. Available online: https://www.bis.org/bcbs/publ/d295.htm (accessed on 12 November 2021). Batool, Maryam, Huma Ghulam, Muhammad Azmat Hayat, Muhammad Zahid Naeem, Abdullah Ejaz, Zulfiqar Ali Imran, Cristi Spulbar, Ramona Birau Icon, and Tiberiu Hora t , iu Gorun. 2020. How COVID-19 has shaken the sharing economy? An analysis using Google trends data. Economic Research-Ekonomska Istraživanja 34: 2374–86. [CrossRef] BCBS. 2013. BCBS 239—Principles for Effective Risk Data Aggregation and Risk Reporting. Basel: Basel Committee on Banking Supervision, Bank for International Settlements, January. Available online: https://www.bis.org/publ/bcbs239.pdf (accessed on 12 November 2021). Bellotti, Tony, and Jonathan Crook. 2009. Support vector machines for credit scoring and discovery of significant features. Expert Systems with Applications 36: 3302–8. [CrossRef] Bijak, Katarzyna, and Anna Matuszyk. 2017. Bayesian models of car lease frauds. Paper presented at the Credit Scoring and Credit Control XV, Edinburgh, UK, August 30–September 1. Bijak, Katarzyna, and Lyn Thomas. 2015. Modelling LGD for unsecured retail loans using Bayesian methods. Journal of the Operational Research Society 66: 342–52. [CrossRef] Crone, Sven F., and Steven Finlay. 2012. Instance sampling in credit scoring: An empirical study of sample size and balancing. International Journal of Forecasting 28: 224–38. [CrossRef] 120
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risks Article Bankruptcy Prediction with a Doubly Stochastic Poisson Forward Intensity Model and Low-Quality Data Tomasz Berent * and Radosław Rejman Citation: Berent, Tomasz, and Radosław Rejman. 2021. Bankruptcy Prediction with a Doubly Stochastic Poisson Forward Intensity Model and Low-Quality Data. Risks 9: 217. https://doi.org/10.3390/risks9120217 Academic Editor: Mercedes Ayuso Received: 14 October 2021 Accepted: 22 November 2021 Published: 2 December 2021 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Capital Markets Department, Warsaw School of Economics, 02-554 Warszawa, Poland; [email protected].pl *Correspondence: tber[email protected].pl Abstract: With the record high leverage across all segments of the (global) economy, default prediction has never been more important. The excess cash illusion created in the context of COVID-19 may disappear just as quickly as the pandemic entered our world in 2020. In this paper, instead of using any scoring device to discriminate between healthy companies and potential defaulters, we model default probability using a doubly stochastic Poisson process. Our paper is unique in that it uses a large dataset of non-public companies with low-quality reporting standards and very patchy data. We believe this is the first attempt to apply the Duffie–Duan formulation to emerging markets at such a scale. Our results are comparable, if not more robust, than those obtained for public companies in developed countries. The out-of-sample accuracy ratios range from 85% to 76%, one and three years prior to default, respectively. What we lose in (data) quality, we regain in (data) quantity; the power of our tests benefits from the size of the sample: 15,122 non-financial companies from 2007 to 2017, unique in this research area. Our results are also robust to model specification (with different macro and company-specific covariates used) and statistically significant at the 1% level. Keywords: default; bankruptcy risk; Poisson process; doubly stochastic assumption; ROC curve; accuracy ratio; leverage 1. Introduction In the world ravaged by the pandemic, with a fragile macro-economic outlook, low interest rates, and record high leverage, any academic research on bankruptcy is welcome. As the authors of this paper, we are neither professionally prepared nor interested in the debate on the degree of macro fragility or the effectiveness of the unprecedented stimulus packages adopted worldwide. Mentioning the unparalleled global leverage positions or the global health crisis, we merely acknowledge the emergence of the almost unmatched global uncertainty. In contrast to more optimistic views, exemplified by the stock exchange post- COVID-19 valuations, we believe the uncertainty is the only certain thing around us these days. Understanding the process of going down (in these circumstances) seems to us more than critical. Throughout this paper, bankruptcy and default are used interchangeably. Below are some universally available leverage statistics (Altman 2020). Global nonfinancial corporate debt increased from the pre-Global Financial Crisis level of $42 trillion to $74 trillion in 2019. The government debt position more than doubled from $33 trillion in 2007 to $69 trillion in 2019. Even the financial sector increased its leverage from the record high pre-crisis level to $62 trillion. Households increased their debt globally from $34 trillion to $48 trillion. With the exception of the financial sector, debt also grew in relation to global GDP. It increased to 93% for non-financials (up from 77%), to 88% for governments (up from 58%), and to 60% for households (up from 57%). Despite this, as Altman (2020) notes, the corporate high-yield bond default rate was surprisingly low at 2.9% in 2019, below a 3.3% historic average, the recovery rate of 43.5% was quite in line with the historic average of 46%, with the high-yield spreads lagging behind historic averages, too. Consequently, Altman believes that the pre-COVID-19 debt market, in contrast to the current state, was still at a benign cycle stage. However, the very levels of debt Risks 2021,9, 217. https://doi.org/10.3390/risks9120217 https://www.mdpi.com/journal/risks 122
Risks 2021,9, 217 globally, coupled with the increased appeal of a very long end of the yield curve and a massive increase in the BBB issuance, makes the debt markets and the global economy quite vulnerable, even without the health crisis. The unconventional monetary policies and the low interest environment also lead to the proliferation of “zombie” firms. Regardless of the precise definition, these companies are kept alive rather artificially thanks to the availability of cheap debt. Banerjee and Hofmann (2018) estimate as much as 16% of US listed firms may have “zombie” status—eight times more than in 1990. Acharya et al. (2020) estimate that 8% of all loans may also be infected with the “zombie” virus. Needless to say, COVID-19 and the resultant generous governmental relief packages do not help mitigate the problem. Bankruptcy research, in all its guises, has been truly impressive and has produced many insightful results for some decades now. Such results include the classical structural models of Merton (1974), Fischer et al. (1989), and Leland (1994), numerous reduced-form models ranging from the simple scoring methods of Beaver (1966, 1968) and Altman (1968), qualitative response models, such as the logit of Ohlson (1980) and probit of Zmijewski (1984), to the third generation of the reduced form, the duration-type models of, for e.g., Shumway (2001), Kavvathas (2000), Chava and Jarrow (2004), and Hillegeist et al. (2004). They all propose various and divergent econometric methods and methodological approaches, with an impressive sectorial and geographic empirical coverage (see Berent et al. 2017). To discriminate healthy from unhealthy firms is one challenge; to predict the (multiperiod) bankruptcy probabilities is another. One way to address the problem is to model default as a random counting process. A Poisson process is such an example. In the bankruptcy literature, it is the Poisson process with stochastic intensities that is frequently used. In the doubly stochastic setting, the stochastic intensity depends on some state variables which may be firm-specific or macroeconomic, also called “internal” or “external” in the works on the statistical analysis of the failure time data (Lancaster 1990; Kalbfleisch and Prentice 2002). We adopt the Duffie–Duan model, as described in Duan et al. (2012), who, with their forward intensity approach and the maximum pseudo-likelihood analysis, follow in the footsteps of Duffie et al. (2007). In 2007, Duffie et al. (2007) first formulated a doubly stochastic Poisson multi-period model with time-varying covariates and Gaussian vector autoregressions. Duan et al. (2012) resolve some specification and estimation challenges inherent in Duffie et al. (2007). With their forward intensity concept, Duan et al. (2012) no longer need a high-dimension state variable process to be assumed, but instead use the data known at the time of making predictions. Both Duan et al. (2012) and Duffie et al. (2007) are well grounded in the doubly stochastic hypothesis literature debated in, for e.g., Collin-Dufresne and Goldstein (2001), Giesecke (2004), Jarrow and Yu (2001), and Schoenbucher (2003). Duffie et al. (2007) apply their model to US-listed industrial firms. Duan et al. (2012) use also US public companies traded on NYSE, AMEX, and Nasdaq. Other researchers use the Duffie–Duan model to assess the default risk of public firms and/or in the context of developed (e.g., Caporale et al. 2017), or emerging markets (Duan et al. 2018). In this paper, we demonstrate that the Duffie–Duan model not only successfully describes a default process for public companies from developed countries with well-functioning capital markets, but is also equally successful in the context of privately owned equity markets with frequently patchy, low-quality data, operating in an emerging market characterized by lower transparency and governance standards (Aluchna et al. 2019). Compared to Duan et al. (2012) and Duffie et al. (2007), we apply the model to a significantly larger dataset of over 15,000 firms. As it is the applicability of the model rather than the discrimination itself that is our priority, we are not optimizing any cut-off point to maximize the accuracy of discrimination (typically made within an in-sample estimation context), but we make use of the out-of-sample accuracy measure calculated across all cut-off points, as is done in the context of the ROC analysis. 123
Risks 2021,9, 217 First, we collect a unique dataset for as many as 15,122 non-financial companies in Poland over the period 2007–2017. We make a huge effort to cross-check and cleanse the data so that the intricate estimation procedures could be run on this (initially) patchy input. Then, we document the performance differential (in the form of financial ratios) between the healthy and the (future) bankrupt firms one, two, and three years before default. In the next stage, company-specific variables (liquidity, profitability, leverage, rotation, and size) and macroeconomic variables (GDP growth, inflation, and interest rates) are used as state variables to estimate the default forward intensity employed in the doubly stochastic Poisson formulation. Partly due to the size of the dataset, we believe, we are able to exploit the differences between the attributes of the two groups. What we lose in the (data) quality, we seem to regain in (data) quantity. Our results surpassed our expectations. Not only are the estimated covariate parameters in line with the expectations and the literature, but the out-of-sample accuracy ratios produced—85% one year before default, 81% two years before default, and 76% three years before default—are at least as high, if not better, than those obtained for the high-quality public companies from developed countries. All our results are statistically significant and robust to the (state variable) model specification. We hasten to repeat that this paper is not about searching for the determinants of default, neither is it about the maximization of the discrimination power between the two groups at any optimal cut-off point. In particular, we are not interested in artificially lifting up the in-sample fit. The main objective is to prove that the doubly stochastic Poisson model can be successfully used in the context of low-quality data for non-public companies from emerging markets. We believe this objective has been fully achieved. We are not aware of any similar effort in this area. The rest of the paper is organized as follows. Below, still within the introduction section, we briefly introduce Poland’s bankruptcy law, an important ingredient, given the recent overhaul of the legislation framework. In the Materials and Methods section, we describe our unique dataset, introduce the model and the micro and macro covariates, and then we define the accuracy ratio, our preferred goodness-of-fit measure, the ROC curves, and the statistical tests applied. In the Results section, we first produce and comment on the descriptive statistics, separately for survivors and defaulters, one, two, and three years prior to bankruptcy. We then analyze the estimated covariate parameters and accuracy ratios, in- and out-of-sample. The critical discussion of our results, in the context of the literature, follows in the Discussion section. We conclude with some proposals for future research in the Conclusions section. Poland’s Bankruptcy Law With regard to Poland’s bankruptcy law, it was not until 2003, nearly one and a half decades after the end of communism in Poland, that the new legislation came into force. The new Bankruptcy and Rehabilitation Act replaced the pre-war ordinance of the President of the Republic of Poland, dated as far back as 1934. The new law was universally praised for bringing together, under one umbrella, two separate bankruptcy and restructuring (composition) proceedings, hitherto governed by the two separate legal acts. It is paradoxical that the essence of the latest changes in Poland’s bankruptcy law consisted in the carving out of the rehabilitation part into once again a separate Restructuring Act, which came into force in 2016. Apart from some substantial changes to the proceedings (e.g., the extension of both the time as well as the list of persons entitled/obliged to file for bankruptcy), the new law gave a debtor the option to choose, depending on the severity of insolvency, between four distinct ways to reach an agreement with the creditors. Given the discontinuity/alteration of the default definition brought upon the changes in the legal frameworks, care must be taken while conducting research in the bankruptcy field in Poland. The motivation for the new 2016 law was clear, as the number of liquidation proceedings dwarfed the restructurings by the ratio of 5:1. As Figure 1 illustrates, the effort was worth making, as the number of restructuring proceedings has significantly improved ever 124
Risks 2021,9, 217 since. In 2020, restructuring proceedings outnumbered liquidations, partly due to COVID- 19-driven regulations. The trend is generally assumed to remain even after the pandemic. 888 807 750 606 591 615 586 587 212 348 469 466 800 0 200 400 600 800 1000 1200 1400 1600 2013 2014 2015 2016 2017 2018 2019 2020 Restructuring proceedings Liquidation proceedings Figure 1. The number of liquidation proceedings vs. restructuring proceedings in Poland (pre-2016 restructuring proceedings not recorded) (Polish Institute of Credit Management). 2. Materials and Methods 2.1. Data 2.1.1. Companies’ Financial Data Our sample is quite unique in that it is large and dominated by non-public companies. It consists of two subsets. The former is the dataset of financial accounts, and the latter is the dataset on default events. Both are provided by Coface Group, the world’s leading credit insurance provider and the owner of sensitive data on defaulters. Other data on, for e.g., macro statistics are obtained from publicly available sources such as Statistics Poland (GUS). As for companies’ financial statements, we assembled financial accounts for as many as 15,122 non-financial Polish companies. According to the Statistical Classification of Economic Activities in the European Community (NACE), 39.8% of our companies come from manufacturing, 30.8% represent the wholesale and retail trade, and the repair of motor vehicles and motorcycles, 12.2%—construction, 5.5%—transportation and storage, 2.8%— information and communication, 2.7%—professional, scientific, and technical activities, and 1.7%—other. All our entities are limited companies, with limited liability companies outnumbering joint stock companies by the ratio of 5:1. The dataset consists of 193,420 company periods from 2006 to 2018. We concede the data are of poor quality in that many missing cells are encountered or contradictory records reported (e.g., subtotals in the balance sheets do not add up). We made a substantial effort to validate, cross-check, and, if necessary, correct the dataset. As a result, we identified 143,451 useable annual companyyears, i.e., a modest 73% of all company-years possible assuming all companies produced annual numbers for 2006–2018. Given the minuscule size of the 2006 and 2018 sub-samples, we arbitrarily excluded these years from our sample (see Figure 2). Consequently, when the period of analysis is limited to 2007–2017, the completeness of our dataset significantly improves to 86%. We regard this as satisfactory, as 100% is impossible by definition—some entities went down or exited for any other reason during the sample period. As shown in Figure 2, the number of company-years decreases towards the end of the period, which we associate with the fact that many non-public companies publish their accounts with a big lag. Moreover, some financial accounts arrive in multi-year packages, caused by 125
Risks 2021,9, 217 Table 4. Cash/TA one, two, and three years before default. Cash/TA tau = 1 tau = 2 tau = 3 Survivors 25 0.0037 0.0066 0.0078 0.0162 50 0.0159 0.0202 0.0222 0.0574 75 0.0462 0.0514 0.0587 0.1646 Table 5. CA/CL one, two, and three years before default. CA/CL tau = 1 tau = 2 tau = 3 Survivors 25 0.3736 0.6701 0.7777 1.0663 50 0.7376 0.9138 1.0188 1.4895 75 1.0585 1.1735 1.3080 2.4051 (a) (b) 0.0000 0.0200 0.0400 0.0600 25 50 75 Cash/TA tau=1 tau=2 tau=3 0.0000 0.0500 0.1000 0.1500 25 50 75 Cash/TA tau=3 Survive Figure 4. Cash to total asset: (a) default companies; (b) survivors vs. default companies three years before default. The conclusions barely change when liquidity is measured in terms of current assets to current liabilities. The closer to default, the lower the ratio, with the survivors well ahead of the bankrupt firms three years before default (Figure 5). (a) (b) 0.0000 0.5000 1.0000 1.5000 25 50 75 CA/CL tau=1 tau=2 tau=3 0.0000 1.0000 2.0000 3.0000 25 50 75 CA/CL tau=3 Survive Figure 5. Current assets to current liabilities: ( a ) default companies; ( b ) survivors vs. default companies three years before default. 3.1.2. Profitability The conclusions on profitability are as uncontentious as on liquidity (see Tables 6 and 7). In contrast to the survivors (always profitable on both net and operating levels), losses on both net and operating levels are reported for bankrupt companies in the lowest quartile already three years before default. As for the medians, they are negative for both NP/TA and EBIT 132
Risks 2021,9, 217 margins one year before default. The closer to default, the smaller the net profit (in relation to assets) at each quartile. Similarly, the operating margins get worse towards default. In short, the closer to default, both the return on assets and the operating margins deteriorate. Table 6. NP/TA one, two, and three years before default. NP/TA tau = 1 tau = 2 tau = 3 Survivors 25 −0.2888 −0.1027 −0.0390 0.0091 50 −0.0970 0.0034 0.0097 0.0454 75 0.0059 0.0238 0.0341 0.1052 Table 7. EBIT/Rev one, two, and three years before default. EBIT/Rev tau = 1 tau = 2 tau = 3 Survivors 25 −0.1804 −0.0466 −0.0089 0.0123 50 −0.0416 0.0133 0.0192 0.0376 75 0.0218 0.0344 0.0414 0.0806 Figures 6a and 7a graphically illustrate the miserable financial condition of the bankrupt companies one year before default in terms of their profitability, particularly in the first quartile. Figures 6b and 7b show that the distance in profitability between the surviving and the bankrupt companies in our sample, even three years before default, could hardly be bigger. (a) (b) -0.4000 -0.3000 -0.2000 -0.1000 0.0000 0.1000 25 50 75 NP/TA tau=1 tau=2 tau=3 -0.0500 0.0000 0.0500 0.1000 25 50 75 NP/TA tau=3 Survive Figure 6. Net profit to total assets: (a) default companies; (b) survivors vs. default companies three years before default. (a) (b) -0.2000 -0.1500 -0.1000 -0.0500 0.0000 0.0500 0.1000 25 50 75 EBIT/Rev tau=1 tau=2 tau=3 -0.0200 0.0000 0.0200 0.0400 0.0600 0.0800 0.1000 25 50 75 EBIT/Rev tau=3 Survive Figure 7. EBIT margin: (a) default companies; (b) survivors vs. default companies three years before default. 133
Risks 2021,9, 217 3.1.3. Leverage The leverage ratios (ND/E and ND/EBIT) are more difficult to interpret (see Tables 8 and 9, Figures 8 and 9). The companies with financial problems may have both huge (net) debt and low, potentially negative EBIT and equity. In contrast, healthy companies may have low, potentially negative net debt and highly positive EBIT and E. After scanning both the default firms and the survivors in our sample in terms of the net debt position, we find that as much as 55% of healthy companies have more cash and cash equivalents than debt, hence they have a negative net debt position. This drops to 30%, 25%, and 15% for companies facing bankruptcy within three, two, and one year, respectively. Similarly, negative equity is not practically reported for the survivors in our sample. Yet, for the bankrupt companies, as many as 30% of firms show negative equity one year prior to default, dropping to around 10% two and three years before default. With regard to EBIT, 25%, 35%, and 55% of defaulters have negative operating profit three, two, and one year prior to default, respectively. Within surviving firms, less than 5% are in the red on the operating level. Table 8. ND/E one, two, and three years before default. ND/E tau = 1 tau = 2 tau = 3 Survivors 25 −1.1764 −0.4346 −0.3620 −0.4701 50 0.3232 0.4436 0.2082 −0.1363 75 2.1259 1.4931 1.2056 0.3250 Table 9. ND/EBIT one, two, and three years before default. ND/EBIT tau = 1 tau = 2 tau = 3 Survivors 25 −3.4364 −2.5609 −1.7182 −2.5117 50 −0.9796 −0.1704 0.5084 −0.5766 75 1.7503 3.4877 3.6871 1.6281 (a) (b) -2.0000 -1.0000 0.0000 1.0000 2.0000 3.0000 25 50 75 ND/E tau=1 tau=2 tau=3 -1.0000 -0.5000 0.0000 0.5000 1.0000 1.5000 25 50 75 ND/E tau=3 Survive Figure 8. Net debt to equity: (a) default companies; (b) survivors vs. default companies three years before default. As a result, for example, the bankrupt companies one year before default post the most negative value of ND/E in the first quartile, and the highest positive value in the third (Table 8, Figure 8a). There is very little order in ND/E over time (to default). In terms of ND/EBIT (Table 9 and Figure 9b), the survivors frequently exhibit the lowest values of the ratio. 134
Risks 2021,9, 217 (a) (b) -4.0000 -2.0000 0.0000 2.0000 4.0000 6.0000 25 50 75 ND/EBIT tau=1 tau=2 tau=3 -4.0000 -2.0000 0.0000 2.0000 4.0000 25 50 75 ND/EBIT tau=3 Survive Figure 9. Net debt to EBIT: (a) default companies; (b) survivors vs. default companies three years before default. 3.1.4. Rotation As illustrated in Tables 10 and 11 and Figures 10 and 11, the assets rotation is not a strong discriminator, regardless of whether we compute the total asset or the shortterm receivables rotation ratios. For most cases, the revenue of (future) bankrupt firms in relation to assets shrinks as the company moves towards default. The sample distributions across time are (surprisingly) close to each other. Revenue tends to be 1.0–1.2, 1.6–1.8, and 2.5–2.7 times higher than the total assets for, respectively, the first, the second, and the third quartile, regardless of whether the rotation is measured one, two, or three years before default. The multiples for the survivors fit well into these ranges, too. As illustrated by Table 11 and Figure 11b, the short-term receivables rotations are even more homogeneous, with little discrimination between the survivors and the defaulters. Table 10. Rev/TA one, two, and three years before default. Rev/TA tau = 1 tau = 2 tau = 3 Survivors 25 0.9733 1.1009 1.2409 1.1839 50 1.5727 1.7264 1.8018 1.7991 75 2.6691 2.5298 2.7008 2.6765 (a) (b) 1.0000 1.5000 2.0000 2.5000 3.0000 25 50 75 Rev/TA tau=1 tau=2 tau=3 1.0000 1.5000 2.0000 2.5000 3.0000 25 50 75 Rev/TA tau=3 Survive Figure 10. Total assets rotation: (a) default companies; (b) survivors vs. default companies three years before default. 135
Risks 2021,9, 217 Table 11. Rev/STR one, two, and three years before default. Rev/STR tau = 1 tau = 2 tau = 3 Survivors 25 3.6326 3.9797 4.1633 4.3510 50 5.9690 5.8769 6.2982 6.3908 75 10.7425 9.7118 10.2449 10.1043 (a) (b) 3.0000 5.0000 7.0000 9.0000 11.0000 25 50 75 Rev/STR tau=1 tau=2 tau=3 4.0000 6.0000 8.0000 10.0000 25 50 75 Rev/STR tau=3 Survive Figure 11. Short-term receivables rotation: ( a ) default companies; ( b ) survivors vs. default companies three years before default. 3.1.5. Size As Tables 12 and 13 and Figures 12a and 13 show, the companies that went bust during our sample period had lower revenue and lower assets one year before default compared to what they had earlier (and what was recorded for the survivors, on average) for only the first quartile. Surprisingly, the medians and the values for the third quartile are higher one year prior to default and do not differ materially from the values for the surviving firms. The survivors are also (marginally) smaller than some future bankrupt firms, according to the first quartile statistics (see Figures 12b and 13b). We are not able to easily explain this finding, but comment later on the ambiguity of the size statistics found in the bankruptcy literature. Table 12. Rev one, two, and three years before default (PLN). Rev tau = 1 tau = 2 tau = 3 Survivors 25 9,943,760 12,024,161 13,391,353 13,041,557 50 28,098,943 21,865,540 22,341,462 28,603,362 75 72,078,970 58,552,894 52,935,266 76,376,322 Table 13. TA one, two, and three years before default (PLN). TA tau = 1 tau = 2 tau = 3 Survivors 25 5,757,452 6,628,929 7,228,960 7,049,281 50 15,068 820 13,947,311 15,023 695 17,191,949 75 51,063,916 48,831,692 37,612,128 50,360,517 136
Risks 2021,9, 217 (a) (b) 0 20,000,000 40,000,000 60,000,000 80,000,000 25 50 75 Rev tau=1 tau=2 tau=3 0 20,000,000 40,000,000 60,000,000 80,000,000 100,000,000 25 50 75 Rev tau=3 Survive Figure 12. Revenue: (a) default companies; (b) survivors vs. default companies three years before default. (a) (b) 0 20,000,000 40,000,000 60,000,000 25 50 75 TA tau=1 tau=2 tau=3 0 20,000,000 40,000,000 60,000,000 25 50 75 TA tau=3 Survive Figure 13. Total assets: (a) default companies; (b) survivors vs. default companies three years before default. 3.2. Parameter Estimates In Table 14, we present the maximum pseudo-likelihood estimates for α ( τ ). These parameters quantify the impact of various firm-specific factors on its default probability. The set of α ( τ ) is estimated separately for tau = 1, tau = 2, and tau = 3. Given the rather generous and overlapping representation of the various firm attributes in our model, which makes the parameters estimates vulnerable to problems related to multicollinearity, we are more than encouraged to see that the signs of the parameters are almost perfectly realigned with what we expected. In particular, as Table 14 shows, the higher the liquidity of the company, be it in the form of cash or working capital, the lower the probability of the company being unable to pay back its debt and interest on it—hence, the lower the probability of default. In other words, the forward default intensities are estimated to increase, as expected, with the decrease of cash to assets and current assets to current liabilities ratios. Interestingly, the estimated negative α -s for both Cash/TA and CA/CL increase (in absolute values) with every year nearer default. This would suggest, unsurprisingly, the recorded drop in liquidity is more and more punishing when approaching financial distress. Similar results are reported for profitability. All parameters are negative, as expected, for both return on assets and operating margins; i.e., the higher the profitability, the lower the default intensity and the probability of default. The parameters are also negative for all time horizons, i.e., one, two, and three years before default, with the strength of the sensitivity of default to the drop in profitability (proxied by the return on assets) increasing with the time approaching default. 137
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