Equity risk and return across hidden market regimes

Endovitsky, Dmitry A.; Korotkikh, Viacheslav V.; Khrispushin, Denis A. Article Equity risk and return across hidden market regimes Risks Provided in Cooperation with: MDPI – Multidisciplinary Digital Publishing Institute, Basel Suggested Citation: Endovitsky, Dmitry A.; Korotkikh, Viacheslav V.; Khrispushin, Denis A. (2021) : Equity risk and return across hidden market regimes, Risks, ISSN 2227-9091, MDPI, Basel, Vol. 9, Iss. 11, pp. 1-21, https://doi.org/10.3390/risks9110188 This Version is available at: https://hdl.handle.net/10419/258272 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/4.0/ risks Article Equity Risk and Return across Hidden Market Regimes Dmitry A. Endovitsky *, Viacheslav V. Korotkikh and Denis A. Khripushin   Citation: Endovitsky, Dmitry A., Viacheslav V. Korotkikh, and Denis A. Khripushin. 2021. Equity Risk and Return across Hidden Market Regimes. Risks 9: 188. https:// doi.org/10.3390/risks9110188 Academic Editor: Mogens Steffensen Received: 28 June 2021 Accepted: 7 September 2021 Published: 22 October 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/). Faculty of Economics, Voronezh State University, 394018 Voronezh, Russia; kor[email protected] (V.V.K.); [email protected] (D.A.K.) *Correspondence: endovitsky[email protected] Abstract: The key to understanding the dynamics of stock markets, particularly the mechanisms of their changes, is in the concept of the market regime. It is regarded as a regular transition from one state to another. Although the market agenda is never the same, its functioning regime allows us to reveal the logic of its development. The article employs the concept of financial turbulence to identify hidden market regimes. These are revealed through the ratio of the components, which describe single changes of correlated risks and volatility. The combinations of typical and atypical variates of correlational and magnitude components of financial turbulence allowed four hidden regimes to be revealed. These were arranged by the degree of financial turbulence, conceptually analyzed and assessed from the perspective of their duration. The empirical data demonstrated ETF day trading profits for S&P 500 sectors, covering the period of January 1998–August 2020, as well as day trade profits of the Russian blue chips within the period of October 2006–February 2021. The results show a significant difference in regard to the market performance and volatility, which depend on hidden regimes. Both sample data groups demonstrated similar contemporaneous and lagged effects, which allows the prediction of volatility jumps in the periods following atypical correlations. Keywords: correlation surprise; financial turbulence; Mahalanobis distance; hidden regimes of stock markets 1. Introduction The year 2020 was a real challenge for all global stock markets. The spread of the new virus, COVID-19, beyond the borders of China and the follow-up pandemic had a negative impact on the global economy and triggered a serious economic crisis. According to extensive research (Matos et al. 2021;Naidu and Ranjeeni 2021;O’Donnell et al. 2021; Seven and Yılmaz 2021), its consequences may well be compared with those during the contemporary history of economics, particularly, Black Monday of 1987, the Asian Financial Crisis of 1997, the Russian Financial Crisis of 1998, the Dotcom Bubble Crash of 2000 and, of course, the Global Financial Crisis of 2008–2010. The ex-post analysis of such events fails to answer a number of questions about how to model the dynamics of stock market performance in order, for example, to predict stock market turnarounds. Although the reasons for such events may be different, the events themselves are assumed to reveal similar patterns and follow almost the same logic. Thus, both the participants of stock markets and the academic community seek opportunities to identify the common pattern of all crises observed in developed and emerging markets. Due to price volatility implied greater risks in trading, such as political risk, inflation rate and change or exchange rate, financial investments conducted in emerging markets are regarded as risky. However, the investors can take higher risk for obtaining higher risk premium in comparison with developed markets. What is more, fast growing potential of emerging markets contributes to the high return of financial investments. The primary focus of this research is on the S&P 500 market index measured the performance of the most capitalized companies in the most developed stock market. The secondary focus is on the main Russian equity index, the RTSI index, which measured the performance of the most capitalized companies in the emerging markets of BRIC. Risks 2021,9, 188. https://doi.org/10.3390/risks9110188 https://www.mdpi.com/journal/risks Risks 2021,9, 188 2 of 21 In regard to this, it seems really important to develop a methodology which can help to forecast economic crises and create a system for their early prevention based on the understanding of hidden regimes (Costa and Kwon 2019;Nystrup et al. 2018). The functioning of stock markets is regarded as a sustainable regime-switching framework, involving the alternation of states. Throughout the dynamics of market performance, the regime detects comparable changes, or shifts. Thus, the regime characterizes the regular shifts rather than the particular state of the market. Although it is believed that the observed regime of any stock market follows a particular stage of the economic cycle at a point of time, it is difficult to use it as a basis for investment decisions. In this paper, we use the concept of a hidden regime with a view to describing complex dynamics of the market via the dynamics of financial turbulence. The latter is not a regular and, therefore, observable phenomenon. There are many reasons that account for such a deep interest in stock market regimes in the sphere of financial modeling. First, the idea of regime-switching framework is inherent for the market and, therefore, intuitively understandable. Hidden regimes were first mentioned in connection with the description of business cycles (Hamilton 1989). The aim was to predict recession and recognize long-term trends in business activities. Second, the modeling of the market processes across its regime enables us to consider nonlinear effects and, thus, ensure more accurate forecasting of more complicated processes. One of the basic tools used to identify the latent changes in a market’s behavior is the Hidden Markov Model, introduced by Hamilton (1989) and Diebold et al. (1993). While Hamilton used the model with regular probabilities of switching from one state to another, Diebold assumed there could be a model with probabilities changing over the time. At present, there are ongoing lively discussions among scholars on the subject of using the concept of hidden regimes to explain some theoretical and practical financial issues. 2. Literature Review In regard to the former, the obtained results demonstrate the specifics of modeling and forecasting market performance and volatility. For example, Paolella et al. (2019) developed a multivariate model of financial asset returns across a switching framework, which takes into account asymmetry and heavy-tailed distribution. The use of the hidden regime concept allows more accurate predictions of risk assessment and may help develop the strategy of dynamic risks control, thus considerably reducing losses when the regime switches. Another study (Van Beek et al. 2020) discussed the options of generalizing the hidden Markov model in case of self-similar processes. Liu et al. (2020) modified the GARCH model by applying the Markov switching model. The results of the study are consistent with the volatility timeline structure. The application of a regime-switching framework does not necessarily mean using the Markov models. Szulczyk and Zhang (2020) delivered another quite interesting approach towards the development of switching regression models. These are more effective in explaining the situations and phenomena in comparison with the well-known linear models with factor specifications. In regard to the applied research issues, Nystrup et al. (2018) obtained promising results after using the hidden Markov model with time-varying parameters to forecast the numerical characteristics of the returns distribution in the framework of a dynamic approach for the evaluation of portfolio performance. The study demonstrates the effectiveness of this approach through the review of risk assets in the portfolio across the detected regime. This idea was further developed in the study by Costa and Kwon (Costa and Kwon 2019). In addition to the applied portfolio’s performance, the hidden regime concept is used in order to find arbitrage opportunities in a stock market across the dynamics of the corresponding futures market (Alemany et al. 2020). Most of the studies mentioned above (see, among others, Chevallier and Goutte 2015; Kirkby and Nguyen 2020), consider hidden regime-switchers in the context of jump risks. However, jump risks should be regarded as a result of regime switching, revealing neither their character nor their reasons. Risks 2021,9, 188 3 of 21 We assume that the change of another undiversified risk, namely, correlation risk, is what underlies the mechanism of regime switching. Thus, it is logical to conduct a further analysis in terms of correlation and its impact on financial turbulence. At present, correlation mechanisms are widely used by economists when dealing with applied tasks in stock markets both from a static perspective (when diversifying idiosyncratic risks in non-turbulent periods of correlation consistency) and a dynamic perspective (if it is necessary to account for losses across failed diversification (Andersson et al. 2008;Engle 2002;Endovitsky et al. 2017;Endovitsky et al. 2018)). This approach was developed in the study by Page and Panariello (2018). The authors analyzed the correlations between financial tools from a dynamic perspective, thus clearly demonstrating that diversification definitely requires considering risks resulting from events which refer to the left tail of the returns distribution. This is where the portfolio performance is most sensitive. On the basis of their calculations as well as the results obtained by Baumeister and Johnson (Baumeister et al. 2001;Johnson et al. 2014), Page and Panariello showed that conditional correlations between asset classes are considerably higher for left tail returns than for right tail returns or the distribution in general. The study concludes that in order to increase the efficiency of the investment strategy, it is necessary to dynamically optimize them by the degree of downside risk. While Page and Panariello did not consider cryptocurrencies as financial tools, the high interest in cryptocurrencies creates threats to the investment industry. Referring to Yuneline (2019), despite the discussions surrounding the nature of cryptocurrency, its legal and economic perspectives and whether it can qualify as money in a real economy, cryptocurrency may be considered as an investment asset rather than a currency. On the one hand, as an asset that is not issued by any central authorities, its values are not directly influenced by monetary policy. Corbet et al. (2018) document the increase regarding them as an investor “save heaven” or “protection asset”. On the other hand, cryptocurrency has no intrinsic value and it is not backed with any assets. Furthermore, the high price volatility and other risks may lead to the bubble panic and destroying investment value. Liu (2018) particularly focused on the influence of cryptocurrencies on portfolio diversification. Nunez (Núñez et al. 2019), however, provided a convincing argument showing that cryptocurrencies fail to maintain diversification in the case of a market crash. More recently, Foglia and Dai (2021) provided fresh evidence of the dynamic connectedness between economic policy uncertainty index (EPU; Baker et al. (2016) ) and the cryptocurrency price uncertainty index. The authors found that EPUs have positive predictive power for cryptocurrency uncertainty, i.e., dictate the behavior in the cryptocurrency market. The investors who are likely to diversify their portfolio between the conventional assets or just trade in the cryptocurrency market should keep their eyes on the regular news, including economic growth, policy changes or any crises to predict dramatic price fluctuations. The focus of this study is to develop a methodology for detecting the hidden regimes of stock markets caused by financial turbulence patterns, as well as the analysis of their impact on risk and return values. The paper is hereafter structured as follows. Section 3presents a consideration of the financial turbulence concept, with a focus on the methods of its calculation and decomposition into correlations and magnitudes. Section 4describes a methodology for risk analyses and forecasting based on stock market hidden regimes, and whether the constructs of the financial turbulence demonstrate atypical patterns in comparison with the norms for a particular area. The calculations are based on the mechanism of a rolling estimation of current values of financial turbulence and its constructs for a given opportunity space. This section on approbation of the suggested approach delivers the results of a practical evaluation based on its application to the US and Russian stock markets. The practical relevance of the research lies in obtaining additional data on areas of investment from the components of financial turbulence with the help of simultaneous and lagged effects, which are typical of a market regime. These data allow us to increase the explanatory Risks 2021,9, 188 4 of 21 power and forecasting capacity of stock market analysis for investors. Section 5provides the discussion of the significance of our findings. Section 6draws the conclusions. 3. Methodology As a rule, any discussions, including those among scholars, about the features of turbulent periods and regime switching are preceded by the “black swans” phenomenon, fraught with various financial crises (see, among others, Chow et al. 1999;Kritzman and Li 2010;Kritzman et al. 2012;Kinlaw and Turkington 2014). Each of these crises are unique in their reasons and the mechanism of development. However, all of them have one common feature, namely, the emergence and spread of abnormal trends in the market. The identification of Chow’s turbulent periods (Chow et al. 1999) was suggested on the basis of multivariate outliers found with the Mahalonobis distance (Mahalanobis 1927; Mahalanobis 1936), and was initially applied to archaeology for the classification of human skulls: Dt=(rt−µ)TΣ−1(rt−µ), (1) where Dt is a multivariate outlier at a time point t ; rt=r1 t,r2 t, . . . ,rn t is the vector of security asset returns for a time period t ; µ=µ1,µ2, . . . µn is the vector of average historical return on assets; Σ=σi,j is the sample covariance matrix of historical asset returns. Although the approach suggested by Chow et al. was to mainly generalize the Markowitz portfolio theory and observe various stock market regimes with a view to improving its sustainability, on the whole, it was the Mahalanobis distance concept that became the basis for developing special measures for measuring financial turbulence in a market. The financial turbulence concept is well-developed in the paper by Kritzman and Li (2010), published almost 10 years later and following yet another financial crisis. The authors linked financial turbulence with the level of deviations in the complex multivariate system of the stock market. They developed a special system of measures to be used in a particular opportunity space for assessing the level of correlations and, thus, the investment capacity. According to Kritzman and Li, this would help to identify the deviation periods in which the patterns of security assets behave uncharacteristically. As a result, asset prices may fluctuate dramatically, thus weakening the correlations among some assets and strengthening them among others. In order to measure financial turbulence, the Mahalanobis distance should be averaged by the number of assets allocated in a particular opportunity space: FTt=(rt−µ)TΣ−1(rt−µ)/n, (2) where FTt is the financial turbulence at a particular time point t ; n is the the number of assets in a particular investment opportunity space. The obtained variate FTt can be regarded as a measure of uncharacteristic asset behavior at the considered time point in regard to the preceding historical perspective. In other words, it is the measure of deviation at a particular time point. It is important to distinguish financial turbulence from cross-sectional volatility, which measures the average cross-sectional dispersion of stocks returns (see, among others, Bali et al. 2011;Fu 2009). However, it fails to consider the average return on particular assets. Moreover, turbulence differs from the rolling volatility of a portfolio of stocks (see, among others, McMillan and Speight 2004;Fouque et al. 2017). This difference comes from the fact that turbulence describes deviations at a particular time point rather than the volatility of a portfolio of stocks over an extended period. Kinlaw and Turkington (2014) extended the idea of Kritzman and Li (2010) and suggested a method for the decomposition of financial turbulence into correlations and magnitudes. The correlation components give a general description of the correlations in a Risks 2021,9, 188 5 of 21 particular investment opportunity space and shows how the correlations change over a historical period of time, i.e., the changes in market correlation risks. The correlational component of financial turbulence is identified through the factorization of the “full-scale” financial turbulence into magnitude components: CSt=FTt MSt, (3) MSt=(rt−µ)TΣ−1 d(rt−µ)/n. (4) where MSt is the magnitude contribution for a time period t ; Σd=σ2 i is the random diagonal asset dispersion matrix from a historical perspective. As follows from the expression (4) above, MSt is a mean of standard asset returns for a particular time point. It only shows whether the deviation of asset returns for this time period is large or small relative to their historical means, i.e., it captures the extent of the price movement. By using the empirical distribution of MSt , we can identify the time periods of atypical magnitude, which is more appropriate to regard as a jump risk. Financial instruments demonstrate magnitude surprise at periods when the observed values of MSt are more to the right of the upper unilateral quantile of u level of MSt distribution: MShigh =MS |MS >MS+ u, PrMS ≥MS+ u=u. The uquantile is set exogenously. We can observe the events with CS > 1, called “correlation surprise”, when security assets demonstrate atypical correlations, i.e., correlations between some assets are weaker and between other assets are stronger. The episodes with CS ≤ 1 (absence of “correlation surprise”) prove the correlations typical. Such an approach seems convenient for, at least, two reasons. Firstly, it summarizes and unifies the general atypicality of correlational interactions over a period of time in any investment opportunity space. Secondly, when calculating the correlation surprise, we focus not on whether the correlation is high or low but rather on its deviation from historical norms, whatever they were. It is by this that we detect changes in market correlation risks. To develop intuition around the concept of correlation surprise, let us consider a single asset with an expected zero-beta return and finite variance σ2 . The turbulence of this asset is a squared standard value of its return: FTt=rtσ2−1rt=rt σ2=z2 t. (5) Since the correlation coefficient for one asset is, by definition, equal to 1, the correlation surprise will equal precisely the financial turbulence. If we consider two assets with zero-beta, it is easy to show that the financial turbulence is also a standardized variable: FTt=r1 t,r2 tTσ2 1ρσ1σ2 ρσ2σ1σ2 2−1r1 t,r2 t. (6) Thus, the correlation in the financial turbulence of the two assets will look as follows: CSt=r1 t,r2 tTσ2 1ρσ1σ2 ρσ2σ1σ2 2−1 r1 t,r2 t r1 t,r2 tTσ2 10 0σ2 2−1 r1 t,r2 t =1 1−ρ2 1−ρz1z2 0.5z2 1+z2 2!. (7) The expression (7) demonstrates that the correlation contribution in the financial turbulence is a functional derivative only from the correlation coefficient and standard values of asset returns, i.e., values which are factorized in relation to volatility. Thus, the Risks 2021,9, 188 6 of 21 correlation surprise contains information not about risks but about how coordinated the price movement is in a given space. If the asset returns are orthogonal ( ρ= 0), the correlation surprise is equal to one, which means we should not expect any movement. If correlation interaction grows in a particular investment space, investors regard it as typical, and in this case the correlation value will be less than one. By contrast, in the case of a large correlational deviation, correlation will become increasingly atypical. It is possible to observe it through the values of correlation surprise as they will exceed one and, thus, increase the degree of market correlation risk. Following these considerations, we can correlate the observed actual state of the market with one of the four hidden regimes from the perspective of whether there are any atypical patterns in the constructs of financial turbulence: 1. The regime of full-scale financial turbulence. This is identified through atypical values of its two components. Deviations responsible for such a regime demonstrate the anticipated exposure to increasing risk. As the market correlational risks grow, asset returns among previously uncorrelated instruments may become positive, thus making the diversification effects shrink to zero. After a regime-switch, the lagged volatility grows and achieves an all-time high. During such periods, returns are low or even negative, which is why this regime may precede downward trends. Typically, this regime in the stock market accounts for about 5–8% of all regimes, which enables us to assume that it is due to the crisis phenomena (which are rare events). We also assume that during such periods, the developing markets can experience capital outflow, while the developed markets are able to control this process and ensure the outflow of capital into safe assets. 2. The regime of financial turbulence across atypical correlations. This is highly frequent and accounts for 55–60% of all regimes. The changes in correlational risks revealed through atypical values of correlations in the financial turbulence do not largely affect the market exposure to the systemic risks. In such a regime, we can observe low values of both returns and volatility. The price performance is connected with low return magnitudes around means, which resembles some kind of random volatility. The absence of significant changes in asset prices allows the effective use of a portfolio optimization in risk management. 3. The regime of financial turbulence across atypical magnitude. This is characterized by atypical price performance. The market correlational risks do not exceed the historical norms, and the asset returns change insignificantly, thus making the diversification effective in idiosyncratic risks management. Such dynamics fill market participants with optimism and make the risk premium higher. During such a regime, the market demonstrates the highest asset returns in contrast with the other regimes. Although the returns deviate from their historical means, they remain positive, thus showing the anticipation of upward trends. Usually, it accounts for 10–15% of all regimes. 4. The regime with laminar conditions. It is characterized by the absolute absence of any abnormalities in the financial turbulence structure and fits within its historical means. In such a regime, the market, as a rule, follows regular patterns because the price movement is not strong enough to produce deviations. Alternatively, such a regime can be characterized as the situation of anticipation before changes start. Usually, it accounts for 17–30% of all regimes. Let us examine the features of the above-mentioned stock market regimes. This research is based on two groups of data describing an attractive investment space, which corresponds to ETFs for the S&P 500 index and the blue-chip space, included in the RTSI index (Table 1). Risks 2021,9, 188 7 of 21 Table 1. Description of source data. Panel A: Time Series Data S&P 500 sector ETFs RTSI equities Size of sliding window 2250 daily returns (9 year span) 1250 daily returns (5 year span) Time datum 22 December 1998 1 October 2006 Finishing time point 31 December 2020 31 December 2020 Data source sector indices S&P 500 MOEX Index components used in financial turbulence calculations ETF for sector indices S&P 500 by sectors: “Consumer discretionary stocks”; “Convenience goods”; “Energy”; “Finances”; “Healthcare”; “Industry”; “Information technology”; “Materials”; “Municipal services” Corporate equities of: PAO (PJSC) “Gazprom”, PAO (PJSC) Mining and Metallurgical Company “Norilsk Nickel”, PAO (PJSC) “Severstal”, PAO (PJSC) “LUKOIL Oil Company”, PAO “(PJSC) Magnit”, PAO (PJSC) “MTC”, PAO (PJSC) “Novatek”, PAO (PJSC) “Oil Company «Rosneft”, PAO “(PJSC) Sberbank”, PAO (PJSC) “Surgutneftegas”, PAO (PJSC) “Tatneft”, VTB Bank (PAO (PJSC). Panel B: Market Index Returns Descriptive Statistics min median mean max St.dev. skewness kurtosis S&P 500 index −0.1198 0.0007 0.0004 0.1158 0.0123 −0.2742 13.8221 RTSI index −0.1910 0.0012 0.0005 0.2238 0.0203 −0.1666 11.4171 We made experimental calculations for both groups of investment options. The experiments included the following stages: 1. Calculations of historical means of financial turbulence. 2. Decomposition of financial turbulence into correlations and magnitudes, and calculation of their historical distribution. 3. Division of observations of a sample into two groups: a. Showing atypical magnitude, i.e., located more to the right of the 20% upper (unilateral) quantile: MShigh =nMS |MS >MS+ 0,20o, PrMS ≥MS+ 0,20=0.2; b. Showing typical magnitude, i.e., located more to the left of the 20% upper (unilateral) quantile: MSlow =nMS |MS <MS+ 0,20o, PrMS ≥MS+ 0,20=0.2; 4. Division of observations of a sample into two groups: a. Showing atypical correlations (CS >1); b. Showing typical correlations (CS ≤1); 5. Formation of samples which correspond to the above-mentioned market regimes at the cross point of the two independent universes. 6. Analysis of contemporaneous and lagged effects, determined by the hidden market regimes. 4. Results 4.1. Analysis of the Dynamics with Hidden Market Regimes Consistent with the logic of our methodology, we computed the values of financial turbulence and its unobservable components for both groups of investment options, as shown in Figure 1. The charts show the effects of clustered values of financial turbulence and its magnitude components. The clusters with high values demonstrate the most turbulent periods in the stock market. The dynamics of correlation components is not so highly clustered. Thus, it is consistent with the assumption that both components are orthogonal, i.e., they demonstrate different information about the contemporaneous market regime. Risks 2021,9, 188 8 of 21 Risks 2021, 9, x FOR PEER REVIEW 8 of 22 and its magnitude components. The clusters with high values demonstrate the most turbulent periods in the stock market. The dynamics of correlation components is not so highly clustered. Thus, it is consistent with the assumption that both components are orthogonal, i.e., they demonstrate different information about the contemporaneous market regime. (а) (b) Figure 1. Financial turbulence and its components for spaces of the (a) S&P 500 index and (b) RTSI index. To identify the hidden regimes, we use two independent period groupings by the observable values of financial turbulence components. As a result, we have four samples, whose sizes are presented in Table 2. The first value in brackets refers to the space of the S&P 500 index and the second value refers to the space of the RTSI index. The ratios of the regimes, as we see, do not differ much. Table 2. The number of observations in the regime-based samples. 𝑪𝑺>𝟏 𝑪𝑺≤𝟏 𝑀𝑆 Full-scale turbulence regime (175; 240) Regime of financial turbulence across atypical magnitude (465; 268) 𝑀𝑆 Regime of financial turbulence across atypical correlation (2095; 1701) Laminar regime (466; 331) The examination of the features of hidden market regimes is based on the four respective groups of observations. Figure 1. Financial turbulence and its components for spaces of the (a) S&P 500 index and (b) RTSI index. To identify the hidden regimes, we use two independent period groupings by the observable values of financial turbulence components. As a result, we have four samples, whose sizes are presented in Table 2. The first value in brackets refers to the space of the S&P 500 index and the second value refers to the space of the RTSI index. The ratios of the regimes, as we see, do not differ much. Table 2. The number of observations in the regime-based samples. CS > 1 CS ≤1 MShigh Full-scale turbulence regime (175; 240) Regime of financial turbulence across atypical magnitude (465; 268) MSlow Regime of financial turbulence across atypical correlation (2095; 1701) Laminar regime (466; 331) The examination of the features of hidden market regimes is based on the four respective groups of observations. Let us consider the contemporaneous effects resulting from atypical magnitudes and atypical correlations, i.e., the effects within the full-scale financial turbulence and financial turbulence with atypical magnitude. Table 3demonstrates the magnitude means for the considered samples. Interestingly, the samples with correlation surprise, on average, demonstrate a lower magnitude value than those without correlation surprise. This empirical evidence confirms that when volatility is high, we can observe typical correlation rather than atypical. The detected differences between the samples and, therefore, regimes have a statistical relevance. Risks 2021,9, 188 15 of 21 Table 16. Daily returns distribution for the RTSI index during switches among four Markov regimes in the COVID-19 crisis. Hidden Market Regime in Previous Day Annualized Mean Return Standard Deviation (Annualized) Days with Positive Returns (Up Days) Laminar regime 0.6679 0.0829 0.8 Regime of financial turbulence across atypical correlation −0.8846 0.1591 0.2 Regime of financial turbulence across atypical magnitude −0.9216 0.3445 0.2 Full-scale turbulence regime −0.9023 0.5691 0.3334 These results suggest that our hidden market regimes contain incremental information about future return and volatility. Our four hidden market regimes, from the perspective of whether there are any atypical patterns in the constructs of financial turbulence, are useful candidates to devise an early warning system that is able to anticipate highly fluctuating Markov regime switching. 4.3. The Analysis of Market Hidden Regimes in Modern History It seems important to turn now to some episodes and details in modern history. It will help to appreciate the practical implications of understanding the impact that hidden regimes, the full-scale regime in particular, have produced on stock market. One of the most striking examples of full-scale turbulence was the stock market crash in 2008, caused by liquidity failures of major US banks in the context of the preceding subprime mortgage crisis. Figure 4demonstrates the stock market diagram for the S&P 500 index’s performance as well as the components of financial turbulence observed in the autumn of 2008. The horizontal lines in the charts mark the threshold values. If exceeded, they signal the occurrence of correlation surprise or magnitude surprise, respectively, or, in other words, full-scale financial turbulence. Within the considered timeline, the surprise correlation exceeded one nine times as much: it was observed on the 2nd, 3rd, 5th, 10th, 12th, 16th, 19th, 24th and 26th of September. Interestingly, the day Lehman Brothers, the biggest bank in US history, declared bankruptcy was preceded both by atypical correlation and atypical magnitude. On the very day of the officially declared bankruptcy, the 15th of September, the correlation surprise did not exceed 1. However, there was a volatility jump, reflected in the magnitude surprise on that day. The average daily mean of the magnitude surprise for the days following a correlation surprise was 6.78, and the mean of the S&P 500 index’s performance reached 3.36%. By contrast, the average daily mean of the magnitude surprise for the days following periods without correlation surprise was 3.55, and the mean of the S&P 500 index’s performance reached 0.71%. The biggest loss was observed on 29 September and reached 8.81%. The magnitude surprise on this particular day reached its all high—24.48. On the eve of this event, the correlation surprise was 1.65, but on 29 September, it struggled to reach 0.61. The charts illustrate that the correlation surprise lasted for nine trading days. Thus, in the considered month, it is possible to observe not only atypical volatility, but also underlying changes in the asset correlation affected by the hidden regimes. Let us consider another episode in the history of financial turbulence, namely, the US stock market crash in 2018 (Figure 5). In light of negative investment expectations resulting from monetary policy mistake by the Federal Reserve, rising interest rates, large amount of uncertainty in the global economy and tariffs on imported goods policy introduced by the Trump administration (Burggraf et al. 2020), the S&P 500 index lost almost 4% on just one day, the 10th of October. The crash was preceded by atypical correlation and magnitude, which are characteristics of full-scale financial turbulence. On the day before the crash, the correlation surprise reached almost its record of 4.19, but on the day of the crash, the 10th Risks 2021,9, 188 16 of 21 of October, it struggled to reach 0.45. The magnitude surprise changed its value from 0.64 on the day before the crash and became 7.71 on the day of the crash. Finally, let us consider a third episode which relates to the market crash in the spring of 2020 (Figure 6). Atypical correlation and magnitude could be observed on the 26th of February. This was followed by a volatility jump the next day and the resulting loss reached 4.41%, according to the S&P 500 index. It was the most dramatic drop since September 2008. On the 6th of March atypical correlation and almost atypical risk was observed. The next day, losses reached 7.60%, according to the S&P 500 index. Next, on the 18th of March, many logically expected that the market had reached its minimum, and therefore, there was very little chance of sinking further as the correlation surprise did not exceed 1 and the magnitude surprise, though high, demonstrated a downward trend. However, on the 19th of March, both the correlation surprise and magnitude surprise showed high values, which meant there was an approaching period of financial turbulence. Over the next two days, the losses reached 6%, according to the S&P 500 index. Now we will consider the first six months of 2020 for the Russia Stock Market. On the 20th–21st of January, the market experienced both atypical correlation surprise and magnitude, which provided evidence of full-scale financial turbulence (Figure 7a). These dates were then followed by sharp risk jumps and the index price dropped for four trading days in a row. The magnitude was highest on the fourth day (27th of January). The total loss over that period was slightly under 5%, according to the RTSI index. Risks 2021, 9, x FOR PEER REVIEW 16 of 22 Within the considered timeline, the surprise correlation exceeded one nine times as much: it was observed on the 2nd, 3rd, 5th, 10th, 12th, 16th, 19th, 24th and 26th of September. Interestingly, the day Lehman Brothers, the biggest bank in US history, declared bankruptcy was preceded both by atypical correlation and atypical magnitude. On the very day of the officially declared bankruptcy, the 15th of September, the correlation surprise did not exceed 1. However, there was a volatility jump, reflected in the magnitude surprise on that day. The average daily mean of the magnitude surprise for the days following a correlation surprise was 6.78, and the mean of the S&P 500 index’s performance reached 3.36%. By contrast, the average daily mean of the magnitude surprise for the days following periods without correlation surprise was 3.55, and the mean of the S&P 500 index’s performance reached 0.71%. The biggest loss was observed on 29 September and reached 8.81%. The magnitude surprise on this particular day reached its all high—24.48. On the eve of this event, the correlation surprise was 1.65, but on 29 September, it struggled to reach 0.61. The charts illustrate that the correlation surprise lasted for nine trading days. Thus, in the considered month, it is possible to observe not only atypical volatility, but also underlying changes in the asset correlation affected by the hidden regimes. Figure 4. Analysis of the financial turbulence, September 2008. Figure 4. Analysis of the financial turbulence, September 2008. Risks 2021,9, 188 17 of 21 Risks 2021, 9, x FOR PEER REVIEW 17 of 22 Let us consider another episode in the history of financial turbulence, namely, the US stock market crash in 2018 (Figure 5). In light of negative investment expectations resulting from monetary policy mistake by the Federal Reserve, rising interest rates, large amount of uncertainty in the global economy and tariffs on imported goods policy introduced by the Trump administration (Burggraf et al. 2020), the S&P 500 index lost almost 4% on just one day, the 10th of October. The crash was preceded by atypical correlation and magnitude, which are characteristics of full-scale financial turbulence. On the day before the crash, the correlation surprise reached almost its record of 4.19, but on the day of the crash, the 10th of October, it struggled to reach 0.45. The magnitude surprise changed its value from 0.64 on the day before the crash and became 7.71 on the day of the crash. Figure 5. Analysis of the financial turbulence, October 2018. Finally, let us consider a third episode which relates to the market crash in the spring of 2020 (Figure 6). Atypical correlation and magnitude could be observed on the 26th of February. This was followed by a volatility jump the next day and the resulting loss reached 4.41%, according to the S&P 500 index. It was the most dramatic drop since September 2008. On the 6th of March atypical correlation and almost atypical risk was observed. The next day, losses reached 7.60%, according to the S&P 500 index. Figure 5. Analysis of the financial turbulence, October 2018. Risks 2021, 9, x FOR PEER REVIEW 18 of 22 Figure 6. Analysis of the financial turbulence, February–March 2020. Next, on the 18th of March, many logically expected that the market had reached its minimum, and therefore, there was very little chance of sinking further as the correlation surprise did not exceed 1 and the magnitude surprise, though high, demonstrated a downward trend. However, on the 19th of March, both the correlation surprise and magnitude surprise showed high values, which meant there was an approaching period of financial turbulence. Over the next two days, the losses reached 6%, according to the S&P 500 index. Now we will consider the first six months of 2020 for the Russia Stock Market. On the 20th–21st of January, the market experienced both atypical correlation surprise and magnitude, which provided evidence of full-scale financial turbulence (Figure 7a). These dates were then followed by sharp risk jumps and the index price dropped for four trading days in a row. The magnitude was highest on the fourth day (27th of January). The total loss over that period was slightly under 5%, according to the RTSI index. The next sharp drop caused by full-scale financial turbulence occurred on the 4th of March (Figure 7b). The magnitude slightly exceeded the threshold value. Over the next five trading days, the RTSI index decreased by almost 40% and the magnitude surprise on the 10th of March showed one of its records of 46.68. Figure 6. Analysis of the financial turbulence, February–March 2020. Risks 2021,9, 188 18 of 21 Risks 2021, 9, x FOR PEER REVIEW 19 of 22 (a) (b) Figure 7. Analysis of the financial turbulence: (a) January–February, (b) March 2020. 5. Discussion The conducted research contributes to the global knowledge pool, at minimum, in three aspects. First, we suggest our own classification of the stock market hidden regimes. The examined regimes were given a consistent consideration and interpretation. We also used statistical tests to compare and contrast the stock market features within different regimes. The article provides the analysis of some episodes of regime switching occurring in financial history. The results obtained across the S&P 500 sample are consistent with the research conducted by many analysts (Ang and Timmermann 2012; Kinlaw and Turkington 2014). Armstrong and Bradfield (2015) revealed similar effects across African stock markets. This paper provides the data on regime switching patterns detected on the Russian stock market with reference to the events which took place in 2020. Second, we propose a methodology to detect hidden market regimes. The methodology is based on capturing single changes in the degree of non-diversifiable orthogonal components of financial turbulence that describe correlation and jump risks. This study extends and summarizes the results of research into hidden market regimes in terms of correlation (Kritzman and Li 2010; Kinlaw and Turkington 2014) and volatility jumps (Chevallier and Goutte 2015; Kirkby and Nguyen 2020). The insight into the intrinsic features of the hidden market regimes provides fuller evidence about their characters and the reasons for behavioral patterns. Third, we describe the impact that hidden market regimes have on asset risks and returns. The obtained results can be used to develop strategies for a turbulence-resistant investment portfolio with reference to the type of market regime (Page and Panariello Figure 7. Analysis of the financial turbulence: (a) January–February, (b) March 2020. The next sharp drop caused by full-scale financial turbulence occurred on the 4th of March (Figure 7b). The magnitude slightly exceeded the threshold value. Over the next five trading days, the RTSI index decreased by almost 40% and the magnitude surprise on the 10th of March showed one of its records of 46.68. 5. Discussion The conducted research contributes to the global knowledge pool, at minimum, in three aspects. First, we suggest our own classification of the stock market hidden regimes. The examined regimes were given a consistent consideration and interpretation. We also used statistical tests to compare and contrast the stock market features within different regimes. The article provides the analysis of some episodes of regime switching occurring in financial history. The results obtained across the S&P 500 sample are consistent with the research conducted by many analysts (Ang and Timmermann 2012;Kinlaw and Turkington 2014). Armstrong and Bradfield (2015) revealed similar effects across African stock markets. This paper provides the data on regime switching patterns detected on the Russian stock market with reference to the events which took place in 2020. Second, we propose a methodology to detect hidden market regimes. The methodology is based on capturing single changes in the degree of non-diversifiable orthogonal components of financial turbulence that describe correlation and jump risks. This study extends and summarizes the results of research into hidden market regimes in terms of correlation (Kritzman and Li 2010;Kinlaw and Turkington 2014) and volatility jumps (Chevallier and Goutte 2015;Kirkby and Nguyen 2020). The insight into the intrinsic Risks 2021,9, 188 19 of 21 features of the hidden market regimes provides fuller evidence about their characters and the reasons for behavioral patterns. Third, we describe the impact that hidden market regimes have on asset risks and returns. The obtained results can be used to develop strategies for a turbulence-resistant investment portfolio with reference to the type of market regime (Page and Panariello 2018; Nystrup et al. 2018;Paolella et al. 2019), the systems of early predictive capacity (Golub et al. 2018;Liu et al. 2020) and also in exploring the patterns and dependency of different sectors of a financial market (Alemany et al. 2020). 6. Conclusions It is obvious that stock markets are constantly developing, changing and updating themselves. This refers not only to institutional aspects but, first of all, to statistic aspects. Although unobservable, the latter aspects have quite tangible effects on the performance of assets and investment opportunities. Thus, their detection requires a specially designed methodology. In this article, we provide a developed classification of hidden market regimes as well as providing a proper consideration of these from the perspective of contemporaneous and lagged effects, which affect the investment characteristics of financial instruments. In order to detect a hidden market regime, it is necessary to decompose the financial turbulence into correlation and magnitude components. The magnitude allows detecting atypical values of returns volatility in relation to their history. Correlations, irrespective of magnitudes, show the degree of atypical assets interaction over a time period. In other words, they show a risk correlation baseline in the stock market. The research finds that the detection of a stock market regime provides additional evidence for future changes of assets performance. The particular examples of the stock markets in the US and Russia, both conceptually and empirically, show that these data have a predictive capacity to forecast volatility jumps over time periods following atypical correlations. The study also demonstrates that the considered hidden regimes have at least one different statistic criterion, i.e., that of returns or volatility. The suggested methodology has a number of important empirical applications. If taken into consideration, a hidden regime pattern can ensure a proper decision-making model and, thus, improve the efficiency of asset risk algorithms. Obviously, a number of issues are yet to be addressed. First, it is necessary to explore the clustering of the effects, resulting from regime switches. Second, it is important to investigate methods for forecasting the duration of the detected contemporaneous and lagged effects during a regime switch. 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