Estimation of Counterparty Credit Risk Impact under IFRS Requirements: A modelling proposal under a quantitative market information-based approach
Abstract
Counterparty credit risk is one of the main financial risk to be monitored by financial and non-financial institutions, worldwide. It entails a huge impact in areas as diverse as Business, Finance, Risk management, Funding & Liquidity management, Treasury, Trading, Solvency control, Accounting, Reporting, etc. Concerning valuation and accounting matters, counterparty credit risk is present throughout IFRS rules, with emphasis on a particular way under IFRS 9, IFRS 13 and IFRS 16. Under the IFRS 9, entities must estimate the PD (Probability of Default) for all financial assets (and other elements) not measured at Fair Value through Profit & Loss in turn to compute the Expected Credit Loss for those assets. Also, regarding the potential impact that a modification in a debt instrument terms (i.e., debt restructuring) may have under IFRS 9, the original debt could have to be derecognized and replaced with the present value of the modified debt, which should be computed by discounting its cash-flows with a robust, liquid yield curve according to the company´s credit quality and instrument seniority. Likewise, under IFRS 13 framework, the expected counterparty credit risk should be incorporated to the value of a derivative which is measured at Fair Value. In this case, the derivative credit risk will be determined for both counterparty (CVA – Credit Value Adjustment) and own credit risk (DVA – Debt Value Adjustment). Therefore, the counterparty credit quality (and subsequent PD) and the own PD for the entire life of the instrument should be estimated. A common problem in this regard is that there is no quoted credit instruments nor credit rating information of a company. For such cases, I propose a regression model that provides a theoretical credit rating for a counterparty as a first, necessary step when estimating the PD or the discounting curve. The model is new in a certain extent in comparison with other recent models in several aspects, such as the size and composition of the database used to calibrate the model variables (financial ratios percentiles within a sector distribution) and the fact that is intended to provide a “forward-looking” risk approach. The initial assumption is that financial ratios are a reliable source of information to estimate a rating letter when those are efficiently combined, with no necessity of qualitative nor additional company´s management-related information. I demonstrate that, with a granular sectorial database and by applying optimization in variables via Stepwise AIC process, the model output is reliable and robust to estimate the credit rating for a given company. On the other hand, under IFRS 16, entities must discount future lease payments to value the leased asset or liability. The discount rate is generally understood as the lessee’s IBR (Incremental Borrowing Rate). IFRS 16 states the IBR must consider that the hypothetical loan is collateralized by the leased asset. In this regard, there is a lack of accounting and finance literature focused on analysing how the IBR should be calculated taking into consideration both the counterparty credit risk of the lessee and the quality of the collateral. The starting hypothesis is that this quality is mainly determined by the underlying asset’s expected LGD (Loss-Given Default) so that the relationship between the IBR and the LGD could be modelled. In this thesis I propose two quantitative models based on CDS (Credit Default Swap) spreads and liquid bond prices to estimate the IBR given the lessee credit rating and collateral-linked LGD. The results are statistically robust and demonstrates that the relationship between CDS spreads or bonds yield-to-maturity and the LGD implied in their market prices can be translated as a sensitivity measure to estimate the IBR for a lease contract by pivoting from a standard market yield curve.
Full text
Universidad de Sevilla – Escuela Internacional de Doctorado Doctoral Program in Economics and Business Science Thesis for Doctor of Philosophy degree achievement Estimation of Counterparty Credit Risk Impact under IFRS Requirements A modelling proposal under a quantitative market information-based approach David Delgado-Vaquero Directors: Dr. José Morales-Díaz, Professor at Financial Administration and Accounting Department Universidad Complutense de Madrid Dr. Constancio Zamora-Ramírez, Professor at Accounting and Financial Economics Department University of Seville June 2022
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 1
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 2 ACKNOWLEDGEMENTS
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 3
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 4 Estimation of Counterparty Credit Risk Impact under IFRS Requirements A modelling proposal under a quantitative market information-based approach Abstract: Counterparty credit risk is one of the main financial risk to be monitored by financial and nonfinancial institutions, worldwide. It entails a huge impact in areas as diverse as Business, Finance, Risk management, Funding & Liquidity management, Treasury, Trading, Solvency control, Accounting, Reporting, etc. Concerning valuation and accounting matters, counterparty credit risk is present throughout IFRS rules, with emphasis on a particular way under IFRS 9, IFRS 13 and IFRS 16. Under the IFRS 9, entities must estimate the PD (Probability of Default) for all financial assets (and other elements) not measured at Fair Value through Profit & Loss in turn to compute the Expected Credit Loss for those assets. Also, regarding the potential impact that a modification in a debt instrument terms (i.e., debt restructuring) may have under IFRS 9, the original debt could have to be derecognized and replaced with the present value of the modified debt, which should be computed by discounting its cash-flows with a robust, liquid yield curve according to the company´s credit quality and instrument seniority. Likewise, under IFRS 13 framework, the expected counterparty credit risk should be incorporated to the value of a derivative which is measured at Fair Value. In this case, the derivative credit risk will be determined for both counterparty (CVA – Credit Value Adjustment) and own credit risk (DVA – Debt Value Adjustment). Therefore, the counterparty credit quality (and subsequent PD) and the own PD for the entire life of the instrument should be estimated. A common problem in this regard is that there is no quoted credit instruments nor credit rating information of a company. For such cases, I propose a regression model that provides a theoretical credit rating for a counterparty as a first, necessary step when estimating the PD or the discounting curve. The model is new in a certain extent in comparison with other recent models in several aspects, such as the size and composition of the database used to calibrate the model variables (financial ratios percentiles within a sector distribution) and the fact that is intended to provide a “forward-looking” risk approach. The initial assumption is that financial ratios are a reliable source of information to estimate a rating letter when those are efficiently combined, with no necessity of qualitative nor additional company´s management-related information. I demonstrate that, with a granular sectorial database and by applying optimization in variables via Stepwise AIC process, the model output is reliable and robust to estimate the credit rating for a given company. On the other hand, under IFRS 16, entities must discount future lease payments to value the leased asset or liability. The discount rate is generally understood as the lessee’s IBR (Incremental Borrowing Rate). IFRS 16 states the IBR must consider that the hypothetical loan is collateralized by the leased asset. In this regard, there is a lack of accounting and finance literature focused on analysing how the IBR should be calculated taking into consideration both the counterparty credit risk of the lessee and the quality of the collateral. The starting hypothesis is that this quality is mainly determined by the underlying asset’s expected LGD (LossGiven Default) so that the relationship between the IBR and the LGD could be modelled. In this thesis I propose two quantitative models based on CDS (Credit Default Swap) spreads and liquid bond prices to estimate the IBR given the lessee credit rating and collateral-linked LGD. The results are statistically robust and demonstrates that the relationship between CDS spreads or bonds yield-to-maturity and the LGD implied in their market prices can be translated as a sensitivity measure to estimate the IBR for a lease contract by pivoting from a standard market yield curve. Keywords: IFRS 9, IFRS 13, IFRS 16, Probability of Default (PD), Credit Rating, Credit Value Adjustment (CVA), Debt Value Adjustment (DVA), Incremental Borrowing Rate (IBR), Recovery Rate (RR), LossGiven Default (LGD), Yield-to-Maturity (YTM), Credit Default Swap (CDS), Stepwise AIC, Libor Market Model (LMM), Swaptions. JEL Classification: C13, C33, C52, G33, M41.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 5
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 6 TABLE OF CONTENTS ACKNOWLEDGEMENTS ....................................................................................................................... 2 TABLE OF CONTENTS ........................................................................................................................... 6 LIST OF ABBREVIATIONS .................................................................................................................... 9 LIST OF FIGURES .................................................................................................................................. 11 LIST OF TABLES .................................................................................................................................... 13 CHAPTER 1: INTRODUCTION ........................................................................................................... 16 1.1. General context and motivation of this doctoral thesis ........................................................ 16 1.2. IFRS framework and the counterparty credit quality estimation requirement ................ 18 1.3. Objective and starting hypotheses: the necessity of modelling solutions under IFRS 9, 13 & 16 frameworks when there is a lack of counterparty credit quality information ...................... 19 1.3.1 Credit rating, PD and YTM estimation under IFRS 9 & 13 frameworks ......................... 20 1.3.2 Incremental Borrowing Rate estimation for leasing valuation under IFRS 16 ................ 22 1.4. Structure of the doctoral thesis .............................................................................................. 24 CHAPTER 2: METHODOLOGY OF RESEARCH ............................................................................. 26 2.1. Introduction ................................................................................................................................... 26 2.2. Questions to initial hypotheses and research methodology ....................................................... 26 2.3. Sample and data input collection for modelling purposes ......................................................... 27 2.5. Final considerations ...................................................................................................................... 28 CHAPTER 3: LITERATURE REVIEW ............................................................................................... 30 3.1. IFRS 9: Financial Assets Expected Loss Provision and Liabilities restructuring to Fair Value ............................................................................................................................................................... 31 3.1.1 Expected Credit Loss ........................................................................................................ 32 3.1.2 The Effective Interest Rate for Liabilities restructuring ................................................... 34 3.2. The Counterparty Risk in Derivatives trades: IFRS 13 and CVA ........................................... 36 3.2.1 CVA definition .................................................................................................................. 37 3.2.2 IFRS 13: Fair value hierarchy and the relevancy of credit risk data ............................... 38 3.3. Lease accounting and valuation under IFRS 16 ......................................................................... 39 3.3.1 Introduction to IFRS 16.................................................................................................... 40 3.3.2 The role of collateral ........................................................................................................ 42 3.3.3 LGD for lease operations ................................................................................................. 44 3.3.4 IFRS discount rates .......................................................................................................... 44 CHAPTER 4: INDUSTRY MODELLING REVIEW ........................................................................... 48 4.1. Rating agencies and Credit Rating letter models ....................................................................... 48 4.1.1 Qualitative and Quantitative Scorecard/Grid .................................................................. 48 4.1.2 Scorecard Factors and Weighting .................................................................................... 49 4.1.3 Mapping Scorecard Factors to a Numerical Score .......................................................... 50 4.1.4 Determining the Overall Scorecard - Indicated Outcome ................................................ 50 4.2. Probability of Default Analytical Models .................................................................................... 56
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 7 4.2.1 Z-Score model .................................................................................................................. 56 4.2.2 Ohlson model ................................................................................................................... 58 4.3. KMV Structural model ................................................................................................................. 59 4.3.1 Concepts and preliminary basis ....................................................................................... 59 4.3.2 Model theory (I): lognormal property of equity prices and Montecarlo simulation ........ 59 4.3.3 Model theory (II): the Company as a call option and the equity-assets relationship ....... 60 4.3.4 Model implementation: from default probabilities to short-term Credit Ratings and additional considerations .................................................................................................................. 64 4.4. Exposure projection for IFRS 13 CVA estimation ..................................................................... 65 4.4.1 Potential exposure ............................................................................................................ 66 4.4.2 Projecting interest rates-linked exposure ......................................................................... 67 4.4.3 Libor Market Model ......................................................................................................... 69 4.4.4 Swaption Mark-to-Market as a proxy for an IRS Potential Exposure .............................. 72 4.5. Conclusions .................................................................................................................................... 75 CHAPTER 5: PROPOSED MODEL TO ESTIMATE CREDIT RATING AND PD UNDER IFRS 9: FRS MODEL ............................................................................................................................................ 78 5.1. Methodology and model theory development ............................................................................. 80 5.1.1 Step 1 – Definition of potential financial ratios ............................................................... 80 5.1.2 Step 2 – Calculation of peers’ general score ................................................................... 83 5.1.3 Step 3 – Calculation of the specific score for each financial ratio for all peers .............. 84 5.1.4 Step 4 – Panel data construction and Model calibration: regression and variable selection through Stepwise AIC ........................................................................................................................ 84 5.1.5 Step 5 – Obtaining the model credit rating and the expected PD for the company ......... 95 5.2. Model implementation and performance measurement ............................................................ 97 5.2.1 Full dataset OLS Regression and analysis ....................................................................... 99 5.2.2 Full dataset GLS Regression and analysis ..................................................................... 105 5.2.3 Stepwise AIC and selection of AIC-optimized variables ................................................ 106 5.2.4 Final Optimized Models ................................................................................................. 107 5.2.5 Ultimate model output: implied Probabilities of Default as input for IFRS ECL and CVA figures 110 5.2.6 Starting hypothesis checkpoint and conclusion: explanatory variables used by Rating Agencies are aligned with the ones used by the optimized model .................................................... 111 5.3. Model dataset distribution testing ............................................................................................. 112 5.4. Back-testing ................................................................................................................................. 116 5.4.1 Out-of-sample testing ..................................................................................................... 116 5.4.2 Cross-validation process ................................................................................................ 117 CHAPTER 6: PROPOSED IBR MODELS UNDER IFRS 16 ........................................................... 123 6.1. Theoretical basis .......................................................................................................................... 123 6.2. Model hypotheses ........................................................................................................................ 126 6.3. Bond price-based model: Methodology, model theory development and implementation ... 127 6.3.1 Default tree implementation example ............................................................................. 129 6.3.2 Specific aspects of leasing contracts .............................................................................. 131
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 8 6.3.3 A practical example ........................................................................................................ 133 6.3.4 Model implementation and Performance measurement ................................................. 135 6.3.5 Out-of-sample model testing and training ...................................................................... 141 6.4. CDS price-based model: Methodology, model theory development and implementation .... 144 6.4.1 CDS pricing framework ................................................................................................. 144 6.4.2 A practical example ........................................................................................................ 147 6.4.3 Model implementation and Performance measurement ................................................. 150 6.4.4 Out-of-sample model testing and training ...................................................................... 153 CHAPTER 7: CONCLUSIONS AND FUTURE LINES OF RESEARCH ....................................... 157 7.1. Credit Rating and Probability of Default estimation model.................................................... 157 7.2. Leasing valuation and IBR estimation model ........................................................................... 159 7.3. Comments and Modelling limitations ....................................................................................... 160 7.4. Future lines of research .............................................................................................................. 162 LIST OF REFERENCES....................................................................................................................... 164
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 15
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 16 CHAPTER 1: INTRODUCTION 1.1. General context and motivation of this doctoral thesis Counterparty credit risk, or in general, credit risk, is the risk of a loss arising from a failure (or default) of a counterparty to meet its contractual obligations (McNeil et al., 2015). Credit risk is one of the main financial risks to be monitored by many companies, worldwide. It entails a relevant impact in areas as diverse as Business, Finance, Risk Management, Funding & Liquidity Management, Treasury, Trading, Solvency Control, Accounting, Reporting, etc. The counterparty credit risk, which is directly translated in potential monetary impact for an institution as a decrease in the value of its assets due to a loss from unpayment (i.e., a “credit loss”), and a source of capital and reserves requirement, is usually understood through two main concepts: a) Probability of Default (PD): following most of the definitions given by supranational entities (ECB, EBA, etc.) or the definition of default contained in the CRR, it can be said that the Probability of default is the term that describes the likelihood of a default of a counterparty over a particular time horizon. More specifically, the PD provides an estimate of the likelihood that a borrower will be unable to meet its debt obligations. Although the definition of “default” can be polysemic, for this research it is not crucial. Hereinafter, we will assume that “default” means “being unable to meet the obligation of payment arising from a debt product (i.e., a loan, a bond, etc.)”. Therefore, we will work under the assumption that the PD provides the expected times a default can occur from a borrower in a predefined time horizon. b) Loss-Given Default (LGD): this concept is inherent to the probability of a default occurrence, and is equally relevant to measure the credit loss, as it represents de amount of losses occurred once the default has taken place. This is, the unrecovered losses once a default has occurred from an obligor. This concept has implicitly attached the concept of Recovery Rate, which is the metric that provides the estimated amount recovered once a default occurs. This is, LGD = (1 - Recovery Rate). These concepts will be referenced in this thesis in an indistinct way. These two concepts are needed to measure the credit loss for an investment between time t-1 and time t: Potential Credit Loss (t-1, t) = PD (t-1, t) * LGD (t-1, t)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 17 A proportional error in either the probability of default or LGD affects potential credit losses identically. Yet, much more resources and efforts are employed in the industry to estimate probability of default. Many different modelling techniques are applied to default probability; from statistical methods based on accounting data to structural models or hybrid approaches. The main reason is that PD are changing over time, and it depends in a wide extent on the rating, sector and geography to which the company belongs. Below is shown a chart of the implied PDs in CDSs 1 per rating letter and maturity, in Europe. Figure 1. Cumulative Probability of Default curves per Rating letter, 20/04/2022 Source: Refinitiv However, in sharp contrast, LGD is typically estimated by appealing to historical averages, usually segregated by debt type (loans, bonds and preferred stock) and seniority (secured, senior unsecured, subordinated, etc.). Although its levels depend not only on the seniority of the product but on the sector-specific and macroeconomic variables as well, its sensitivity to such factors is not as notable as in the case of PD. Likewise, PD is widely expected to change even between companies of the same sector and rating grade, however historical LGDs, in average, are more static on their seniorities, and even their implicit values in market-traded products, like CDSs and bonds, are assumed to be flat. The main reason for that is that even for same seniority tranches, the LGD could be too much “entity-specific”, and therefore there could be a serious lack of information for a correct modelling. Because of that, LGD uses to be assumed flat and LGD averages per seniority are usually the main input used when estimating potential credit losses. 1 Credit Default Swap
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 18 Figure 2. Loss-Given Default rates on instrument prices, per instrument seniority 2 Source: Moody`s (2014) In this context, a correct estimation of the PD and LGD for a given client or counterparty and financial product is therefore a key when measuring its credit risk. It is widely known that financial and non-financial companies face many information-related issues when computing figures for PD and LGD. This is mostly linked to lack of information about the credit quality for a counterparty which usually has no credit-related data available but its own financial statements. This is, there are no credit ratings given by an agency rating, credit-linked instruments with available prices in a financial venue nor historical series of bonds or loans that may provide with a reliable data about the market estimation of the credit quality for such a counterparty. This problem lead companies, auditors, banks and other entities to do a research process to estimate PD and LGD figures for counterparties and clients. The main issue in this case is that the estimation methodology should comply with several accounting criteria and minimum methodological standards that are difficult to reach in an efficient way. In this regard, the motivation of this doctoral thesis is to cover those main modelling gaps found in the academic and industry practice related to the lack of credit quality information and propose new modelling solutions which directly concern the concepts of PD and LGD under the IFRS 3 framework for financial valuation, reporting and accounting. 1.2. IFRS framework and the counterparty credit quality estimation requirement Over the last ten years, IFRS accounting standards have changed significantly in areas such as fair value, financial instruments, lease accounting, and revenue recognition. Generally, the new standards entail a higher use of judgment and estimations, which renders the role of financial 2 It highlights the variability of recoveries for several seniority classes. The shaded boxes cover the inter-quartile range with the median marked as a white horizontal line. Squared brackets cover the data range except for outliers that are marked as horizontal lines 3 International Financial Reporting Standards (IFRS) issued by the International Accounting Standards Board (IASB). In Europe, IFRS are applied by quoted entities for the preparation of their consolidated financial statements See http://www.ifrs.org/use-aroundthe-world/use-of-ifrs-standards-by-jurisdiction/ for a detailed study on the use of IFRS standards by jurisdiction.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 19 analysts and auditors far more difficult. According to Heidhues and Patel (2011), the exercise of accountants’ professional judgment has increasingly been recognized as an important and controversial topic. In this sense, for one purpose or another, several recently issued standards require entities to estimate the credit quality of a third party or their own credit quality. Specifically, IFRS 9 (“Financial Instruments”) requires the estimation of an impairment from a potential credit loss in the assets (i.e., the Expected Credit Loss or ECL). Likewise, following the implementation of IFRS 13 (“Fair Value Measurement”), when measuring derivatives’ fair value, entities must consider the counterparty credit risk adjustment, which generally entails estimating the PD of the derivative’s counterparty and the own PD, among other inputs. Furthermore, under IFRS 16 (“Leases”), when a lessee discounts future lease asset cash-flows, if the implicit lease rate is not available, the entity must estimate its own borrowing rate for buying a specific asset with a specific maturity. In some cases, the inputs required (PD or the bond interest rate/YTM 4 ) can be directly estimated from observable market information, such as CDS spread quotes or the issuer bond price quotes 5 . In other cases, however, this information is not available. The counterparty whose credit quality needs to be estimated may not have quoted CDSs nor bonds, nor a credit rating 6 issued by an independent credit rating agency (CRA). In such cases 7 , entities need to implement a methodology for internally estimating the credit quality (credit rating) of a company as a basis for obtaining a PD or a YTM/discount rate curve, and also a method to correctly calibrate the adjustments needed on those PD or discount curves due to some particularities of the asset or the counterparty. Hence, in this thesis I will provide with modelling solutions to tackle the issues arising from the non-existence of indicators of credit quality for a given company nor market information on discounting curves, so that the gaps to comply with the PD and discount rates can be covered under the IFRS 9, 13 and 16 frameworks. 1.3. Objective and starting hypotheses: the necessity of modelling solutions under IFRS 9, 13 & 16 frameworks when there is a lack of counterparty credit quality information My background and professional experience in the field of financial valuation and risk management have provided me with awareness and expertise on the main problems that companies, both financials and corporates, have when dealing with the compliance of IFRS 9, 13 4 Yield-To-Maturity. 5 Or even from internal information such as the yield-to-maturity of a recently obtained, representative banking debt. 6 Credit ratings are a summary of a firm’s expected future creditworthiness. They represent an evaluation of the credit risk of company, i.e., they are related to the probability that a company will default. The higher the rating, the lower the expected credit risk, and the lower the estimated PD. There are independent credit rating agencies that issue public credit ratings for companies/governments or specific bonds issuances. Relevant rating issuers are S&P (Standard & Poors), Moody’s, Fitch or DBRS (Dominion Bond Rating Service). 7 See IFRS 13 fair value hierarchy in Chapter 3.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 20 and 16 rules, particularly when the lack of financial and market information about counterparties is relevant. Market models to derivate standard PD values or vanilla YTM curves for companies with credit risk information available are widely known among practitioners. However, when there is no such an information, which is a common issue, new model approaches are needed. In fact, even when there is information on standard credit instruments for a company but no rating nor YTM for longer tenors or non-standard debt seniority tranches, modelling adjustments are duly required. Bearing this in mind, several solutions to cope with these problems are explained, which have been brough together, enhanced and tested alongside my research period, crystallizing in this doctoral thesis. 1.3.1 Credit rating, PD and YTM estimation under IFRS 9 & 13 frameworks Within the field of finance literature, the interest in counterparty credit risk and credit rating estimation has particularly increased since the 2008 subprime financial crisis. There is a line of research in which authors propose models for obtaining an internal credit rating to challenge the official credit rating issued by CRAs, or to use it in the event that there is no official credit rating available. The first historical work was that by Altman (1968), which used five financial ratios in order to predict bankruptcy. Since then, many authors have also proposed models in which financial variables are used for estimating credit risk. See, for example, Merton (1974); Kaplan and Urwitz (1979); Ohlson (1980); Ederington (1985); Longstaff and Schwartz (1995); Duffee (1999); and Kamstra et al. (2001). More recently, Creal et al. (2014) proposed a marked-based rating which makes direct use of the prices on traded assets. The authors use asset pricing data to impute a term structure of risk neutral survival functions or default probabilities. Firms are then clustered into ratings categories based on their survival functions using a functional clustering algorithm. They compare their ratings to S&P and find that, over the period 2005 to 2011, their ratings consistently lead to S&P ones for firms that ultimately default. Tsay and Zhu (2017) proposed a two-step algorithm involving ARIMA-GARCH modelling and clustering to obtain a market-based credit rating by using easily obtained public information. The algorithm is applied to 3-year CDS spreads of 247 publicly listed firms. The authors compare the ratings obtained with the ratings given by agencies, and show that such market-based credit rating performs reasonably well. Jansen and Fabozzi (2017), assuming a given recovery rate, use the CDS-implied default probabilities to cluster them in rating groups. However, there are still present in the financial literature several issues concerning the PD modelling for accounting and reporting purposes, with a relatively global application. Few proposed models for obtaining an internally developed credit rating fulfil all (or most of) the following criteria at the same time: i. Specifically addressed to accounting purposes (i.e., for complying with accounting requirements) under IFRS, which affect most of companies not reporting under US GAAP.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 21 ii. Specifically focused on complying with IFRS 9 expected loss requirements. The IFRS 9 PD should be based not only on historical information but should also consider forwardlooking information. By way of example, Altman’s and Merton’s models do not incorporate forward-looking information (related to market quotes). iii. Able to be applied to non-quoted/non-rated entities. Few models have mainly been developed for non-quoted companies (Beever, 1968; Ohlson, 1980; Campbell et al., 2008; Chava and Jarrow, 2004) iv. Comparable, so that the results can be compared to market or credit rating information. v. Able to be applied to one specific counterparty/company within a given sector. vi. Applicable in any jurisdiction. vii. Able to be implemented by obtaining public information which is readily available, such as the entity’s sector; the credit rating issued by official CRAs for other companies in the same sector/country; the entity’s financial statements, etc. viii. The output provided is a credit rating under a scale comparable to the ratings used by CRAs: S&P, Moody’s and Fitch. This will make it easier to find companies with similar credit quality and which also have a public credit rating. ix. Updatable: it provides an updated output based on the current market/sectorial framework. x. Able to be extrapolated, as the main output could be translated into a Rating Letter, a PD rate, a yield-to-maturity curve, or a credit spread. This fact leads to a solution for lack of counterparty credit information under the IFRS 13 and IFRS 16 frameworks as well. In this regard, the first objective of this doctoral thesis is to propose a model that provides with a credit rating under the IFRS requirements. Hence, Chapter 5 presents a model that provide a robust output (as a credit rating, a PD or even as a discount rate) to be used as input needed to impairment calculation (ECL) and debt restructuring valuation figures under IFRS 9, as well as CVA and DVA metrics to be estimated under IFRS 13. That model is expected to meet most of above criteria and is intended to provide consistent outputs in this regard. The model provides the output via a regression scheme which retrieves a theoretical credit rating for a counterparty as a first, necessary step when estimating the PD or the discounting curve. The model is new in a certain extent in comparison with other academic models in several aspects, such as the size and composition of the database used to calibrate the model variables (financial ratios percentiles within a sector distribution for several years in a row) and the fact that is intended to provide a “forward-looking” risk approach. The assumption that can be taken as an initial hypothesis is that historical financial ratios are a reliable source of information to estimate a rating letter when those are efficiently combined, with no necessity of qualitative nor additional company´s management-related information. I demonstrate that, with a granular sectorial database and by applying optimization in variables via Stepwise AIC process, the model output is reliable and robust to estimate the credit rating of a given company. Therefore, once the
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 22 database is accurately treated, the model can be easily implemented and used for different sector and geographies, with a forward-looking approach and able to cover the changes in rating criteria throughout time, hence available to be used for accounting and reporting purposes under different audit exercises. The model has been tested by comparing its output for entities already given with an official credit rating with credit rating agencies (Moody’s, Fitch, or Standard & Poor’s). Therefore, we obtain a unified framework which incorporates a firm’s specific features along with its sectorial and regional factors, and which enables market assessments of credit risk to be incorporated into the book value of financial assets. 1.3.2 Incremental Borrowing Rate estimation for leasing valuation under IFRS 16 On the other hand, the second objective on this thesis is to provide a modeling framework that copes with the necessity of adapting the discounting curve to value leasing contracts with different assets as collateral. It know that entities must discount future lease payments to value the leased asset or liability to comply with IFRS 16 rules. The discounting rate is generally understood as the lessee’s IBR (Incremental Borrowing Rate). IFRS 16 states the IBR must consider both the counterparty credit risk of the lessee and the quality of the collateral. Therefore, in this document two quantitative models based on CDS spreads and liquid bond prices are presented, so that the IBR can be estimated given the lessee credit rating and collateral-linked LGD. This work contributes to the previous literature in three main drawbacks widely found among the industry practice: - Firstly, the models proposed can be used by researchers when estimating the impact of IFRS 16 on a certain jurisdiction or entity. Studies prior to the issue of IFRS 16 use a unique rate for discounting lease payments (Beattie, et al., 1998; Bennett and Bradbury, 2003; Duke et al., 2009; Ely, 1995; Imhoff and Lipe, 1997; Singh, 2012; Wong and Joshi, 2015); or discount rates used for pensions and other provisions (Fülbier et al., 2008; Pardo et al., 2017); or directly use a benchmark rate plus a firm credit spread (Durocher 2008; Fitó et al., 2013). Therefore, the method provided for the estimation of lease IBR is in fact more accurate for research purposes because it provides a solution to adapt the IBR at lease-level and contingent LGD, rather than using benchmarks. - Secondly, the previous literature related to LGD estimation is not directly applicable to this matter. Although certain authors do present models for estimating the LGD or for analysing the relationship between loan prices and collateral value (with a given sample of loans at a certain date by Akguen and Vanini, 2007; Silagui et al., 2020), none of them present a model that explains how a standard yield curve can be adjusted to reflect the sensitivity to a LGD adapted to the collateral quality. - Thirdly, the models can be used by IFRS 16 practitioners in order to adjust “standard” IBR to the IBR applicable to different lease assets associated with different LGDs. As
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 23 previously mentioned, there is a gap in the existing literatures in this regard, and entities do not disclose this information in their financial statements. It is worth noting that the model presented is also applicable in many other contexts, such as estimating the fair value of a loan/bond that includes an asset as a collateral (for accounting, trading, valuation, or other purposes). In this case, the model can be used to adjust the discount curve and correctly reflect the higher (or lower) recovery rate expected from the asset. Another potential use would be the calculation of the interest rate of a collateralized loan transaction between a lender and a borrower; in this case the model can be used for adjusting the standard interest rate to the collateral value, calculate additional liquidity margins, etc. As a summary, it can be said that there is a modelling gap in the accounting and finance literature when analysing how the IBR should be calculated taking into consideration both the counterparty credit risk of the lessee and the quality of the collateral. The starting hypothesis in this regard is that this quality is mainly determined by the underlying asset’s expected LGD (Loss-Given Default) so that the relationship between the IBR and the LGD could be modelled. In this research it is demonstrated that the modelling results are statistically robust and demonstrates that the relationship between CDS spreads or bonds yield-to-maturity and the LGD implied in their market prices can be translated as a sensitivity measure to estimate the IBR for a lease contract by pivoting from a standard market yield curve. Moreover, it is demonstrated that the model functions by using real market data of quoted bonds, i.e., by applying the models to a real sample of quoted bonds and CDS prices, and subsequently analyse whether the model predicts the change in YTM when a change in the recovery rate occurs. Figure 3. Modelling framework proposal to estimate counterparty credit risk impact under IFRS Source: Compiled by the author
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 24 1.4. Structure of the doctoral thesis In Chapter 1, the introduction to the problems found in the counterparty credit risk treatment under IFRS framework is presented, including the main objectives of the research and the required fulfilment of the starting hypotheses made. In Chapter 2, I review the main methodology of research steps made and the relevant topics to be outlined within the research period. Chapter 3 covers the global literature review on the IFRS 9, 13 and 16 topics related to the credit risk estimation and its implications under the IFRS space, presenting the main conclusions and gaps found which the models presented aim to fix. Chapter 4 summarizes the main models currently used in the financial industry related to the credit risk estimation, including several approaches. In Chapter 5, I propose a credit rating estimation model named FRS model, that has been developed and improved during my research period, to cover some of the limitations found in the literature. It includes model theory and development, implementation examples, statistical testing and back-testing. Chapter 6 presents the models proposed concerning the IBR estimation under IFRS 16 requirements, also including model theory and development, hypotheses made, implementation and statistical testing. Finally, Chapter 7 includes the doctoral research conclusions, model limitations and future lines of research.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 31 3.1. IFRS 9: Financial Assets Expected Loss Provision and Liabilities restructuring to Fair Value IFRS 9 is the financial instruments accounting standard that has replaced IAS 39 for annual reporting periods commencing on or after 1st January 2018. One of the areas in which IFRS 9 will have a higher impact is the new impairment model (applicable to financial assets not measured at fair value through profit and loss, lease receivables, contract assets and financial guarantee contract - see IFRS 9.5.5.1). IAS 39 followed an incurred loss model: an impairment loss could not be recognized until it was incurred. Additionally, in terms of the "generic" provision, only what was known as Incurred But Not Reported (IBNR) losses could be recognized: losses related to debtors for which, at the date of the financial statements, the credit event has occurred but has not yet been revealed/reported. Conversely under IFRS 9, as soon as the debt instrument is recognized, at least part of the expected losses should be recognized. Loans are classified in three steps: step 1, step 2 and step 3. In step 1, 12-month expected credit losses are recognized, while lifetime expected credit losses are recognized in steps 2 and 3. Broadly speaking, the expected credit losses are calculated as 𝐸𝐴𝐷𝑡·𝑃𝐷𝑡·𝐿𝐺𝐷𝑡, where 𝐸𝐴𝐷𝑡 represents the Exposure at Default (expected instrument exposure) at time t; 𝑃𝐷𝑡 represents the Probability of Default at time t; 𝐿𝐺𝐷𝑡 represents the Loss Given Default at time t. 𝐿𝐺𝐷𝑡 represents at the same time the following: (1 – Recovery Rate) Therefore, one of the necessary inputs for calculating the expected credit losses is the PD of the borrower. However, IFRS 9 has introduced several changes with respect to IAS 39. For example, the categories for financial assets are different to those of IAS 39 (classification criteria is also different), and changes have been made to hedge accounting rules. One aspect significantly affected by the IFRS 9 changes is loan loss provisioning (impairment rules). For many entities, this has proved to be the most important change (that with the highest impact). It is not only banks that have been impacted by the new impairment rules; in fact all kinds of entities are making changes to their provisioning criteria (EY, 2018; EY, 2016; NovotnyFarkas, 2016; Beerbaum, 2015; Hronsky, 2010). The IAS 39 impairment model was based on “incurred losses”. Several regulators and authorities argued that this model led to procyclical effects, and asked standard issuers to develop a new model that entailed a more forward-looking provisioning (e.g. BCBS, 2009; FCAG, 2009; G20, 2009). The new IFRS 9 model is based on “expected losses” instead of “incurred losses”; however, it is not a full expected loss model.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 32 With certain exceptions 9 , under IFRS 9 all financial assets 10 not measured at fair value through profit or loss should be classified in three different “stages”. For financial assets included in stage 1, 1-year expected loss should be estimated and recognized. For financial assets included in stages 2 and 3, expected loss until maturity should be estimated and recognized. In other words, for all financial assets (and other elements) subject to IFRS 9 impairment rules, the entity should estimate a PD for 1 year or maturity. The measure of the loan loss allowance will require the use of data not previously considered under IAS 39 (Holt & McCarroll, 2015). 3.1.1 Expected Credit Loss As previously stated, IFRS 9 impairment rules are based on an expected loss model (in contrast with the IAS 39 incurred loss model). All financial assets subject to IFRS 9 impairment rules (with certain exceptions), are classified in three different stages. Depending on the stage involved, the impairment calculation is based on 1 year expected loss (“12-month expected credit losses”), or on expected loss until maturity (“lifetime expected credit losses”). In theory, all financial assets are included in stage 1. They progress to stage 2 when “credit risk on that financial instrument has increased significantly since initial recognition” (IFRS 9 paragraph 5.5.3). Finally, they are classified as stage 3 when the loss is incurred. The general formulas for estimating impairment (ECL) according to the stage to which the instrument belongs are as follows: 𝑆𝑡𝑎𝑔𝑒 1: 𝐸𝐶𝐿12𝑚=𝐸𝐴𝐷12𝑚⋅𝑃𝐷12𝑚⋅𝐿𝐺𝐷12𝑚⋅𝐷𝐹(0,1) 𝑆𝑡𝑎𝑔𝑒 2: 𝐸𝐶𝐿𝐿𝑖𝑓𝑒𝑡𝑖𝑚𝑒= ∑𝐸𝐴𝐷𝑡⋅𝑃𝐷𝑡⋅𝐿𝐺𝐷𝑡⋅𝐷𝐹(0,𝑡) 𝑛 𝑡=1 𝑆𝑡𝑎𝑔𝑒 3: 𝐸𝐶𝐿𝐿𝑖𝑓𝑒𝑡𝑖𝑚𝑒= 𝐸𝐴𝐷𝑀𝑎𝑡⋅𝐿𝐺𝐷𝑀𝑎𝑡⋅𝐷𝐹(0,𝑀𝑎𝑡) where 𝐸𝐴𝐷𝑡 represents the Exposure at Default (expected instrument exposure) at time t; 𝐸𝐴𝐷12𝑚 is the Exposure at Default at 12 months; 𝐸𝐴𝐷𝑀𝑎𝑡 represents the Exposure at Default at maturity; 𝑃𝐷𝑡 represents the Probability of Default at time t; 𝐿𝐺𝐷𝑡 represents the Loss Given Default at time t. LGD is calculated as (1 – Recovery Rate); 𝐷𝐹(0,𝑡) represents the discount factor from the calculation date to t. t is 1 year in stage 1 (or less than 1 year if the instruments mature in less than 1 year) and the time in years to maturity in stage 2 and stage 3. In stages 2 and 3, t can be divided into sub-periods (always considering all periods to maturity of the instruments). 9 For example, purchased or originated credit-impaired financial assets (IFRS 9 paragraphs 5.5.13 and 5.5.14), or trade receivables, contract assets and lease receivables to which the simplified model is applied (IFRS 9 paragraphs 5.5.15 and 5.5.16). 10 IFRS 9 impairment rules do not only apply to financial assets; they also apply to lease receivables (under IFRS 16); to contract assets (under IFRS 15); and in many cases to loan commitment and financial guarantee contracts (IFRS 9 paragraphs 2.1, 4.2.1(c), 4.2.1(d) and 5.5.1). (1) (2) (3)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 33 In Chapter 1 we saw that LGD value depends on several factors and is not even a certain value for a counterparty but depends on the loan’s seniority and the value of any specific guarantee at a given time period. In practice, if no information is available, LGD is assumed to be 60% (the recovery rate being 40%) 11 . In the following table the average corporate debt recovery rates measured by trading prices from 1983 to 2017 is shown. This type values can be used as a robust source to estimate the LGD for most of seniorities: Table 1: Average corporate debt recovery rates measured by trading prices Class Average recovery rate 1st Lien Bank Loan 63.74% 2nd Lien Bank Loan 27.73% Sr. Unsecured Bank Loan 40.21% 1st Lien Bond 53.80% 2nd Lien Bond 43.63% Sr. Unsecured Bond 33.48% Sr. Subordinated Bond 26.34% Subordinated Bond 27.55% Jr. Subordinated Bond 13.97% Source: Moody’s 2018. Also, it should be noted that IFRS 9 establishes that the estimated PD must include not only past due information, but also forward-looking information (in relation to expected changes in default rates). In this sense, observed past default rates should be adapted to changes in macroeconomic variables and market expectations. With the above context clear, it can be said that, generally, there are several methods for obtaining a PD depending on the availability of market and financial reliable sources: i. If market information of quoted inputs is available, the PD can be directly calibrated from quoted CDS spreads, quoted bonds yields or by using official credit rating and peer information. In theory, it is assumed that this market information already incorporates forward-looking adjustments. ii. A PD can also be obtained by using internal historical default data adjusted by forwardlooking estimations. This data is generally held by large corporate and banking companies. iii. Finally, if no market or internal historical information is available, an internal model can be used for estimating the PD based on other companies’ default rates, or on information from the company’s financial statements or from other sources. The models can be split into two groups: 11 See Ou et al. (2016) and Koulafetis (2017) for an empirical study of average recovery rates according to collateral.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 34 o Structural models: based on Merton (1974) and on Black and Scholes (1973) option pricing models. o Non-structural (analytical) models (as Altman et al. 1977). With regard to the abovementioned third method (which is the focus of this research), several authors have proposed internal models for estimating a company’s probability of default. Altman (1968) proposed an initial analytical model in which he used financial metrics (accounting ratios) for predicting an entity’s default. Other authors have proposed structural and analytical models for estimating credit risk or default probability, such as Merton (1974); Kaplan and Urwitz (1979); Ederington (1985); Longstaff and Schwartz (1995); Duffee (1999); and Kamstra et al. (2001). In this regard, there are also lines of research by other authors proposing a model whereby they obtain their own internal credit rating for a counterparty (also known as an “unofficial” or “shadow” rating). They compare this rating with the official credit rating (in order to challenge the official credit rating). The most recent papers in this area are those by Creal et al. (2014), Tsay and Zhu (2017), and Jiang (2018). Nonetheless, there is a lack of studies focused on non-quoted/non-rated entities. According to Duan et al. (2018), the relative paucity of academic attention is partly due to the lack of publicly available data on privately held firms. Even if accounting data for private firms is available, the lack of market data such as stock prices entails an additional obstacle to studying their defaults, since recent advancements in the credit risk model typically require some form of market information. Duan et al. (2018) propose a model for such cases. They obtain the distance-to-default (DTD) for quoted companies, and then identify macro and firm-specific factors related to the DTDs. Subsequently they locate macro and firm-specific values for private firms, and utilize the coefficients estimated from public firms to obtain the public-firm equivalent DTDs for the private firms. In addition, they improve the efficiency of estimating the default probabilities by adopting the newly developed doubly stochastic Poisson forward intensity model suggested in Duan et al. (2012). Cappon et al. (2018) propose an alternative model which they apply to Brazilian banks. They develop a regression model to estimate the “synthetic rating” of Brazilian banks from financial variables. They achieve an R2 higher than 80% to explain the ratings. However, they do not disclose the main internal aspects of the model. Ivanovic et al. (2015) also propose a model for obtaining a “shadow rating”, but it is focused on countries (and not on entities). 3.1.2 The Effective Interest Rate for Liabilities restructuring Although the main objective in this dissertation is the credit rating modelling with regards to the Expected Credit Loss estimation, in should be noted that IFRS 9 also includes the abovementioned rule on recognition of changes in a liability measured at amortized cost. In July 2017 the IASB
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 35 confirmed the accounting for modifications of financial liabilities under IFRS 9. That is, when a financial liability measured at amortized cost is modified without this resulting in derecognition, a gain or loss should be recognized in profit or loss. The gain or loss is calculated as the difference between the original contractual cash flows and the modified cash flows discounted by the original effective interest rate. (IFRS 9, paragraph B5.4.6) This is consistent with the tentative agenda decision of the IFRS Interpretations Committee (‘IC’). However, the IC decided not to finalize this decision on the grounds that an agenda decision was not an appropriate mechanism to address the issue. The Board has decided instead to amend the Basis for Conclusions to IFRS 9 to highlight that the accounting under IFRS 9 is clear and that no changes to the standard are required. This will impact all preparers, particularly those applying a different policy for recognizing gains and losses today. Under IAS 39, Financial instruments: Recognition and measurement, many preparers did not recognize a gain or loss at the date of modification of a financial liability. Instead, the difference between the original and modified cash flows was amortized over the remaining term of the modified liability by re-calculating the effective interest rate. This will need to change on transition to IFRS 9 because the accounting will change. Whilst it is not expected that entities will be required to change their existing accounting policy under IAS 39, the impact on transition to IFRS 9 should be considered. IFRS 9 is required to be applied retrospectively, therefore modification on gains and losses arising from financial liabilities that are still recognized at the date of initial application (e.g., 1st January 2018 for calendar year end companies) would need to be calculated and adjusted through opening retained earnings on transition. Although changes in debt terms are common in today’s environment and at first glance, it may appear that IFRS 9 does not change the accounting for financial liabilities as it retains almost all the existing guidance under IAS 39. However, IFRS 9 has introduced new guidance on how to account for changes in debt terms and this new requirement is expected to result in a significant change in practice for many companies. Modifications to debt can occur when the borrower and lender agree on changes to the contractual terms of the liability, e.g., changing the interest coupon or extending the expiration date. Under IAS 39, a change that is considered “substantial” would be assumed to be extinguishing, which means that the initial liability is derecognized, implying a gain or loss to be recorded in profit & loss, and subsequently that a new financial liability will be recorded based on the new terms. If the change is not considered “substantial”, then the original liability remains on the books and no profit and loss impact will be recorded. Nonetheless, under IFRS 9, a gain or loss at the date of the modification will be recognized notwithstanding if the change in contractual terms is substantial or not. This entails that the original liability will have to be derecognized and replaced with the present value of the modified liability. Also, if there were any costs or fees incurred to change the terms, they would be adjusted to the carrying amount of the modified debt and amortized over the remaining term of the modified debt. This means that the modified debt should be measured at fair value. This leads to the problem of looking for a reliable, adapted YTM curve. This curve should reflect the credit risk inherent to the debtor, so that the yield curve used should be in line with its credit rating. Hence, the model to estimate credit rating which is to be
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 36 presented in next chapters not only covers the ECL calculation itself, but provides with the credit rating that can be used to look for a YTM curve to discount cash-flows of a modified debt. To provide a hint about the relevance of being accurate when estimating the credit rating for a given company, see the below chart which provides a view on the difference between YTM curves per rating notch, for the same currency and sector (in this example, Automobile sector): Figure 4. Automobile & auto parts sector, EUR-denominated YTM curves (%) per Rating notch, 18/04/22 Source: Refinitiv 3.2. The Counterparty Risk in Derivatives trades: IFRS 13 and CVA From 2008, new, innovative financial regulation was implemented and was increasingly focusing on counterparty risk and OTC derivatives. The US Dodd–Frank Reform and Consumer Protection Act 2009 (Dodd–Frank) and European Market Infrastructure Regulation (EMIR) were designed to enhance the stability of OTC derivative markets. Basel III rules were introduced to strengthen bank capital bases and introduce new requirements on liquidity and leverage. Although not specifically driven by the effects from the 2008 crisis, IFRS 13 accounting rules were introduced from 2013 to replace IAS 39. IFRS 13 rules provide a single framework around fair value measurement for financial instruments and started to create convergence in practices around CVA. In particular, IFRS 13 uses the concepts of fair value and exit price, which entails the usage of market-implied quantitative information as much as possible. This is particularly relevant in default risk estimation, as market credit spreads must be used instead of historical default probabilities (somehow following the principle of forward-looking estimation approach). “Exit price” also introduces the notion of “own credit risk” and leads to DVA as the CVA charged by a replacement counterparty when exiting a transaction. The IFRS 13 standard was issued in 2011 and came into effect for annual reporting periods commencing on or after 1st January 2013. This standard represents a general fair value framework. If another IFRS requires or permits the use of fair value as a measurement basis, generally the entity should follow IFRS 13 for measuring the fair value (with the exceptions included in paragraphs 6 and 7 of IFRS 13). -1,00 0,00 1,00 2,00 3,00 4,00 5,00 6,00 7,00 3M 6M 1Y 2Y 3Y 4Y 5Y 6Y 7Y 8Y 9Y 10Y YTM (%) AA A BBB BB
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 37 3.2.1 CVA definition Prior to IFRS 13, and as a general rule, in order to measure the fair value of a financial derivative, future cash flows were estimated using different techniques, and these cash-flows were subsequently discounted using a "risk free" curve (based on interbank rates, such as the EURIBOR 6M swap curve or OIS curves). In this regard, it was assumed that the potential credit risk adjustment that could arise was not material, or that the credit risk assigned to both counterparties was netted. An adjustment for credit risk was only carried out in those scenarios where incurred losses had to be provisioned. In these cases, the positive value of the derivative was priced downwards to reflect an estimated recoverable amount. IFRS 13 clarified that when measuring the fair value of derivatives, credit risk must always be considered (see paragraphs 3, 42 - 44 and 69 of IFRS 13). This includes both the risk that the derivative may end with a positive value and the counterparty does not meet its obligations (which means, inherently, the inclusion of the Credit Value Adjustment or commonly, CVA) 12 , as well as the risk that the derivative may end with a negative value and the company itself does not meet its obligations (Debt Value Adjustment or DVA, which was not considered prior to IFRS 13). Credit Value Adjustment (hereinafter, CVA) measurement is similar to the one shown for the case of ECL under IFRS 9, although there is a critical difference concerning the Exposure at default amount. In the case of IFRS 9 impairment the EAD amount could be assumed as the amortized cost of the asset, constant for the remaining lifetime of the contract. However, the exposure to be taken into account for CVA should be understood as a double way exposure, i.e., bilateral. A derivative can take positive or negative values for both counterparties throughout its life span. Hence, it is necessary to model not only the default risk of each counterparty, but also the potential exposure values the derivative might have until maturity. This is understood as the potential exposure amount, which determines the amount of CVA for each counterparty to be subtracted to the current derivative Mark-to-Market. Therefore, the Fair value (i.e., the exit price) for a derivative at time t under IFRS 13 would be: 𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒 𝐹𝑎𝑖𝑟 𝑉𝑎𝑙𝑢𝑒𝑡=𝑀𝑡𝑀𝑡−𝐶𝑉𝐴𝑡+𝐷𝑉𝐴𝑡 where 𝑀𝑡𝑀𝑡 the derivative mark-to-market at time t, 𝐶𝑉𝐴𝑡 the Credit-Value Adjustment and 𝐷𝑉𝐴𝑡 the Debt-Value Adjustment at valuation time t. The CVA metric is relevant for OTC derivatives that have no full collateralization, i.e., there is no full hedge of counterparty risk, meaning that there is no full collateral posted daily for both counterparties to hedge the current CVA value. For those derivatives that need the CVA included in its fair value calculation, the future exposure estimation is critical. The CVA/DVA would be calculated as follows 13 : 12 CVA is not specifically mentioned in IFRS 13. Nevertheless, the standard states that an entity should measure the fair value of an asset or a liability using the assumptions that market participants would use when pricing the asset or liability, assuming that market participants act in their economic best interest. CVA is considered by market participants when pricing the derivative. 13 See Kenyon and Stamm (2012), Morales (2015) or Gregory (2015) among others, for further details on CVA/DVA estimation (4)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 38 𝐶𝑉𝐴/𝐷𝑉𝐴=(1−𝑅)∫𝐸𝑡ℚ 𝑇 0[(𝐷𝐹(0,𝑡)∙𝑉(𝑡)+]∙𝑃𝐷𝑐(𝑡)𝑑𝑡 where 𝐸𝑡ℚ[(𝐷𝐹(0,𝑡)∙𝑉(𝑡)+] is the expected discounted value of the derivative’s positive exposure 𝑉(𝑡)+ under a probability measure ℚ; 𝑃𝐷𝑐(𝑡) is the conditional PD at t; and 𝑅 is the estimated Recovery Rate. Therefore, it can be seen that one of the necessary inputs for CVA estimation is the conditional PD of the counterparty between 𝑡=0 and 𝑡=𝑇 while in the case of DVA estimation, one of the necessary inputs is the own conditional PD in the same context. For this, the model proposed in this dissertation for credit risk estimation is fully useful for those counterparties that have no rating nor credit instruments with liquid prices. However, the estimation of the future exposure is something critical to be modelled. In the next chapter, some current market modelling solutions to cope with this issue are presented, for interest rate vanilla and non-vanilla derivatives. 3.2.2 IFRS 13: Fair value hierarchy and the relevancy of credit risk data The way in which a company should consider the corresponding credit quality in the situations described in section 3.1.1., and the way in which the inputs are developed should be consistent with the fair value hierarchy included in IFRS 13. Fair value hierarchy refers to the inputs used in order to measure fair value. IFRS 13 prioritises observable inputs over those that are not observable (i.e., that are internally developed by an entity). There are three levels within IFRS 13 fair value hierarchy (IFRS 13 Appendix A): ▪ Level 1 inputs: quoted prices in active markets for identical assets or liabilities that the entity can access at the time of measurement. ▪ Level 2 inputs: inputs other than quoted prices included within Level 1 that are observable for the asset or liability, either directly or indirectly. ▪ Level 3 inputs: unobservable or difficult-to-obtain model inputs for the asset or liability. IFRS 13 focuses on prioritizing the inputs used in the valuation techniques and not the techniques themselves (see IFRS 13.74), (however, the availability of inputs could affect the valuation technique used). Therefore, as stated above, when obtaining a PD or a YTM within this context, it is important to consider fair value hierarchy. For example, to obtain a PD for a specific counterparty and maturity: 1. The best input would be the PD calibrated with CDS spreads (on bonds issued by the same counterparty with the same maturity), quoted in a liquid market. 2. Should that information not be available, other potential sources in order to estimate the PD are: (5)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 39 o The quoted YTM of bonds issued by the same counterparty with the same maturity in an active market. o The quoted CDSs spread (over bonds issued by the same counterparty with the same maturity) in a non-active market. o The quoted YTM of bonds issued by the same counterparty with the same maturity in a non-active market. o The quoted CDSs spread (over bonds issued by the same counterparty with similar maturity) in a non-active market. The spread should be adjusted for the difference in maturity. o The quoted YTM of bonds issued by the same counterparty with similar maturity in an active or non-active market. The PD is adjusted for the difference in maturity. 3. Should the specific counterparty not have quoted CDSs or bonds, nor a public credit rating, it could be internally estimated a credit rating for the specific counterparty in order to obtain the PD from quoted CDSs or bonds of companies with the same rating and characteristics (sector, country, size, etc.). In both cases, as much market information as possible should be used. The model proposed in Chapter 5 to estimate credit rating and PD would only be used in the case of this last scenario. 3.3. Lease accounting and valuation under IFRS 16 IFRS 16 is the new lease accounting standard that will replace the current IAS 17 for annual reporting periods commencing on or after 1st January 2019. The implementation of IFRS 16 will specifically affect contracts in which the entity is the lessee. In the majority of these contracts, the entity will have to apply the so-called “capitalization model” which the new standard introduces. In the capitalization model, the lease asset (right-of-use) and the lease liability are initially measured by discounting future lease payments. Subsequently, the asset is depreciated (in most cases on a straight-line basis), and the liability is accounted for as a debt in which the financial expense is accrued based on the discount rate used. In addition, in case of subsequent modification of the lease payments (due to changes in variable payments, changes in the lease term, etc.), the lease liability should be recalculated; that is, future cash-flows should be discounted once again (using the original interest rate in some cases and a new interest rate in others). IFRS 16 establishes the following in relation to the interest rate to be used by a lessee when discounting future lease payments (IFRS 16.26, 41 and 45):
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 40 - 1) In principle, the so-called “implicit interest rate in the lease” should be used. This is the rate that the lessor obtains from the financing transaction implied by the lease. - 2) The IASB recognizes that in many cases, the lessee will not be able to obtain the interest rate implicit in the lease because he/she does not possess information on aspects such as the initial costs incurred by the lessor or the residual value of the asset at the end of the lease period (IFRS 16. BC161). In these cases, IFRS 16 allows for the use of the “lessee’s incremental borrowing rate”. This is the rate that the lessee would have to pay on a debt in order to buy the leased asset while taking into consideration the following aspects (IFRS 16.BC161): - Moment in time. - The maturity of the lease. - The economic environment in which the transaction occurs. - The credit quality of the lessee. - The nature and quality of the collateral. Generally speaking, it is expected that many entities will use the incremental borrowing rate instead of the lease implicit rate (see Morales and Zamora, 2017). Therefore, an estimation of the lessee’s credit quality is required in order to obtain the borrowing rate. 3.3.1 Introduction to IFRS 16 Under IFRS 16 (as well as under ASC 14 Topic 842), a lessee must apply the capitalization model for the accounting of all lease transactions (except if two voluntary exceptions are applied) (Morales-Díaz and Zamora-Ramírez, 2018a). The capitalization model entails recognizing an asset (“right-of-use”) and a liability (“lease liability”) in the statement of financial position. Both elements are initially measured as the present value of future lease payments for the duration of the lease term. In order to discount future lease payments (and calculate the present value), IFRS 16 (along with ASC Topic 842) offers the lessee two options (IFRS 16, paragraph 26/ASC Topic 842-20-30-3): A) “Interest rate implicit in the lease” which is defined as “the rate of interest that causes the present value of (a) the lease payments and (b) the unguaranteed residual value to equal the sum of (i) the fair value of the underlying asset and (ii) any initial direct costs of the lessor” (IFRS 16 Appendix A; the ASC Topic 842 definition is similar). B) In those cases where the implicit rate “cannot be readily determined”, a lessee may use what IFRS 16 names as the “lessee’s incremental borrowing rate” (IBR), defined as “the rate of interest that a lessee would have to pay to borrow over a similar term, and with a similar security, the funds necessary to obtain an asset of a similar value to the right-of-use asset in a similar economic environment” (IFRS 16 Appendix A; the ASC Topic 842 definition is similar5). 14 Accounting Standards Codification
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 47
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 48 CHAPTER 4: INDUSTRY MODELLING REVIEW In this chapter, we will see a review on some of the main models used in the financial industry related to counterparty credit risk and probability of default estimation. It is a summary of the methodologies used by rating agencies and practitioners at a high-level approach. This means that these methodologies may provide a robust, initial grounding to model developers, but additional modelling aspects are surely considered to adapt them to particular industries and data sources. In fact, the contribution to the credit rating and PD estimation field in this document is partially based on the Moody´s credit rating models presented in next sections. Likewise, in this chapter we will see some modelling solutions used in the financial industry which cope with the Exposure at Default (EAD) estimation for derivatives concerning IFRS 13. Although the models developed during my doctoral research period have been mainly focused on the credit rating estimation and the subsequent modelling of the IBR, it is important to highlight the relevancy of a robust estimation of the exposure concerning CVA calculation under IFRS 13, as outlined in section 3.2.1. 4.1. Rating agencies and Credit Rating letter models Credit rating agencies, like Moody’s, publish research and methodology for a wide spectrum of casuistries related to credit analysis, rating methodologies, credit markets, among others. In this section, the basic, public Moody’s rating methodology will be shown 15 for the telecommunication sector. It describes the key qualitative and quantitative considerations that are usually most important for assessing credit risk in a given sector. These considerations can be understood as a set of guidance to assigning ratings backed by conceptual background. Also, it is explained through a step-by-step basis: 4.1.1 Qualitative and Quantitative Scorecard/Grid The main tool that the rating assignment process leverages is a scorecard or grid, which is a reference that can be used to approximate credit profiles within this sector in most cases and to explain, in summary, the factors that are generally most important in assigning ratings to companies in each industry. The scorecard is a summary that does not include every rating consideration, and other quantitative or qualitative considerations. The weights shown for each 15 Visit www.moodys.com for further information and public papers on methodology for rating estimation for different sectors.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 49 factor in the scorecard represent an approximation of their importance for rating decisions, but actual importance may vary substantially between companies and sectors. Although the telecommunication sector to be explained is an example of the different sectors for which variable rating methodologies can be applied, the below factors use to be common when using the grid: 1) Company’s Scale 2) Business Profile 3) Profitability and Efficiency 4) Leverage and Coverage 5) Company’s Financial Policy 4.1.2 Scorecard Factors and Weighting The below table summarizes the Telecommunications sector scorecard published by Moody’s in their rating assignment methodology summaries (Moody’s, 2018). This scorecard assigns a weight to a given rating concept or metric, so that the weighted average of all the scores will represent the credit rating. Table 2: Scorecard Factors and relative weights, Telecommunications sector Rating Factors Factor weight Subfactors Subfactor Weight Company's Scale 12.5% Revenue 12.5% Business Profile 27.5% Business Model, Competitive Environment and Technical Positioning 12.5% Regulatory Environment 7.5% Market Share 7.5% Profitability and Efficiency 10% Revenue Trend and Margin Sustainability 10% Leverage and Coverage 35% Debt/EBITDA 15% Retained Cash/Debt 10% (EBITDA-CAPEX)/Interest Expense 10% Financial Policy 15% Financial Policy 15% Total 100% Total 100% Source: Moody’s (2018). In the development of the credit rating and PD model proposed in this dissertation, the potential correlation between the quantitative variables used by rating agencies (the scorecard factors above) and the ones used as explanatory variables within the model will be checked. As a matter of fact, and as previously outlined in Chapters 1 and 2, one of the initial hypotheses on the model is that the variables used in its construction should be somehow aligned to the ones used by rating agencies.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 50 4.1.3 Mapping Scorecard Factors to a Numerical Score After estimating or calculating each sub-factor, the outcomes for each of the sub-factors are mapped to a broad Moody’s rating category (Aaa, Aa, A, Baa, Ba, B, Caa, or Ca, also called alpha categories) and to a numerical score. Qualitative factors are scored based on the description by broad rating category in the scorecard. The numeric value of each alpha score is based upon the scale below. Table 3: Possible numerical outputs for qualitative metrics and related rating, Telecommunications sector. Rating Aaa Aa A Baa Ba B Caa Ca Numeric value 1 3 6 9 12 15 18 20 Source: Moody’s. Quantitative factors are scored on a linear continuum. For each metric, the scorecard shows the range by alpha category. The scale below is used to convert the metric, based on its placement within the scorecard range, to a numeric score, which may be a fraction. Table 4: Possible numerical outputs for quantitative metrics and related rating, Telecommunications sector. Rating Aaa Aa A Baa Ba B Caa Ca Numeric value 0.5-1.5 1.5-4.5 4.5-7.5 7.5-10.5 10.5-13.5 13.5-16.5 16.5-19.5 19.5-20.5 Source: Moody’s. 4.1.4 Determining the Overall Scorecard - Indicated Outcome The numeric score for each sub-factor (or each factor, when the factor has no sub-factors) is multiplied by the weight for that sub-factor (or factor), with the results then added to produce an aggregate numeric score. The aggregate numeric score is then mapped back to an alphanumeric scorecard indicated outcome based on the ranges in the table below.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 51 Table 5: Aggregated numeric score and mapping to alphanumeric scorecard Scorecard indicated outcome (Rating) Aggregate Weighted Factor Score Aaa 0 < x ≤ 1.5 Aa1 1.5 < x ≤ 2.5 Aa2 2.5 < x ≤ 3.5 Aa3 3.5 < x ≤ 4.5 A1 4.5 < x ≤ 5.5 A2 5.5 < x ≤ 6.5 A3 6.5 < x ≤ 7.5 Baa1 7.5 < x ≤ 8.5 Baa2 8.5 < x ≤ 9.5 Baa3 9.5 < x ≤ 10.5 Ba1 10.5 < x ≤ 11.5 Ba2 11.5 < x ≤ 12.5 Ba3 12.5 < x ≤ 13.5 B1 13.5 < x ≤ 14.5 B2 14.5 < x ≤ 15.5 B3 15.5 < x ≤ 16.5 Caa1 16.5 < x ≤ 17.5 Caa2 17.5 < x ≤ 18.5 Caa3 18.5 < x ≤ 19.5 Ca 19.5 < x ≤ 20.5 C x > 20.5 Source: Moody’s. For example, an issuer with an aggregate weighted factor score of 11,7 would have a Ba2 scorecard-indicated outcome. Concerning the final rating, the below criteria is used by Moody’s to assign each scorecard outcome and therefore, the credit rating (concerning the Telecommunications sector):
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 52 Table 6: Qualitative and quantitative factors and scale by their outcome (I), Telecommunications sector. Table 6: Qualitative and quantitative factors and scale by their outcome (I), Telecommunications sector. Source: Moody’s
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 53 Table 7: Qualitative and quantitative factors and scale by their outcome (II), Telecommunications sector. Table 7: Qualitative and quantitative factors and scale by their outcome (II), Telecommunications sector. Source: Moody’s
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 54 Table 8: Qualitative and quantitative factors and scale by their outcome (III), Telecommunications sector Table 8: Qualitative and quantitative factors and scale by their outcome (III), Telecommunications sector. Source: Moody’s
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 55 Table 9: Qualitative and quantitative factors and scale by their outcome (IV), Telecommunications sector. Table 9: Qualitative and quantitative factors and scale by their outcome (IV), Telecommunications sector. Source: Moody’s
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 56 4.2. Probability of Default Analytical Models 4.2.1 Z-Score model The Z-Score model, commonly referred to as the Altman Z-Score, was developed by Professor Edward I. Altman in 1968. Although Altman et al. have subsequently modified the original ZScore model to create the Z’-Score Model, the Z”-Score Model, and the Zeta Model, the Z-Score model is still a common component of many credit rating systems. The Z-Score is constructed from six accounting values and one market-based value. These seven values are combined into five ratios which are the pillars that comprise the Z-Score. The five pillars are combined using the equation below to result in each company’s Z-Score (Altman 2002). 𝑍−𝑆𝑐𝑜𝑟𝑒=1.2𝛽1+1.4𝛽2+3.3𝛽3+0.6𝛽4+1.0𝛽5 where 𝛽1=𝑊𝑜𝑟𝑘𝑖𝑛𝑔 𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠 𝛽2=𝑅𝑒𝑡𝑎𝑖𝑛𝑒𝑑 𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠 𝛽3=𝐸𝐵𝐼𝑇 (𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 𝐵𝑒𝑓𝑜𝑟𝑒 𝐼𝑛𝑡𝑒𝑟𝑒𝑠𝑡 𝑎𝑛𝑑 𝑇𝑎𝑥𝑒𝑠) 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠 𝛽4=𝑀𝑎𝑟𝑘𝑒𝑡 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝐸𝑞𝑢𝑖𝑡𝑦 𝐵𝑜𝑜𝑘 𝑉𝑎𝑙𝑢𝑒 𝑜𝑓 𝑇𝑜𝑡𝑎𝑙 𝐿𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠 𝛽5=𝑆𝑎𝑙𝑒𝑠 𝑇𝑜𝑡𝑎𝑙 𝐴𝑠𝑠𝑒𝑡𝑠 This formula appeals to the practitioner’s intuition because each pillar describes a different and relevant aspect (from the point of view of its credit health) of a company. Liquidity, cumulative profitability, asset productivity, market based financial leverage, and capital turnover are addressed by the five ratios respectively. The Z-Score presumes that each ratio is linearly related to a company’s probability of bankruptcy. The Working capital/Total assets ratio is a measure of the net liquid assets of the firm relative to the total capitalization. Working capital is defined as the difference between current assets and current liabilities. When a firm is experiencing consistent operating losses, current assets will decrease in relation to total assets. In different analysis, 𝛽1 proved to be more valuable than the current ratio and the quick ratio. This ratio explicitly considers liquidity and size dimensions. The Retained Earnings/Total assets ratio refers to the earned surplus of a firm over its entire life. This measure of cumulative profitability over time is one of the two (the other is the use of the market value of equity, instead of the book value) “new” ratios evaluated by Altman for the latest ZScore model. It considers implicitly the age of the firm due to its cumulative nature and the use of leverage in order to finance the asset growth of the firm. The Earnings before interest and (6)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 63 Φ(𝑑2)=𝑆𝑢𝑟𝑣𝑖𝑣𝑎𝑙 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 hence, 1−Φ(𝑑2)=𝐷𝑒𝑓𝑎𝑢𝑙𝑡 𝑃𝑟𝑜𝑏𝑎𝑏𝑖𝑙𝑖𝑡𝑦 When using and calibrating models like (18), two factors are intrinsically critical: the company’s asset growth and the volatility of the asset. The company’s assets growth represents the average return expected for the assets, in such a way that the higher the drift, the higher the expected asset value and therefore the lower default probability. It can be estimated as the annualized return the assets have had during the last 5 years. Regarding asset volatility, it is clear that it is a factor that is not observable, and not very reliable given the frequency at which financial statements are issued. However, as previously described, assets’ volatility is affected by the equity value. Hence, one needs to figure out the value of assets volatility given by the equity volatility: this calculation relies on the Black-Scholes differential equation: 𝑟𝑓=𝜕𝑓 𝜕𝑡+𝑟𝑆𝜕𝑓 𝜕𝑆+12𝜎2𝑆2𝜕2𝑓 𝜕𝑆2 where 𝑓 is the derivative price on a contingent underlying 𝑆 which follows the stochastic process and 𝑟 is the risk-free rate. (23) can be approximated by a Taylor series expansion giving ∆𝑓=𝜕𝑓 𝜕𝑡∆𝑡+𝜕𝑓 𝜕𝑆∆𝑆+12𝜕2𝑓 𝜕𝑆2∆𝑆2+12𝜕2𝑓 𝜕𝑡2∆𝑡2+𝜕2𝑓 𝜕𝑆𝜕𝑡∆𝑆∆𝑡+⋯ (24) states the relationship between the derivative price and the risk factors involved in its pricing. The first term on the right-hand side states how much the price of the derivative changes for each change in a time unit. This partial derivative is known as Theta (Θ). The second one, Delta (Δ), relates the price change of the derivative with the underlying price change. The third one, Gamma (Γ), is the second partial derivative of the price of the derivative with respect to the underlying price, to capture the convexity effect, as can be seen in Figure 5. Subsequently, additional and cross-partial derivatives can be computed. Ignoring the Theta term, and option price change can be understood as the following: ∆𝑓=𝐷𝑒𝑙𝑡𝑎 ∆𝑆 +12𝐺𝑎𝑚𝑚𝑎 ∆𝑆2 Hence, we can establish the relationship between asset and equity volatility absolute quantities as 𝜎𝑒𝑞𝑢𝑖𝑡𝑦𝐸𝑞𝑢𝑖𝑡𝑦𝑡0=Δ𝐸𝑞|𝑉 𝜎𝑉𝑉0+12Γ𝐸𝑞|𝑉 𝜎𝑉𝑉02 where 𝜎𝑒𝑞𝑢𝑖𝑡𝑦 is the historical or implied annualized equity market price volatility, 𝐸𝑞𝑢𝑖𝑡𝑦𝑡0 is the company’s equity market price at the calculation moment, Δ𝐸𝑞|𝑉 is the delta of the Equity on the company’s assets, Γ𝐸𝑞|𝑉 is the gamma in the same context, 𝑉0 is the company’s assets value, (21) (22) (23) (24) (25) (26)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 64 and 𝜎𝑉 is the assets volatility to be calibrated. Knowing that on European options, the BlackScholes framework gives 𝐷𝑒𝑙𝑡𝑎𝑐𝑎𝑙𝑙= Φ(𝑑1) 𝐺𝑎𝑚𝑚𝑎𝑐𝑎𝑙𝑙=Φ(𝑑1) 𝑆0𝜎√𝑡 we can calibrate 𝜎𝑉 by rearranging the terms in (26), and get the volatility to be used in (19) and (20). 4.3.4 Model implementation: from default probabilities to short-term Credit Ratings and additional considerations Following Refinitiv database, the below table relates the 1-year probability of default and the rating letter assigned. Table 11: Implied 1y Probability of Default & Rating Source: Refinitiv, 2021 Some topics to be considered when implementing this model are: 1) Entities are generally more likely to default when their asset value reaches a certain critical level somewhere between the value of total liabilities and the value of short-term debt. Therefore, in practice, using only the short-term debt or the total liabilities as a strike might not be an accurate measure of the actual probability of default. The strike selection will also depend on the debt structure and the leverage ratio sensitivity, among others. However, a widespread solution is to set the strike, so-called Default Point (DPT), as 𝐷𝑃𝑇=𝑆ℎ𝑜𝑟𝑡 𝑇𝑒𝑟𝑚 𝐷𝑒𝑏𝑡+0.5 𝐿𝑜𝑛𝑔 𝑇𝑒𝑟𝑚 𝐷𝑒𝑏𝑡 Probability of Default (Lower Limit) Probability of Default (Upper Limit) Implied Letter Rating 0,0000% 0,0010% AAA 0,0010% 0,0020% AA+ 0,0020% 0,0040% AA 0,0040% 0,0080% AA0,0080% 0,0150% A+ 0,0150% 0,0250% A 0,0250% 0,0380% A0,0380% 0,0540% BBB+ 0,0540% 0,0730% BBB 0,0730% 0,1110% BBB0,1110% 0,1870% BB+ 0,1870% 0,3060% BB 0,3060% 0,4720% BB0,4720% 0,8700% B+ 0,8700% 1,5600% B 1,5600% 2,5000% B2,5000% 3,6900% CCC+ (27) (28) (29)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 65 2) Unlike in the Merton concept, the KMV μ is no longer a risk-free rate related return, but the expected rate of the return of the company's asset. This is, the relative logarithmic return between 𝐴𝑠𝑠𝑒𝑡𝑠𝑡−1 and 𝐴𝑠𝑠𝑒𝑡𝑠𝑡. 3) The Distance-to-Default equation can be approximated by DTD=E(𝑉𝑡)−𝐷𝑃𝑇 𝜎 when drift is very low and time-to-default (t) is also short, being E(𝑉𝑡)=𝑉𝑡 𝑒𝜇𝑡. The below example is shown in turn to clarify the model implementation. Say that, once the company’s latest balance sheet has been analyzed, we have the following information: - Total Assets: 40.000.000€ - Short-term debt book value: 15.000.000€ - Long-term debt book value: 18.000.000€ - Drift: 0.8%, annualized - Asset volatility already calibrated: 16% - Time-to-default: 1 year We consider the DPT = 15m € + 0.5·18m € = 24m € Thus, we use the above information to compute 𝑑2: 𝑑2=𝐿𝑛(4024 ⁄ )+(0.008−0.162 2)1 0.16√1=3.16 so that 1−Φ(𝑑2)=1−99.92%=0.08% Following Table 11, the 1-year default probability leads to an estimated credit rating BBB-. This is an example on how to use financial and market information within the model. Obviously, further financial and accounting analysis is highly recommended to accurately set the risk factors within the model. This is, there could be some items which maybe could be adjusted or not considered, for instance, longest-term debt. 4.4. Exposure projection for IFRS 13 CVA estimation As previously discussed in section 3.2.1., a derivative can have positive or negative values for both counterparties throughout its life span. Therefore, for the CVA calculation, it is necessary to model the exposure in the future, assuming that it is not constant, opposite to the case of a bond or a loan which are expected to pay coupons and notional like an “amortized cost”. This is (30)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 66 understood as the potential exposure amount, which determines the amount of CVA for each counterparty to be subtracted to the current derivative Mark-to-market. 4.4.1 Potential exposure Depending on the type of derivative, the risk factors that affect its value will be different. For example, if we are long on a currency forward, the evolution of exchange and interest rates will be the factors to be estimated; if we buy an IRS, we must estimate the evolution of the corresponding interest rates, while if we are exposed to an equity swap, both interest rates and the price of the corresponding equity underlying must be projected. Therefore, the EAD will not be “flat” but will be different in the many different moments into the future. So, the Fair Value of the derivative would be given by the sum of the current exposure and the future default risk exposure: MtM - CVA 17 : 𝐹𝑉𝐷𝑒𝑟𝑖𝑣𝑎𝑡𝑖𝑣𝑒=𝑀𝑡𝑀𝑡−𝐶𝑉𝐴=𝑀𝑡𝑀𝑡−(1−𝑅)∫𝐸𝑡ℚ 𝑇 0[(𝐷𝐹(0,𝑡) 𝑉(𝑡)+]∙𝑃𝐷𝑐(𝑡)𝑑𝑡 where 𝐸𝑡ℚ[(𝐷𝐹(0,𝑡)∙𝑉(𝑡)+] is the expected discounted value of the derivative’s positive exposure 𝑉(𝑡)+ under a probability measure ℚ; 𝑃𝐷𝑐(𝑡) is the conditional probability of default at t; and 𝑅 is the estimated Recovery Rate. As the above expression is “continuous”, this means that in practice, the discretized CVA expression would be: 𝐶𝑉𝐴=(1−𝑅)∑ 𝐷𝐹(0,𝑡) 𝑉(𝑡)+ ∆𝑃𝐷𝑡−1,𝑡 𝑇 𝑡=0 Our concern lies in a robust estimate of the potential risk: for a given current MtM, we need to project its future value to estimate the exposure that we will have to manage. In words, estimate the exposure of the given derivative at every future time until maturity. Hence, we need to project that expected discounted value of the derivative’s positive exposure: 𝑉(𝑡)+ (also called Expected Positive Exposure or EPE) at any future point t in the above expression. Usually, the points on which the EPE is computed and multiplied by the conditional default probability ∆𝑃𝐷 are assumed monthly or quarterly, matching with the times when coupons of the derivative are paid off. To project the EPE, we must determine the market risk factors (interest rates, exchange rates, equity returns, volatility, etc.) that affect the valuation of the derivative and project its evolution over time. This evolution can be determined by generating numerous 'evolution' scenarios for the corresponding risk factors, according to different stochastic processes and models (Montecarlo, Vasicek, Hull&White, LMM, etc.) that best fit the historical distribution of the risk factor values, as well as adjusting due to the macroeconomic situation that affects the evolution of these factors. 17 For the sake of simplicity, we will work with the assumption that only CVA is taken as counterparty risk, not considering the own default risk (DVA). However, as seen in section 3.2., DVA should also be considered, therefore the own PD and also the Expected Negative Exposure (i.e., the Expected Positive Exposure for the counterparty) should be computed as DVA inputs. (31) (32)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 67 4.4.2 Projecting interest rates-linked exposure Although there are many different risk factors to which a derivative can have exposure, in this section we will focus on two different models to project interest rate exposures, as interest rate derivatives are, by far, the most relevant derivatives in the OTC market. In the figure below it is shown the global OTC market notional outstanding, split by asset class 18 . Figure 7. Notional amount outstanding (USD trillions), OTC derivatives Source: BIS, 2021 Also, it should be known that, although most of corporate and investment banking players have exposure to many different risk factors, interest rate risk is common among many types of hedges and strategies. Likewise, a relevant portion of the CVA amount in the financial sector arises from the hedging trades sold to corporates and non-financial counterparties, which vastly uses IRSs and Cross-Currency swaps as hedging instruments. Figure 8. CVA amount share of global OTC derivatives by asset class Source: Solum Financial, 2013 Focusing on the potential models to be applied, if we take as an example the valuation of the future exposure of a EURIBOR 3M-linked IRS, we should establish as a risk factor the evolution 18 IRD means Interest-Rate Derivative
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 68 of the market EURIBOR 3M to model forward rates, and also the discounting curve (e.g., ESTR swap curve). Therefore, the curves evolution would have to be projected, so we should generate projection scenarios of those underlyings, and then translate them into the corresponding future MtM at every single future point (e.g., every three months) to maturity. Figure 9. Example of interest rate simulation paths Source: compiled by the author Applying each interest rate projected scenario to, for instance, an Interest-Rate Swap (IRS) valuation, we would obtain a series of MtM scenarios as follows: Figure 10. Example of interest rate swap MtM simulation paths Source: compiled by the author where we would have to keep in mind the positive regions, which represent the positive exposure in each time period (i.e., if the derivative has positive value, then we have counterparty risk as the counterparty “owes” value to us). As we need to estimate the expected positive exposure (EPE), then the average of the exposure at any time t would represent that EPE. Other exposure profiles, like the Peak Exposure (representing the 99th percentile of the MtM future distribution) can be used for calculating additional metrics, in this case the CVA VaR.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 69 Figure 11. Example of interest rate swap MtM simulation paths, EPE and Peak Exposure Source: compiled by the author Therefore, the steps to compute the Expected Positive Exposure would be: - Choice of the corresponding risk factors for the derivative price - Scenario generation according to a well-fitted stochastic model - Valuation of the derivative in all scenarios - Compute the average of the positive exposures at any calculation time t to obtain the vector of EPEs to be used to compute the CVA amount. 4.4.3 Libor Market Model When generating the scenarios of interest rates, a well-known Montecarlo-based simulation methodology is widely used among risk management practitioners. The model is known as Lognormal Forward-Libor Model, or Libor Market Model (LMM) (Brace, Gatarek and Musiela, 1997), and can be very useful in the field of CVA or Montecarlo VaR when simulating interest rates, for the reasons listed below: - This model simulates the entire forward curve and discount factors from current forward quotes, so this feature allows to directly price floating interest rate products; - The model risk factors are directly observed in the market (or they can be calibrated from quoted data), opposite to, for instance, models like Hull-White or Cox-Ingersoll-Rox (CIR), for which risk factors like mean-reversion should be calibrated depending on time series length; - This model is derived from the Black-76 option pricing framework. Therefore, quoted Black volatilities can be used to strip the volatility surface, so this model is also consistent with the prices directly observed in the market;
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 70 - The model entails using the so-called forward volatilities, which depend on cap forward volatilities quoted in EUR, GPB or USD option markets. This fact provides the model with soundness in terms of market expectations when generating future scenarios, being compliant with the forward-looking requirements under IFRS. The LMM, in terms of risk-neutral dynamics, can be written as 𝑑𝐹𝑘(𝑡)=𝜇𝑘(𝑡)𝐹𝑘(𝑡)𝑑𝑡+𝜎𝑘(𝑡)𝐹𝑘(𝑡)𝑑𝑍𝑘(𝑡) where 𝐹𝑘(𝑡) is each generic forward rate bucket 𝐹(𝑡;𝑇𝑘−1,𝑇𝑘); 𝜇𝑘 is the forward rate drift (computed as the average forward rate annual return for simplification purposes) 19 ; 𝜎𝑘(𝑡) 20 is the instantaneous volatility at time t for the forward rate 𝐹𝑘, which will be the caplet forward volatility; and 𝑍𝑘(𝑡) is a standard Brownian motion. Under the probability measure of the numeraire 𝑃(𝑡,𝑡+∆𝑡) (used to compute 𝐹𝑘(𝑡)), the lognormal behaviour of 𝐹𝑘(𝑡) will be determined by Ito’s formula, as 𝑑ln (𝐹𝑘(𝑡))=𝜇𝑘(𝑡)𝑑𝑡−𝜎𝑘(𝑡)2 2𝑑𝑡+𝜎𝑘(𝑡)𝑑𝑍𝑘(𝑡) so that discretizing we have ln (𝐹𝑘(𝑡+∆𝑡))=ln (𝐹𝑘(𝑡))+𝜇𝑘(𝑡)∆𝑡−𝜎𝑘2(𝑡) 2∆𝑡+𝜎𝑘(𝑡)(𝑍𝑘(𝑡+∆𝑡)−𝑍𝑘(𝑡)) and, in terms of the generic forward rate jump from 𝑡 to ∆𝑡: 𝐹𝑘(𝑡+∆𝑡)=𝐹𝑘(𝑡) 𝑒 (𝜇𝑘−𝜎𝑘2 2)∆𝑡+𝜎𝑘𝑍𝑘√∆𝑡 As EUR rates have had many forward rate tenors in negative regions so far, the market provides prices for option volatilities in the Black environment as well. This entails including the shift 𝛼 so as negative rate scenarios can be avoided when applying the model 21 (Beinker and Stapper, 2012). 𝐹𝑘(𝑡+∆𝑡)=(𝐹𝑘(𝑡)+𝛼) 𝑒 (𝜇𝑘−𝜎𝑘2 2)∆𝑡+𝜎𝑘𝑍𝑘√∆𝑡−𝛼 Therefore, we can generalize for the entire forward curve simulation the above expression. This means that we can simulate each forward rate tenor 𝐹𝑘(𝑡) to which a swap has exposure over time, until each forward rate in the floating leg is paid. Moreover, discount factors are simulated based on the simulated forwards, following their risk-neutral relationship 19 The drift can be inputted in the model as a volatility-dependent factor, but it has been assumed as a constant annualized return for each forward bucket, for simplification purposes. 20 Caplet volatilities are subject of a time-variance treatment as 𝜎𝑘2(𝑡) is a function of time in a Montecarlo simulation framework, and therefore 𝜎𝑘 does not exactly represent each caplet volatility at t0. For further information on this treatment, see Hull (2012) or Brigo & Mercurio (2006). 21 The Black-Scholes model and the derived simulation models, like LMM, depend on the lognormal relationship between the underlying price and the strike price. This means that when one of them turns negative, the model would not work. Hence, this drawback can be saved applying a “shift” to the underlying forward rate to make it positive, before simulating or valuing an option under the Black-76 environment. (33) (34) (35) (36) (37)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 71 𝑃(0,𝑡+∆𝑡)=𝑃(0,𝑡) 1+𝐹𝑘(𝑡+∆𝑡) Implied ATM caplet volatilities calibration As explained in above paragraphs, 𝜎𝑘(𝑡) represents the caplet volatility for each 𝐹𝑘(𝑡) to be simulated. However, the options market only provides with volatilities implied in caps per strike and maturity, not volatilities for every single caplet composing the cap (i.e., not for each forward rate we need to simulate). Then, we need to carry out a bootstrapping process to calibrate the caplet volatilities implied in the cap volatility ATM skew. Under the Black-76 model, the call option (cap) value is 𝑁 ∆𝑡 𝑃(0,𝑡𝑘+1) [(𝐹𝑘+𝛼)𝛷(𝑑1)−(𝐾𝑘+𝛼)𝛷(𝑑2)] whereas the put option (floor) value is 𝑁 ∆𝑡 𝑃(0,𝑡𝑘+1) [−(𝐹𝑘+𝛼)𝛷(−𝑑1)+(𝐾𝑘+𝛼)𝛷(−𝑑2)] where 𝑑1=𝐿𝑛((𝐹𝑘+𝛼)(𝐾𝑘+𝛼) ⁄)+𝜎𝑘2 2𝑡𝑘 𝜎𝑘√𝑡𝑘 𝑑2=𝑑1−𝜎𝑘√𝑡𝑘 and 𝐹𝑘 is the forward interest rate at time 0 for the period between time 𝑡𝑘 and 𝑡𝑘+1, 𝐾𝑘 is the strike, α is the curve shift (3% given the market convention for EUR), 𝜎𝑘 is the shifted Black cap volatility for 𝑡𝑘 and 𝐾𝑘, ∆𝑡 is the accrual for each caplet/floorlet (payment accrual), 𝑃(0,𝑡𝑘+1) is the discount factor, and 𝑁 is the notional amount. Namely, 𝐶𝑎𝑝𝑀𝐾𝑇(0;𝐾+𝛼;𝜎𝑗𝑐𝑎𝑝)=∑𝐶𝑎𝑝𝑙𝑒𝑡(𝐹𝑘(0);∆𝑡;𝐾+𝛼; 𝑗 𝑘=1 𝜎𝑐𝑎𝑝𝑙𝑒𝑡𝑘|𝜎𝑗𝑐𝑎𝑝) where 𝜎𝑐𝑎𝑝𝑙𝑒𝑡𝑘|𝜎𝑗𝑐𝑎𝑝 is the caplet volatility for each caplet that makes their sum equal to the hypothetical market Cap price with constant 𝜎𝑗𝑐𝑎𝑝 for a maturity j. Although there is a unique volatility for a cap strike and maturity, there could be different caplet volatilities depending on the option maturity, as they represent, in average, such a cap volatility. With this framework, each entire caplet volatility time structure would be stripped iteratively, from the first caplet – which will be equal to the cap – to the latest one based on a target cap price and maturity 𝐶𝑎𝑝𝑀𝐾𝑇(0;𝐾+𝛼;𝜎𝑗𝑐𝑎𝑝). For European option pricing, either 𝜎𝑗𝑐𝑎𝑝 or its corresponding 𝜎𝑐𝑎𝑝𝑙𝑒𝑡𝑘|𝜎𝑗𝑐𝑎𝑝 can be used (as caplets/floorlets are accepted to be priced using a unique cap/floor volatility for a certain maturity as well), but this issue matters regarding forward curve simulation. For instance, the EOD 29/12/2021 shifted Black forward volatilities quoted for caps and their corresponding caplet volatilities calibrated following (41) on a cap maturity in 2030 and 𝐾𝑘= 0% are shown below: (38) (39) (40) (41)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 72 Figure 12. EUR6M Cap and Caplet vols, K 0%, Cap Maturity Dec ‘30 Source: Bloomberg and compiled by the author As it can be seen, caplet volatilities are different to the ones from cap market. It is totally convenient to use caplet vols in the LMM so that each forward rate is simulated under its own expected volatility. 4.4.4 Swaption Mark-to-Market as a proxy for an IRS Potential Exposure Following Figure 7 and Figure 8, it is well noted that interest-rate derivatives are the ones most used across the financial world. Within this asset class, IRSs represent a vast amount of those outstanding derivatives, both cleared and bilateral. Therefore, in this subsection we cover one modelling solution particularly used by consulting firms and non-financial companies to project the Expected Exposure for this kind of derivatives. An interest rate swap is a contractual agreement entered into between two counterparties where they agree to exchange fixed for variable interest rates, periodically, for an agreed period of time and with a notional amount of principal. The principal amount is “notional” as there is no need to exchange actual amounts of principal (although in Cross-Currency Swap this practice is common). However, the notional amount is required in order to compute the actual cash amounts that will be periodically exchanged. The valuation of an IRS is pretty simple: on the one side we have the floating leg (the leg which is paid or received by a counterparty which is composed by floating payments), whose payments are projected with the forward rates corresponding to the contractual floating reference rate (e.g., EURIBOR 3M), whereas the fixed leg is simply the array of fixed payments upon the fixed rate already specified in the contract. The difference between the discounted value of the sum of payments from each leg is the IRS markto-market (depending on the direction and amount of the payments, one counterparty will have positive MtM whereas the another will have negative MtM). Therefore, the problem arises not when the MtM should be calculated at time 0, but when it should be projected into the future. One solution would perfectly be the LMM, explained in section 4.4.3. However, there already exists a closed formula to estimate the EPE for a given IRS.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 79 According to Cappon et al. (2018), credit ratings are “opinions” issued by rating agencies regarding the credit worthiness of corporate, municipal, and sovereign borrowers. Agencies generally avoid claiming that credit ratings predict probabilities of default. Nevertheless, they do publish detailed default studies which show historical ratings migration and default events as a function of the initial rating and time horizon. Analysts and risk managers routinely use default study data as estimates of default probabilities. In practice, it is assumed that a rating generally matches a range of default probabilities. The FRS model is intensive in terms of data collection (as we will see, it is necessary to create a distribution of sector companies). However: - It can be considered to be highly consistent since the model’s inputs are calibrated with the financial information of companies which do have an agency rating. - It is not as intensive in terms of data sources and input data treatment, as other structural models (see Chapter 4). Among the ratios considered by the model (which may also vary from one sector to another), those with higher relevance in terms of credit risk are those related to debt and interest coverage, leverage or liquidity. In other words, the relative debt level of a company is generally the factor with most influence on its credit risk. Growth and profitability are also considered but linked to liabilities and equity. The model proposed uses quantitative data as its main inputs (financial ratios) are obtained from the entity’s financial statements. In theory, qualitative data is not directly used in the model, fundamentally due to the following factors: - Qualitative factors or metrics are difficult to measure and to model due to several reasons such as the fact that the same information is not available for all entities, and they entail a significant level of subjectivity, etc. In this sense, as the model aims to be both robust and relatively easy to implement at the same time, it does not consider subjective qualitative factors (at least not directly). - In recent years, financial and market information (pure quantitative factors) has tended to be more reliable. This makes quantitative factors more effective when estimating a probability of default or assigning a credit rating. In fact, in terms of default events and recovery rates, quantitative models have been taking new assumptions into account and covering recent scenarios (by way of example see Moody’s reports on default risk and recovery rates - Moody’s, 2017). As will be observed throughout the conclusions, when the model is well calibrated and financial ratios used as inputs are representative enough, the explanatory power for certain ratios is highly related with the criteria used by rating agencies in terms of ratios used to assess on the credit risk within a given sector.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 80 5.1. Methodology and model theory development As previously stated, the FRS model is based on reflecting the position (score) of a company within a representative group of rated companies, so as to provide the company with a credit rating in line with its associated score. With regards to this score: - It may also be considered as a “percentile” in the model context (in fact, it is a percentile within a sectorial group). It is configured on a basis that value “1” represents the worst position and “100” the best position within a financial metric for a given sector or peer group. - It will depend on the financial ratios selected, and therefore on the position of each financial ratio within its group (hereinafter also named as “distribution”). - Therefore, the model will need to be composed by exogenous variables (financial ratios) with enough explanatory power. For this, Stepwise AIC optimization technique is chosen, in order to select the most representative ratios for a given sector. - It should be noted that the exogenous variables are transformed and used in the model as percentiles (as explained, all type of rations ranging from 1 to 100). This is done this way to avoid variable transformation. When the ratios are translated to percentiles, we avoid any problem with variables under different distribution regimes (e.g., working with variables in absolute differences or log differences instead of variables in levels). The construction of the FRS model consists of five main steps: • Step 1 – Definition of potential financial ratios • Step 2 – Calculation of peers’ general score • Step 3 – Calculation of the specific score for each potential financial ratio for all the peers • Step 4 – Model calibration: regression, variable selection through a variable-optimization method (in this case, Stepwise AIC will be used) • Step 5 – Obtaining the model credit rating and the expected PD for the company 5.1.1 Step 1 – Definition of potential financial ratios In this first step, a group of key financial ratios is defined as potential explanatory variables of the credit letter for the sector to which the company belongs. Generally, these ratios are related to metrics such as coverage, leverage, liquidity, profitability, and growth. Initially, it is recommended to use a wide range of ratios as a first step, before optimizing the model. These ratios are widely used by analysts (Fazzini, 2018) and by rating agencies (see Moody’s 2017b, for example), since they represent the key financial dimensions that act as drivers for a rating profile. They are easy to calculate using the financial information included in the public financial statements issued by companies.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 81 Nevertheless, it should be noted that additional ratios could be included for specific sectors according to the nature of their business, such as Passenger Load in the commercial airlines sector, or Loan Default Rate in the banking sector, etc. As will be explained in subsequent sections, the intrinsic characteristics of a sector are disclosed when calibrating the ratio weights, hence to a certain extent the “sector” variable is covered by this methodology. Table 12: Example of set of Ratios that can be used in the FRS model Financial Ratio Pretax Income /Sales Debt / EBITDA Free Funds from Ops / Debt EBIT/ Interest Expense EBITDA / Assets Return on Equity Net Margin Return on Assets Interest Exp. / Sales Debt / Equity Debt / Assets Cash / Total Debt Short Term Debt /Total Debt Quick Ratio Source: Compiled by the author. Some relevant ratios that are used as risk factors by the main CRAs models are the following: - “Interest expense/Sales” and “EBITDA/Interest Expense” (coverage ratios) focus on to what extent interest expenses related to debt are “covered” by income from normal business operations. The higher the interest expense in relation to sales or EBITDA, the weaker the financial position of the company. In other words, the ratio analyzes to what extent the entity generates sufficient resources in order to be able to pay the interests related to external debt. • In the first ratio, the higher the level, the lower the coverage (less sales income is available to pay the interest expense). • In the second ratio, the higher the ratio level, the higher the generated surplus (and the higher the coverage). In general terms, the model places much importance on coverage ratios as a default event is usually understood as the situation in which a company is not able to entirely pay the short-term debt. In this sense, coverage ratios can act as signals of credit problems. - Pre-tax income as a percentage of sales. It provides a metric on the company’s effectiveness with regard to the cost structure and its capability to reach yield premiums in comparison with peer companies. The capital-intensive nature of the transportation industry makes it important to include interest expense when considering profitability, as
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 82 capital costs are as relevant as operating costs. Therefore, while this ratio may be relevant for modelling purposes, correlation and significance should also be checked. - Financial leverage and coverage metrics are indicators of a company’s financial capacity and long-term viability. Financial flexibility is critical to this sector as it indicates the degree of stress a company would suffer during an economic downturn. In addition, leverage affects a company’s ability to reinvest in the business, as a highly leveraged company may not have the same access to capital (new funds) as other companies with a lower leverage level. Furthermore, leverage partly affects the capacity to deal with changing market conditions in the highly cyclical business operations to which this type of company may be exposed. Financial leverage and coverage are additionally represented in the model by the following ratios: o Debt/EBITDA ratio is an indicator of debt serviceability and leverage, and is commonly used in this sector as a proxy for comparative financial strength. o Funds from Operations (Free Cash Flows from Operations minus Capex) to Debt is an indicator of a company’s ability to repay principal on its outstanding debt. This ratio compares cash flow generation from operations before working capital movements to outstanding debt. o EBIT to Interest Expense is an indicator of a company’s ability to cover its ongoing costs of borrowing. - “(Liabilities - Cash & Securities)/Assets” statically analyzes the company’s leverage level (or relative debt level). It compares the assets (that could be used to pay the debt) with the net debt (net of cash and liquid securities). The higher the ratio result, the higher the relative debt level (and the higher the credit risk). - “Retained Earnings/Liabilities” compares the company’s result with its debt level. It analyzes the company’s leverage level more dynamically. The higher the ratio result, the lower the credit risk. - “Current Assets/Current Liabilities” is known as working capital. Depending on the sector involved, the interpretation of the result may vary. Generally speaking, the higher the ratio, then the higher the liquidity level. Nevertheless, in the retail sector, a low ratio may be interpreted in a positive way, i.e. the entity is being financed by its suppliers (the average collection period is lower than the average payment period). - “Cash & Securities/Current Assets” analyzes to what extent current assets are composed of liquidity (the higher the ratio level, the higher the liquidity level).
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 83 - ROA and ROE analyzes the profitability of the company. They calculate return in relation to assets (ROA), and return in relation to equity (ROE). 5.1.2 Step 2 – Calculation of peers’ general score This step consists in creating a database including a portfolio of companies (“peers”) which possess an official credit rating (issued by a rating agency) and giving a general score to each of them. Where possible, companies included in the database should belong to the same sector and country as the company under analysis and should have recently been rated by a relevant credit rating agency (i.e., Moody’s, Fitch or S&P). Alternatively, given the limited number of rated companies over the sectors, the database can also be created by using the credit letter issued by Refinitiv or Bloomberg upon their internal models. In some cases, it can be difficult to find peers since companies are highly diversified and act in many different industries and markets at the same time. Nevertheless, it is recommended the inclusion of as many peers as possible. A score is assigned to each peer company in the portfolio, and each company is ranked according to its position (a percentile between 1 and 100) within the entire portfolio of companies. This position represents the general score. By way of example, for a specific real case (in a specific sector), we included the information required in a database in order to build the cumulative distribution function, deriving the following figure: Figure 14. Example of Score distribution per Credit Rating Source: Compiled by the author. As it can be seen in the above distribution, the credit rating is directly related to the score (“position” or “percentile”) within the distribution. This distribution was created using Refinitiv information on rated companies. Certain companies with an equal rating are scored slightly differently according to their outlook, size and debt coverage. In the example above, this means that there are 13 companies with the same rating (BBB-) between percentile 25 and 37. This is normal given the fact that there are more companies rated between BBBand BBB+ than in any other rating bucket. Figure 14 above represents a cumulative distribution of 63 rated companies. Its corresponding probability density function is shown in Figure 15: - 20 40 60 80 100 Percentile
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 84 Figure 15. Example of Density function of Credit Rating Source: Compiled by the author. 5.1.3 Step 3 – Calculation of the specific score for each financial ratio for all peers In this step, it is needed to assign a score to each peer company in the portfolio in relation to each ratio. In other words, each company has on the one hand a general score (step 2), and on the other a specific score for each ratio (step 3). Therefore: - We calculate every ratio included in Table 12 for all of the companies in the sample. - Hence, a distribution for each ratio according to the results is created. - Then, each company is given a score (percentile) for each ratio depending on its position within the distribution. 5.1.4 Step 4 – Panel data construction and Model calibration: regression and variable selection through Stepwise AIC A percentile-composed matrix is prepared which shows the relationship between the comparable companies’ rating, their general score, and the score given to each ratio within the entire peer sample. In order to make the model “temporal unbiased”, it is necessary to build a panel data matrix given that the modelled variable (the general score) depends not only on the selected variables but also on its inherent variation. Consequently, the peer sample is structured in a cross-sectional matrix (panel data), in which the rows present the values for each company within the sectorial group as of December of several past years. The following table presents an example:
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 85 Table 13: Example of Scoring Panel Data (general and specific scores) Company General Score Specific Score for each ratio Agency Rating General Score ROE ROA EBITDA / Interest Expense Net Debt / Assets Etc. Company A Year T-3 BBB25 37 40 28 48 … Company A Year T-2 BBB+ 52 65 61 54 65 … Company A Year T-1 BB+ 16 12 7 20 22 … Company A Year T BBB25 15 12 32 29 … Company B Year T-3 AA+ 94 95 97 86 56 … Company B Year T-2 AAA 98 96 98 87 67 … Company B Year T-1 AA 93 94 95 85 58 … Company B Year T AA+ 96 92 96 84 61 … … … … … … … … … Company N Year T BB+ 13 6 9 16 4 … Source: Compiled by the author. The above table should be fed with the following inputs: - The name of each peer company in the portfolio. - The rating and general score of each peer company in the portfolio. - The specific score of each peer company in the portfolio for each ratio. Once the Panel data is built, then the following algorithm to create the regression model over the sectorial ratios is followed: 5.1.4.1 Model selection algorithm Selection algorithm consists of several steps that are presented in the following scheme and described in detail below. This algorithm describes the main steps to be taken in turn to select the best model in terms of regressors and their representative within the model. The steps cover an initial OLS model calibration with all available explanatory variables (ratios) and then continues to end up with the final, optimal model:
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 86 Figure 16. Model selection algorithm Source: compiled by the author 1. Data Cleansing and normalization First of all, it should be noted that there could be incomplete information for some of the companies within the sample, as well as companies with financial statements containing rare figures. Subsequently, a data cleansing and normalization process should be applied to the database before continuing with the model optimization. The following steps would be followed: 1. Identify missing values from historical financial statements 2. Delete companies for which financial variables are rare or non-existing 3. Homogenize rating information. Some companies could be rated by Moody´s, whose rating scales is different to the one used by S&P and Fitch. Also, some companies could be rated with short-term rating values, which are in a different scale than long-term rating values. 4. Delete the companies that belong to geographies too dissimilar in comparison with the whole dataset, in order to avoid geographical noise (e.g., when most of companies in the dataset belong to Europe or America, it is convenient to exclude a company that could be based on Vietnam or Madagascar, for example.). 5. Use the same currency and FX rate for those financial variables in foreign currency. 6. Use international scale to translate those ratings from local scale. For instance, Argentina or Peru have local rating scale provided by CRAs whose rating notches do not match with the ones used in Europe or America, which are by default international-scaled ratings.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 87 2. Full dataset - OLS regression Due to the fact that the panel data is structured with many entities and over several years, the paradigm of traditional time-series analysis is subject to more profound changes. In this case, we have several sets of endogenous variables to be used to model the General Score, since there are several individual entities for which the explanatory variables may present different behaviors. That is to say: 𝑦𝑖𝑗=𝛼+𝑥1𝑖𝑗𝛽1𝑖𝑗+𝑥2𝑖𝑗𝛽2𝑖𝑗+⋯+𝑥𝑛𝑖𝑗𝛽𝑛𝑖𝑗…+𝜂𝑖𝑗+𝜀 where 𝑦𝑖𝑗 is the dependent variable (General Score) for the individual 𝑖 and timeframe of observation 𝑗; 𝑥𝑛𝑖𝑗 is the value for the explanatory variable 𝑛 (Specific Score) for a given individual 𝑖 of the observation period 𝑗; 𝛽𝑛𝑖𝑗 is the coefficient of each explanatory variable in the same context; and 𝜂𝑖𝑗 represents the potential unobservable, correlated differences for the values of each explanatory variable 𝑥𝑛 at each observation node in 𝑗. Given the heterogeneity of the entities within our sample, it is possible that entities with similar characteristics may display different behaviors. In fact, it is possible that a single entity may present different behaviors for the given timeframe data set. Therefore, first of all it is necessary to analyze the existence of any potential unobservable factors which may influence consistency in the output parameters and may entail autocorrelation and heteroskedasticity in the residuals. These unobservable factors (which may be either fixed or stochastic for a given data set) are expected to result in biased model coefficients for a given timeframe and entity, hence this must be treated accordingly. One solution is to assume that all 𝛼 and each coefficient 𝛽𝑛𝑖𝑗 are constant for the entire data set and for each individual 𝑖. In this case, it would be possible to calibrate the model via Ordinary Least Squares (OLS). However, this method could lead to problems of autocorrelation and heteroskedasticity, given that the error variance may vary among individuals or even for a given timeframe and individual. In turn, this problem would be solved by calibrating the model via a Generalized Least Squares method (GLS). Alternatively, it may be assumed that intercept 𝛼 varies among individuals and over time. Therefore, it is necessary to verify that the source of said unobservable factors is the difference occurring in intercept 𝛼. In this case, the model should be transformed as follows, where each explanatory variable will be the deviation with respect to its average, for each individual: (𝑦𝑖𝑗−𝑦𝑖 )=∑𝛽𝑛𝑖𝑗 𝑁 𝑛=1 (𝑥𝑛𝑖𝑗−𝑥𝑛𝑖)+𝜀 where 𝑦𝑖𝑗 is the dependent variable for the individual 𝑖, and 𝑥𝑛𝑖 is the time average of each explanatory variable for each individual. (46) (47)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 88 3. OLS Regression analysis In order to determine which solution should be adopted, we need to firstly ran a regression calibrated via OLS over all of the several variables available in our data set. This means that, with high probability, we are going to end up, in a first stage, with model that incorporates heteroskedasticity and correlated residuals, and secondly, with too many variables with low explanatory power and highly correlation between each other. However, this previous step is necessary in order to identify what are the potential issues that the initial data set can bring into the output estimation. The main regression tests performed over the model are the following: - Parameter representativeness: it is checked what p-value and t-Student value have each explanatory variable, so that the main representative variables can be identified. - Normality in residuals, mainly via Q-Q Plot and Jarque-Bera test, Shapiro-Wilk test and Anderson-Darling test. 5% threshold value holds for hypothesis acceptation/rejection for each of the tests. If the p-value of a test result for normality of residuals is higher than 5%, it is considered that the test fails to reject the null hypothesis that the errors are normally distributed. Since three tests are used for testing normality of residuals, it is required to have p-values for all the tests to be higher than 5% in order to establish the fact that residuals are normally distributed and thus, the model can be considered as a valid method for related predictions. - Heteroskedasticity: Heteroskedasticity in errors is tested with the Breusch-Pagan test. As the result of F-statistic, if p-value is greater than 5%, it is considered that the test fails to reject the null hypothesis that the results having homoskedasticity. - Multicollinearity: correlation between explanatory variables is checked, as it would affect the resulting model and may provide with spurious results and arbitrary goodness-of-fit values. Also, VIF (Variance-inflation Factor) is computed for each variable. If VIF is over a value of “10”, the variable will be a candidate to be removed, although it is fully recommended to wait until the final step in the model calibration (Stepwise AIC) as in that step many of the initial variables are directly removed. - Autocorrelation: an additional assumption that residuals should not be serially correlated is tested in order to establish consistency and asymptotic normality. The assumption tested and respective tests used are the Ljung-Box test and the BreuschGodfrey test. 5% threshold holds true for p-values of the Ljung-Box test and the Breusch-Godfrey test for serial correlation of residuals. If both tests provide p-values greater than 5% thus, fail to reject the null hypotheses that residuals are not serially correlated so that additional solutions need to be assessed in order to fix this problem. Also, Partial ACF plots are used to assess on the presence of autocorrelation in residuals, in order to detect not only autocorrelation, but the lag between correlated
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 95 6. Final model form and composition Once the Stepwise AIC process has been run on both OLS and GLS model forms, the best model in terms of regression tests and better AIC with a maximum number of variables is selected (this limits the potential multicollinearity problems). When dealing with panel datasets, the most possible outcome is to have a Stepwise-optimized model calibrated with GLS with the form of AR(p), covering the potential autocorrelation found in the initial regression models, if any. 5.1.5 Step 5 – Obtaining the model credit rating and the expected PD for the company The final output of the model will be of the following form: 𝐶𝑜𝑚𝑝𝑎𝑛𝑦 𝐺𝑒𝑛𝑒𝑟𝑎𝑙 𝑆𝑐𝑜𝑟𝑒=𝛼+𝑋1𝛽1+𝑋2𝛽2+⋯+ 𝑋𝑛𝛽𝑛+𝜀 Where 𝑋1,2,…,𝑛 represent the Score for all the X ratios selected in the optimal model, and 𝛽1,2,…,𝑛 represent the coefficient given to the corresponding ratio score by the AIC-based optimization process. By following the cumulative distribution shown in Figure 14, then the general, final score can be directly associated to its most probable credit letter. However, the Expected Credit Loss and the CVA and DVA metrics are needed to be fed with the PD for a given timeframe. Therefore, it is needed to map all the potential credit letters to its implied PD cumulative curve. As one of the IFRS rules is that, when using variables to calculate the Expected Credit Loss, the output should be forward-looking, historical PDs cannot be used. Conversely, implied PDs in Credit Default Swaps or liquid senior bonds can be used in this regard. The usage of PDs implied in market quotes provides the model output with robustness in terms of default market future expectations for a given entity, sector, or rating letter. Therefore, it is necessary to build a matrix of PD cumulative curve which provide the default rate per rating letter and tenor. In this research I have used the PD curves that are quoted by Refinitiv. Refinitiv provides, through its SECTORCDS function, the forward default probability rates implied in market Credit Default Swaps spreads. Refinitiv provides several tables with PD curves constructed upon different single name CDSs, according to sector, rating, and geography. This market information already implicitly incorporates a forward-looking approach. For instance, the BBB-rated CDS spread curve for the Telecommunications sector in Europe, together with its implied default probability curve and estimated Recovery Rate is the following: (69)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 96 Figure 17. BBB-rated CDS spread curve, Telecommunications sector, 17/03/2022 Source: Refinitiv This CDS curve is built as an average of single-name CDSs quoted on senior unsecured bonds, for the relevant sector and geography, and it is a reliable source for PDs containing forwardlooking default expectations that can be used in several fields of counterparty credit risk, e.g., for ECL or CVA calculation. Table 14 therefore is composed by all the sectorial PDs implied in CDS spread curves for every single rating letter and is used in the model implementation shown in section 5.2. For those intermediate notches, linear interpolation has been used: Table 14: CDS-implied cumulative PDs (%) and Recovery Rates (%), Telecommunications sector, 31/12/2021 Rating 6M 1Y 2Y 3Y 4Y 5Y 7Y 10Y 20Y 30Y Recovery Rate AAA 0,07 0,15 0,40 0,76 1,33 2,15 4,37 7,72 16,07 25,52 40,00 AA+ 0,07 0,15 0,41 0,81 1,42 2,26 4,43 7,80 16,78 26,54 40,00 AA 0,06 0,14 0,41 0,85 1,51 2,36 4,48 7,88 17,49 27,55 40,00 AA0,07 0,17 0,48 0,99 1,73 2,70 5,09 8,80 19,38 30,21 39,91 A+ 0,08 0,19 0,55 1,12 1,96 3,04 5,69 9,71 21,26 32,88 39,81 A 0,09 0,22 0,62 1,26 2,18 3,38 6,30 10,63 23,15 35,54 39,72 A0,11 0,27 0,77 1,54 2,67 4,13 7,61 12,62 26,62 39,71 39,61 BBB+ 0,14 0,32 0,91 1,83 3,16 4,89 8,92 14,62 30,09 43,88 39,49 BBB 0,16 0,37 1,06 2,11 3,65 5,64 10,23 16,61 33,56 48,05 39,38 BBB0,25 0,61 1,74 3,41 5,80 8,65 14,83 22,66 42,25 57,06 39,13 BB+ 0,35 0,84 2,42 4,70 7,96 11,67 19,44 28,71 50,93 66,08 38,87 BB 0,44 1,08 3,10 6,00 10,11 14,68 24,04 34,76 59,62 75,09 38,62 BB0,78 1,89 5,01 9,09 14,20 19,61 29,54 40,74 65,43 79,06 37,73 B+ 1,13 2,70 6,91 12,17 18,29 24,55 35,04 46,71 71,24 83,02 36,83 B 1,47 3,51 8,82 15,26 22,38 29,48 40,54 52,69 77,05 86,99 35,94 B2,47 5,26 11,58 18,78 26,14 33,00 43,43 54,26 75,34 83,89 29,37 CCC 3,46 7,01 14,33 22,29 29,90 36,51 46,32 55,82 73,62 80,78 22,80 Source: Refinitiv
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 97 5.2. Model implementation and performance measurement So as to assess on the modelling expected outcome, a representative set of companies within a given sector has been selected in order to apply the model. The outcome is expected to be similar to the overall ratings, or much closer to those provided by the market (credit rating agencies - CRAs). Also, not only the outcome but the variables used in the model are expected to be similar to the ones used by CRAs. The chosen sector is “Telecommunications”, for which overall ratings are issued by Moody’s, S&P or Fitch. Following the steps detailed throughout previous section, the following ratios and the inherent percentile within the sample for each company and ratio are computed: Pre-tax Income to Sales; Debt to EBITDA; Funds from Operations to Debt; EBIT to Interest Expense; Return On Equity; Net Margin; Return On Assets; EBITDA to Interest Expense; Debt to Equity; Debt to Assets, Cash to Total Debt; Short Term Debt to Total Debt; and Quick Ratio. In terms of sectorial companies, I directly took all the companies provided as “peers” of Telefónica, S.A., by Refinitiv, in turn to ensure comparability. Some of these peers have no information published to compute some of the ratios, so previously these companies were deleted from the dataset. The following companies were finally chosen from the sample in order to calibrate the model factors, since these peers possess the most liquid, updated financial information in line with the financial statements date used (31/12/2020): Table 15: Sectorial companies used to implement the FRS model for Telecommunications sector Company Names used in the model construction BCE Inc Singapore Telecommunications Ltd BT Group PLC Solusi Tunas Pratama Tbk PT Chorus Ltd Sri Lanka Telecom PLC Cogent Communications Holdings Inc Sunrise Communications Group AG Deutsche Telekom AG Swisscom AG EI Towers SpA Talktalk Telecom Group Ltd Emirates Telecommunications Group Company PJSC Tata Communications Ltd Far Eastern New Century Corp Tata Teleservices (Maharashtra) Ltd Hellenic Telecommunications Organization SA Telecom Argentina SA Iliad SA Telecom Italia SpA Koninklijke KPN NV Telefonica SA KT Corp Telekom Austria AG Lumen Technologies Inc Telekom Malaysia Bhd Nippon Telegraph and Telephone Corp Telenet Group Holding NV NOS SGPS SA Telia Company AB Ooredoo QPSC Telus Corp Orange SA True Corporation PCL PLDT Inc Verizon Communications Inc Proximus NV Vodafone Group PLC Rostelekom PAO Windstream Holdings Inc Saudi Telecom Company SJSC Zayo Group Holdings Inc Shaw Communications Inc Ziff Davis Inc Source: Refinitiv, compiled by the author
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 98 The following figure shows the general and particular percentiles for each sample company and ratio within the sectorial database used: Table 16: Sector companies and their ratio percentiles from the sample Source: Compiled by the author; Refinitiv. It should be highlighted that the global score (percentile) for each company was assigned by a random number within a confidence interval of percentile for the corresponding company rating, in order to test the capacity of the model to cover the existing percentile dispersion within the Company Global Percentile PreTax Income / Sales Debt / EBITDA Funds from Ops / Debt EBIT / Int Expense EBITDA / Assets ROE Net Margin ROA EBITDA / INTEREST EXPENSE D/E D/A Cash to Debt ST DEBT / TOTAL DEBT QR BCE Inc_2017 38 87 58 54 73 67 71 81 80 58 54 47 923 7 BCE Inc_2018 35 87 56 54 70 63 68 79 77 56 57 49 531 14 BCE Inc_2020 63 75 46 50 57 45 63 74 64 44 53 46 266 27 BT Group PLC_2017 52 57 78 75 74 65 88 61 73 66 47 80 63 28 25 BT Group PLC_2018 35 62 73 72 78 64 85 63 78 71 49 73 75 44 51 BT Group PLC_2019 28 64 63 58 74 55 87 68 76 67 41 64 79 56 75 BT Group PLC_2020 25 58 35 43 64 39 60 59 55 64 37 30 76 49 77 Chorus Ltd_2018 27 70 33 125 32 44 64 33 17 27 32 695 16 Chorus Ltd_2019 25 44 20 220 25 31 43 20 13 22 23 37 38 8 Chorus Ltd_2020 38 39 22 619 32 33 42 20 15 20 16 048 2 Cogent Communications Holdings Inc_2017 8 33 16 41 23 92 426 47 9 6 2 82 86 98 Cogent Communications Holdings Inc_2018 52 43 16 45 26 95 344 60 11 5 1 82 87 99 Cogent Communications Holdings Inc_2019 64 56 11 44 29 85 454 63 11 4 3 87 89 100 Cogent Communications Holdings Inc_2020 12 15 336 13 60 915 16 6 2 1 81 87 99 Deutsche Telekom AG_2017 50 34 53 71 45 47 58 37 47 42 35 57 28 54 32 Deutsche Telekom AG_2018 50 35 47 73 47 41 39 23 27 56 32 53 27 49 34 Deutsche Telekom AG_2019 26 52 44 71 49 66 63 38 44 60 25 29 29 46 38 Deutsche Telekom AG_2020 33 47 33 51 43 53 59 32 29 46 18 20 37 60 67 Emirates Telecommunications Group Company PJSC_2017 90 94 95 97 86 56 84 88 88 84 89 96 96 32 78 Emirates Telecommunications Group Company PJSC_2018 91 98 96 98 87 67 83 89 90 84 91 96 98 673 Emirates Telecommunications Group Company PJSC_2019 91 93 94 95 85 58 81 90 88 82 88 93 98 15 76 Emirates Telecommunications Group Company PJSC_2020 91 96 92 96 84 61 80 92 89 80 86 89 97 470 Hellenic Telecommunications Organization SA_2017 19 24 85 21 37 74 20 18 22 57 78 81 95 559 Hellenic Telecommunications Organization SA_2018 19 47 89 51 71 82 41 37 50 74 81 84 94 11 61 Hellenic Telecommunications Organization SA_2019 19 19 88 81 39 92 52 41 57 73 66 72 92 552 KT Corp_2017 38 20 91 88 56 62 22 20 29 75 88 89 88 21 70 KT Corp_2018 54 25 92 93 68 51 29 24 42 78 92 92 94 29 85 KT Corp_2019 50 22 89 80 67 43 26 22 35 81 89 92 88 43 80 KT Corp_2020 69 22 85 84 67 48 26 22 38 81 85 87 89 27 82 Lumen Technologies Inc_2017 16 18 425 16 615 16 14 15 44 27 491 58 Lumen Technologies Inc_2018 5 4 5 44 5 8 8 5 5 6 34 24 488 31 Lumen Technologies Inc_2019 15 2 2 38 2 2 1 2 2 2 25 19 21 76 28 Lumen Technologies Inc_2020 16 6 9 43 712 6 6 6 9 23 19 373 10 Nippon Telegraph and Telephone Corp_2017 99 72 94 92 98 50 46 55 60 98 95 95 73 22 87 Nippon Telegraph and Telephone Corp_2018 99 77 96 95 99 54 50 60 70 99 96 98 67 22 84 Nippon Telegraph and Telephone Corp_2019 78 74 91 81 100 40 50 58 64 100 94 94 71 986 Nippon Telegraph and Telephone Corp_2020 99 71 87 70 99 37 49 56 61 99 91 91 70 471 NOS SGPS SA_2018 31 60 78 92 83 85 67 66 80 89 64 59 125 26 NOS SGPS SA_2019 35 61 70 90 82 87 70 67 74 88 51 42 262 37 NOS SGPS SA_2020 38 37 50 89 75 73 48 50 52 86 43 28 38 61 51 Orange SA_2017 97 36 29 27 46 25 36 30 34 39 38 37 78 19 33 Orange SA_2018 50 40 30 22 46 26 37 31 33 40 36 35 61 14 35 Orange SA_2019 51 58 29 30 57 35 54 51 48 57 30 25 68 37 64 Orange SA_2020 74 54 30 37 54 29 73 74 68 61 35 32 70 32 63 Proximus NV_2019 82 51 86 65 85 79 66 53 66 94 71 79 43 71 40 Proximus NV_2020 80 73 88 78 91 91 84 71 87 95 69 75 40 72 44 Saudi Telecom Company SJSC_2017 79 95 99 100 98 78 74 96 94 97 100 99 99 50 90 Saudi Telecom Company SJSC_2018 71 97 100 99 96 74 75 96 95 96 9100 100 75 93 Saudi Telecom Company SJSC_2019 89 94 99 99 95 75 78 95 92 95 99 99 96 51 89 Saudi Telecom Company SJSC_2020 64 92 98 98 97 77 78 94 93 96 99 98 99 18 92 Shaw Communications Inc_2017 44 80 76 56 58 49 47 75 58 49 84 82 44 98 43 Shaw Communications Inc_2018 23 21 51 17 26 15 14 15 15 29 83 81 35 93 21 Shaw Communications Inc_2019 35 83 63 49 61 39 58 85 72 45 80 74 77 20 47 Shaw Communications Inc_2020 31 84 61 69 62 51 56 81 67 54 73 66 46 78 62 Singapore Telecommunications Ltd_2017 72 78 71 89 81 16 68 97 92 72 96 88 25 13 24 Singapore Telecommunications Ltd_2018 91 98 90 91 88 49 80 99 98 83 98 91 22 39 33 Singapore Telecommunications Ltd_2019 88 70 69 91 81 13 54 94 86 68 97 90 26 37 49 Singapore Telecommunications Ltd_2020 75 71 54 80 76 15 21 51 43 67 90 83 36 12 30 Swisscom AG_2017 70 86 81 77 88 84 86 84 91 87 67 70 32 29 36 Swisscom AG_2018 66 85 84 74 89 80 81 82 89 91 76 76 31 53 60 Swisscom AG_2019 64 78 72 68 90 75 82 87 91 93 65 63 19 40 49 Swisscom AG_2020 70 84 75 76 91 77 73 86 85 92 74 67 25 59 63 Talktalk Telecom Group Ltd_2018 6 6 4 40 410 2 6 4 7 18 16 23 64 37 Talktalk Telecom Group Ltd_2019 10 11 23 53 13 30 56 19 39 16 21 20 33 91 19 Talktalk Telecom Group Ltd_2020 10 50 57 52 51 94 98 70 94 36 26 13 23 69 15 Telecom Italia SpA_2017 49 51 25 36 36 20 29 46 30 20 49 39 57 47 54 Telecom Italia SpA_2018 10 5 6 35 6 4 9 5 6 13 47 40 44 30 30 Telecom Italia SpA_2019 7 56 25 33 37 22 25 39 24 26 45 34 48 58 56 Telecom Italia SpA_2020 10 49 20 19 34 19 90 100 97 29 59 36 65 50 68 Telefonica SA_2017 51 49 35 37 50 52 77 43 49 50 20 22 50 42 29 Telefonica SA_2018 53 65 39 39 64 59 74 49 51 63 22 29 53 36 43 Telefonica SA_2019 44 28 27 57 40 33 28 18 18 48 19 26 56 35 46 Telefonica SA_2020 49 30 26 53 44 35 61 25 25 59 12 21 55 39 81 Telekom Austria AG_2017 35 45 68 60 72 81 67 58 70 78 53 49 40 99 65 Telekom Austria AG_2018 49 42 77 64 73 83 51 46 56 79 60 62 668 46 Telekom Austria AG_2019 49 60 54 47 75 78 64 57 61 77 44 25 13 26 54 Telekom Austria AG_2020 49 65 71 75 77 82 69 65 75 77 54 52 42 16 35 Telenet Group Holding NV_2017 21 31 18 50 24 88 636 41 19 4 6 5 74 2 Telenet Group Holding NV_2018 19 76 17 63 42 95 570 73 21 1 2 8 68 4 Telenet Group Holding NV_2019 14 73 18 55 38 93 567 65 20 3 4 10 65 4 Telenet Group Holding NV_2020 19 79 21 64 47 96 282 84 33 2 5 8 65 3 Telia Company AB_2017 38 67 32 57 55 13 51 80 63 38 77 68 80 82 96 Telus Corp_2017 60 81 49 47 68 65 79 75 78 54 40 35 16 61 12 Telus Corp_2018 65 82 51 42 69 57 72 76 77 53 50 47 12 77 41 Telus Corp_2019 60 81 37 34 63 46 76 80 71 46 36 30 11 73 39 Telus Corp_2020 40 64 27 33 49 27 53 61 53 42 40 33 18 74 42 True Corporation PCL_2017 49 17 36 20 23 816 17 15 32 73 84 51 213 True Corporation PCL_2018 50 44 36 35 52 11 30 34 27 55 58 78 50 320 True Corporation PCL_2019 50 27 12 10 33 925 30 22 26 39 55 71 43 60 True Corporation PCL_2020 52 12 822 12 12 16 13 13 14 15 14 29 23 19 Verizon Communications Inc_2017 49 85 53 46 70 68 93 73 81 47 24 39 784 64 Verizon Communications Inc_2018 38 80 57 70 65 64 92 78 83 44 29 50 13 77 65 Verizon Communications Inc_2020 32 89 50 73 77 40 89 87 82 62 32 56 60 80 91 Vodafone Group PLC_2017 26 29 42 68 50 21 7 3 4 68 84 71 81 16 23 Vodafone Group PLC_2018 25 46 52 79 66 29 38 71 62 73 85 69 80 20 25 Vodafone Group PLC_2019 28 4 7 59 4 4 8 4 5 22 78 42 92 71 95 Vodafone Group PLC_2020 27 15 19 61 15 24 11 7 9 34 55 22 78 45 72 Windstream Holdings Inc_2017 1 2 1 14 1 1 99 2 2 1 6 5 1 83 17 Windstream Holdings Inc_2018 1 5 14 16 888 97 4 3 5 5 4 14 0 0 Windstream Holdings Inc_2019 1 1 0 5 1 0 100 1 1 0 1 12 12 70 53 Ziff Davis Inc_2017 70 88 67 87 61 73 71 85 85 33 71 56 84 100 97 Ziff Davis Inc_2018 60 77 64 94 59 70 64 73 79 36 72 60 67 98 94 Ziff Davis Inc_2019 38 75 48 87 60 47 75 88 84 41 61 51 86 15 77
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 99 same notch, particularly for ratings from BB+ to BBB+. The way this percentile dispersion works is presented in section 5.3. 5.2.1 Full dataset OLS Regression and analysis The first step is to run an OLS regression on the entire panel data set. The output on the linear model, following (69) is the below: Table 17: OLS Regression statistics – Total Sample of Ratio percentiles Source: Compiled by the author The results show that the explanatory power of these regressors altogether is poor, with only Income to Sales as a good significant variable with a 95% of confidence. Although R2 is relatively high (0.8872), F-value is not as high as desired in a multivariate linear model (58.28) and therefore there could be spurious conclusions from this. Figure 18 and Figure 19 below show how the model performs in terms of performance and goodness of fit. There is high dispersion over the average, and some of the estimations are out of the real values (e.g., one estimation with percentile < 0). This means that the model needs to be improved in terms of regressors used and the performance for near-to-boundary estimations. Estimator Coefficient t value Pr(>|t|) Significance IncomeToSales 0.525415 2.026 0.0458 * DtEBITDA -0.165742 -0.673 0.5028 FFOpsToDebt 0.008746 0.074 0.9414 EBITtoInterest 0.512611 1.266 0.2089 EBITDAtoAssets -0.157808 -1.233 0.2209 ROE -0.018395 -0.211 0.8332 NetMargin -0.516259 -1.437 0.1543 ROA 0.231903 0.710 0.4797 EBITDAtoInterest 0.053609 0.187 0.8518 DtoE 0.056223 0.419 0.6766 DtoA 0.139830 0.601 0.5493 CashToDebt 0.082911 0.777 0.4391 STDebtToDebt 0.012775 0.164 0.8699 QuickRatio 0.047713 0.406 0.6854 --- Residual standard error 17.75 Adjusted R-squared 0.8872 F-Statistic 58.28 p-value <2.2e-16 Significance codes: 0 ‘***’, 0.001 ‘**’, 0.01 ‘*’, 0.05 ‘.’, 0.1 ‘ ’
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 100 Figure 18. Actual Percentile vs. Model Predicted Percentile – Total Sample of Ratio dataset. Source: Compiled by the author Figure 19. OLS goodness of fit– Total Sample of Ratio dataset Source: Compiled by the author As it can be seen below, there is no conclusion when dealing with too many variables in the model, as no explanatory relationship is even found when regressing each of them with the rest as exogenous variables:
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 101 Figure 20. Added-variable plots for Total Sample of Ratio dataset Source: compiled by the author In terms of heteroskedasticity identification, it should also be noted that evidence of heteroskedasticity was not found as per the result of the Breusch-Pagan test (assuming a constant linear relationship), with a p-value of 0.093. Concerning normality in residuals, both Jarque-Bera and Anderson-Darling tests resulted in p-values over 5%. Also, Normal Q-Q plot is the following, upon which the assumption of normality would not be rejected neither:
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 102 Figure 21. Normal Q-Q Plot – Total Sample of Ratio dataset Source: Compiled by the author In addition, we verified that no outliers were identified among the sample, hence they all fall within the Cook distance lines: Figure 22. Cook’s distance Plot – Total Sample of Ratio dataset Source: Compiled by the author However, when testing Multicollinearity, several issues arise from using too many variables, some of them similar by nature. In this sense, Table 18 below summarizes the Variance Inflation Factor (VIF) for each of the regressors show that for many of them, it is found a high correlation with all the others regressors (values over 10), particularly Income to Sales, EBITDA to Interest, Net Margin and ROA:
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 103 Table 18: VIF matrix – Total Sample of Ratio dataset Source: Compiled by the author Likewise, the correlation matrix for the entire dataset of ratios and historical figures shows that for many pairs of ratios there is a relevant correlation found, hence several regressors are to be deleted as explanatory variables: Figure 23. Correlation heatmap – Total Sample of Ratio dataset Source: Compiled by the author Furthermore, as indicated at the beginning of this section, the use of panel data with OLS methods may lead to models being biased due to the existence of autocorrelation. Due to the fact that the errors are unobservable in the linear model, particularly as regards panel data where relevant variables can be missed, the detection method should focus on the best available estimator, i.e., the residuals created in the regression. Therefore, we first performed the analysis by checking residual autocorrelation and partial autocorrelation plots: IncomeToSales DtEBITDA FFOpsToDebt EBITtoInterest EBITDAtoAssets ROE NetMargin 81,33 68,88 18,59 205,02 17,66 8,34 154,3 EBITDAtoInterest DtoE DtoA CashToDebt STDebtToDebt QuickRatio ROA 97,71 20,79 62,64 12,61 61,05 14,97 132,05
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 104 Figure 24. Residual autocorrelation and partial autocorrelation – Total Sample of Ratio dataset. Source: Compiled by the author The dashed horizontal lines on the plots correspond to approximately 95% confidence limits. The general pattern of the autocorrelation and partial autocorrelation functions is suggestive of an autoregressive process of order 3 - AR(3) -. Additionally, a Ljung-Box test was performed in order to quantitatively analyze the weight of the autocorrelation for the given lags. Assuming the autoregressive process is of order 3, the statistic is 10.32, which is above that expected for a 95% confidence interval. This is another indicator of existing correlation in residuals.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 111 Table 22: Regression statistics for Market CDS-implied 5Y PDs vs. Modeled CDS-implied 5Y PDs under GLS – Optimal variables with Stepwise AIC selection Source: compiled by the author Figure 32. Model performance for Market CDS-implied 5Y PDs vs. Modelled CDS-implied 5Y PDs under GLS – Optimal variables with Stepwise AIC selection Source: compiled by the author 5.2.6 Starting hypothesis checkpoint and conclusion: explanatory variables used by Rating Agencies are aligned with the ones used by the optimized model As it has been observed, when the model variables are optimal the output from the model (measured either in General Scores, in rating letters or even in PDs) is robust and consistent. Therefore, my starting hypothesis was that, if the model uses optimal variables, and the output is aligned to the sample actual ratings, therefore those optimal explanatory variables should be similar in nature to the ones used in the rating agencies criteria, at least in a certain extent (due to the fact that qualitative factors are also used and they are not present in the model, at least explicitly). If we recall the information published by Moody´s in Table 2, it can be noted that the main quantitative metrics or ratios used by Moody’s in their credit rating assessment for the Telecommunications sector are the same as, or quite similar to, the optimal variables used in the model implementation shown for such a sector: Estimator Coefficient t value Pr(>|t|) Significance Model PD 5Y 0.95757 30.65 <2e-16 *** --- Residual standard error 0.03114 Adjusted R-squared 0.9098 F-Statistic 939.20 p-value <2.2e-16 Significance codes: 0 ‘***’, 0.001 ‘**’, 0.01 ‘*’, 0.05 ‘·’, 0.1 ‘ ’
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 112 Table 23: financial metrics used by Moody´s in rating assignment criteria vs GLS optimal variables Financial metric used in Moody´s credit rating assessment Weight in the model output Model optimal variables Revenue 12.5% → Income / Sales Revenue Trend and Margin Sustainability 10% → Net Margin Debt / EBITDA 15% - Retained Cash / Debt 10% → Cash / Debt (EBITDA-CAPEX) / Interest Expense 10% → EBIT&EBITDA / Interest Expense 57.5% Source: Moody´s and compiled by the author The only metric which is not shared at all between Moody’s criteria and the optimized model is Debt/EBITDA, which is out of the AIC-optimal variables set for both OLS and GLS models, although Debt/Assets is a ratio of similar interpretation which is used in GLS model. As a conclusion, it is demonstrated that, with a high degree of certainty, the initial hypothesis is met. The model replicates in a relevant extent the quantitative criteria used by the rating agency, which is a conclusion to take into consideration also in the sense that the model could be applicable as long as the agency criteria does not change in a substantial way. Also, it is worth mentioning that the model has been implemented by using a heterogeneous company dataset, including several geographies, currencies, and a wide range of ratings from different agencies. This means that the model assumptions are robust to cover companies from different countries and credit quality, as it is demonstrated in some extent in section 5.4. Backtesting / Out-of-sample testing. However, it should be noted that the range of applicability could be limited for companies from particular jurisdictions (e.g., from least developing countries), for companies whose local rating could be difficult to be translated to a global rating scale, or for companies in geographies with special situations (e.g., close-to-default countries), as there are many other qualitative factors present in the rating assessment that are not directly contemplated in financial ratios. 5.3. Model dataset distribution testing As it was outlined in the model implementation section 5.1., there exists a range of percentiles for a given rating notch. This means that companies with different percentiles but within the same range of percentiles for a given rating notch would be rated with the same letter. For instance, following the distribution of companies and percentiles provided by Refinitiv, a company which is ranked 41 would have a rating of BBB, but another company with score 47 will be rated BBB as well. For the telecommunications sector it was previously explained that the assignment of the global percentile from the rating letter was done by applying a random process. The randomness upon which a company global percentile is assigned was initially applied by using the following sample distribution:
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 113 Figure 33. In – sample distribution function for Telecommunication sector Source: Compiled by the author; Refinitiv. By way of simplification, it is assumed that the percentile distribution follows therefore a normal distribution function, so that the random expected dispersion within each rating notch has been applied following a normal distribution and a standard deviation according the above distribution. This makes sense following the historical distributions of rating letters given by the main CRAs (see, for instance, Hirk; 2020 27 , for further detail on rating letters historical distribution functions) which follow quasi-normal distribution as shown in Figure 33. The figure below illustrates the simulation process applied to every company’s score from the starting percentile level (the average for its corresponding agency rating). It has been performed by computing many random scenarios for each company based on a standard deviation upon a normally-distributed Brownian motions: 27 Hirk, R (2020): “Multivariate ordinal models in credit risk: Three essays”. Available on https://epub.wu.ac.at/7508/
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 114 Figure 34. Percentile dispersion simulation from Probability Density Function Figure 34: Percentile dispersion simulation calculated from its Probability Density Function Source: compiled by the author
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 115 It may be noted that, generally speaking, higher dispersion occurs in mid-to-lower quality notches (i.e., for scores at the beginning of the simulation below 60), with both the highest investment grades and highly speculative grades remaining almost unchanged, as expected according to the below rating migration matrix: Table 24: Average One-Year Alphanumeric Rating Migration Rates, 1983-2017 Source: Moody’s (2018); Compiled by the author. This is a testing process used to demonstrate that the random dispersion assumed among company scores is logical for modelling purposes. From\To Aaa Aa1 Aa2 Aa3 A1 A2 A3 Baa1 Baa2 Baa3 Ba1 Ba2 Ba3 B1 B2 B3 Caa1/2/3/ Default Aaa 91,08% 5,42% 2,38% 0,56% 0,28% 0,15% 0,02% 0,06% 0,00% 0,02% 0,01% 0,01% 0,00% 0,00% 0,00% 0,00% 0,00% Aa1 1,73% 80,96% 8,21% 6,10% 1,50% 0,94% 0,19% 0,13% 0,08% 0,01% 0,04% 0,00% 0,01% 0,04% 0,03% 0,01% 0,04% Aa2 1,06% 4,35% 78,22% 10,25% 3,59% 1,68% 0,40% 0,09% 0,16% 0,07% 0,03% 0,02% 0,00% 0,03% 0,01% 0,02% 0,02% Aa3 0,16% 1,05% 4,19% 80,75% 8,58% 3,66% 0,85% 0,24% 0,25% 0,13% 0,03% 0,03% 0,02% 0,01% 0,00% 0,00% 0,05% A1 0,05% 0,10% 1,01% 5,12% 81,14% 7,78% 2,88% 0,67% 0,48% 0,22% 0,19% 0,13% 0,05% 0,06% 0,02% 0,01% 0,10% A2 0,06% 0,03% 0,21% 1,06% 5,78% 80,62% 7,46% 2,67% 1,04% 0,39% 0,18% 0,14% 0,17% 0,06% 0,03% 0,01% 0,10% A3 0,05% 0,05% 0,10% 0,31% 1,58% 6,33% 79,96% 6,95% 2,81% 0,92% 0,38% 0,16% 0,13% 0,11% 0,04% 0,02% 0,12% Baa1 0,03% 0,03% 0,08% 0,12% 0,21% 1,68% 6,75% 79,62% 7,17% 2,44% 0,65% 0,36% 0,24% 0,28% 0,06% 0,04% 0,24% Baa2 0,04% 0,04% 0,02% 0,07% 0,18% 0,59% 2,05% 6,52% 80,39% 6,60% 1,41% 0,66% 0,47% 0,34% 0,20% 0,09% 0,32% Baa3 0,03% 0,01% 0,02% 0,04% 0,08% 0,18% 0,50% 1,93% 8,59% 78,66% 4,90% 2,17% 1,04% 0,74% 0,30% 0,25% 0,58% Ba1 0,02% 0,00% 0,02% 0,02% 0,16% 0,13% 0,22% 0,76% 2,58% 9,97% 73,05% 5,09% 4,27% 1,62% 0,64% 0,54% 0,93% Ba2 0,00% 0,00% 0,02% 0,03% 0,09% 0,12% 0,17% 0,39% 0,72% 3,81% 7,91% 72,37% 6,82% 3,80% 1,34% 0,95% 1,48% Ba3 0,00% 0,01% 0,01% 0,01% 0,07% 0,18% 0,18% 0,10% 0,47% 0,81% 2,85% 6,63% 73,52% 7,39% 3,24% 1,89% 2,64% B1 0,01% 0,01% 0,02% 0,01% 0,05% 0,03% 0,08% 0,10% 0,22% 0,32% 0,73% 2,88% 6,44% 73,96% 6,17% 4,45% 4,53% B2 0,00% 0,01% 0,00% 0,01% 0,02% 0,02% 0,10% 0,13% 0,14% 0,27% 0,21% 0,68% 2,06% 7,26% 71,83% 7,94% 9,32% B3 0,01% 0,00% 0,02% 0,00% 0,03% 0,03% 0,06% 0,03% 0,05% 0,11% 0,14% 0,22% 0,63% 2,27% 6,27% 71,56% 17,75% Caa1 0,00% 0,01% 0,00% 0,00% 0,00% 0,02% 0,00% 0,02% 0,00% 0,03% 0,07% 0,13% 0,22% 0,40% 1,35% 7,68% 90,08%
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 116 5.4. Back-testing Back-testing is performed to measure the accuracy and effectiveness of the model. In general, back testing is a technique to compare the model outcome based on historical data with the actual realization. As the model is not intensive in historical data depth but on the data quality, the backtesting is focused on two main techniques: Out-of-sample testing and Cross-validation. 5.4.1 Out-of-sample testing To test the predictive ability of the model, 3 companies belonging to the Telecommunication sector are randomly selected from different geographies, rating agencies and currencies, and with financial information cut-off date as of different years as well. This way we are testing the model by using several dimensions in data (i.e., several CRAs, years, currencies, and geographies in the same dataset). If the model is robust enough, it should ensure a certain level of accuracy when modeling the global percentiles of companies which are not in the initial model calibration dataset. Firstly, we calculate the financial ratios score for the three companies on the optimized GLS model regressors, for which optimal ratios are: PreTax Income/Sales; EBITDA/Assets, Net Margin; EBITDA/Interest Expense; Debt/Assets and Cash/Debt. The table below summarizes the information used to feed the model: Table 25: Out-of-sample tested companies and ratio percentiles for optimal regressors under GLS Source: Refinitiv (31/05/2022), compiled by the author Then, the optimized GLS model (Model B) is applied with the percentiles of the corresponding ratios for the three companies: Table 26: Optimal ratios and coefficients, GLS model Ratio percentile AIC-optimized coefficients under GLS PreTax Income / Sales 0,5860 EBITDA / Assets -0,1386 Net Margin -0,2057 EBITDA / Int. Expense 0,2409 Debt / Assets 0,2561 Cash / Debt 0,0912 Source: compiled by the author As can be seen below, the application of the model to those companies retrieves a good estimation power, particularly for Sunrise Communications and Telekom Malaysia, for which the model provides the same rating notch as estimation, whereas for Ooredoo QPSC there is a difference of 2 notches. Company Agency globalscale rating Agency Information Year PreTax Income / Sales EBITDA / Assets Net Margin EBITDA / Int. Expense Debt / Assets Cash / Debt Ooredoo QPSC AFitch Dec 2018 59 35 40 32 43 90 Sunrise Communications Group AG BBBS&P Dec 2020 20 44 25 69 40 41 Telekom Malaysia Bhd BBB+ Fitch Dec 2020 67 70 68 47 61 91 Percentiles
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 117 Table 27: Out-of-sample back-testing output Source: Refinitiv (31/05/2022), compiled by the author The relevant impact of the model accuracy is on the IFRS 9 and 13 output, which is the PD, for which the explanatory power is relatively high for the 5Y PD estimation. 5.4.2 Cross-validation process We have already seen that the model replicates in a relevant way the actual rating letter for a significant set of companies. Likewise, the model has demonstrated a robust predictive power for some out-of-sample companies. Now, it is needed to test the model accuracy with a combination of in-sample and out-of-sample companies, by randomly changing the dataset used to calibrate it. This way the performance and predictive power of the model is tested by altering the sample with multiple variations, sizes, and combinations of different subsets of inputs, i.e., by implementing cross-validation or resampling methods. The fundamental principle behind these cross-validation techniques consists of dividing the data into two sets: - the training set: used to train (i.e., build) the model. - the testing set (or validation set): used to test (i.e., validate) the model by estimating the prediction error on the general percentile with a sample of the entire company population used initially. Company Agency globalscale rating Agency Model Percentile Model Rating Diff. Notches Agency ratingimplied 5Y PD (%) Model ratingimplied 5Y PD (%) Diff. (%) Ooredoo QPSC AFitch 48,29 BBB+ 2 4,13 4,89 0,75 Sunrise Communications Group AG BBBS&P 31,01 BBB0 8,65 8,65 0,00 Telekom Malaysia Bhd BBB+ Fitch 50,62 BBB+ 0 4,89 4,89 0,00 Model Output and differences
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 118 Figure 35. Example on how cross-validation technique works by resampling the model input data Source: Moody’s (2011) Three main methods are used for cross-validating the model performance to assess its predictive power: - Leave One Out - Cross Validation: LOOCV - Bootstrapping - Repeated K-Folds The main outputs to be analyzed from these methods are the following: - The R-squared (R2), representing the squared correlation between the observed outcome values and the values predicted by the model. The higher the adjusted R2, the better the model. - Root Mean Squared Error (RMSE) which measures the average prediction error made by the model in predicting the outcome for an observation. That is, the average difference between the observed known outcome values and the values predicted by the model. The lower the RMSE, the better the model. RMSE=√∑ (𝑦𝑖− 𝑦𝑖)2 𝑛 𝑖=1 𝑛 - Mean Absolute Error (MAE) which is an alternative to the RMSE that is less sensitive to outliers. It corresponds to the average absolute difference between observed and predicted outcomes. The lower the MAE, the better the model. (70)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 119 MAE =∑ |𝑦𝑖− 𝑦𝑖| 𝑛 𝑖=1 𝑛 In the above equations, 𝑦𝑖 denotes the ith observation in the sample where 𝑦𝑖 denotes the ith prediction of the model and n is the number of observations/predictions. In order to prevent any possible overfitting, it is assessed whether there is considerable difference between the prediction errors of training data and the prediction errors of test data for each validation subset, as well as the average error results for all of the subset assessed. Although the initial model output is the company global score, the goal of the model is to predict the PD to be used in the IFRS framework. Therefore, the accuracy of the model will be measured in terms of 5Y PD, so that we can ensure the accuracy of the output to be used in as an input for ECL or CVA figures. Regarding the techniques used to test the model estimation power, they have been implemented in the following way: - LOOCV: the sample is split into two sections, one of n-1 data points which is used to reproduce a regression for predicting the value of the remaining data points, for each of which a regression of n-1 is calibrated. Also, the LOOCV has been implemented under a Stepwise AIC optimization approach, for which I leave the process to select from 1 to 7 maximum number of variables, so that there will be three dimensions of randomness: type of regressor, number of regressors and degrees of freedom. The output averages are the following: • RMSE: 0.03411986 • R2: 0.7281695 • MAE: 0.02076997 with an optimal number of variables = 5. - Bootstrapping: this method randomly selects a sample of n observations from the original data set. This subset is then used to evaluate the model. In this case, the sampling is performed with replacement, which means that the same observation can occur more than once in the bootstrap data set. It has been also performed with Stepwise AIC. This provides the advantage of having a large number of potential subsets to simulate data samples. 1,000 scenarios are simulated with the following average output: • RMSE: 0.03186692 • R2: 0.7972403 • MAE: 0.01903913 (71)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 120 Figure 36. Residuals fitting for Bootstrap resampling on Predicted 5Y Probability of Default Source: compiled by the author - Repeated K-folds: this method divides the data into k buckets of almost equal size. Of these k folds, one is used as a validation set while the others are involved in calibrating the regression. In this regard, 1,000 regression folds are simulated so as to be able to generate sufficient prediction scenarios, in order to confirm whether the model’s predictive power is robust enough. This method can be considered less unbiased than the above since it uses random data for both regression subsamples, including thousands of combinations of training and validation data sets. For a K-fold implementation with the sample divided into 10 buckets, the average output for the Stepwise AIC-based k-fold is as follows: • RMSE: 0.02669951 • R2: 0.8835198 • MAE: 0.01684332 Figure 37. Residuals fitting for Repeated K-Folds on Predicted 5Y Probability of Default Source: compiled by the author
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 127 depending on the state of the economy. This also includes geographical issues. In short, the LGDs assumed for a given issuer/issuance may vary throughout time (EBA 28 , 2017). 5. Secured debt is less sensitive to the default risk and to the general state of the economy than unsecured debt. This applies to the majority of the different classes of assets and represents the pivotal point of the models introduced. More specifically, issuances with more liquid collaterals behind them are expected to have higher recovery rates than those with less liquid collaterals (Benmelech and Bergman, 2009; Cerquerio et al., 2016, Duo and Meder, 2020; Lara-Rubio et al., 2016; Matias and Dias, 2015, Moody’s, 2018). 6. Fixed income and credit markets are assumed to be the most reliable sources of information, including updates in every risk factor used. The relationship between LGDs, YTMs and default risk is understood through market instruments (Schonbucher, 2003). 7. The model does not cover lease contract liquidity and sovereign risk, as explained in the following subsections. 6.3. Bond price-based model: Methodology, model theory development and implementation The first modelling proposal is based on the pricing of traded debt instruments issued by the lessee (or similar peers in terms of rating and sector) following a default-tree model. A binomial tree can be constructed in order to calculate the debt instrument’s value at each tree node 29 , taking into account the conditional default probabilities [𝑆𝑃𝑖−𝑆𝑃𝑖−1] existing at each node 𝑖. Namely, Figure 38. Default-tree model algorithm Source: compiled by the author 28 EBA: European Banking Authority. 29 See, for instance, Castagna, A., and Fede, F. (2013).
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 128 where 𝐶𝐹(𝑡𝑖−1,𝑡𝑖) is the risk-free cash-flow to be paid by the instrument; 𝑆𝑃(0,𝑡𝑖) is the survival probability of the product between 𝑡0 and 𝑡𝑖; 1−𝑆𝑃(0,𝑡𝑖) is the default probability for the same period; and RR (𝑡𝑖−1,𝑡𝑖) is the estimated recovery rate of the debt instrument for each period. This tree shows that bonds payments have a survival probability at each node 𝑡𝑖, but they are complemented with their default probability at the same node, where the payment value will be the only estimated recovery. That is to say, at every node 𝑡𝑖 a default event may occur, or the obligor will continue until the next date 𝑡𝑖+1. Following default, the non-defaulted path continues (indicated by the upper continuation of the tree), but the defaulted security only earns, for a certain node, its recovery payoff and ceases to exist from there on (represented by dashed lines). The sum of the payment scenarios (indicated by red dots), weighted by the probability of their occurrence, is equal to the instrument fair value. The aforementioned also means that the probabilities attached to the branches of the tree are only the conditional default and survival probabilities at this node as seen from t = valuation date. Therefore, under the above model, the defaultable debt instrument price is as follows: where 𝐶𝐹 is the default-free cash flow at each node i, and 𝑃(0,𝑡𝑖) is the risk-free discount factor. We can assume (given the objective of the model) that default event (hazard) rates 𝜆𝑡𝑖 for different predefined time intervals [ti-1; ti] of the instrument life are deterministic and constant, so that the instrument survival probability between each time interval is: 𝑆𝑃[0,𝑡𝑖]=𝑒(−𝜆𝑡𝑖) Hence, if we already know the market price (fair value) of the product and the recovery rate linked to its seniority, we can carry out an initial calibration of the factor 𝜆 to the instrument market price. This is the market price (fair value) as shown in (72). Once the hazard rate has been calibrated, then all the risk factors of this model have been defined: 𝐵𝑜𝑛𝑑 𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒=𝑓[𝐶𝐹,𝜆,𝑅𝑅, 𝑃(0,𝑡𝑖)]. Therefore, we can analyze the sensitivity of the price to the recovery rate as follows: - We already possess a bond’s market price with the implied hazard rate, and we will assume that the hazard rates are constant, and therefore 𝑆𝑃 only increases over time. - Once the default-tree has been constructed, the initial recovery rate RR may be changed to the chosen recovery rate estimated upon the collateral backing the leasing contract. - Hence, this change in the RR implies a change in the bond price and, therefore, in the bond price sensitivity to the Recovery Rate, assuming that there is no immediate (73) (72)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 129 correlation between Recovery Rates and probability of default (although it does exist in the long-term). - The price change can be translated into the Yield-to-Maturity or curve change, following the general framework of bond pricing: 𝐵𝑜𝑛𝑑 𝑚𝑎𝑟𝑘𝑒𝑡 𝑣𝑎𝑙𝑢𝑒= ∑𝐶𝐹𝑡𝑖 𝐵(0,𝑡𝑖) 𝑛 𝑖=1 where 𝐵(0,𝑡𝑖)= 1 (1+𝑌𝑇𝑀)𝑡𝑖 The new bond price will be given by 𝑓[𝐶𝐹,𝜆,𝑅𝑅(𝑛𝑒𝑤), 𝑃(0,𝑡𝑖)] following (74), and subsequently the implied change in the Yield-to-Maturity (∆𝑌𝑇𝑀) will be obtained by calibrating the YTM to the new bond price, following (72) and (73). 6.3.1 Default tree implementation example Our scenario assumes a senior unsecured bond corresponding to a certain issuer that matures in 2025. We know that today’s bond market mid-price is 99.50%, paying a semiannual coupon of 3% with bullet amortization. The coupon payments will be made on every 30th September and every 31st March, and the valuation date is 30/09/2021. The nodes of the tree correspond to the payment times, for simplification purposes. 𝑃[0,𝑡𝑖] will be constructed by using the €STR curve as of the valuation date. Assuming that the recovery rate for the bonds is 40%, the default tree can be constructed as of 30/09/2021, while the hazard rate required to obtain the bond market price (99.50%) must be calibrated, following (72) and (73), against the market price. Calibrating 𝜆𝑖 results in an implied hazard rate of 6.0875%, and the final tree would be as follows: Table 32: Default tree scenarios and bond Net Present Value for a standard RR = 40% Tree scenarios Cash-flows NPV Scenario probability conditional to 𝝀𝒊 default 31/03/2022 40.27% 3.031% default 30/09/2022 41.90% 2.955% default 30/03/2023 43.54% 2.834% default 30/09/2023 45.17% 2.793% default 30/03/2024 46.81% 2.679% default 30/09/2024 48.44% 2.626% default 30/03/2025 50.07% 2.504% default 30/09/2025 51.68% 2.469% no default 30/09/2025 114.57% 78.110% Bond market value 99.50% Source: compiled by the author (74)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 130 As a result, we obtain the bond market price which has been computed from the tree by using its corresponding recovery rate (40%) and by calibrating its implied hazard rate. Table 32 above represents the value of each tree branch and its probability occurrence, in line with Figure 38 and (72). For instance, the first default node has a cash-flow NPV of 40.27% (40% of notional recovery * risk-free discount factor), with a default probability of 3.031% (1− 𝑆𝑃[0,𝑡1]). The second node works in the same way, and now includes the first coupon previously received at 31/03/2022 plus the recovery rate of the notional to be received at the next default date scenario (30/09/2022), all risk-free discounted and weighted by its conditional default probability of 2.955% (𝑆𝑃[0,𝑡2]−𝑆𝑃[0,𝑡1]). The rest of the defaulting branches represent the same scenario (i.e., cash-flows received until default plus the notional recovery rate at default date, all risk-free discounted and weighted by their conditional probability rate). The final node represents the survival scenario, where no Recovery Rate occurs, and only the total cash-flows, including notional, are risk-free discounted, as shown in (72). In order to assess the sensitivity of the bond price to the recovery rate, only a change in the recovery rate of the tree is required. For instance, assuming the bond has a recovery rate of 50%, then the tree would return the following figures: Table 33: Default tree scenarios and bond Net Present Value for a new RR = 50%. Tree scenarios Cash-flows NPV Scenario probability conditional to 𝝀𝒊 default 31/03/2022 50.34% 3.031% default 30/09/2022 52.00% 2.955% default 30/03/2023 53.66% 2.834% default 30/09/2023 55.31% 2.793% default 30/03/2024 56.98% 2.679% default 30/09/2024 58.63% 2.626% default 30/03/2025 60.28% 2.504% default 30/09/2025 61.90% 2.469% no default 30/09/2025 114.57% 78.110% Bond market value 101.72% Source: compiled by the author As can be seen, the net present value for any single branch of the tree has increased, given the higher expected recovery rate, whereas the default and no default probability for each branch remain constant (the bond seniority and the issuer are the same). As previously mentioned, in the case that the objective of the model implementation is to assess the change in the instrument YTM, then firstly the original bond YTM should be computed. In this specific situation, the original bond market price (99.50%) provides a YTM of 3.1563%. With the new bond market price (101.72%), the corresponding YTM is 2.5668%, meaning that the change in YTM or ΔYTM = -0.5895%. This is a practical example to show how the model works, providing information on the change in the YTM resulting from a shift in the Recovery Rate of a given asset, which is precisely the main objective of this study with regard to IBR computation for leased assets. That is to say, the change arising in an instrument’s YTM following a change in the Recovery Rate can be
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 131 applied to the IBR of a leased asset with similar issuer/borrower (in this case, the lessee) rating, and maturity. This will be applied to an entire set of bonds with liquid prices in turn to test the model performance. 6.3.2 Specific aspects of leasing contracts In terms of leasing contracts and IBR estimation, many companies do not have credit ratings nor liquid bonds issued in order to estimate the standard IBR (Step 1 as explained in Section 6.1). If a company is not able to estimate the standard IBR, then it cannot calculate the change in the standard IBR if said IBR is applied to a different recovery rate (Step 2 in Section 6.1). In these cases, the most frequent solution is to estimate a theoretical credit rating for the issuer and to use sectorial bond prices or yield curves from comparable issuers (with a similar rating and maturity). Therefore, it is critical to use a model that provides a consistent rating for the lessee. In this regard, the proposed model in Chapter 5 covers this issue in a relevant extent. By way of example, a leasing contract for which the IBR must be estimated has machinery as the underlying asset (the collateral). The lessee has been estimated to have a BB rating and belongs to the “basic materials” sector. The company has no liquid bonds nor similar debt instruments quoted on the market. First of all, a standard IBR curve is required, representing the company credit risk. Bloomberg and Refinitiv provide liquid indexed yield curves for many sectors and geographies. In this case, for the Basic Materials sector, the BB yield curve provided by Refinitiv (RIC 0#BBEURMATBMK=) is as follows: Figure 39. Basic Materials sector, BB-rated standard YTM curve (%), 30/09/21 Source: Refinitiv The company’s leasing contract matures in 5 years (September 2026), and therefore the YTM (IBR) required pertaining to liquid bonds maturing in 5 years is approximately 1.10%. The recovery rate for these bonds is assumed to be 40% (since they are senior, unsecured vanilla bonds), and the average mid-price is 106.81%, paying an average coupon of 2.587%. for that maturity. See next table for further information on the Refinitiv curve constituents: 0,00 0,20 0,40 0,60 0,80 1,00 1,20 3M 6M 1Y 2Y 3Y 4Y 5Y 6Y 7Y
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 132 Table 34: Basic Materials sector, BB-rated YTM curve bond constituents, 30/09/21 Issuer Name Coupon (%) Maturity Bid Ask Swap Spread Asset Swap ISIN SEALED AIR 4.50 15/09/2023 107.259 107.674 70.5 76.1 XS1247796185 BALL 4.38 15/12/2023 109.331 109.630 56.8 58.6 XS1330978567 BALL 0.88 15/03/2024 101.109 101.488 79.7 77.6 XS2080317832 WIENERBERGER 2.00 02/05/2024 104.672 105.073 57.9 58.7 AT0000A20F93 CROWN EURO 2.63 30/09/2024 104.957 105.412 102.7 103.8 XS1490137418 TITAN GLOBAL 2.38 16/11/2024 103.413 104.413 145.6 144.8 XS1716212243 CROWN EURO 3.38 15/05/2025 107.745 108.007 121.2 125.4 XS1227287221 WIENERBERGER 2.75 04/06/2025 107.516 108.216 86.4 89.7 AT0000A2GLA0 METINVEST 5.63 17/06/2025 105.889 107.389 415.4 420.7 XS2056722734 CROWN EURO 2.88 01/02/2026 106.750 107.121 137.8 141.1 XS1758723883 SYNGENTA FIN 3.38 16/04/2026 109.834 110.162 129.8 135.3 XS2154325489 BALL 1.50 15/03/2027 102.486 104.486 121.2 120.5 XS2080318053 TITAN GLOBAL 2.75 09/07/2027 105.955 106.827 178.3 179.9 XS2199268470 SYNGENTA FIN 1.25 10/09/2027 101.021 101.425 122.9 121.7 XS1199954691 ASHLAND SVC 2.00 30/01/2028 104.183 104.690 142.5 143.3 XS2103218538 VERALLIA 1.63 14/05/2028 103.490 103.966 117.9 118.3 FR0014003G27 Source: Refinitiv Using this information, we are able to calibrate a default-tree similar to the one shown in Table 32, obtaining an implied hazard rate of 2.7365% and with the tree already prepared for a shift in the recovery rate. As previously stated, the leased asset (used as collateral) is a machinery-type asset. Based on historical data from Hartmann-Wendels et al. (2014) seen in Table 31, this asset has a recovery rate of approximately 50.91%. Therefore, all that is required is a shift from 40% to 50.91% to be made in the Recovery Rate used in the tree and, as a result, the new bond price would be 108.25%, meaning a ΔYTM = -0.1789% or -17.89 basis points, thus decreasing from the original YTM (1.10%) to the new lower YTM (0.9211%). This change could hence be applied proportionally to all available, liquid maturities of the standard YTM curve for a given sector and rating in order to make the adjustment required, thereby resulting in a new YTM curve adapted to the required recovery rate. Figure below simulates this shift from the original YTM curve to the new curve adapted to the machinery recovery rate, for all available maturities:
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 133 Figure 40. Basic Materials sector, BB-rated standard and shifted YTM curves, 30/09/2021 Source: Refinitiv and Compiled by the author 6.3.3 A practical example I have performed several analyses using quoted bonds, applying the model by using prices of bonds issued by companies that maintain quoted bonds with different recovery rates. The starting YTM used is the one belonging to the senior unsecured bond, and subsequently we analyze whether it correctly predicts the change in YTM for a similar bond in terms of contractual features but with a different recovery rate. The bonds contractual data (duration, currency, coupon frequency and type, market conventions, etc.) pertaining to each of the issuers must be similar enough for them to be comparable, thus permitting the main driver behind the differences seen in their YTMs and credit spreads to be their implied LGD (or implicitly, the Recovery Rate), due to the difference in the credit tranche. In order to illustrate the assessment of the model, two isolated use cases have been performed (which have been subsequently extended to a wider sample). The first test has been carried out using quoted bonds issued by BBVA (BBVA.MC). I selected three bonds which were highly similar to each other in terms of issuer, currency and duration, but which belonged to different seniority tranches: Table 35: Several outstanding bonds for BBVA, SA, for several seniority tranches, 30/09/21 Issuer ISIN Maturity Coupon Currency Seniority Issuance Rating Implied Recovery Rate BBVA, SA XS2013745703 21/06/2026 1.000% EUR Senior Unsecured BBB+ (FTC) 40% BBVA, SA ES0413211915 22/11/2026 0.875% EUR Senior Secured (Covered Bond) Aa1 (Moody's) 65% BBVA, SA XS1562614831 10/02/2027 3.500% EUR Subordinated Unsecured Baa2 (Moody's) 30% Source: Refinitiv In this case, we have a standard bond (Sr. Unsecured) with an implied market recovery rate of 40%. Furthermore, BBVA has issued other bonds with similar maturity and currency but belonging to the Senior Secured and Subordinated Unsecured tranches, with recovery rates of 0,00% 0,20% 0,40% 0,60% 0,80% 1,00% 1,20% 3M 6M 1Y 2Y 3Y 4Y 5Y 6Y 7Y YTM w/ RR = 40% YTM w/ RR = 50.91%
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 134 approximately 65% and 30% respectively, in line with historical data from Moody’s (Table 28 and Table 29). If we use the proposed default-tree model and simulate the impact on the YTM by changing the original recovery rate as per the Sr. Unsecured note by the recoveries for the other tranches, we obtain the results shown in the table below: Table 36: Several outstanding bonds for BBVA, SA, for several seniority tranches, and model outputs, 30/09/2021 Issuer ISIN Maturity Coupon Currency Seniority Issuance Rating Implied Recovery Rate Market Price Model Price Actual YTM Actual ΔYTM (from Sr. Unsec. Bond) Model YTM Model ΔYTM (from Sr. Unsec. Bond) BBVA, SA XS2013745703 21/06/2026 1.000% EUR Senior Unsecured BBB+ 40% 104.30% 104.30% 0.0795% 0.0795% BBVA, SA ES0413211915 22/11/2026 0.875% EUR Senior Secured (Covered Bond) Aa1 65% 105.50% 105.50% -0.1980% -0.2775% -0.1650% -0.2445% BBVA, SA XS1562614831 10/02/2027 3.500% EUR Subordinated Unsecured Baa2 30% 115.71% 115.71% 0.5030% +0.4235% +0.4709% +0.3914% Source: Refinitiv and Compiled by the author As it can be seen, we obtain similar results when comparing the actual YTM for any single bond with the YTM obtained when replacing the original Sr. Unsecured bond recovery rate in the default-tree model (40%) by the corresponding recoveries for the covered bond and the subordinated, unsecured note. This effect can be seen in the case of CaixaBank (CABK.MC), for example. In the table below three outstanding bonds with similar contractual details have been taken, with seniority constituting the sole notable difference between them: Table 37: Several outstanding bonds for CaixaBank, for several seniority tranches, 30/09/2021 Issuer ISIN Maturity Coupon Currency Seniority Issuance Rating Implied Recovery Rate CaixaBank ES0213307053 09/07/2026 0.750% EUR Senior Unsecured A- (FTC) 40% CaixaBank XS2013574038 19/06/2026 1.375% EUR Senior Non-Preferred BBB+ (FTC) 35% CaixaBank ES0440609339 11/01/2027 1.250% EUR Senior Secured (Covered bond) AAA (FTC) 65% Source: Refinitiv The results when shifting the recovery rate in the default-tree model from 40% to 35% and 65% achieve a change in the YTM similar to those directly seen in the quoted YTMs:
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 135 Table 38: Several outstanding bonds for CaixaBank, for several seniority tranches, and model outputs, 30/09/21 Issuer ISIN Maturity Coupon Currency Seniority Issuance Rating Implied Recovery Rate Market Price Model Price Actual YTM Actual ΔYTM (from Sr. Unsec. Bond) Model YTM Model ΔYTM (from Sr. Unsec. Bond) CaixaBank ES0213307053 09/07/2026 0.750% EUR Senior Unsecured A40% 102.81% 102.81% 0.1290% 0.1235% CaixaBank XS2013574038 19/06/2026 1.375% EUR Senior NonPreferred BBB+ 35% 104.83% 104.83% 0.2910% +0.1620% 0.2539% +0.1304% CaixaBank ES0440609339 11/01/2027 1.250% EUR Senior Secured AAA 65% 107.28% 107.28% -0.1724% -0.3014% -0.1451% -0.2685% Source: Refinitiv, compiled by the author 6.3.4 Model implementation and Performance measurement In order to assess the robustness of the model along with its predictive power, the above analysis is done for a sample of outstanding bonds issued in EUR, USD and GBP. I extensively researched Refinitiv to locate issuers that have issued more than one bond with different estimated recovery rates (belonging to different seniority tranches) but issued in the same currency, with similar duration and paying a similar coupon. In other words, the bonds under analysis would be so similar in nature that the main explanatory variable for the gap between their YTMs would have to be the seniority tranche. This is necessary in order to analyze whether the model correctly predicts the change in YTM when a change in recovery rate occurs. A sample with outstanding bonds from the world’s principal bond markets is constructed. Table 39 shows the number of bonds initially included in the sample by exchange market. Only fixed rate bonds are included, issued by corporates or financial institutions, with maturity dates between 2026 and 2040. For this reason (i.e., the fact that we can only use issuers that have issued more than one bond with different estimated recovery rates), several bond markets with hundreds of potential bonds have been analyzed, so that to build a database with sufficient bonds to test model outputs. For the most part, the potential population of quoted bonds is expected to be highly limited and to belong to financial entities. More specifically, using a manual selection process, 91 bonds issued by 43 issuers (Table 40) are used, all of which complied with the criteria of same issuer, maturity year and different debt seniority (unsecured vs. subordinated/nonpreferred/mortgage/secured).
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 136 Table 39: number of bonds initially included in the sample by exchange market Exchange Bonds Deutsche Boerse AG 2,853 Dublin 1,380 Euronext.liffe Paris 771 London 1,264 Luxembourg 1,927 NYSE 3,191 Singapore 596 Vienna Stock Exchange 341 TOTAL 12,323 Source: Compiled by the author Table 40: Bonds used for model testing, 30/09/2021 Bond Maturity Seniority ISIN Coupon (%) Mod. Duration Bayerische Landesbank 2016 1.4% 29/06/29 2029 Senior Unsecured DE000BLB32E3 1.4 7.3428 Bayerische Landesbank 2018 1 3/4% 17/10/28 2028 Subordinated Unsecured DE000BLB6TV4 1.75 6.5154 Dekabank Deutsche Girozentrale 2018 1.33% 25/01/30 2030 Senior Unsecured DE000DK0PDR8 1.33 7.8796 Dekabank Deutsche Girozentrale 2020 1 1/4% 01/04/30 2030 Senior NonPreferred DE000DK0T1B2 1.25 8.0626 Dekabank Deutsche Girozentrale 2020 1.1% 25/11/30 2030 Subordinated Unsecured DE000DK0T2A2 1.1 8.6042 Deutsche Bank AG 2011 4 1/4% 14/09/26 2026 Senior Unsecured DE000DB7XNA3 4.25 4.5877 Deutsche Bank AG 2016 4.2% 15/06/26 2026 Subordinated Unsecured DE000DL19S19 4.2 4.209 Aareal Bank AG 2018 0.8% 05/09/28 2028 Mortgage DE000A2E4CE8 0.8 6.8061 Aareal Bank AG 2019 0.87% 28/06/29 2029 Senior NonPreferred DE000A2E4CV2 0.87 7.4798 ABN Amro Bank NV 2016 1% 13/04/31 CBB16 2031 Senior Secured XS1394791492 1 9.1608 ABN Amro Bank NV 2021 1% 02/06/33 Regulation S 2033 Senior NonPreferred XS2348638433 1 10.9892 Altice Financing SA 2021 4 1/4% 15/08/29 Regulation S 2029 Senior Secured XS2373430425 4.25 6.6425 Altice France Holding 2020 4% 15/02/28 Regulation S 2028 Senior Unsecured XS2138140798 4 5.5535 Argentum Capital SA 2019 2.1% 19/01/26 2026 Senior Secured XS1947921075 2.1 4.0979 Argentum Capital SA 2020 1.7% 27/01/27 2027 Senior Unsecured XS2090803466 1.7 5.0289 Bayerische Landesbank 2016 1/2% 24/03/26 2026 Mortgage DE000BLB3Z54 0.5 4.4736 Bayerische Landesbank 2017 0.55% 09/08/27 2027 Senior Unsecured DE000BLB43N1 0.55 3.3615 Banque Nationale de Paris Paribas SA 2016 2 1/4% 11/01/27 Regulation S 2027 Subordinated Unsecured XS1470601656 2.25 4.9962 Banque Nationale de Paris Paribas SA 2018 1 1/8% 11/06/26 Regulation S 2026 Senior NonPreferred XS1748456974 1,125 4.6158 Commerzbank AG 2018 7/8% 06/06/28 2028 Mortgage DE000CZ40MV5 0.875 6.542 Commerzbank AG 2019 0.85% 15/08/29 2029 Senior NonPreferred DE000CZ40N95 0.85 7.6003 Deutsche Bank AG 2015 1 3/4% 09/04/35 2035 Senior Unsecured DE000DB7XLM2 1.75 11.9416 Deutsche Bank AG 2018 1.405% 04/11/33 2033 Mortgage DE000DL19T91 1,405 11.165 DZ Bank AG Deutsche 2016 0.67% 18/05/27 2027 Senior Secured DE000DG4T8R7 0.67 5.5727 DZ Bank AG Deutsche 2017 0.725% 21/06/27 2027 Senior Unsecured DE000DG4UAZ5 0.725 5.6353
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 143 Figure 48. Residuals fitting for Repeated K-Folds on Predicted ΔYTM, 30/09/2021 Source: Compiled by the author Excluding the outliers, the values are: - RMSE: 0.00170 - R2: 0.93541 - MAE: 0.00138 Figure 49. Residuals fitting for Repeated K-Folds on Predicted ΔYTM, without outliers, 30/09/2021 Source: Compiled by the author As shown above, the cross-validation process has provided with robust results. This means that, using many different samples in terms of components and size, the model is robust enough, so that the explanatory variables chosen in the optimization process are representative for a good estimation power with the current input dataset.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 144 6.4. CDS price-based model: Methodology, model theory development and implementation In the proposed model, we analyze the sensitivity of a credit-linked instrument in relation to the recovery rate. CDS prices are used, with the default probability embedded in a CDS price, and the CDS spread sensitivity to changes in the expected recovery rate. The theory is similar to the one presented for the Bond-price model in section 6.3, in the sense that we measure the sensitivity of a fixed-income product price to changes made to the Recovery Rate. However, in this case we will propose using quoted CDS spreads as a metric directly providing the change in the YTM. In this context, we firstly need to understand the model framework for standard CDS pricing. 6.4.1 CDS pricing framework A standard CDS is a contract in which one counterparty (the protection buyer) pays a regular fee (the CDS spread), while the other counterparty (the protection seller) must pay a default payment if a credit event occurs with respect to a reference entity. The default payment is designed to approximate the loss that the holder of a bond issued by the reference entity would suffer at the default event. Therefore, it is necessary to calculate the default event’s probability of occurrence by using a specific distribution function (Harb and Louhichi, 2017). Default event models, just like many other models used to infer occurrence probability, may be understood to follow an intensity-based process N: an event probability with an occurrence rate 𝜆 for a time period (𝑇 – 𝑡)=Δt. That is, 𝑃[N(𝑡+Δ𝑡)−N(𝑡)=1]=𝜆Δt so that 𝑃[N(𝑡+Δ𝑡)−N(𝑡)=0]=1−𝜆Δt We subdivide the interval [t, T] into n subintervals of length Δt = (𝑇 – 𝑡). In each of these subintervals, the process N has a jump with probability 𝜆Δt. If we conduct n independent binomial experiments, each with a probability of 𝜆Δt for a “jump” outcome, the probability of no jump at all in [t, T] is given by 𝑃[N(𝑇)=N(𝑡)]=(1−𝜆Δt)𝑛=(1−1 𝑛𝜆(𝑇−𝑡))𝑛 And since (1−𝑥 𝑛)𝑛→ 𝑒𝑥 if 𝑛→∞, this converges to a Poisson process with no event between each subinterval n: 𝑃[N(𝑇)=N(𝑡)]=𝑒(−𝜆(𝑇−𝑡)) (75) (76) (77) (78)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 145 Translated into default probabilities, and considering different occurrence (hazard) rates 𝜆𝑖 for different predefined time intervals [𝑡𝑖−𝑗,𝑡𝑖] of the instrument life, the instrument survival probability between t and t + Δt is 𝑆𝑃[𝑡,𝑡 + Δ𝑡 ]=𝑒(−𝜆𝑖Δ𝑡) and therefore, the cumulative PD in the same context will be 𝑃𝐷[𝑡,𝑡 + Δ𝑡 ]=1−𝑒(−𝜆𝑖Δ𝑡)=1−𝑆𝑃[𝑡,𝑡 + Δ𝑡 ] If we assume that there exist different hazard rates for different time intervals, we will obtain a discretized distribution of hazard rates for each time interval as follows: 𝐻𝑎𝑧𝑎𝑟𝑑 𝑟𝑎𝑡𝑒Δ𝑡𝑖= { 𝜆1, 𝑖𝑓 Δ𝑡𝑖∈[0,𝑡1) 𝜆2, 𝑖𝑓 Δ𝑡𝑖∈[𝑡1,𝑡2) 𝜆3, 𝑖𝑓 Δ𝑡𝑖∈[𝑡2,𝑡3) ⋮ ⋮ 𝜆𝑇, 𝑖𝑓 Δ𝑡𝑖∈[𝑡𝑇−1,𝑡𝑇) From this we will obtain the Survival Probability Curve (SPC), i.e., the cumulative survival rate to be used in the CDS pricing framework: 𝑆𝑃𝐶0,𝑇= { 𝑆𝑃[0,𝑡1)=𝑒−𝜆1Δ𝑡1, 𝑖𝑓 𝑇∈[0,𝑡1) 𝑆𝑃[0,𝑡2)=𝑒−𝜆1Δ𝑡1−𝜆2Δ𝑡2, 𝑖𝑓 𝑇∈[0,𝑡2) 𝑆𝑃[0,𝑡3)=𝑒−𝜆1Δ𝑡1−𝜆2Δ𝑡2−𝜆3Δ𝑡3, 𝑖𝑓 𝑇∈[0,𝑡3) ⋮ ⋮ 𝑆𝑃[0,𝑡𝑇)=𝑒−𝜆1Δ𝑡1−𝜆2Δ𝑡2−𝜆3Δ𝑡3−⋯−𝜆𝑇−1Δ𝑇−1−𝜆𝑇Δ𝑇 𝑖𝑓 𝑇∈[0,𝑡𝑇) where 𝛥𝑡𝑖 is the time interval for each 𝜆𝑖. Returning to the CDS note pricing, the protection buyer pays the CDS spread as an insurance fee in order to hedge the potential default of a reference entity. This implies therefore that the protection buyer pays the CDS related to said reference entity over a predefined period of time. The present value of the protection “leg” – assuming that the potential default events occur between every two payment dates – is estimated as follows in (83) and (84) below: 𝑃𝑟𝑜𝑡.𝐿𝑒𝑔=𝑁·𝑆𝑝𝑟𝑒𝑎𝑑· ∆𝑡∑ 𝑆𝑃[0,𝑡𝑖] 𝑃(0,𝑡𝑖) +12 𝑇 𝑖=1 [𝑆𝑃[0,𝑡𝑖−1]−𝑆𝑃[0,𝑡𝑖]] 𝑃(0,(𝑡𝑖−1+𝑡𝑖)2 ⁄) where 𝑁 is the contract notional; 𝑆𝑝𝑟𝑒𝑎𝑑 is the spread of the CDS for the predefined period of time (maturity) 𝑖; 𝑆𝑃[0,𝑡𝑖] is the cumulative survival probability at each payment time, with the particularity that each payment time will have different hazard rates. In other words, the CDS is modeled with as many different hazard rates as payment nodes. This implies that the survival probability curve gains convexity and adapts each payment interval to the expected default probability that exists within it. Conversely, the default leg is expected to be as follows: (83) (79) (80) (81) (82)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 146 𝐷𝑒𝑓𝑎𝑢𝑙𝑡 𝑙𝑒𝑔=𝑁 (1−𝑅)∑[𝑆𝑃[0,𝑡𝑖−1]−𝑆𝑃[0,𝑡𝑖]] 𝑇 𝑖=1 𝑃(0,(𝑡𝑖−1+𝑡𝑖)2 ⁄) with 𝑆𝑃[0,𝑡𝑖−1]−𝑆𝑃[0,𝑡𝑖] representing the conditional probability in the CDS life-time filtration that the default time of the entity underlying the CDS will occur in the middle of the interval (𝑡𝑖−1, 𝑡𝑖] (given survival until 𝑡𝑖−1); and where 𝑅 is the recovery rate, assumed constant for the entire CDS extension. Therefore, the CDS price at any point in time will be the difference between the two legs (from the protection buyer’s point of view): 𝐶𝐷𝑆 𝑝𝑟𝑖𝑐𝑒= 𝐷𝑒𝑓𝑎𝑢𝑙𝑡 𝑙𝑒𝑔−𝑃𝑟𝑜𝑡𝑒𝑐𝑡𝑖𝑜𝑛 𝑙𝑒𝑔 The CDS is usually priced at par at inception, meaning that 𝐷𝑒𝑓𝑎𝑢𝑙𝑡 𝑙𝑒𝑔=𝑃𝑟𝑜𝑡𝑒𝑐𝑡𝑖𝑜𝑛 𝑙𝑒𝑔 𝑖𝑓 𝑡=0 with a spread that makes the protection leg equal to the default leg. Hence, if we solve for the equilibrium spread, leaving the notional out of this scope, the aforementioned equation becomes the following: 𝑆𝑝𝑟𝑒𝑎𝑑=(1−𝑅)∑[𝑆𝑃[0,𝑡𝑖−1]−𝑆𝑃[0,𝑡𝑖]] 𝑇 𝑖=1 𝑃(0,(𝑡𝑖−1+𝑡𝑖)2 ⁄) ∆𝑡∑ 𝑆𝑃[0,𝑡𝑖] 𝑃(0,𝑡𝑖) +12 𝑇 𝑖=1 [𝑆𝑃[0,𝑡𝑖−1]−𝑆𝑃[0,𝑡𝑖]] 𝑃(0,(𝑡𝑖−1+𝑡𝑖)2 ⁄) The term in the numerator is the cumulated probability of default for the CDS life extension, whereas the term in the denominator is the cumulated survival probability, which may also be understood as the CDS price sensitivity to a bp (basis point) of spread, 𝑆𝑝01: 𝑆𝑝𝑟𝑒𝑎𝑑=(1−𝑅)𝐶𝑢𝑚𝑢𝑙𝑎𝑡𝑒𝑑 𝑃𝐷 𝑆𝑝01 Assuming that we already know the underlying bond recovery rate 𝑅, the next step in this method will be to calibrate the different hazard rates. This process will entail that each 𝜆𝑖 will be calibrated starting from a standard initial period, for instance 6 months, in such a way that the Survival Probability nodes are defined from the earliest to the latest, arriving at the equality shown in the equation above. (84) (85) (86) (87) (88)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 147 Using this framework, the sensitivity of the spread to the Recovery Rate is relatively easy to analyze. The basis will also consist of finding fixed vanilla bonds issued by entities similar to the lessee in terms of rating, currency and sector. However, we also need to find CDSs which are similar in this same context. Bonds and CDSs used for the analysis need to be unquestionably linked because the CDSs spread will determine the market YTM. If we find a liquid vanilla bond for which a quoted CDS curve exists (or, at least, a CDS curve for its rating and sector), we can then price the bond price with accuracy by using the formula below: 𝐵𝑜𝑛𝑑 𝑝𝑟𝑖𝑐𝑒=∑𝐶𝐹𝑖1 (1+𝑟𝑓𝑖+𝑠𝑝𝑖)𝑖 𝑛 𝑖=1 where 𝑟𝑓𝑖 is the risk-free rate and 𝑠𝑝𝑖 is the market CDS spread at each cash-flow 𝐶𝐹𝑖 payment date 𝑖. Hence, if a senior unsecured vanilla bond has a market price x, this price can be accurately replicated by using an adequate risk-free curve and a related CDS spread curve in terms of sector, rating and currency. The CDS spread represents, in terms of credit risk, the premium over the risk-free rate required by the market to buy the underlying bond. Therefore, the CDS spread can be understood to be the portion of yield with idiosyncratic credit risk. Thus, we can deduce why this spread should be added to the risk-free rate in order to price the underlying bond, given that it consists of the premium paid off in the CDS trade due to the default probability. The previous assumption comes from the fact that a CDS is designed so that a combined position of a CDS with a defaultable bond issued by a counterparty is very well-hedged against default risk and should therefore trade close to the price of an equivalent default-free bond. This means that the sum of the CDS and the risk-free bond should be equal to the defaultable bond price. 6.4.2 A practical example Below we analyze how the bond price changes as well as the subsequent change in the YTM once the recovery rate changes at the same time. By way of example, imagine that our lessee is a company within the transportation and logistics sector. It needs to arrange a leasing contract maturing in 4 years, with technical electric equipment as collateral, and with an average expected recovery rate of approximately 33% in line with the information presented in Table 31. The rating of the company is BBB, and it does not have liquid debt instruments quoted on the market; therefore, we should be able to find comparable peers with liquid bonds and credit default swaps. The Refinitiv EUR BBB Transportation CDS curve reference and its risk factors are as follows, as of 20/01/2022 (RIC 0#BBBTRACDBMK=): (89)
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 148 Table 41: EUR BBB Transportation sector CDS index curve, 20/01/2022 Bid Spread (bps) Default Prob. (%) Sp01 Recovery Rate (%) 6M 20/07/2022 17.26 0.12 416.25 40.00 12M 20/01/2023 20.37 0.31 922.22 40.00 2Y 20/01/2024 33.46 1.08 1918.89 40.00 3Y 20/01/2025 46.76 2.28 2894.20 40.00 4Y 20/01/2026 64.06 4.18 3836.55 40.00 5Y 20/01/2027 81.87 6.66 4743.69 40.00 7Y 20/01/2029 105.40 11.79 6446.88 40.00 10Y 20/01/2032 123.12 18.91 8725.03 40.00 20Y 20/01/2042 137.41 36.59 14493.10 40.00 30Y 20/01/2052 147.21 51.80 18288.80 40.00 Source: Refinitiv and compiled by the author. For this rating, sector and currency, the bond market gives the following YTM curve (RIC 0#BBBEURTRABMK=): Figure 50. EUR BBB Transportation sector YTM curve, 20/01/2022 Source: Refinitiv and Compiled by the author. According to the bonds constituting the 4y tenor for the above curve as at valuation date, the average market price is approximately 103.35%, with an average YTM of 0.52%, and an average maturity date of 17/06/2026 with an annual coupon of 1.38%. Using this structure, we firstly replicate the price by using the BBB Transportation CDS curve quoted by Refinitiv (Table 41), and subsequently by using the Euribor 6M zero coupon curve plus the CDS spreads in order to verify that the CDS curve to be used fits the expected pricing: Table 42: EUR BBB Transportation sector 4Y Maturing bond pricing 20/01/2022 20/01/2023 20/01/2024 20/01/2025 20/01/2026 Coupon 1.39% 1.408% 1.408% 1.411% 101.408% Discount Factor 100.272% 99.821% 98.782% 97.485% Market price 103.46% Price using CDS spread 103.07% Source: Refinitiv and compiled by the author -1,00% -0,50% 0,00% 0,50% 1,00% 1,50% 2,00% 2,50% 3M 6M 1Y 2Y 3Y 4Y 5Y 6Y 7Y 8Y Standard curve
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 149 As expected, the convergence between the market price and the price derived from using the CDS spreads proves sufficiently quantitative for modelling purposes. This can only occur if the CDS curve is sufficiently representative in terms of rating, sector and geography as regards the bonds used to calibrate the yield curve. There is a discrepancy of only 39 bps in price, but it should be noted that the constituents of the Refinitiv CDS curve are not the same as those constituting the yield curve, apart from other slight differences in market conventions. Once this convergence has been checked, the next step required is to measure the sensitivity of the bond price to the recovery rate. To this end, firstly we need to measure the expected change in the credit spreads arising from a change in the recovery rate. Hence, as per equation 88, the change in the recovery rate from 40% to 33.96% entails the following increase in the credit spread curve (given a constant PD and Sp01): Table 43: BBB Transportation CDS curve adjusted with a Recovery Rate = 33.96% under the proposed model, 20/01/2022 New Mid Spread with RR = 33.96% (bps) Change (bps) 6M 17.36 1.53 12M 21.13 1.87 2Y 35.79 3.17 3Y 52.63 4.66 4Y 75.95 6.72 5Y 99.01 8.76 7Y 132.98 11.77 10Y 159.55 14.12 Source: compiled by the author. This shift means that the bond will be priced at 102.47% which, translated into the YTM change, results in a shift of + 24.35 bps (from 0.5240% to 0.7675%). This process should also be carried out for the representative maturities in the yield curve. The necessary similarity between the bonds compounding the yield curve and the CDSs used for the bond pricing regarding rating and sector is clear. As a result, the new curve is as follows: Figure 51. EUR BBB Transportation sector standard and adjusted YTM curves (%), 20/01/2022 Source: Refinitiv and compiled by the author. -1,00% -0,50% 0,00% 0,50% 1,00% 1,50% 2,00% 2,50% 3M 6M 1Y 2Y 3Y 4Y 5Y 6Y 7Y 8Y Standard curve Adjusted curve
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 150 The adjusted curve is higher due to the fact that the lower recovery rate should be compensated via an increase in the return for the lessor, assuming that the default rate does not change. Certain assumptions for this framework related to the CDS valuation should be taken into consideration: - As mentioned above, a CDS is designed as a combined position of a CDS with a defaultable bond issued by a counterparty. - In order to ease the computations, we assume that each payoff occurs at the time of each default. - The delivery option which is embedded in a CDS with physical delivery is ignored. We consider that CDSs hedge the corresponding defaultable bonds, and therefore the same recovery rates are intrinsic for the bonds and the hedging CDS. If this were not the case, the necessary matching between yield and corresponding CDS curves under sector and rating would not occur. - It is assumed that the CDS is triggered by an individual obligors’ default (despite the fact that the obligor is a basket in terms of the model, we consider it as a whole for the purpose of sector/rating CDS curve treatment). 6.4.3 Model implementation and Performance measurement In order to test the initial hypothesis and to corroborate the model robustness, several analyses have been performed by using quoted bonds with CDSs issued on them. As in the case of the Bond-price model, I have searched for issuers that maintain quoted bonds with different recovery rates (due to different seniority levels, different guarantees, etc.) and similar maturities for the same sample shown in Table 40 of section 6.3, but also having CDSs issued. The sample decreases in 6 inputs as there were no CDSs quoted for every company in the sample. Then it is checked whether the model predicts the change in the bonds’ YTM in response to a change in the estimated recovery rate. Once the theoretical YTM change was computed for each pair of bonds following the CDS spread change model outlined in the previous section, a regression analysis on the model output is performed – i.e., the theoretical predicted ΔYTM as per the CDS spread model change vs. the actual ΔYTM currently seen in the market for each pair of bonds – as of same banking day (20/01/2022). Figure 52 below contains a summary of the main results for an Ordinary-Least Squares regression:
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 151 Figure 52. OLS regression, Predicted ΔYTM via CDS Spread change vs Actual ΔYTM, 20/01/2022 (bps) Source: Compiled by the author. The statistical outputs reflect a robust goodness-of-fit of the predicted ΔYTM compared to the actual one. For an OLS linear regression with the modeled YTM as the explanatory variable, R2 reaches 0.7251, taking into account that there are certain outliers identified in the series which penalize the final outcome. The estimator is 1.0786, being significative with a p-value of 6.4e-14 and t-test value of 10.773 for 44 degrees of freedom. It should also be noted that no evidence of heteroskedasticity in the Breusch-Pagan test (assuming linear relationship) has been identified. However, full normality in residuals cannot be assumed as per the Jarque-Bera test output and Q-Q plot, due to the four outliers already identified in the regression outcome. Figure 53. Normal Q-Q Plot, Predicted ΔYTM via CDS Spread change vs Actual ΔYTM, 20/01/2022 Source: Compiled by the author. As in the case of the model presented in section 6.3., the abovementioned outliers within the bond sample are issuances from Deutsche Bank, Bayerische Landesbank and Erste Group. If we eliminate the outliers from the sample, we obtain the regression output shown in the figure below.
Estimation of Counterparty Credit Risk Impact under IFRS Requirements David Delgado-Vaquero 152 Figure 54. OLS regression without outliers, Predicted ΔYTM via CDS Spread change vs Actual ΔYTM, 20/01/2022 (bps) Source: Compiled by the author. The goodness-of-fit of the predicted ΔYTM increases considerably, with R2 reaching 0.9118. For an OLS linear regression with the modeled YTM as the explanatory variable, the estimator is 0.9418, with the t-test value equal to 20.336 and p-value < 6.49e-16. It is now possible to assume the normality in residuals with a Jarque-Bera test output of 1.3397 and a p-value = 0.5118, with the following Q-Q plot and Cook’s distance: Figure 55. Normal Q-Q Plot for regression residuals w/out outliers, Predicted ΔYTM via CDS Spread change vs Actual ΔYTM, 20/01/2022 Source: Compiled by the author.