credit risk

In this paper we investigate the information in corporate credit ratings relevant to investors concerned about credit risk. We show that ratings relate to two economically di¤erent aspects of credit risk: raw default probability (expected payo¤) and systematic default risk, or the tendency to default in bad times (discount rate). We …rst demonstrate that ratings are not an optimal predictor of default probability: they are dominated by a simple default prediction model based on publicly available accounting and market based measures; they explain little of the variation in default probability across …rms; and they fail to capture the considerable variation in default probabilities and empirical failure rate over the business cycle. This means that either credit ratings are simply not at the frontier of default prediction or that delivering optimal default probability forecasts is not the sole objective of rating agencies. We present evidence that the latter is the case. In particular, we show that ratings are strongly related to systematic risk, as measured by failure beta, and that systematic risk is economically distinct from long-run idiosyncratic default risk. It should perhaps not be surprising that ratings re‡ect systematic risk: in theory, a diversi…ed risk-averse investor should care about both default probability and systematic risk, and we show empirically that systematic default risk is priced in CDS risk premia. Nevertheless, this relationship between rating and systematic risk has not been well-appreciated or explored in the previous literature.

The primary objective of credit risk models is to treat credit risk on a “Portfolio” a basis to address issues, such as, qualifying aggregate credit risk, identifying concentration risk, quantifying marginal risk, i.e., the effect on portfolio risk on account of the addition of a single asset, setting risk limits, and last but not least, quantifying economic and regulatory capital. The traditional techniques for managing credit risk, the use of limits. The common limits used by banks are individual/group borrower limits, which seek to control the size of exposure, concentration limits, which seek to control concentration within industry, instrument type, country, tenor limits, which seek to control the maximum maturity of exposures to borrowers, etc. While the limit system takes care of the various factors, which contribute to the magnitude of credit risk, viz., size of exposure, concentration risk of the borrowers, the maturity of the exposure, etc., on a “stand-alone” basis, it does not provide a satisfactory measure of the “concentration risk” and “diversification benefits” of a portfolio of exposures.

In order to take advantage of credit portfolio management opportunities, however, management must first answer several technical questions: What is the risk of a given portfolio? How do different macroeconomic scenarios, at both the regional and the industry sector level, affect the portfolio’s risk profile? What is the effect of changing the portfolio mix? How might risk-based pricing at the individual contract and the portfolio level be influ- enced by the level of expected losses and credit risk capital? This paper describes a new and intuitive method for answering these technical questions by tabulating the exact loss distribution arising from correlated credit events for any arbitrary portfolio of counterparty exposures, down to the individual contract level, with the losses measured on a marked-to-market basis that explicitly recognises the potential impact of defaults and credit migrations. 1 The importance of tabulating the exact loss distribution is highlighted by the fact that counterparty defaults and rat- ing migrations cannot be predicted with perfect foresight and are not perfectly correlated, implying that manage- ment faces a distribution of potential losses rather than a single potential loss. In order to define credit risk more precisely in the context of loss distributions, the financial industry is converging on risk measures that summarise management-relevant aspects of the entire loss distribu-

– Definition of Credit Risk – Probability of Default (PD) – Loss Given Default (LGD) – Exposure at Default (EAD) – Expected Loss (EL) – Value-at-Risk (VaR) – Unexpected Loss (UL)7. [r]

which means that the ratio between the intensities are constant over time. However, as argued in Jarrow, Lando and Turnbull (2001) and Yu (2002), simply taking this constant µ as the default jump risk premium is doubtful. First, the constant ra- tio would imply a simple dependent structure between the term structure of credit spreads and default rates which is inconsistent with the actual market data. More- over, as demonstrated in Delianedis and Geske (2001), and Huang and Huang (2003), credit risk accounts for only a small fraction of the observed corporate-Treasury yield spreads for investment grade bonds of all maturities, while a major portion of the spread is attributable to some non-Default factors such as taxes, liquidity and market risk factors. In order to refine the default risk factor, Jarrow et al. (2001) propose to subtract the average value of the Aaa-implied intensity from the intensities implied from other ratings. Yu (2002) further suggests to subtract the non-default factor from the default intensity, although a fully specified model of non-default sources of the spread remains elusive.

This module extends the credit risk analytic techniques to those that incorporate or make use of the prices in traded securities markets to assess creditworthiness. As such, the approach in this module extends firm-specific analysis in that the models make use of the prices at which transactions take place in the financial markets. Prices in these markets reflect the market’s best estimate of the value of the securi- ties and the underlying obligor’s credit risk. That is, they incorporate the market’s collective judgement about the security’s credit risk that is embedded within the security price. The analytic tools in this – and the next – module have been devel- oped to reveal this information and make use of it in determining credit risk and the probability of default.

Credit risk rating is summary indicator of a bank’s Credit risk rating is summary indicator of a bank’s individual credit exposure. An internal rating individual credit exposure. An internal rating system categorizes all credits into various classes system categorizes all credits into various classes on the basis of underlying credit quality An internal on the basis of underlying credit quality An internal rating framework can be used for a number of rating framework can be used for a number of

In recent years, value at risk (VaR) has become a heavily used risk management tool in the banking sector. Roughly speaking, the value at risk of a portfolio is the loss in market value over a risk horizon that is exceeded with a small probability. Bank management can ap- ply the value at risk concept to set capital requirements because VaR models allow for an estimate of capital loss due to market and credit risk (see, e.g., Duffie/Pan 1997, Jackson/Maude/Perraudin 1997, Jorion 1997, Saunders 1999, Friedmann/Sanddorf-Köhle 2000, Hartmann-Wen- dels/Pfingsten/Weber 2000, and Simons 2000). The aim of our study is to answer the question what is the optimum amount of equity capital of a ban- king firm under the value at risk concept in the presence of credit risk?

When considering a new instrument to be traded as part of a certain book, one needs to take into account the impact of the new deal in the credit risk profile at the time the deal is considered. An increase of risk exposure should lead to a higher premium or to a deal not being authorized. A decrease in risk exposure could lead to a more

Borio, Furfine, and Lowe (2001) contains a detailed discussion of procyclicality and banking regulator responses. There has been a lot of discussion about the impact of capital requirements on the cyclical behavior of banks. 20 Here, we want to focus on loan loss provisions since we think that they are the proper instrument to deal with expected losses. Thus, we propose a new prudential provision that addresses the fact that credit risk builds up during credit boom peri- ods. This new provision is in addition to the already existing specific and general provisions. The general provision can be interpreted as a provision for the inherent or latent risk in the portfolio—that is, an average provision across the cycle. The new loan loss provision (or the third component of the total loan loss provision) is based on the credit-cycle position of the bank in such a way that the higher the credit growth of the individual bank, the more it has to provision. On the contrary, the lower the credit growth, the more provisions the bank can liberate from the previously built reserve. Analytically, we can write

When comparing the results for the pre-crisis sample versus the post-crisis sample, we find that the explanatory power of the variables decreased. For example, for the comprehensive models, from the before-crisis period to the after-crisis periods, the adjusted R-squared falls from 77% to 62%. This may reflect the increased volatility in latent factors that has not been captured by our accounting and market variables. One such factor could be the liquidity risk predominating in the financial sector during the crisis period. Focusing on the banking sectors, Gefang et al. (2011) suggest the importance of the liquidity risk relative to the credit risk to the financial crisis in explaining the LIBOR-OIS (overnight index swap) rate. They find that, particularly at the 1 month and 3 month terms, the role of the liquidity risk is much more important than that of the credit risk. Alternatively, the decline in the model fit may reflect an increase in the sensitivity of the CDS pricing to the perceived counter-party risk in these OTC derivatives contracts.

Basically the main goal of this paper is to develop a su¢ ciently wide model for corporate bonds with credit risk, and develop a set of mathematical tools and results that would allow the practitioner to simplify this framework and conditions in order to implement these models according to the speci…c needs of the market (with or without continuity and with or without jumps, with or without credit migration or under di¤erent types of default).

In this paper we use the industrial economics approach to the microeconomics of banking to analyze the management of credit risk for the case of a large bank active in the deposit and loan markets. While this approach does not explicitly account for informational problems, our analysis of credit and macro derivatives which do not exactly offset the bank’s credit risk nevertheless captures in a stylized way features of optimal bank behavior under asymmetric information. For example, the combination of uncertainty and asymmetric information suggests that the bank retain some of the risk in order to give an incentive for proper monitoring. This retention of risk will be included in all but one of our analyses. We follow the lead of Wong (1997) and supplement the industrial economics approach by risk aversion and uncertainty, more specifically credit risk in our case. As for the assumption of risk aversion and the need of active corporate risk management we refer our readers to the seminal work of Froot et al. (1993) and Froot and Stein (1998). Pausch and Welzel (2002) provide an application to the banking industry, showing that even a per se risk neutral bank exhibits risk averse behavior, if there is capital adequacy regulation. Our two main objectives are the following: First, we want to help close the gap between theoretical analysis and practice of credit derivatives as hedging instruments. We explicitly model a credit default swap as the main instrument traded and show how the design of the derivative affects its hedge properties and optimal bank decisions. Second, we split up credit risk into a systematic and a specific part and introduce the notion of a macro derivative used to hedge against systematic risk. Both the credit default swap and the macro derivative extend the scope of banking from a mere buy–and–hold strategy to active management of credit risk.

• The analysis of theoretical and empirical literature seeking to reveal the pecularities oc credit risk mangement enabled to draw the following conclutions; Firstly, level of the credit risk depends on the single credit union policy guidelines (lending policy and priorities, composition of the credit portfolio, amounts of the operating income etc). Secoundly, credit unions making investment decisions should involve the estimation the concentration of credit risk in order to escape high delinquencies and foreclosure of loans. Thirdly, funds allocating process are very sophisticated and risk mangement systems should take into consideration a wide range of features related to liquidity needs, geografic concentrations, unemployment trends and business infrastructure in the region etc. All these aspect should be stated in the corporate risks management strategies.

Borio, Furfine, and Lowe (2001) contains a detailed discussion of procyclicality and banking regulator responses. There has been a lot of discussion about the impact of capital requirements on the cyclical behavior of banks. 20 Here, we want to focus on loan loss provisions since we think that they are the proper instrument to deal with expected losses. Thus, we propose a new prudential provision that addresses the fact that credit risk builds up during credit boom peri- ods. This new provision is in addition to the already existing specific and general provisions. The general provision can be interpreted as a provision for the inherent or latent risk in the portfolio—that is, an average provision across the cycle. The new loan loss provision (or the third component of the total loan loss provision) is based on the credit-cycle position of the bank in such a way that the higher the credit growth of the individual bank, the more it has to provision. On the contrary, the lower the credit growth, the more provisions the bank can liberate from the previously built reserve. Analytically, we can write

The current regulation of credit risk capital in banks, based on the 1988 Basel Ac- cord and presently endorsed by more than 100 countries, establishes rules that set capital requirements for banks in relation to the amount of credit risk in their portfolios. In- terestingly, these rules do not take into account the risk reduction bene…ts of credit risk diversi…cation. The credit risk of each security in a bank portfolio is assessed indepen- dently of the other securities in the portfolio. The reason behind this over-simplistic approach has to do with the objectives of the G8 countries that agreed the Accord back in 1988. At that time, there was not a uniform regulatory treatment of bank capital across countries and the purpose of the Accord was to lay down a level playing …eld in which minimum standard were guaranteed internationally. Since no international rules were in place before, and national regulatory systems di¤ered substantially in aims and sophistication, the obvious and practical solution was to come up with a simple set-up that could allow everybody involved to align their system to the agreed standard. It was also understood that the Accord would have to be re…ned over time. Indeed, modi…cations and additions have been numerous since its inception (see, for example, Basel Committee on Banking Supervision (BCBS) 1996). In fact, the Basel Committee on Banking Super- vision, the forum that originated the Accord and is now responsible for its revisions, is now considering updating capital regulation for credit risk. A proposal for a new capi- tal adequacy regime, which was released this year for comments from the industry (see BCBS 2001), does make an improvement on the previous rules in that it acknowledges the role of diversi…cation in reducing idiosyncratic credit risk. Yet, it does not take into account how diversi…cation across countries and industry sectors may a¤ect portfolio risk. It recognises that a higher number of securities in the portfolio may reduce risk, but treats all securities alike regardless of the country of origin and industry sector of the issuer. So, for example a portfolio of 1000 di¤erent corporate loans all issued by high-tech US companies would attract the same capital charges as a portfolio of 1000 corporate loans distributed geographically and across industries 21 .

The second type of credit risk model is called Contingent Claim Analysis (CCA) by Jones et al (1984) [29]. Basically, CCA is a generalization or extension of Black- Scholes’ option pricing model pioneered by Black and Scholes (1973) [11]. A bor- rower’s liabilities are viewed as contingent claims issued against underlying asset value which is assumed to follow a stochastic differential process with known expected rate of asset return and variance of return. Merton (1974) [35] defines a default event occurrence when a borrower’s asset value falls below its total liability. The model is well known as Black-Scholes-Merton model. Since then, similar CCA models are pro- posed by Black and Cox (1976) [10], Santomero and Vinso (1977) [38], Scott (1981) [39], Chance (1990) [18] and Shimko et al(1993) [40]. Hull and White (1995) [24], redefine default process as the borrower’s asset value hit some specified boundary. A current commercial software employing CCA modeling is KMV (1993) [1].

During the recent financial crisis, we observed a dramatic increase in the credit spreads quoted on the market. This is true for both the spreads implicit in the corporate bond market and those paid to buy protection in the CDS market. This rise in the spreads can be interpreted as an increase in the risk neutral default probability of the considered companies since such a dramatic change in the expected recovery rate does not seem plausible. One first question that arises is therefore whether such high values of the default probability can be considered systematic or specific and thus diver- sifiable. Another question concerns the change in the role of systematic components of credit risk during the crisis period. We investigate such ques- tions in the CDS market. This choice is justified by the high liquidity of the credit derivatives market and by the huge volume of outstanding contracts. According to the ISDA Market Survey of June 2010, the total outstanding notional covered by CDS contracts amounts to more than 26 trillions in the first half of 2010. Although this number is huge, it is well below the historical maximum of outstanding notional, which is equal to more than 62 trillions in the second half of 2007. Another justification of the choice can also come from the wider and wider use of indexes of CDS contracts. Here we focus only on the US market and consider only the CDX as a comprehensive index. The first contribution of the paper is therefore to propose a model that separates the systematic and specific components of risk in the CDS market. The second objective is to analyze in depth the evolution of systematic credit risk before and during the financial crisis. This is done both on the entire sample of firms and considering the same data grouped by sector. The change in risk is investigated also with respect to the “extreme systematic” risk, measured in terms of extreme tail dependence.

endogeneity of the key independent variable, the data used in the credit risk model was modified. The dependent variable was replaced with the result of a random number generator, the SAS Ranuni function, designed so that about the same number of credit losses (180) would be simulated by the random number generator as were in the original dataset. This was done once under the assumption that annual default probabilities were equal (so that a loan observed from 1979 to 1992 had 14 times the probability of a default as did a 1992 loan) and again with the probability of a loan defaulting in the first 2 years set to 0, the probability of the 13 th and 14 th year set to 0, and equal annual default probabilities for the remaining exposure years. The independent variable for the land price shock was then recalculated, and the regression re- estimated. A macro did this for 1000 times, for seed values fed to the random number generator of 1 to 1000. In both cases, 100% of the results showed a negative coefficient, significant at 5%. Coefficients on the other independent variables frequently changed sign and were significant less than 7% of the time.

The most promising route for future research seems to be the introduction of bank capital. In the model considered here, there are no intermediaries with positive equity that could serve as a buffer against loan losses. Introducing bank capital would help make the model more complete, as one could distinguish the portions of the banks’ credit risk borne by the bank owners (the major part or all) and by the depositors (little or none at all), respectively. Another possible extension of the model would introduce lenders with heterogeneous risk attitudes, which would raise the question of the optimal allocation of risks across differently risk-averse agents. Risky collateral would shed further light on optimal risk sharing. These, and possibly further, issues can only be meaningfully addressed in a model with portfolio risk, and we are confident that our results will hold true with a small amount of bank capital, a small second group of consumers with different risk attitude, or uncertain collateral with a small variance.