1 Credit Risk Management Elements of Financial Risk Management Chapter 12 Peter Christoffersen Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Overview • Credit risk can be defined as the risk of loss due to a counterparty’s failure to honor an obligation in part or in full • Credit risk can take several forms • For banks credit risk arises fundamentally through its lending activities • Nonbank corporations that provide short-term credit to their debtors face credit risk as well • Investors who hold a portfolio of corporate bonds or distressed equities need to get a handle on the default probability of the assets in their portfolio Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Overview • Default risk, a key element of credit risk, introduces an important source of nonnormality into the portfolio • Credit risk can also arise in the form of counterparty default in a derivatives transaction • The chapter is structured as follows: • Section provides a few stylized facts on corporate defaults • Section develops a model for understanding the effect on corporate debt and equity values of corporate default Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Overview • Default risk will have an important effect on how corporate debt is priced, but default risk will also impact the equity price The model will help us understand which factors drive corporate default risk • Section builds on single-firm model from Section to develop a portfolio model of default risk The model and its extensions provide a framework for computing credit Valueat-Risk • Section discusses further issues in credit risk including recovery rates, measuring credit quality through ratings, and measuring default risk using credit default swaps Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Figure 12.1: Exposure to Counterparty Default Risk Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Brief History of Corporate Defaults • Credit rating agencies such as Moody’s and Standard & Poor’s maintain databases of corporate defaults through time • In Moody’s definition corporate default is triggered by one of three events: – a missed or delayed interest or principal payment – a bankruptcy filing – a distressed exchange where old debt is exchanged for new debt that represents a smaller obligation for the borrower Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Table 12.1: Largest Moody's-Rated Defaults Company Default Volume ($ mill) Year Industry Country Lehman Brothers $120,483 2008 Financials United States Worldcom, Inc $33,608 2002 Telecom / Media United States GMAC LLC $29,821 2008 Financials United States Kaupthing Bank Hf $20,063 2008 Financials Iceland Washington Mutual, Inc $19,346 2008 Financials United States Glitnir Banki Hf $18,773 2008 Financials Iceland NTL Communications $16,429 2002 Telecom / Media United Kingdom Adelphia Communications $16,256 2002 Telecom / Media United States Enron Corp $13,852 2001 Energy United States Tribune Economy $12,674 2008 Telecom / Media United States Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Figure 12.2: Annual Average Corporate Default Rates for Speculative Grade Firms, 1983-2010 Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Figure 12.2: Annual Average Corporate Default Rates for Speculative Grade Firms, 1983-2010 Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Modeling Corporate Default 10 • The Merton model of corporate default provides important insights into the valuation of equity and debt when the probability of default is nontrivial • The model also helps us understand which factors affect the default probability • Consider the situation where we are exposed to the risk that a particular firm defaults • This risk could arise from the fact that we own stock in the firm, or it could be that we have lent the firm cash, or it could be because the firm is a counterparty in a derivative transaction with us Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Credit Quality Dynamics 55 • The credit quality of a company typically declines well before any eventual default • It is important to capture this change in credit quality because the lower the quality the higher the chance of subsequent default • One way to quantify the change in credit quality is by using the credit ratings provided by agencies such as Standard & Poor’s and Moody’s • The following list shows the ratings scale used by Moody’s for long-term debt ordered from highest to lowest credit quality Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Credit Quality Dynamics 56 • Investment Grades • Aaa: Judged to be of the highest quality, with minimal credit risk • Aa: Judged to be of high quality and are subject to very low credit risk • A: Considered upper-medium grade and are subject to low credit risk • Baa: Subject to moderate credit risk They are considered medium grade and as such may possess certain speculative characteristics Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Credit Quality Dynamics 57 • Speculative Grades • Ba: Judged to have speculative elements and are subject to substantial credit risk • B: Considered speculative and are subject to high credit risk • Caa: Judged to be of poor standing and are subject to very high credit risk • Ca: Highly speculative and are likely in, or very near, default, with some prospect of recovery of principal and interest • C: The lowest rated class of bonds and are typically in default, with little prospect for recovery of principal or interest Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Table 12.2: Average One-Year Rating Transition Rates, 1970-2010 From/To: Aaa Aa A Baa Ba B Caa Ca_C WR Default Aaa 87.395% 8.626% 0.602% 0.010% 0.027% 0.002% 0.002% 0.000% 3.336% 0.000% Aa 0.971% 85.616% 7.966% 0.359% 0.045% 0.018% 0.008% 0.001% 4.996% 0.020% A 0.062% 2.689% 86.763% 5.271% 0.488% 0.109% 0.032% 0.004% 4.528% 0.054% Baa 0.043% 0.184% 4.525% 84.517% 4.112% 0.775% 0.173% 0.019% 5.475% 0.176% Ba 0.008% 0.056% 0.370% 5.644% 75.759% 7.239% 0.533% 0.080% 9.208% 1.104% B 0.010% 0.034% 0.126% 0.338% 4.762% 73.524% 5.767% 0.665% 10.544% 4.230% Caa 0.000% 0.021% 0.021% 0.142% 0.463% 8.263% 60.088% 4.104% 12.176% 14.721% Ca_C 0.000% 0.000% 0.000% 0.000% 0.324% 2.374% 8.880% 36.270% 16.701% 35.451% Notes to Table: The table shows Moody's credit rating transition rates estimated on annual data from 1970 through 2010 Each row represents last year's rating and each column represents this year's rating Ca_C combines two rating categories WR refers to withdrawn rating Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen 58 Credit Quality Dynamics 59 • Table 12.2 shows a matrix of one-year transition rates between Moody’s ratings • The number in each cell corresponds to the probability that a company will transition from the row rating to the column rating in a year • For example, the probability of a Baa rated firm getting downgraded to Ba is 4.112% • The transition probabilities are estimated from the actual ratings changes during each year in the 1970–2010 period • The Ca_C category combines the companies rated Ca and C Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Credit Quality Dynamics 60 • The second-to-last column, which is labeled WR, denotes companies for which rating was withdrawn • More interestingly, the right-most column shows the probability of a firm with a particular row rating defaulting within a year • Notice that the default rates are monotonically increasing as the credit ratings worsen • The probability of an Aaa rated firm defaulting is virtually zero whereas the probability of a Ca or C rated firm defaulting within a year is 35.451% Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Credit Quality Dynamics 61 • Note also that for all the rating categories, the highest probability is to remain within the same category within the year • Ratings are thus persistent over time • The lowest rated firms have the least persistent rating • Many of them default or their ratings are withdrawn • The rating transition matrices can be used in Monte Carlo simulations to generate a distribution of ratings outcomes for a credit risk portfolio Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Credit Quality Dynamics 62 • This can in turn be used along with ratings-based bond prices to compute the credit VaR of the portfolio • JP Morgan’s CreditMetrics system for credit risk management is based on such an approach • The credit risk portfolio model developed in Section can also be extended to allow for debt value declines due to a deterioration of credit quality Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Credit Default Swaps 63 • As discussed earlier, the price of corporate debt such as bonds is highly affected by the probability of default of the corporation issuing the debt • However, corporate bond prices are also affected by the prevailing risk-free interest rate as the Merton model showed us • Furthermore, in reality, corporate bonds are often relatively illiquid and so command a premium for illiquidity and illiquidity risk • Observed corporate bond prices therefore not give a clean view of default risk Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Credit Default Swaps 64 • Fortunately, derivative contracts known as credit default swaps (CDS) that allow investors to trade default risk directly have appeared • CDS contracts give a pure market-based view of the default probability and its market price • In a CDS contract the default protection buyer pays fixed quarterly cash payments (usually quoted in basis points per year) to the default protection seller • In return, in the event that the underlying corporation defaults, the protection seller will pay the protection buyer an amount equal to the par value of the underlying corporate bond minus the recovered value Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Credit Default Swaps 65 • CDS contracts are typically quoted in spreads or premiums • A premium or spread of 200 basis points means that the protection buyer has to pay the protection seller 2% of the underlying face value of debt each year if a new CDS contract is entered into • Although the payments are made quarterly, the spreads are quoted in annual terms • CDS contracts have become very popular because they allow the protection buyer to hedge default risk Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen 66 Credit Default Swaps • They of course also allow investors to take speculative views on default risk as well as to arbitrage relative mispricings between corporate equity and bond prices • Paralleling the developments in equity markets, CDS index contracts have developed as well • They allow investors to trade a basket of default risks using one liquid index contract rather than many illiquid firmspecific contracts • Figure 12.11 shows the time series of CDS premia for two of the most prominent indices, namely the CDX NA (North American) and iTraxx EU (Europe) Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Figure 12.11: CDS Index Premia CDX North America and iTraxx Europe Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen 67 Credit Default Swaps • The CDX NA and iTraxx EU indexes each contain 125 underlying firms • The data in Figure 12.11 are for five-year CDS contracts and the spreads are observed daily from March 20, 2007 through September 30, 2010 • The financial crisis is painfully evident in Figure 12.11 • Perhaps remarkably, unlike CDOs, trading in CDSs remained strong throughout the crisis and CDS contracts have become an important tool for managing credit risk exposures Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen 68 Summary 69 • Credit risk is of fundamental interest to lenders but it is also of interest to investors who face counterparty default risk or investors who hold portfolios with corporate bonds or distressed equities • This chapter has provided some important stylized facts on corporate default and recovery rates • Merton’s seminal model • Vasicek’s factor model structure • Credit Default Swaps Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen ... default risk using credit default swaps Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen Figure 12.1: Exposure to Counterparty Default Risk Elements of Financial Risk. .. estimate of the physical growth rate of firm assets Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen The Risk- Neutral Probability of Default 27 • Default risk is... Christoffersen Figure 12.5: Market Value of Debt as a Function of Asset Value when Face Value of Debt is $50 Elements of Financial Risk Management Second Edition © 2012 by Peter Christoffersen