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## Credit Risk

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**Credit Risk**§ Types of Loans § Return on Loans § Models of Credit Risk measurement**Commercial & Industrial Loans**◆Term ◆Amounts ─ Syndicated Loan ◆Secured & Unsecured ◆Spot Loan & Loan Commitment Is Commercial Loan still important ??**Real Estate Loans**◆Mortgage Loans ◆Revolving Home Equity Loans**Individual Loans**◆Nonrevolving e.g : Auto Loans ; Mobile Home Loans ◆Revolving e.g : Credit Card Other Loans**Return on Loans**Influence Factor : ◆ Interest Rate ◆ Fees ◆ Credit Risk Premium ◆ Other Factors**ROA per dollar lent**1+k=1+｛〔f+(BR+m)〕/〔1-〔b(1-R)〕〕｝ k : Gross Return on the Loan f : Loan Origination fee BR : Base Lending Rate m : Credit Risk Premium b : Compensating Balance Requirement R : Reserve Requirement**Expected Return on a Loan**＊ E (r) = p (l+k) p: probability of repayment of the loan**Credit Risk**Two Dimensions to Control Credit Risk ◆1+k: price or promised return ◆quantity or credit availability**Retail**◆accept or reject ◆sorted by loan quantity Wholesale ◆Both interest rates & credit quantity Credit Decisions**Borrower-specific Factors**◆Reputation ◆Leverage ◆Volatility of Earnings ◆Collateral Market-specific Factors ◆Business Cycle ◆Level of interest rates Default Risk Models – Qualitative Models**Default Risk Models –Credit Scoring Models**◆Linear Probability Model Z i = ∑nj=1βj X ij + error ◆Logit Model F(Zi) =1/(1+e-z)**Default Risk Models –Credit Scoring Models**◆Linear Discriminant Models Z=1.2X1+1.4X2+3.3X3+0.6X4+1.0X5 X1：Working capital /total assets ratio X2 ： Retained earnings/total assets ratio X3 ： EBIT/total assets ratio X4： Market value of equity/book value of long-term debt ratio X5： Sales/total assets ratio**Discriminant Model**Problems ◆discriminate between extreme behavior ◆Are the weights and Xi constant? ◆Ignore hard-to-quantify factors ◆No centralized database**New Models of Credit Risk Measurement and Pricing**• Term Structure Derivation of Credit Risk • Mortality Rate Derivation of Credit Risk • RAROC Models • Option Models of Default Risk**Term Structure Derivation of Credit Risk**• The spreads between risk-free discount bounds issued by the Treasury and discount bounds issued by corporate borrowers of differing quality reflect perceived credit risk exposures of corporate borrowers for single payments at different times in the future. • Probability of default on a one –period debt instrument • Probability of default on a multiperiod debt instrument**Probability of default on a one –period debt instrument**• p = the probability of repayment • = the risk premium • Example 11-4**Probability of default on a one –period debt instrument**• i = 10% • k = 15.8% • In this case, a probability of default of 5% on the corporate bond requires the FI to set a risk premium of 5.8%. • p , 1-p , ( k - i ) = k - i = 5.8%**= the proportion of the loan’s principal and interest**that is collectible on default. > 0 • and are perfect substitutes for each other. • An increase in collateral a decline in**i = 10%**• p = 0.95 • r = 0.9 k = 10% + 0.55276% = 10.55276%**: the probability of the debt surviving in the ith year**Probability of default on a multiperiod debt instrument Cumulative Default probability: The probability that a borrower will default over a specific multiyear period Example**Probability of default on a multiperiod debt instrument**• Marginal Default Probability • No arbitrage • Forward Rate Example**Advantages and Problems**• Advantages • Clearly forward looking and based on market expectations. • Liquid markets for Treasury and corporate discount bonds. • Problems • Treasury markets _ deep • Corporate markets_ small • Discount yield curve**Total value of grade B bonds defaulting in year i of**issues = Total value of grade B bonds outstanding in year i of issues Mortality Rate Derivation of Credit Risk • Mortality Rate • Historical default rate experience of a bond or loan • Marginal Mortality Rate • The probability of a bond or loan defaulting in any given year of issue.**Mortality Rate Derivation of Credit Risk**• MMR curve can show the historic default rate • Any shape to the mortality curve is possible • The higher Mortality rates the lower the rating of the bond**Mortality Rate Derivation of Credit Risk**• Problems • historic or backward-looking measures. • Implied future default probabilities tend to be highly sensitive to the period over which FI manager calculates the MMRs. • The number of issues and the relative size of issues in each investment grade.**One year income on a loan**Loan (asset) risk or capital at risk RAROC (Risk-Adjusted Return of Capital) Models • RAROC = • RAROC > ROE the loan should be made**RAROC Models**• The first problem in estimating RAROC • The measurement of loan risk**RAROC Models**• : The change in the yield spread between corporate bonds of credit rating class i (Ri) and matched duration treasury bonds (RG) over the last year. • Max [ ] : only consider the worst-case scenario.**Example 11-6**AAA borrower 400 publicly traded bonds (AAA) The range of Risk Premium is from -2%~3.5% = 10% = 2.7 Spread = 0.2% * $1m = $2’000 Fees = 0.1% * $1m = $1’000 $2000 + $1000 = 11.1% -(2.7) * ($1m)(0.11/1.1) = RAROC Models**One-year income per dollar loaned**One-year income on loan Unexpected default rate RAROC Models RAROC = Proportion of loan lost on default Expected income per dollar lent = 0.3 cents Unexpected default rate = 4% Proportion of loan lost on default = 80% RAROC = 9.375%**One year income on a loan**RAROC = Loan (asset) risk or capital at risk RAROC Models • Add more interest income or fees • Curtail the size of the loan • Shorten the duration of the loan**Option Models of Default Risk**• The Borrower’s Payoff from Loans • buying a call optionon the assets of the firm • The Debt Holder’s Payoff from Loans • Writing a put optionon the value of the borrower’s assets with B, the face value of debt, as the exercise price.**Payoff to stockholders**B (debt) 0 A1 A2 Assets (A) -S Call option**Payoff to debt holders**A1 0 A2 Assets (A) B (debt) Put option**Option Models of Default Risk**• Applying the Option Valuation Model to the calculation of Default Risk Premium