Credit Risk § Types of Loans § Return on Loans § Models of Credit Risk measurement

金融機構逾放比例

Types of Loans in Taiwan

Types of Loans in Taiwan

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

Residential Mortgage-Lending Process Function Rewards Risks Origination Fees Limited Funding/underwriting Spread Liquidity , interest rate , credit Selling Fees & commissions Servicing Investor Interest & principal

Individual Loans ◆Nonrevolving e.g : Auto Loans ; Mobile Home Loans e.g : Credit Card Other Loans

Credit Card in Taiwan

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

Credit Decisions Retail ◆accept or reject ◆sorted by loan quantity Wholesale ◆Both interest rates & credit quantity

Default Risk Models – Qualitative Models Market-specific Factors ◆Business Cycle ◆Level of interest rates Borrower-specific Factors ◆Reputation ◆Leverage ◆Volatility of Earnings ◆Collateral

Default Risk Models – Credit Scoring Models ◆Linear Probability Model Z i = ∑n j=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 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%

Probability of default on a multiperiod debt instrument Cumulative Default probability: The probability that a borrower will default over a specific multiyear period : the probability of the debt surviving in the ith year Example

Probability of default on a multiperiod debt instrument Marginal Default Probability No arbitrage Forward Rate Example

Advantages and Problems 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

Mortality Rate Derivation of Credit Risk 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. 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 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.

RAROC (Risk-Adjusted Return of Capital) Models One year income on a loan Loan (asset) risk or capital at risk 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.

RAROC Models Example 11-6 = 10% AAA borrower = 2.7 Spread = 0.2% * $1m = $2’000 Fees = 0.1% * $1m = $1’000 Example 11-6 AAA borrower 400 publicly traded bonds (AAA) The range of Risk Premium is from -2%~3.5% $2000 + $1000 -(2.7) * ($1m)(0.11/1.1) = 11.1% =

RAROC Models One-year income on loan One-year income per dollar loaned RAROC Models Unexpected default rate One-year income on loan 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%

RAROC Models RAROC = Add more interest income or fees One year income on a loan Loan (asset) risk or capital at risk RAROC = 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 option on the assets of the firm The Debt Holder’s Payoff from Loans Writing a put option on the value of the borrower’s assets with B, the face value of debt, as the exercise price.

Call option -S Assets (A) Payoff to stockholders A1 B (debt) A2

Put option Payoff to debt holders A1 B (debt) A2 Assets (A)

Option Models of Default Risk Applying the Option Valuation Model to the calculation of Default Risk Premium

Option Models of Default Risk ,T: the maturity date ; t: today the borrower’s leverage ratio the probability that a deviation exceeding the calculated value of h will occur the asset risk of the borrower t = d = = ) ( h N = 2 s

Option Models of Default Risk Required yield on risky debt The lender should adjust the required risk premium as leverage and asset risk change @ Example 11-7

Example 11-7 B = $100,000 = 1 year = 12% i = 5% d = 90%

The required risk spread or premium is 5%+1.33%=6.33%

The lender’s decision matrix : Result Good loan Decision Yes No Bad loan Loan repaid Type 1 error Type 2 error Loan denied Reject H0 Accept H0 H1 is true H0 is true Type 1 error Type 2 error

H0:the customer would default H1:the customer could repay Not Grant H1:the customer could repay Grant TypeⅠ: reject the true H0 Bankrupt Type Ⅱ: accept the wrong H0 Damage reputation

CreditMetrics Credit Risk+

CreditMetrics---Introduction Introduced by J.P. Morgan & its co-sponsors, 1997 Based on the conception of VaR The difficulties to attain the P and σ of loans & Methods to solve this problem Rating Migration---changing credit spread 1.The borrower’s credit rating 2.The rating Migration matrix 3.Recovery rate of default loans 4.Yield spreads in the bond market

CreditMetrics---Rating Migration Eg. 5yr $100m 6% loan for BBB borrower Rating Migration Probabilities Valuation P=6+6/(1+r1+s1)+6/(1+r2+s2)2+ 6/(1+r3+s3)3+106/(1+r4+s4)4 Rating Transition Prob AAA 0.02% AA 0.33% A 5.95% BBB 86.93% BB 5.30% B 1.17% CCC 0.12% Default 0.18%

CreditMetrics---Prob. Distibution Year- End Rating Loan Value AAA $109.37 AA $109.19 A $108.56 BBB $107.55 BB $102.02 B $98.10 CCC $83.64 Default $51.13

CreditMetrics---VaR & Capital Requirements

Credit Risk+---Introduction Developed by Credit Suisse Financial Products (CSFP) Derive from the conceptions of fire insurance Unlike CreditMetrics, Credit Risk+ focus on 1.The frequency of Defaults 2.Severity of Losses

Credit Risk+---Assumptions The prob. of any individual loan defaulting in the portfolio of loans is random The correlation between the defaults on any pair of loans is 0 Poisson Distribution is applied More appropriate for analyzing the default rate on a large portfolio of small loans rather than a portfolio of just a few loans

Credit Risk---pdf 1.Prob. of n defaults=e-m*mn n! m: Historic #of defaults for loans of this type n: # of defaults 2.Severity of Losses---average $ loss per loan defaults

Credit Risk---calculations E.g.. A FI makes 100 loans, each of $10,0000 M=3 Severity of loss:20 cent per$1 Prob. of 4 loans defaulting = e-3*34 4! Dollar loss of 4 loans defaulting=4*20C*$100,000=$80,000 Possible Drawbacks of this model

Loan Portfolio and Concentration Risk

Simple Models of Loan Concentration Risk Risk Grade at Yr End Risk Grade at yr beginning FI widely employed two simple models to measure the credit risk of a loan portfolio : 1.Loan migration matrix 2.Concentration limits 1 2 3 D 0.85 0.10 0.04 0.01 0.12 0.83 0.03 0.02 0.13 0.80 Concentration limit=Maximum loss(% of capital) 1 * Loss rate

KMV Portfolio Manager Model---Conceptions

MPT Applied to Bank Lending Modern Portfolio Theory ALM LINE Purchasing Fed Funds Selling Fed Funds

FI Portfolio Diversification Rp=∑ Xi Ri i=1 C Σσp2=∑Xi2σi2+ ∑∑XiXjσij A B Σσp2=∑Xi2σi2+ ∑∑XiXjρijσiσj

KMV Portfolio Manager Model σi=ULi=σDi* LGDi=√EDFi(1-EDFi) *LGDi Ri=AISi-E(Li)=AISi -(EDFi*LGDi)

Comparing with Benchmark National Bank A Bank B Real Estate 10% 15% C&I 60% 75% 25% Individuals 5% 55% Others 4 σj= ∑(Xij-Xi)2 i=1 N σA=10.61% σB=26.69%

Loan Loss Ratio-Based Models Involves estimating the systematic loan loss risk of a particular section or industry relatives to the loan loss of an FI’s total loan portfolio =α+βi( Total loan losses/Total loans) Sectoral losses in the ith sector Loans to the ith sector

Credit Derivates---Introduction(1/3) Usually OTC, Off-balance sheet contracts Banks can use credit derivatives to achieve more efficient risk-return combinations without hurting customer relationships Four Components Payment of credit derivatives 1.Cash Settlement 2.Physical Delivery 1.The notional amount 2.The term or maturity 3.The reference party whose credit is being traded 4.Reference Assets

Promised int. + Mkt Value Loss Credit Derivates(2/3) Types of credit derivatives Pure-credit (default) Swap Total-return Swap premium Party1 Party 2 Loss Compensation premium Party 2 Party1 Promised int. + Mkt Value Loss

Credit Derivates(3/3) Hedge ratio=LIED for the loan/LIED for the reference assets LIED( loss in the event of default)=1-recovery rate e.g.. A Bank holds a $10m,senior, syndicated, floating rate loan (estimate recovery rate=70%) Reference asset: a Bond with 50% recovery rate Hedge ratio=(1-0.7)/(1-0.5)=60% $10m*60%=6m

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