1. CREDIT RISK MEASUREMENT Classes #14; Chap 11

2. Lecture Outline Purpose: Gain a basic understanding of credit risk. Specifically, how it is measured  Measuring Credit Risk  Qualitative Factors  Quantitative Models Credit Score Models Value-at-Risk (VaR) RAROC Other models (if time permits) 2

3. Measuring Loan Credit Risk 3

4. How Did we Adjust for Credit Risk?  We basically looked at two questions: 1.How much do we lose if the borrower defaults 2.How likely is it that the borrower defaults  We adjust for credit risk by considering (adding) the expected loss  If there is no expected loss then we earn the contractually promised return.  To adjust for credit risk we need to know 2 things 1. What is the probability that the borrower defaults 2. How much can we recover if the borrower defaults 4 Answering these two questions gets us the expected loss i.e., how much do we expect to lose on this loan? What is Recovery (R) What is the probability of default

5. Adjusting for Credit Risk In the credit risk game we need good estimates of: 1.The loan’s probability of default 2.The recovery in default 3.The expected loss  Instead of estimating the probability of default and recovery separately we can take them together and estimate the expected loss directly 5

6. Credit Risk Estimation - Methods 1.Qualitative Factors 2.Quantitative Models  Credit Score Models  Value at Risk (VaR)  RAROC Model  Other Models 6

7. Qualitative Factors 7

8. Qualitative Credit Risk Factors Loan Interest Rate The higher the interest rate on the loan the more difficult it is to make payments and the more likely the borrower is to default. Borrower Reputation From prior borrowing experiences at the bank (high/low quality) From prior borrowing in general – timely bill, rent … payments Collateral Physical assets that can be seized an sold to recover value in default Capital The insolvency buffer capital-to-asset or leverage ratio Economic Conditions How is the borrowers ability to repay affected by the business cycle – type of business (industry), type of project, type of collateral … 8

9.  Capacity  The capacity of the borrower to repay depends on future income  These effects are usually quantified for use in CR models  Loan interest rate → I  Borrower reputation → FICO, credit report …  Collateral → Loan-to-value ratio  Capital → Leverage, Tier I, and Total capital ratios  Exposure to economic conditions → Industry’s Market Beta  Capacity → projected interest coverage ratio (earnings divided by interest expense). 9 Qualitative Credit Risk Factors

10. Quantitative Models of Credit Risk  Credit Score Models  Value at Risk (VaR)  RAROC Model  Other Models 10

11. Credit Score Model  Linear Probability Model  Logit Analysis  Linear Discriminate Model 11

12. Credit Score Model Credit Score Models – Introduction 12 Types of Credit Credit Credit Score Models are models designed to analytically aggregate many dimensions of credit worthiness into a single credit score that represents a borrowers likelihood of default NewCredit Credit Score

13. 13 Credit Score Models – Example FICO Score (Fair Isaac Company) FICO = 0.35 Payment History + 0.30 Amount Owed + 0.15 + 0.10 New Credit Length of credit history Types of credit used FICO = 720 580 Sub-prime

14. How to build a credit score model 14 Credit Score Models – Construction Estimation window – track loans Default = 1 Survive = 0 These characteristics should be related to the borrowers likelihood of default – for example leverage Collect loan/borrower characteristics

15. What do you want to know about the loan/borrower? Loan/borrower characteristics:  Reputation: Years at the bank, borrowing history, # of loans repaid …  Leverage: Leverage ratio, Tier I and Total capital ratios  Future income: Earnings volatility (repayment capacity)  Collateral: Market value of physical assets backing the loan  Loan characteristics: Term, interest rate, type …  Business cycle effects: market beta, earnings sensitivity to GDP or other economic indicators  Interest rates: earnings, profitability, investment … sensitivity to interest rates. 15 Credit Score Models – Construction (Loan\Borrower Characteristics)

16. 16 Credit Score Models – Construction (Basic Estimation) Default = 1 Survive = 0 Estimation: Estimation Window Object is to build a model that we can use to predict default in the next period

17. 17 Credit Score Models – Construction (Basic Estimation) Default = 1 Survive = 0 Estimation: Estimation Window We use this information collected at the beginning of the year to estimate the model parameters (weights) Tier I Ratio # of loans w/ bank Collateral Value Earnings Volatility Loan Covenants Default =           Get loan/borrower information at the beginning of the year

18. 18 Credit Score Models – Construction (Prediction) Default = 1 Survive = 0 Prediction: Estimation Window Tier I Ratio # of loans w/ bank Collateral Value Earnings Volatility Loan Covenants Default =           Default =0      After estimating the model, we can fill in the parameters and the model can be used to forecast loan/borrower defaults

19. 19 Credit Score Models – Construction (Prediction) Default = 1 Survive = 0 Prediction: Estimation Window Tier I Ratio # of loans w/ bank Collateral Value Earnings Volatility Loan Covenants Default =0      Default =0     0.10 3 0.052 0.45 = 0.04 Example: Suppose we collect this information for Netflix at the beginning of 2012 We would expect Netflix to default with a probability of 4% over the next 1 year

20. 20 Credit Score Models – Estimation Default = 1 Survive = 0 Estimation Method Estimation Window Default =   Tier I Ratio   # of loans w/ bank Collateral Value Earnings Volatility Loan Covenants       1010010100 0.04 0.07 0.10 0.02 0.05 0372003720 2.23 0.45 1.23 2.8 1.2 2M 2.3M 0.32M 0.8M 5.2M 4 12 8 6 3 How can you estimate the parameters (weights)? There are many different ways to estimate the parameters Ordinary Least Squares (OLS) regression is the most straight forward Logit regression Discriminate analysis

21. Linear Probability Model  Uses Ordinary Least Squares (OLS) regression to estimate parameters  PROBLEMS: Can predict default probabilities outside of the range from 0-1 OLS should only be used with continuous dependent variables 21 Credit Score Models – Linear Probability Default =   Tier I Ratio   # of loans w/ bank Collateral Value Earnings Volatility Loan Covenants       Default =   X 1   X 2   X 3 …  n  X n  Choose          …  n,  so that the sum of the squared residuals is as small as we can get it (minimized)  Find          …  n to minimize Its impossible to exactly explain default with a model so we allow for an error

22. Logit Model Adjustment to correct for problems with the Linear Probability Model 1. Estimate the probability of default using the Linear Probability Model 2. Transform the probability using the Logit transformation 22 Credit Score Models – Logit Default =   X 1   X 2   X 3 …  n  X n  In practice: (only if you are interested)  In practice, a more sophisticated estimation is used.  We say that follows a Logit distribution, then we use an estimation technique called maximum likelihood to find          …  n,  it is more precise 

23. Linear Discriminate Analysis  Just another way of coming up with          …  n  The estimation technique is more complicated than either the Linear Probability model or the Logit model  The end result is still just a set of parameters  The reason that we talk about it is because there is a famous application called the Altman Z – Score that estimates a firm’s probability of default 23 Credit Score Models – Discriminate Analysis Default =   X 1   X 2   X 3 …  n  X n 

24. Altman Z-score  Used Linear Discriminate Analysis to estimate the model below 24 Credit Score Models – Discriminate Analysis (Altman Z–Score) X 1 = Working Capital/Total Assets X 2 = Retained Earnings/Total Assets X 3 = EBIT/Total Assets X 4 = MV Equity/BV Long-Term Debt X 5 = Sales/Total Assets  Z > 2.99 -“Safe” Zone  1.81 2. 99 -“Grey” Zone  1.81 -“Distress” Zone Calculation: Evaluation:

25. Kaplan Associates has estimated the following linear probability model using loan defaults over the past 4 years. Suppose that North Star restaurant applies for a loan. They have a leverage ratio of 0.25, a FICO score of 720 and a 10 year credit history. 25 a)Calculate the probability that North Star defaults over the next year using the linear probability model b)Calculate the probability that North Star defaults over the next four years using the linear probability model c)Calculate the probability that North Star defaults over the next four years using the Logit model

26. 11-26 Credit Score Models  Problems:  Only considers two extreme cases (default/no default)  Weights need not be stationary over time  Ignores hard to quantify factors including business cycle effects  Database of defaulted loans is not available to benchmark the model

27. Value at Risk (VaR) 27

28. Thinking About Credit Risk What have we done so far:  Followed a group of firms – some defaulted and some did not.  Used the actual defaults vs. non-default to try to understand, in general, what causes a firm to default on its loans.  Problem - we have to wait for firms to default to understand what causes default Another way of thinking:  If no firms defaulted would that mean that there is no credit risk?  The value of a loan can change simply because the probability of default or what we expect to recover in default changes.  This is credit risk! It exists even if no firms default  Value-at-Risk is one method used to measure this 28

29.  VaR asks:  Based on what has happened in the past  On a really bad day, how much will I lose on my loan position?  How to answer this question: 1. Collect past returns – for example, one year of daily returns 2. Calculate the mean and standard deviations of daily returns 3. Assume a normal distribution 4. Declare a significance level – for example 99% 5. Find the Value-at-risk (VaR) – Value that the company’s losses will exceed only 1% of the time – over the return horizon (next day) 29 Value-at-Risk (VaR) – Concept

30.  Returns are considered normally distributed, but this assumption can cause problems  What do we need to define a normal distribution  Mean & Standard deviation – (that’s it!) 30 Value-at-Risk (VaR) – Assumption Mean = 0.0090 Stdev = 0.0034 Is this normal?

31.  Returns are considered normally distributed, but this assumption can cause problems  What do we need to define a normal distribution  Mean & Standard deviation – (that’s it!) 31 Value-at-Risk (VaR) – Assumption Mean = 0.0053 Stdev = 0.046 Is this normal?

32. Find the one-day 95% value at risk for a bond with 1,000 face value if the price is currently $723.98.  First of all, what are we looking for?  We are looking for a threshold value for daily losses that will only be exceeded 5% of the time. That is, we have a 5% chance of losing more than this value tomorrow.  Lets start by collecting a year of historical daily returns  We work with returns because they are usually normally distributed – prices are not! 32 Value-at-Risk (VaR) – Example Based on the data that we have collected, there is a 5% probability of experiencing a return below this threshold tomorrow Once we find this return, we can back out the VaR(95%)

33. Find the one-day 95% value at risk for a bond with 1,000 face value if the price is currently $723.98. Step #1: Calculate the mean and standard deviation Step #2: Find the 95% VaR 33 Value-at-Risk (VaR) – Example Mean = 0.005473 Stdev = 0.009128 Mean = 0.005473 Stdev = 0.009128 We want to find the return that gives us 5% of the area under the curve in the tail 5% How do you do it?

34. Find the one-day 95% value at risk for a bond with 1,000 face value if the price is currently $723.98. Step #2: Find the 95% VaR (continued ) Standard Normal 5% Mean = 0.0 Stdev = 1 34 Value-at-Risk (VaR) – Example These areas and their corresponding z-values are all tabulated for the standard normal distribution. So, we can go to the normal tables and find the z-value for which 5% of the area under the curve is in the left tail. -1.64 What does that tell us? For any normal distribution, this value occurs 1.64 standard deviations below the mean

35. Find the one-day 95% value at risk for a bond with 1,000 face value if the price is currently $723.98. Step #2: Find the 95% VaR (continued ) Standard Normal 5% Mean = 0.0 Stdev = 1 35 Value-at-Risk (VaR) – Example These areas and their corresponding z-values are all tabulated for the standard normal distribution. So, we can go to the normal tables and find the z-value for which 5% of the area under the curve is in the left tail. -1.64 Mean = 0.005473 Stdev = 0.009128 5% Our Distribution X We know that “X” is 1.64 standard deviations below the mean X = 0.005473 Start at the meansubtract 1.64 Standard deviations in this case 0.009128 – 1.64(0.009128) = -0.0095

36. Finds the one-day 95% value at risk for a bond with 1,000 face value if the price is currently $723.98. Step #2: Find the 95% VaR (continued )  There is a 5% chance that the daily return will be less than –0.0095 36 Value-at-Risk (VaR) – Example Mean = 0.005473 Stdev = 0.009128 5% Our Distribution X -0.0095

37. Finds the one-day 95% value at risk for a bond with 1,000 face value if the price is currently $723.98. Step #2: Find the 95% VaR (continued )  There is a 5% chance that the daily return will be less than –0.0095  So your Value-at-Risk is: 37 Value-at-Risk (VaR) – Example Mean = 0.005473 Stdev = 0.009128 5% Our Distribution X -0.0095 VaR = ($723.98)(-0.0095) = –$6.88 There is a 95% chance that the maximum daily loss (tomorrow) will be less than $6.88 OR There is 5% chance that we will lose $6.88 or more tomorrow

38. Lorden Investments has a loan portfolio with a current value of $172M. The mean an variance of the value weighted daily return on their portfolio is 0.0181 and 0.0004 respectively. Find the 99% value at risk for the loan portfolio 38 2.3 3

39. RAROC Model 39

40. RAROC Models Risk Adjusted Return on Capital 1-year net income on the loan: 40 1 year net income on loan Interest Earned Fees Funding cost = – + Accept loan

41. RAROC Models Risk Adjusted Return on Capital Loan Risk:  Option #1  Option #2 Use value at risk to estimate the expected loss in loan value for the extreme case 41 Extreme change in the credit risk premium Accept loan

42. 42 The Lucre Island Community Bank (LICB) is planning to make a loan of $5,000,000 to the Dunder-Mifflin Paper Company. It will charge a servicing fee of 50 bps, the loan will have a maturity of 8 years, and a duration of 7.5 years. The cost of funds (RAROC benchmark) for the bank is 10%. Assume that LICB has estimated the maximum change in the risk premium on the paper processing sector to be approximately 4.2%, The current market interest rate for loans in this sector is 12

43. Lecture Summary 43  We looked at three different ways to measure credit risk:  Measuring Credit Risk  Credit Score Models Linear Probability Logit Model Linear Discriminant  Value-at-Risk (VaR)  Risk Adjusted Return on Capital - RAROC  Other Models

44. Appendix Other Models 44

45. 11-45 Term Structure Based Methods  We can use the credit spread in the market to determine the level of risk probability of default using zero coupons and strips  Suppose the contractual promised return on a corporate bond is k –the expected return is then p (1+ k)+(1-p)(0) Assuming zero recovery  Suppose the FI require a return equal to the risk free rate i p (1+ k)+(1-p)(0)= 1+i

46. Term Structure Based Methods  Then the probability of survival is:  If we allow for recovery as a percent of repayment 46 Suppose we are looking at a corporate bond that has secondary market prices. How would this change? Over what horizon?

47. 11-47 Term Structure Based Methods  May be generalized to loans with any maturity or to adjust for varying default recovery rates  The loan can be assessed using the inferred probabilities from comparable quality bonds

48. 11-48 Mortality Rate Models  Similar to the process employed by insurance companies to price policies; the probability of default is estimated from past data on defaults  Marginal Mortality Rates:  Has many of the problems associated with credit scoring models, such as sensitivity to the period chosen to calculate the MMRs

49. 11-49 Option Models Equity holders:  Equity holders view the bond as the purchase of a call option on the value of the firm Bond Principal (B) If the project fails the managers (equity holders) default on the bond If the project succeeds the managers (equity holders) pay off the bond and keep A-B proceeds Assets (A)

50. 11-50 Option Models Debt holders:  Debt holders view the bond as the sale of a put option Bond Principal (B) If the project fails the Debt holders receive the remaining collateral A If the project succeeds the debt holders receive full repayment (B) Assets (A)

51. 11-51 Applying Option Valuation Model  Merton showed value of a risky loan: where F(  ) = value of risky debt ln = Natural logarithm i = Risk-free rate on debt of equivalent maturity  remaining time to maturity B = principal amount on the bond