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Credit Risk Management Primer

Credit Risk Management Primer. By A. V. Vedpuriswar. September 16, 2009. Introduction to Credit Risk. Credit risk is caused by many factors, including: Borrower's ability to repay Economic conditions Specific events Regional factors. 1. Understanding Credit Risk.

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Credit Risk Management Primer

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  1. Credit Risk Management Primer By A. V. Vedpuriswar September 16, 2009

  2. Introduction to Credit Risk Credit risk is caused by many factors, including: Borrower's ability to repay Economic conditions Specific events Regional factors . 1

  3. Understanding Credit Risk Credit risk is the risk of financial loss owing to the failure of the counterparty to perform its contractual obligations. Lack of diversification of credit risk has been the primary reason for many bank failures. Why is diversification difficult? Banks have a comparative advantage in making loans to entities with whom they have an ongoing relationship. This creates excessive concentrations in geographic or industrial sectors. 2

  4. Banking and trading books The banking book covers credit risk arising from : commercial loans loans to sovereigns and public sector entities consumer (retail) loans Some financial instruments that give rise to credit risk do not appear on a bank's books. These off-balance sheet items include loan commitments and lines of credit. They may be converted later to on-balance sheet items. The trading book covers credit risk arising from exchange traded instruments and OTC derivatives. 3

  5. The Building blocks of Credit Risk Management Probability of default Refers to the likelihood that a borrower will be unable to honor its contractual obligations and is therefore a measure of the expected default frequency. Exposure at default Maximum amount an institution can lose if a borrower or counterparty defaults. Loss given default The percentage of an outstanding claim that cannot be recovered in the event of a default. 4

  6. Probability of Default Probability of Default (PD) is the likelihood of default on obligations. PD typically depends on credit rating and maturity of transaction. Longer maturity implies a higher the probability of default. Shorter maturity increases creditor's flexibility to limit future losses. 5

  7. Estimating Probability of Default The analysis of a borrower's profitability and cash flow may provide early warning signals that default is likely. Qualitative factors such as reputation and market position may be used to estimate PD. Models based on market prices are also used to measure PDs. These models are based on: the market value of the borrower's equity credit spreads 6

  8. Credit Rating Credit ratings can also be a useful source of information on probability of default. External credit assessment institutions (ECAIs) give a credit rating to publicly-traded debt securities. The issuer requests a rating and the ECAI conducts an examination before rating the issue. The rating is reviewed from time to time and altered as the credit quality of the issuer changes. 7

  9. Default events A delay in repayment Restructuring of borrower repayments Bankruptcy 8

  10. Transition Matrices It is also useful to monitor how PDs move over time. This can be done through the use of transition matrices These matrices measure the probability of a given credit rating being upgraded or downgraded over time. Transition matrices are calculated by comparing ratings at the beginning of a reference period with those achieved at the end of the period. 9

  11. Exposure at Default Exposure at Default (EAD) is the maximum (monetary) amount that a lender can lose if an obligor defaults. For many credit instruments, a bank's exposure may not be known with certainty, but depends on the occurrence of some future event. This occurs where credit is optional – the borrower may or may not decide to use the credit at some unknown time in the future. A typical example is a committed line of credit. The customer may or may not use the line of credit. As a result there is uncertainty about future drawdowns. Will the customer draw down and, if so, how much will be drawn down? 10

  12. Loss Given Default LGD is the percentage of the credit exposure that the lender will lose if the borrower defaults. It is also referred to as loss 'severity'. The recovery rate is the percentage of the exposure that is recovered when an obligor defaults. The higher the recovery rate, the lower the LGD. 11

  13. Factors affecting LGD Seniority Collateral Type of borrower/obligation 12

  14. Average cumulative default rates (%), 1970-2003 (Source: Moody’s) 13

  15. Recovery rates on corporate bonds as a percent of face value, 1982-2004. (Source: Moody’s). 14

  16. Problem • There are 10 bonds in a portfolio. The probability of default for each of the bonds over the coming year is 5%.These probabilities are independent of each other. What is the probability that exactly one bond defaults?

  17. Required probability = (10)(.05)(.95)9 = .3151 = 31.51%

  18. Problem • A Credit Default Swap (CDS) portfolio consists of 5 bonds with zero default correlation. One year default probabilities are : 1%, 2%, 5%,10% and 15% respectively. What is the probability that that the protection seller will not have to pay compensation?

  19. Probability of no default = (.99)(.98)(.95)(.90)(.85) = .7051 = 70.51%

  20. Problem • If the probability of default is 6% in year 1 and 8% in year 2, what is the cumulative probability of default during the two years? 19

  21. Solution • Probability of default not happening in both years =(.94) (.92) = = .8648 • Required probability = 1 －.8648 = .1352 • = 13.52% 20

  22. Problem • The 5 year cumulative probability of default for a bond is 15%. The marginal probability of default for the sixth year is 10%. What is the six year cumulative probability of default?

  23. Required probability = 1- (.85)(.90) = .235 = 23.5%

  24. Calculating probability of default from bond yields How can we do this? What is the significance of yield?

  25. Problem • Calculate the implied probability of default if the one year T Bill yield is 9% and a 1 year zero coupon corporate bond is fetching 15.5%. Assume no amount can be recovered in case of default.

  26. Solution • Let the probability of default be p • Returns from corporate bond = 1.155 (1-p) + (0) (p) • Returns from treasury = 1.09. • To prevent arbitrage, 1.155(1-p) = 1.09 p = 1- 1.09/1.155 = 1- .9437 • Probability of default = .0563 = 5.63%

  27. Problem • In the earlier problem, if the recovery is 80% in the case of a default, what is the default probability?

  28. Solution • 1.155(1-p) + (.80) (1.155) (p) = 1.09 • .231p = 0.065 • p = .2814

  29. Problem • If 1 year and 2 year T Bills are fetching 11% and 12% and 1 year and 2 year corporate bonds are yielding 16.5% and 17%, what is the marginal probability of default for the corporate bond in the second year? 28

  30. Solution • Yield during the 2nd year can be worked out as follows: • Corporate bonds: (1.165) (1+i) = 1.172 • i = 17.5% • Treasury : (1.11) (1+i) = (1.12)2 • i = 13.00% • (1- p) (1.175) + (p) (0) = 1.13 • p = 1- .9617 • Default probability = 3.83% 29

  31. Significance of Credit spread Spread is the interest differential vis a vis a risk free instrument. What is the significance of the spread?

  32. Problem • The spread between the yield on a 3 year corporate bond and the yield on a similar risk free bond is 50 basis points. The recovery rate is 30%. What is the cumulative probability of default over the three year period?

  33. Solution • Spread = (Probability of default) (loss given default) • or .005 = (p) (1-.3) • or p = = .00714 = .71% per year • No default over 3 years = (.9929) (.9929) (.9929) = .9789 • So cumulative probability of default = 1 – 9789 = .0211 = 2.11%

  34. Problem • The spread between the yield on a 5 year bond and that on a similar risk free bond is 80 basis points. If the loss given default is 60%, estimate the average probability of default over the 5 year period. If the spread is 70 basis points for a 3 year bond, what is the probability of default over years 4, 5?

  35. Solution • Probability of default over the 5 year period = = .0133 • Probability of default over the 3 year period = = .01167 • (1-.0133)5 = (1-.01167)3 (1-p)2 • or (1-p)2 = = .9688 • or 1 – p = .9842 • or p = .0158 = 1.58%

  36. Problem • A four year corporate bond provides a 4% semi annual coupon and yields 5% while the risk free bond, also with 4% coupon yields 3% with continuous compounding. The bonds are redeemable at a maturity at a face value of 100. • Defaults may take place at the end of each year. • In case of default, the recovery rate is flat 30% of the face value. • What is the risk neutral default probability?

  37. Solution • Risk free bond • So expected value of losses = 103.65 – 96.21 = 7.44

  38. Let the default probability per year = Q. • The recovery rate is flat, 30 % of face value. • So if the notional principal is 100, we can recover 30. • We can work out the present value of losses assuming the default may happen at the end of years 1, 2, 3, 4. • Accordingly, we calculate the present value of the risk free bond at the end of years 1, 2, 3, 4. • Then we subtract 30 being the recovery value each year. • We then calculate the present value of the losses using continuously compounded risk free rate.

  39. Solution (Cont…) • PV factors • e-.015 = .9851 • e-.030 = .9704 • e-.045 = .9560 • e-.060 = .9417 • e-.075 = .9277 • e-.09 = .9139

  40. Solution (Cont…) Time of default = 1 • PV of risk free bond = 2+2e-.015+2e-.030+2e-.045+ 2e-.060+2e-075+ (102)e-.090 • = 2[1+.9851+.9704+.9560+.9417+.9277]+(102)(.9139) • = 11.56 + 93.22 = 104.78 Time of default = 2 • PV of risk free bond • = 2[1+.9851+.9704 +.9560]+(102) (.9417) • = 7.823 + 96.05 = 103.88

  41. Solution (Cont…) Time of default = 3 • PV of risk free bond = 2[1+ .9851] + (102) (.9704) • = 3.97 + 98.98 • = 102.95 Time of default = 4 • PV of risk free bond • = 102

  42. Solution (Cont…) • So we can equate the expected losses: • i.e, 7.44 = 272.68Q • or Q = .0273 = 2.73%

  43. Problem • A bank has made a loan commitment of $ 2,000,000 to a customer. Of this, $ 1,200,000 is outstanding. There is a 1% default probability and 40% loss given default. In case of default, drawdown is expected to be 75%. What is the expected loss? 42

  44. Solution • Drawdown in case of default = (2,000,000 – 1,200,000) (.75) = 600,000 • Adjusted exposure = 1,200,000 + 600,000 = 1,800,000 • Loss given default = (.01) (.4) (1,800,000) = $ 7,200 43

  45. Problem • A bank makes a $100,000,000 loan at a fixed interest rate of 8.5% per annum. • The cost of funds for the bank is 6.0%, while the operating cost is $800,000. • The economic capital needed to support the loan is $8 million which is invested in risk free instruments at 2.8%. • The expected loss for the loan is 15 basis points per year. • What is the risk adjusted return on capital?

  46. Solution • Net profit = 100,000,000 (.085 - .060 - .0015) – 800,000 + (8,000,000) (.028) • = 23,50,000 – 800,000 + 224,000 • = $1,774,000 • Risk adjusted return on capital = 1.774/8 = .22175 = 22.175%

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