Your SlideShare is downloading. ×
0
Credit Risk Management Primer September 16,  2009 By A. V. Vedpuriswar
Introduction to Credit Risk <ul><li>Credit risk is caused by many factors, including: </li></ul><ul><ul><li>Borrower's abi...
Understanding Credit Risk <ul><li>Credit risk is the risk of financial loss owing to the failure of the counterparty to pe...
Banking and trading books <ul><li>The banking book covers credit risk arising from : </li></ul><ul><ul><li>commercial loan...
The Building blocks of Credit Risk Management <ul><li>Probability of default  </li></ul><ul><ul><li>Refers to the likeliho...
Probability of Default <ul><li>Probability of Default (PD) is the likelihood of default on obligations.  </li></ul><ul><li...
Estimating Probability of Default <ul><li>The analysis of a borrower's profitability and cash flow may provide early warni...
Credit Rating <ul><li>Credit ratings can also be  a useful source of information on probability of default. </li></ul><ul>...
Default events <ul><li>A delay in repayment  </li></ul><ul><li>Restructuring of borrower repayments  </li></ul><ul><li>Ban...
Transition Matrices <ul><li>It is also useful to monitor how PDs move over time.  </li></ul><ul><li>This can be done throu...
Exposure at Default <ul><li>Exposure at Default ( EAD) is the maximum (monetary) amount that a lender can lose if an oblig...
Loss Given Default <ul><li>LGD is the percentage of the credit exposure that the lender will lose if the borrower defaults...
Factors affecting LGD <ul><li>Seniority </li></ul><ul><li>Collateral </li></ul><ul><li>Type of borrower/obligation </li></ul>
Average cumulative default rates (%), 1970-2003  ( Source:  Moody’s) Rating Term (Years) 1 2 3 4 5 7 10 15 20 Aaa 0.00 0.0...
Recovery rates on corporate bonds as a percent of face value, 1982-2004.  ( Source : Moody’s). Class Average recovery rate...
Problem <ul><li>There are 10 bonds in a portfolio. The probability of default for each of the bonds over the coming year i...
<ul><li>Required probability  </li></ul><ul><li>= (10)(.05)(.95) 9 </li></ul><ul><li>= .3151 </li></ul><ul><li>=  31.51% <...
Problem <ul><li>A Credit Default Swap (CDS) portfolio consists of 5 bonds with zero default correlation. One year default ...
<ul><li>Probability of no default  </li></ul><ul><li>= (.99)(.98)(.95)(.90)(.85) </li></ul><ul><li>= .7051 </li></ul><ul><...
Problem <ul><li>If the probability of default is 6% in year 1 and  8% in year 2, what is the cumulative probability of def...
Solution <ul><li>Probability  of default not happening in both years  </li></ul><ul><li>=(.94) (.92)  = = .8648 </li></ul>...
Problem <ul><li>The 5 year cumulative probability of default for a bond is 15%. The marginal probability of default for th...
<ul><li>Required probability  </li></ul><ul><li>= 1- (.85)(.90) </li></ul><ul><li>= .235 </li></ul><ul><li>= 23.5% </li></ul>
Calculating probability of default from bond yields <ul><li>How can we do this? </li></ul><ul><li>What is the significance...
Problem <ul><li>Calculate the implied probability of default if the one year T Bill yield is 9% and a 1 year zero coupon c...
Solution <ul><li>Let the probability of default be p </li></ul><ul><li>Returns from corporate bond = 1.155 (1-p) + (0) (p)...
Problem <ul><li>In the earlier problem, if the recovery is 80% in the  case of a default, what is the default probability?...
Solution <ul><li>1.155(1-p) + (.80) (1.155) (p) = 1.09 </li></ul><ul><li>.231p = 0.065 </li></ul><ul><li>p =  .2814 </li><...
Problem  <ul><li>If 1 year and 2 year T Bills are fetching 11%  and 12% and 1 year and 2 year corporate bonds are yielding...
Solution <ul><li>Yield during the 2 nd  year can be worked out as  follows: </li></ul><ul><li>Corporate bonds: (1.165) (1+...
Significance of Credit spread <ul><li>Spread is the interest differential vis a vis a risk free instrument. </li></ul><ul>...
Problem  <ul><li>The spread between the yield on a 3 year corporate bond and the yield on a similar risk free bond is 50  ...
Solution  <ul><li>Spread = (Probability of default) (loss given default) </li></ul><ul><li>or .005 = (p) (1-.3) </li></ul>...
Problem  <ul><li>The spread between the yield on a 5 year bond and that on a similar risk free bond is 80 basis points.  I...
Solution  <ul><li>Probability of default over the 5 year period = = .0133 </li></ul><ul><li>Probability of default over th...
Problem  <ul><li>A four year corporate bond provides a 4% semi annual coupon and yields 5% while the risk free bond, also ...
Solution  <ul><li>Risk free bond </li></ul><ul><li>So expected value of losses = 103.65 – 96.21 = 7.44 </li></ul>Risk free...
<ul><li>Let the default probability per year = Q.  </li></ul><ul><li>The recovery rate is flat, 30 % of face value.  </li>...
Solution (Cont…)  <ul><li>PV factors </li></ul><ul><li>e -.015 = .9851 </li></ul><ul><li>e -.030 = .9704 </li></ul><ul><li...
Solution (Cont…)  <ul><li>Time of default  = 1 </li></ul><ul><li>PV of risk free bond = 2+2e -.015 +2e -.030 +2e -.045 + 2...
Solution (Cont…)  <ul><li>Time of default  = 3 </li></ul><ul><li>PV of risk free bond = 2[1+ .9851] + (102) (.9704) </li><...
Solution (Cont…)  <ul><li>So we can equate the expected losses: </li></ul><ul><li>i.e, 7.44  = 272.68Q </li></ul><ul><li>o...
Problem <ul><li>A bank has made a loan commitment of $ 2,000,000 to a customer.  Of this, $ 1,200,000 is outstanding.  The...
Solution <ul><li>Drawdown in case of default  = (2,000,000 – 1,200,000) (.75) = 600,000 </li></ul><ul><li>Adjusted exposur...
Problem  <ul><li>A bank makes a $100,000,000 loan at a fixed interest rate of 8.5% per annum.  </li></ul><ul><li>The cost ...
Solution <ul><li>Net profit = 100,000,000 (.085 - .060 - .0015) – 800,000 + (8,000,000) (.028) </li></ul><ul><li>  = 23,50...
Problem  <ul><li>Using the Merton Model, calculate the value of the firm’s equity.  </li></ul><ul><li>The current value of...
Solution  <ul><li>Formula is:  St  = V x N(d) – Fe -r(T-t)  x N (d-  T-t) </li></ul><ul><li>d = </li></ul><ul><li>V = va...
Solution  <ul><li>S = 60 x N (d) – (50)e -(.05)(3)  x N (d-(.1)  3) </li></ul><ul><li>d = </li></ul><ul><li>= = 2.005 </l...
Problem <ul><li>In the earlier problem, calculate the value of the firm’s  debt. </li></ul>
Solution  <ul><li>Dt = Fe -r(T-t)  – p t </li></ul><ul><li>= 50e -.05(3)  – p t </li></ul><ul><li>= 43.035 – p t </li></ul...
<ul><li>Consider the following figures for a company. What is the probability of default?  </li></ul><ul><ul><li>Book valu...
<ul><li>Distance to default (in terms of value)  = 13.8 – 1.9  = $11.9 billion </li></ul><ul><li>Standard deviation  = (.2...
<ul><li>Given the following figures, compute the distance to default: </li></ul><ul><ul><li>Book value of liabilities  : $...
<ul><li>Distance to default (in terms of value) =  18.4 – 4.15  = $14.25 billion </li></ul><ul><li>Standard deviation    =...
Upcoming SlideShare
Loading in...5
×

Credit Risk Management Primer

1,831

Published on

Overview of CreditRisk Management for MBA students

Published in: Economy & Finance, Technology
1 Comment
0 Likes
Statistics
Notes
  • Be the first to like this

No Downloads
Views
Total Views
1,831
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
98
Comments
1
Likes
0
Embeds 0
No embeds

No notes for slide

Transcript of "Credit Risk Management Primer"

  1. 1. Credit Risk Management Primer September 16, 2009 By A. V. Vedpuriswar
  2. 2. Introduction to Credit Risk <ul><li>Credit risk is caused by many factors, including: </li></ul><ul><ul><li>Borrower's ability to repay </li></ul></ul><ul><ul><li>Economic conditions </li></ul></ul><ul><ul><li>Specific events </li></ul></ul><ul><ul><li>Regional factors </li></ul></ul><ul><li>. </li></ul>
  3. 3. Understanding Credit Risk <ul><li>Credit risk is the risk of financial loss owing to the failure of the counterparty to perform its contractual obligations. </li></ul><ul><li>Lack of diversification of credit risk has been the primary reason for many bank failures. </li></ul><ul><li>Why is diversification difficult? </li></ul><ul><li>Banks have a comparative advantage in making loans to entities with whom they have an ongoing relationship. </li></ul><ul><li>This creates excessive concentrations in geographic or industrial sectors. </li></ul>
  4. 4. Banking and trading books <ul><li>The banking book covers credit risk arising from : </li></ul><ul><ul><li>commercial loans </li></ul></ul><ul><ul><li>loans to sovereigns and public sector entities </li></ul></ul><ul><ul><li>consumer (retail) loans </li></ul></ul><ul><li>Some financial instruments that give rise to credit risk do not appear on a bank's books. </li></ul><ul><li>These off-balance sheet items include loan commitments and lines of credit. </li></ul><ul><li>They may be converted later to on-balance sheet items. </li></ul><ul><li>The trading book covers credit risk arising from </li></ul><ul><ul><li>exchange traded instruments and </li></ul></ul><ul><ul><li>OTC derivatives. </li></ul></ul>
  5. 5. The Building blocks of Credit Risk Management <ul><li>Probability of default </li></ul><ul><ul><li>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. </li></ul></ul><ul><li>Exposure at default   </li></ul><ul><ul><li>Maximum amount an institution can lose if a borrower or counterparty defaults. </li></ul></ul><ul><li>Loss given default </li></ul><ul><ul><li>The percentage of an outstanding claim that cannot be recovered in the event of a default. </li></ul></ul>
  6. 6. Probability of Default <ul><li>Probability of Default (PD) is the likelihood of default on obligations. </li></ul><ul><li>PD typically depends on credit rating and maturity of transaction. </li></ul><ul><li>Longer maturity implies a higher the probability of default. </li></ul><ul><li>Shorter maturity increases creditor's flexibility to limit future losses. </li></ul>
  7. 7. Estimating Probability of Default <ul><li>The analysis of a borrower's profitability and cash flow may provide early warning signals that default is likely. </li></ul><ul><li>Qualitative factors such as reputation and market position may be used to estimate PD. </li></ul><ul><li>Models based on market prices are also used to measure PDs. </li></ul><ul><li>These models are based on: </li></ul><ul><ul><li>the market value of the borrower's equity </li></ul></ul><ul><ul><li>credit spreads </li></ul></ul>
  8. 8. Credit Rating <ul><li>Credit ratings can also be a useful source of information on probability of default. </li></ul><ul><li>External credit assessment institutions (ECAIs) give a credit rating to publicly-traded debt securities. </li></ul><ul><li>The issuer requests a rating and the ECAI conducts an examination before rating the issue. </li></ul><ul><li>The rating is reviewed from time to time and altered as the credit quality of the issuer changes. </li></ul>
  9. 9. Default events <ul><li>A delay in repayment </li></ul><ul><li>Restructuring of borrower repayments </li></ul><ul><li>Bankruptcy </li></ul>
  10. 10. Transition Matrices <ul><li>It is also useful to monitor how PDs move over time. </li></ul><ul><li>This can be done through the use of transition matrices </li></ul><ul><li>These matrices measure the probability of a given credit rating being upgraded or downgraded over time. </li></ul><ul><li>Transition matrices are calculated by comparing ratings at the beginning of a reference period with those achieved at the end of the period. </li></ul>
  11. 11. Exposure at Default <ul><li>Exposure at Default ( EAD) is the maximum (monetary) amount that a lender can lose if an obligor defaults. </li></ul><ul><li>For many credit instruments, a bank's exposure may not be known with certainty, but depends on the occurrence of some future event. </li></ul><ul><li>This occurs where credit is optional – the borrower may or may not decide to use the credit at some unknown time in the future. </li></ul><ul><li>A typical example is a committed line of credit. </li></ul><ul><li>The customer may or may not use the line of credit. </li></ul><ul><li>As a result there is uncertainty about future drawdowns. </li></ul><ul><li>Will the customer draw down and, if so, how much will be drawn down? </li></ul>
  12. 12. Loss Given Default <ul><li>LGD is the percentage of the credit exposure that the lender will lose if the borrower defaults. </li></ul><ul><li>It is also referred to as loss 'severity'. </li></ul><ul><li>The recovery rate is the percentage of the exposure that is recovered when an obligor defaults. </li></ul><ul><li>The higher the recovery rate, the lower the LGD. </li></ul>
  13. 13. Factors affecting LGD <ul><li>Seniority </li></ul><ul><li>Collateral </li></ul><ul><li>Type of borrower/obligation </li></ul>
  14. 14. Average cumulative default rates (%), 1970-2003 ( Source: Moody’s) Rating Term (Years) 1 2 3 4 5 7 10 15 20 Aaa 0.00 0.00 0.00 0.04 0.12 0.29 0.62 1.21 1.55 Aa 0.02 0.03 0.06 0.15 0.24 0.43 0.68 1.51 2.70 A 0.02 0.09 0.23 0.38 0.54 0.91 1.59 2.94 5.24 Baa 0.20 0.57 1.03 1.62 2.16 3.24 5.10 9.12 12.59 Ba 1.26 3.48 6.00 8.59 11.17 15.44 21.01 30.88 38.56 B 6.21 13.76 20.65 26.66 31.99 40.79 50.02 59.21 60.73 Caa 23.65 37.20 48.02 55.56 60.83 69.36 77.91 80.23 80.23
  15. 15. Recovery rates on corporate bonds as a percent of face value, 1982-2004. ( Source : Moody’s). Class Average recovery rate (%) Senior secured 57.4 Senior unsecured 44.9 Senior subordinated 39.1 Subordinated 32.0 Junior subordinated 28.9
  16. 16. Problem <ul><li>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? </li></ul>
  17. 17. <ul><li>Required probability </li></ul><ul><li>= (10)(.05)(.95) 9 </li></ul><ul><li>= .3151 </li></ul><ul><li>= 31.51% </li></ul>
  18. 18. Problem <ul><li>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? </li></ul>
  19. 19. <ul><li>Probability of no default </li></ul><ul><li>= (.99)(.98)(.95)(.90)(.85) </li></ul><ul><li>= .7051 </li></ul><ul><li>= 70.51% </li></ul>
  20. 20. Problem <ul><li>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? </li></ul>
  21. 21. Solution <ul><li>Probability of default not happening in both years </li></ul><ul><li>=(.94) (.92) = = .8648 </li></ul><ul><li>Required probability = 1 - .8648 = .1352 </li></ul><ul><li>= 13.52% </li></ul>
  22. 22. Problem <ul><li>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? </li></ul>
  23. 23. <ul><li>Required probability </li></ul><ul><li>= 1- (.85)(.90) </li></ul><ul><li>= .235 </li></ul><ul><li>= 23.5% </li></ul>
  24. 24. Calculating probability of default from bond yields <ul><li>How can we do this? </li></ul><ul><li>What is the significance of yield? </li></ul>
  25. 25. Problem <ul><li>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. </li></ul>
  26. 26. Solution <ul><li>Let the probability of default be p </li></ul><ul><li>Returns from corporate bond = 1.155 (1-p) + (0) (p) </li></ul><ul><li>Returns from treasury = 1.09. </li></ul><ul><li>To prevent arbitrage, </li></ul><ul><ul><li>1.155(1-p) = 1.09 </li></ul></ul><ul><ul><li>p = 1- 1.09/1.155 = 1- .9437 </li></ul></ul><ul><li>Probability of default = .0563 = 5.63% </li></ul>
  27. 27. Problem <ul><li>In the earlier problem, if the recovery is 80% in the case of a default, what is the default probability? </li></ul>
  28. 28. Solution <ul><li>1.155(1-p) + (.80) (1.155) (p) = 1.09 </li></ul><ul><li>.231p = 0.065 </li></ul><ul><li>p = .2814 </li></ul>
  29. 29. Problem <ul><li>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? </li></ul>
  30. 30. Solution <ul><li>Yield during the 2 nd year can be worked out as follows: </li></ul><ul><li>Corporate bonds: (1.165) (1+i) = 1.17 2 </li></ul><ul><li> i = 17.5% </li></ul><ul><li>Treasury : (1.11) (1+i) = (1.12) 2 </li></ul><ul><li> i = 13.00% </li></ul><ul><li> (1- p) (1.175) + (p) (0) = 1.13 </li></ul><ul><li> p = 1- .9617 </li></ul><ul><li> Default probability = 3.83% </li></ul>
  31. 31. Significance of Credit spread <ul><li>Spread is the interest differential vis a vis a risk free instrument. </li></ul><ul><li>What is the significance of the spread? </li></ul>
  32. 32. Problem <ul><li>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? </li></ul>
  33. 33. Solution <ul><li>Spread = (Probability of default) (loss given default) </li></ul><ul><li>or .005 = (p) (1-.3) </li></ul><ul><li>or p = = .00714 = .71% per year </li></ul><ul><li>No default over 3 years = (.9929) (.9929) (.9929) = .9789 </li></ul><ul><li>So cumulative probability of default = 1 – 9789 = .0211 = 2.11% </li></ul>
  34. 34. Problem <ul><li>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? </li></ul>
  35. 35. Solution <ul><li>Probability of default over the 5 year period = = .0133 </li></ul><ul><li>Probability of default over the 3 year period = = .01167 </li></ul><ul><li>(1-.0133) 5 = (1-.01167) 3 (1-p) 2 </li></ul><ul><li>or (1-p) 2 = = .9688 </li></ul><ul><li>or 1 – p = .9842 </li></ul><ul><li>or p = .0158 = 1.58% </li></ul>
  36. 36. Problem <ul><li>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. </li></ul><ul><li>Defaults may take place at the end of each year. </li></ul><ul><li>In case of default, the recovery rate is flat 30% of the face value. </li></ul><ul><li>What is the risk neutral default probability? </li></ul>
  37. 37. Solution <ul><li>Risk free bond </li></ul><ul><li>So expected value of losses = 103.65 – 96.21 = 7.44 </li></ul>Risk free bond Corporate bond Year Cash flow PV factor e -(.03)t PV PV factor e -(.05)t PV .5 2 .9851 1.9702 .9754 1.9508 1.0 2 .9704 1.9408 .9512 1.9024 1.5 2 .9560 1.9120 .9277 1.8554 2.0 2 .9418 1.8836 .9048 1.8096 2.5 2 .9277 1.8554 .8825 1.7650 3.0 2 .9139 1.8278 .8607 1.7214 3.5 2 .9003 1.8006 .8395 1.679 4.0 102 .8869 90.4638 .8187 83.51 103.6542 96.21
  38. 38. <ul><li>Let the default probability per year = Q. </li></ul><ul><li>The recovery rate is flat, 30 % of face value. </li></ul><ul><li>So if the notional principal is 100, we can recover 30. </li></ul><ul><li>We can work out the present value of losses assuming the default may happen at the end of years 1, 2, 3, 4. </li></ul><ul><li>Accordingly, we calculate the present value of the risk free bond at the end of years 1, 2, 3, 4. </li></ul><ul><li>Then we subtract 30 being the recovery value each year. </li></ul><ul><li>We then calculate the present value of the losses using continuously compounded risk free rate. </li></ul>
  39. 39. Solution (Cont…) <ul><li>PV factors </li></ul><ul><li>e -.015 = .9851 </li></ul><ul><li>e -.030 = .9704 </li></ul><ul><li>e -.045 = .9560 </li></ul><ul><li>e -.060 = .9417 </li></ul><ul><li>e -.075 = .9277 </li></ul><ul><li>e -.09 = .9139 </li></ul>
  40. 40. Solution (Cont…) <ul><li>Time of default = 1 </li></ul><ul><li>PV of risk free bond = 2+2e -.015 +2e -.030 +2e -.045 + 2e -.060 +2e -075 + (102)e -.090 </li></ul><ul><li>= 2[1+.9851+.9704+.9560+.9417+.9277]+(102)(.9139) </li></ul><ul><li>= 11.56 + 93.22 = 104.78 </li></ul><ul><li>Time of default = 2 </li></ul><ul><li>PV of risk free bond </li></ul><ul><li>= 2[1+.9851+.9704 +.9560]+(102) (.9417) </li></ul><ul><li>= 7.823 + 96.05 = 103.88 </li></ul>
  41. 41. Solution (Cont…) <ul><li>Time of default = 3 </li></ul><ul><li>PV of risk free bond = 2[1+ .9851] + (102) (.9704) </li></ul><ul><li>= 3.97 + 98.98 </li></ul><ul><li>= 102.95 </li></ul><ul><li>Time of default = 4 </li></ul><ul><li>PV of risk free bond </li></ul><ul><li>= 102 </li></ul>
  42. 42. Solution (Cont…) <ul><li>So we can equate the expected losses: </li></ul><ul><li>i.e, 7.44 = 272.68Q </li></ul><ul><li>or Q = .0273 = 2.73% </li></ul>Default point (Years) Expected losses PV 1 (104.78 – 30)Q = 74.78Q (74.78)Qe -.03 = 72.57Q 2 (103.88 – 30)Q = 73.78Q (73.88)Qe -.06 = 69.58Q 3 (102.95 – 30)Q = 72.95Q (72.95)Qe -.09 = 66.67Q 4 (102 – 30)Q = 72 Q (72)Qe -.12 = 63.86Q 272.68 Q
  43. 43. Problem <ul><li>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? </li></ul>
  44. 44. Solution <ul><li>Drawdown in case of default = (2,000,000 – 1,200,000) (.75) = 600,000 </li></ul><ul><li>Adjusted exposure = 1,200,000 + 600,000 = 1,800,000 </li></ul><ul><li>Loss given default = (.01) (.4) (1,800,000) = $ 7,200 </li></ul>
  45. 45. Problem <ul><li>A bank makes a $100,000,000 loan at a fixed interest rate of 8.5% per annum. </li></ul><ul><li>The cost of funds for the bank is 6.0%, while the operating cost is $800,000. </li></ul><ul><li>The economic capital needed to support the loan is $8 million which is invested in risk free instruments at 2.8%. </li></ul><ul><li>The expected loss for the loan is 15 basis points per year. </li></ul><ul><li>What is the risk adjusted return on capital? </li></ul>
  46. 46. Solution <ul><li>Net profit = 100,000,000 (.085 - .060 - .0015) – 800,000 + (8,000,000) (.028) </li></ul><ul><li> = 23,50,000 – 800,000 + 224,000 </li></ul><ul><li> = $1,774,000 </li></ul><ul><li>Risk adjusted return on capital = 1.774/8 = .22175 = 22.175% </li></ul>
  47. 47. Problem <ul><li>Using the Merton Model, calculate the value of the firm’s equity. </li></ul><ul><li>The current value of the firm’s equity is $60 million and the value of the zero coupon bond to be redeemed in 3 years is $50 million. </li></ul><ul><li>The annual interest rate is 5% while the volatility of the firm value is 10%. </li></ul>
  48. 48. Solution <ul><li>Formula is: St = V x N(d) – Fe -r(T-t) x N (d-  T-t) </li></ul><ul><li>d = </li></ul><ul><li>V = value of firm </li></ul><ul><li>F = face value of zero coupon debt </li></ul><ul><li> = firm value volatility </li></ul><ul><li>r = interest rate </li></ul>
  49. 49. Solution <ul><li>S = 60 x N (d) – (50)e -(.05)(3) x N (d-(.1)  3) </li></ul><ul><li>d = </li></ul><ul><li>= = 2.005 </li></ul><ul><li>S = 60 N (2.005) – (50) (.8607) N (2.005 - .17321) </li></ul><ul><li>= 60 N (2.005) – (43.035) N (1.8318) </li></ul><ul><li>= (60) (.9775) – (43.035) (.9665) </li></ul><ul><li>= $17.057 million </li></ul>
  50. 50. Problem <ul><li>In the earlier problem, calculate the value of the firm’s debt. </li></ul>
  51. 51. Solution <ul><li>Dt = Fe -r(T-t) – p t </li></ul><ul><li>= 50e -.05(3) – p t </li></ul><ul><li>= 43.035 – p t </li></ul><ul><li>Based on put call parity </li></ul><ul><li>p t = C t + Fe -r(T-t) – V </li></ul><ul><li>Or p t = 17.057 + 43.035 – 60 = .092 </li></ul><ul><li>D t = 43.035 - .092 = $42.943 million </li></ul><ul><li>Alternatively, value of debt </li></ul><ul><li>= Firm value – Equity value = 60 – 17.057 </li></ul><ul><li>= $42.943 million </li></ul>
  52. 52. <ul><li>Consider the following figures for a company. What is the probability of default? </li></ul><ul><ul><li>Book value of all liabilities : $2.4 billion </li></ul></ul><ul><ul><li>Estimated default point, D : $1.9 billion </li></ul></ul><ul><ul><li>Market value of equity : $11.3 billion </li></ul></ul><ul><ul><li>Market value of firm : $13.8 billion </li></ul></ul><ul><ul><li>Volatility of firm value : 20% </li></ul></ul>Problem
  53. 53. <ul><li>Distance to default (in terms of value) = 13.8 – 1.9 = $11.9 billion </li></ul><ul><li>Standard deviation = (.20) (13.8) = $2.76 billion </li></ul><ul><li>Distance to default (in terms of standard deviation) = 4.31 </li></ul><ul><li>We now refer to the default database. </li></ul><ul><li>If 5 out of 100 firms with distance to default = 4.31 actually defaulted, probability of default = .05 </li></ul>Solution
  54. 54. <ul><li>Given the following figures, compute the distance to default: </li></ul><ul><ul><li>Book value of liabilities : $5.95 billion </li></ul></ul><ul><ul><li>Estimated default point : $4.15 billion </li></ul></ul><ul><ul><li>Market value of equity : $ 12.4 billion </li></ul></ul><ul><ul><li>Market value of firm : $18.4 billion </li></ul></ul><ul><ul><li>Volatility of firm value : 24% </li></ul></ul>Problem
  55. 55. <ul><li>Distance to default (in terms of value) = 18.4 – 4.15 = $14.25 billion </li></ul><ul><li>Standard deviation = (.24) (18.4) = $4.416 billion </li></ul><ul><li>Distance to default (in terms of standard deviation) = 3.23 </li></ul>Solution
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×