1. J. K. Dietrich - FBE 524 - Fall, 2005 Risk Premiums in Interest Rates Week 8 – October 12, 2005

2. J. K. Dietrich - FBE 524 - Fall, 2005 Types of Risk u Holding-period yield risk –Capital gains risk –Reinvestment risk u Default risk –Non-payment of principal –Delayed or reduced payments –Sometimes viewed as embedded option (put) u Call risks –Call risks can be viewed as embedded options (call) u Liquidity or marketability risk –Often measured as bid-ask spread for traded securities

3. J. K. Dietrich - FBE 524 - Fall, 2005 Text Exhibit 8.6 Risky Rates

4. J. K. Dietrich - FBE 524 - Fall, 2005 Holding Period Yield Risk u Bond price is function of expected cash flows and RADR, but usually bond traders define contractual cash flows and yields to maturity u Relationship between YTM and p is a curve defined by equation from last week

5. J. K. Dietrich - FBE 524 - Fall, 2005 Bond Prices and Yields

6. J. K. Dietrich - FBE 524 - Fall, 2005 Holding Period Risk (cont’d) u Zero coupon default risk free bonds held to maturity will earn yield to maturity –If maturity equals holding period, no risk –Future wealth from coupon bonds depends on income from reinvested cash at rates not known now u Bonds which must be sold at end of holding period (maturity does not equal holding period) have risk of capital gains or losses

7. J. K. Dietrich - FBE 524 - Fall, 2005 Measuring Holding-Period Risk u Price sensitivity of bonds is measured in terms of a bond price elasticity u This elasticity is called duration denoted d 1, which is widely used by bond traders and analysts and is often available on quote sheets

8. J. K. Dietrich - FBE 524 - Fall, 2005 Example of Duration u Assume a 10-year 8% coupon bond is priced at 12% yield to maturity and has value of 77.4 and duration of 6.8 u If yields changed immediately from 12% to 10%, that is a 2/112 or 1.8% change in gross yield u The bond price should change about 1.8% * 6.8 = 12.1%

9. J. K. Dietrich - FBE 524 - Fall, 2005 Duration as Time Measure u Macauley noted that maturity was not relevant measure of timing of payments of bonds and defined his own measure, duration u The definition of duration is (p. 192):

10. J. K. Dietrich - FBE 524 - Fall, 2005 Duration has two interpretations u Elasticity of bond prices with respect to changes in one plus the yield to maturity u Weighted average payment date of cash flows (coupon and interest) from bonds u Duration measure –Can be modified to be a yield elasticity by dividing by (1+yield to maturity) –Can be redefined using term structure of yields (Fisher-Weil duration noted d 2 )

11. J. K. Dietrich - FBE 524 - Fall, 2005 Alternative Duration Calculation u Duration is widely used by bond traders and fixed income portfolio managers u Duration values are available from information services like Bloomberg u Calculated is three ways –Macauley’s formula (but combersome) –Calculate two prices and rates, divide changes –Closed-form solution, e.g. Dietrich formulation:

12. J. K. Dietrich - FBE 524 - Fall, 2005 Duration is an Approximation Yield to Maturity Price (Par=1.0) 0 Derivative is used in calculating duration Change predicted by duration Actual price change

13. J. K. Dietrich - FBE 524 - Fall, 2005 Duration as Risk Measure u Good –Balances reinvestment yield risk against capital gains risk –Widely used and clear mathematical expression assessing holding-period yield risk u Bad –Approximation and theoretical issues –Convexity adjustment only approximate improvement

14. J. K. Dietrich - FBE 524 - Fall, 2005

15. Default or Credit Risk Example of 8% 3-year bond with risk-adjusted discount rate (RADR) of 12%:

16. J. K. Dietrich - FBE 524 - Fall, 2005 Effect of Credit Risk Change u RADR constant at 12%: u Note price and yield change –Could be a change in one industry or firm –Default risk could be diversified in this case

17. J. K. Dietrich - FBE 524 - Fall, 2005 Pricing Default-Risky Bond u Discount expected cash flows (related to default probabilities) to obtain value –Default probabilities may be related to bond ratings –Change in default probability will change expected cash flows and yield to maturity u Risk-adjusted discount rate (RADR) may or may not change with change in default risk

18. J. K. Dietrich - FBE 524 - Fall, 2005 Risk Premiums in RADRs u Diversifiable or avoidable risks –Hedge portfolios can reduce or eliminate –Unsystematic risks are not priced (do not increase discount rate) u Priced versus non-priced risk –Systematic risks are unavoidable –Risk aversion (declining marginal utility of wealth) is underlying assumption

19. J. K. Dietrich - FBE 524 - Fall, 2005 Short and Long Risk Premia

20. J. K. Dietrich - FBE 524 - Fall, 2005 Default Risk Premiums u Vary over the business cycle –Can be changes in default risk probabilities or in the market price of risk u Current default risk premiums are very high relative to historical experience u Development of bond markets internationally is believed to promise substantial growth and risk analysis of private borrowers will be very important

21. J. K. Dietrich - FBE 524 - Fall, 2005 Liquidity Risk u Unusual securities in often cannot be sold readily –Reflected in dealers’ spreads –If no market makers, can only be estimated –Thin markets require price concessions for quick transactions despite intrinsic values u Examples –Structured notes and Orange County –Drexel Burnam and junk bonds in 1980s –The Russian debt market collapse in 1998

22. J. K. Dietrich - FBE 524 - Fall, 2005 Developments in Credit-risk u Usual interpretation of credit risk is default on a loan or bond u New views of credit risk are focused on the change in the credit-worthiness of debt instruments as well as default u Risk changes will be reflected in the value of a portfolio over time as write-downs or downgrades short of default reduce value of claims

23. J. K. Dietrich - FBE 524 - Fall, 2005 Default u Private debt (corporate and household) may not pay cash flows as promised –Late payments –Nonpayment of interest or principal u Other default or credit events –Violation of covenants and other creditor interventions in operations –Change in risk of default (e.g. highly leveraged transactions)

24. J. K. Dietrich - FBE 524 - Fall, 2005 Credit Events u Probability of default (PD) can change affecting the value of default-risky securities u Upgrades and downgrades reflecting changes in PD are credit events u Recent progress has been made in quantifying these probabilities

25. J. K. Dietrich - FBE 524 - Fall, 2005 Bond and Debt Ratings u Rating agencies –Standard and Poor’s (AAA to D) –Moody’s (Aaa to C) –Fitch and Duff and Phelps u Migration of ratings, e.g. from BBB to BB (investment grade to below investment grade) represents credit risk u For example, change from BBB to BB has historical probability of 5.3% (S&P, 1996)

26. J. K. Dietrich - FBE 524 - Fall, 2005 Risk of Fixed Incomes Future Value of Debt Probability Maximum value=F

27. J. K. Dietrich - FBE 524 - Fall, 2005 Credit Losses u Three elements in credit losses –Estimated default probability (PD) –Loss given default (LGD) –Exposure at default (EAD) u Credit losses = PD*LGD*EAD u Investors in debt securities will be concerned about all these elements in managing their risks

28. J. K. Dietrich - FBE 524 - Fall, 2005 Credit Risk Analysis u Credit risk has become a major focus of rating agencies, regulators, and investors –Very important to capital market development (e.g. asset securitizations, loan syndications) –Enron, Global Crossing, and GE exemplify different stages of concern with these issues u Consulting industry in credit analysis –RiskMetrics (formerly J.P. Morgan) –KMV (academic based research) –Others (KPMG, PricewaterhouseCoopers, etc.)

29. J. K. Dietrich - FBE 524 - Fall, 2005 Example of Steps to estimate PD u Default occurs when value of assets less than value of liabilities (insolvency) u Example of analysis used by KMV uses simplified estimates of variables u Must calculate market value of assets (market value of debt and equity) and variability of market value u Identify book value of liabilities

30. J. K. Dietrich - FBE 524 - Fall, 2005 Motorola: Debt and Equity Total Market Value

31. J. K. Dietrich - FBE 524 - Fall, 2005 Distance to Default: Example u Motorola 2001-II (billions) Value of long-term debt = $ 7.3 Book value of current liabilities= 12.9 Total value of liabilities= $20.2 Market value of assets= $56.6 Standard deviation of change in market value= 16.4% u Market value  standard deviation of percent change = $9.3 billion

32. J. K. Dietrich - FBE 524 - Fall, 2005 Reduced Probability of Default? u Estimated default point in example is midway between book value of current liabilities and long-term debt u Theory is that long-term debt does not require immediate payment, short-term liabilities may allow some flexibility u KMV uses historical data to fine-tune this estimate

33. J. K. Dietrich - FBE 524 - Fall, 2005 Estimated Distance to Default $56.6$20.2 $12.9 TMVCL+LTDCL Default point (estimated as midpoint) = $16.6 Market value to default point = $40.0

34. J. K. Dietrich - FBE 524 - Fall, 2005 Distance to Default: 12-31-02 u Total Value of Assets (from “Capital Structure” and Financial Statements): E + LTD + CL = TA $33.9 + $ 8.1 + $9.7 = $ 51.7 u Book value of LTD and CL $8.4 and $9.7 Midpoint estimate of default point = $13.9 Std Dev = 16.4% * $51.7 = $8.48

35. J. K. Dietrich - FBE 524 - Fall, 2005 Probability of Default u KMV has used historical data to relate distance from default to probability of default u That measure is proprietary (not available) u As example, Motorola is rated A3 by Standard and Poors, historically associated with a default rate of about.82% over next five years

36. J. K. Dietrich - FBE 524 - Fall, 2005 Credit Risk in Portfolios u Individual assets have probability of default and risk and discussed last week u Loans in portfolios will have an interdependent risk structure due to correlations in defaults u Credit risk within portfolio context is a major advance in credit risk management u Search for a summary measure of portfolio risk led to the concept of value at risk

37. J. K. Dietrich - FBE 524 - Fall, 2005 Value at Risk (VAR) u Value at risk (VAR) looks at risk of portfolio accounting for covariance of assets u Risk is defined in terms of likelihood of losses

38. J. K. Dietrich - FBE 524 - Fall, 2005 Portfolio Credit Risk u Credit risk different than usual portfolio risk analysis –Returns are not symmetric –Concentrations of exposure complicate losses u Major issue is correlation of defaults and losses given default –We will discuss approach followed by CreditMetrics –Other approaches exist (including KMV)

39. J. K. Dietrich - FBE 524 - Fall, 2005 Credit Risk as Rating Changes u Increased credit riskDefault CCC B BB u Same credit risk (BBB)BBB A AA u Less credit risk

40. J. K. Dietrich - FBE 524 - Fall, 2005 Rating Migrations (BBB rating) Source: Standard & Poors

41. J. K. Dietrich - FBE 524 - Fall, 2005 Two Bond Rating Migrations

42. J. K. Dietrich - FBE 524 - Fall, 2005 Probability of Default: Two Firms Value of Firm A Value of Firm B Default Point A Default Point B Probability = 1/100% Probability = 1/2% Probability = 1/10%

43. J. K. Dietrich - FBE 524 - Fall, 2005 Loss Given Default

44. J. K. Dietrich - FBE 524 - Fall, 2005 Simplified “Road Map” Compute exposure profile Of each asset Compute the volatility Of value caused by Up (down)grades and defaults Compute correlations Portfolio value-at-risk due to credit Source: Introduction to CreditMetrics (1997)

45. J. K. Dietrich - FBE 524 - Fall, 2005 Required Resources u Default probabilities (or ratings) u Migration probabilities –Historical data requirements –Approaches to estimating correlations u Complete data on types of credits and estimations of losses given defaults u Exposures to classes of risks u Models and simulations of value changes given credit events

46. J. K. Dietrich - FBE 524 - Fall, 2005 Credit Portfolio Risk Frequency Return Frequency Return One AssetMany Assets 00

47. J. K. Dietrich - FBE 524 - Fall, 2005 Incremental Risk u Introduction to CreditMetrics provides good examples (in Section 5) u Importance portfolio risk is the marginal risk u Marginal risk considers portfolio risk implications 10% $ Credit Exposure High risk and large size $ 10mm 

48. J. K. Dietrich - FBE 524 - Fall, 2005 Next Week – October 19, 2005 u Take-home midterm examination due; 90- minute examination is open book and open note u Examination must be completed without discussion with anyone and a declaration to that effect and time spent turned in with examination u Prepare Chapter 9 u Arrange a meeting regarding project progress if you have not talked to me