"Risk Premiums in Interest Rates"
Risk Premiums in Interest Rates Week 8 – October 12, 2005 J. K. Dietrich - FBE 524 - Fall, 2005 Types of Risk Holding-period yield risk – Capital gains risk – Reinvestment risk Default risk – Non-payment of principal – Delayed or reduced payments – Sometimes viewed as embedded option (put) Call risks – Call risks can be viewed as embedded options (call) Liquidity or marketability risk – Often measured as bid-ask spread for traded securities J. K. Dietrich - FBE 524 - Fall, 2005 Text Exhibit 8.6 Risky Rates J. K. Dietrich - FBE 524 - Fall, 2005 Holding Period Yield Risk Bond price is function of expected cash flows and RADR, but usually bond traders define contractual cash flows and yields to maturity Relationship between YTM and p is a curve defined by equation from last week c 1 1 p0 (1 ) y (1 y) m (1 y) m J. K. Dietrich - FBE 524 - Fall, 2005 Bond Prices and Yields Bond Prices and Yields 1.6 1.4 1.2 1 Bond Price (Par = 1.0) 0.8 0.6 0.4 0.2 0 0.03 0.05 0.07 0.09 0.11 0.13 0.15 Yie ld to M aturity c=8%, m=10 years c=8%, m=20 years c=6%, m=10 years c=6%, m=20 years J. K. Dietrich - FBE 524 - Fall, 2005 Holding Period Risk (cont’d) 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 Bonds which must be sold at end of holding period (maturity does not equal holding period) have risk of capital gains or losses J. K. Dietrich - FBE 524 - Fall, 2005 Measuring Holding-Period Risk Price sensitivity of bonds is measured in terms of a bond price elasticity % price d1 % (i yield ) This elasticity is called duration denoted d1, which is widely used by bond traders and analysts and is often available on quote sheets J. K. Dietrich - FBE 524 - Fall, 2005 Example of Duration 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 If yields changed immediately from 12% to 10%, that is a 2/112 or 1.8% change in gross yield The bond price should change about 1.8% * 6.8 = 12.1% J. K. Dietrich - FBE 524 - Fall, 2005 Duration as Time Measure Macauley noted that maturity was not relevant measure of timing of payments of bonds and defined his own measure, duration The definition of duration is (p. 192): n It (t ) (1 y)t D d1 t 1 n It (1 y)t t 1 J. K. Dietrich - FBE 524 - Fall, 2005 Duration has two interpretations Elasticityof bond prices with respect to changes in one plus the yield to maturity Weighted average payment date of cash flows (coupon and interest) from bonds 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 d2) J. K. Dietrich - FBE 524 - Fall, 2005 Alternative Duration Calculation Duration is widely used by bond traders and fixed income portfolio managers Duration values are available from information services like Bloomberg Calculated is three ways – Macauley’s formula (but combersome) – Calculate two prices and rates, divide changes – Closed-form solution, e.g. Dietrich formulation: 1 i 1 1 d1 M cM M 1 i pi (1 i ) J. K. Dietrich - FBE 524 - Fall, 2005 Duration is an Approximation Derivative is used in calculating duration p i Actual price change Change predicted by duration 0 J. K. Dietrich - FBE 524 - Fall, 2005 i Yield to Maturity Duration as Risk Measure Good – Balances reinvestment yield risk against capital gains risk – Widely used and clear mathematical expression assessing holding-period yield risk Bad – Approximation and theoretical issues – Convexity adjustment only approximate improvement J. K. Dietrich - FBE 524 - Fall, 2005 Duration Calculation J. K. Dietrich - 2005 Coupon Bonds Formula: 1 i 1 1 d M cM i pi (1 i) M 1 Calculation: i= 10.0% M= 10 d1 = 6.759 p= 1.0000 c= 10.0% Level Payment Loans Formula 1 i M d i (1 i) 1 M Calculation i= 10.0% M= 30 d1 = 9.1762 J. K. Dietrich - FBE 524 - Fall, 2005 Default or Credit Risk Example of 8% 3-year bond with risk-adjusted discount rate (RADR) of 12%: 1 2 3 ($849.12) 80 80 1080 Probability of payment 0.9 0.9 0.9 Default cash flow 0 0 500 Expected cash flow 72 72 1022 Price $849.12 RADR 12.00% YTM=IRR 14.56% J. K. Dietrich - FBE 524 - Fall, 2005 Effect of Credit Risk Change RADR constant at 12%: Probability Price YTM 0.9 849.12 14.56% 0.8 794.32 17.36% 0.7 739.52 20.45% Note price and yield change – Could be a change in one industry or firm – Default risk could be diversified in this case J. K. Dietrich - FBE 524 - Fall, 2005 Pricing Default-Risky Bond 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 Risk-adjusted discount rate (RADR) may or may not change with change in default risk J. K. Dietrich - FBE 524 - Fall, 2005 Risk Premiums in RADRs Diversifiable or avoidable risks – Hedge portfolios can reduce or eliminate – Unsystematic risks are not priced (do not increase discount rate) Priced versus non-priced risk – Systematic risks are unavoidable – Risk aversion (declining marginal utility of wealth) is underlying assumption J. K. Dietrich - FBE 524 - Fall, 2005 Short and Long Risk Premia Baa and Commerc i al Paper Ri s k Premi a 5 4 3 2 1 0 72 74 76 78 80 82 84 86 88 90 92 94 96 98 BA ARIS KPR CP RISK PR J. K. Dietrich - FBE 524 - Fall, 2005 Default Risk Premiums Vary over the business cycle – Can be changes in default risk probabilities or in the market price of risk Current default risk premiums are very high relative to historical experience Development of bond markets internationally is believed to promise substantial growth and risk analysis of private borrowers will be very important J. K. Dietrich - FBE 524 - Fall, 2005 Liquidity Risk 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 Examples – Structured notes and Orange County – Drexel Burnam and junk bonds in 1980s – The Russian debt market collapse in 1998 J. K. Dietrich - FBE 524 - Fall, 2005 Developments in Credit-risk Usual interpretation of credit risk is default on a loan or bond New views of credit risk are focused on the change in the credit-worthiness of debt instruments as well as default 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 J. K. Dietrich - FBE 524 - Fall, 2005 Default Private debt (corporate and household) may not pay cash flows as promised – Late payments – Nonpayment of interest or principal Other default or credit events – Violation of covenants and other creditor interventions in operations – Change in risk of default (e.g. highly leveraged transactions) J. K. Dietrich - FBE 524 - Fall, 2005 Credit Events Probability of default (PD) can change affecting the value of default-risky securities Upgrades and downgrades reflecting changes in PD are credit events Recent progress has been made in quantifying these probabilities J. K. Dietrich - FBE 524 - Fall, 2005 Bond and Debt Ratings Rating agencies – Standard and Poor’s (AAA to D) – Moody’s (Aaa to C) – Fitch and Duff and Phelps Migration of ratings, e.g. from BBB to BB (investment grade to below investment grade) represents credit risk For example, change from BBB to BB has historical probability of 5.3% (S&P, 1996) J. K. Dietrich - FBE 524 - Fall, 2005 Risk of Fixed Incomes Maximum value=F Future Value of Debt J. K. Dietrich - FBE 524 - Fall, 2005 Credit Losses Three elements in credit losses – Estimated default probability (PD) – Loss given default (LGD) – Exposure at default (EAD) Credit losses = PD*LGD*EAD Investors in debt securities will be concerned about all these elements in managing their risks J. K. Dietrich - FBE 524 - Fall, 2005 Credit Risk Analysis 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 Consulting industry in credit analysis – RiskMetrics (formerly J.P. Morgan) – KMV (academic based research) – Others (KPMG, PricewaterhouseCoopers, etc.) J. K. Dietrich - FBE 524 - Fall, 2005 Example of Steps to estimate PD Default occurs when value of assets less than value of liabilities (insolvency) Example of analysis used by KMV uses simplified estimates of variables Must calculate market value of assets (market value of debt and equity) and variability of market value Identify book value of liabilities J. K. Dietrich - FBE 524 - Fall, 2005 Motorola: Debt and Equity Motorola Total Market Values 1991-1 to 2001-2 140000 120000 100000 Total Market Value 80000 60000 40000 20000 0 91 92 93 94 95 96 97 98 99 00 MVE LTDANDCL TMV CL J. K. Dietrich - FBE 524 - Fall, 2005 Distance to Default: Example 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% Market value standard deviation of percent change = $9.3 billion J. K. Dietrich - FBE 524 - Fall, 2005 Reduced Probability of Default? Estimated default point in example is midway between book value of current liabilities and long-term debt Theory is that long-term debt does not require immediate payment, short-term liabilities may allow some flexibility KMV uses historical data to fine-tune this estimate J. K. Dietrich - FBE 524 - Fall, 2005 Estimated Distance to Default $56.6 $16.6 Dis tan ce to default 4.3 $9.3 Market value to default point = $40.0 $12.9 $20.2 $56.6 CL CL+LTD TMV Default point (estimated as midpoint) = $16.6 J. K. Dietrich - FBE 524 - Fall, 2005 Distance to Default: 12-31-02 Total Value of Assets (from “Capital Structure” and Financial Statements): E + LTD + CL = TA $33.9 + $ 8.1 + $9.7 = $ 51.7 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 $51.7 $13.9 Dis tan ce to default 4.5 $8.48 J. K. Dietrich - FBE 524 - Fall, 2005 Probability of Default KMV has used historical data to relate distance from default to probability of default That measure is proprietary (not available) As example, Motorola is rated A3 by Standard and Poors, historically associated with a default rate of about .82% over next five years J. K. Dietrich - FBE 524 - Fall, 2005 Credit Risk in Portfolios Individual assets have probability of default and risk and discussed last week Loans in portfolios will have an interdependent risk structure due to correlations in defaults Credit risk within portfolio context is a major advance in credit risk management Search for a summary measure of portfolio risk led to the concept of value at risk J. K. Dietrich - FBE 524 - Fall, 2005 Value at Risk (VAR) Value at risk (VAR) looks at risk of portfolio accounting for covariance of assets Risk is defined in terms of likelihood of losses Value at Risk Probability Maximum value=F Future Value of Portfolio J. K. Dietrich - FBE 524 - Fall, 2005 Portfolio Credit Risk Credit risk different than usual portfolio risk analysis – Returns are not symmetric – Concentrations of exposure complicate losses Major issue is correlation of defaults and losses given default – We will discuss approach followed by CreditMetrics – Other approaches exist (including KMV) J. K. Dietrich - FBE 524 - Fall, 2005 Credit Risk as Rating Changes Increased credit risk Default CCC B BB Same credit risk (BBB) BBB A AA AAA Less credit risk J. K. Dietrich - FBE 524 - Fall, 2005 Rating Migrations (BBB rating) Year-End Rating Probability (%) AAA 0.02 AA 0.33 A 5.95 BBB 86.93 BB 5.30 B 1.17 CCC 0.12 Default 0.18 Source: Standard & Poors J. K. Dietrich - FBE 524 - Fall, 2005 Two Bond Rating Migrations Obligor # 2 (Single-A) AAA AA A BBB BB B C Default Obligor #1 (BBB) 0.09 2.27 91.05 5.52 0.74 0.26 0.01 0.06 AAA 0.02 0.00 0.00 0.02 0.00 0.00 0.00 0.00 0.00 AA 0.33 0.00 0.04 0.29 0.00 0.00 0.00 0.00 0.00 A 5.95 0.02 0.39 5.44 0.08 0.01 0.00 0.00 0.00 BBB 86.93 0.07 1.81 79.69 4.55 0.57 0.19 0.01 0.04 BB 5.30 0.00 0.02 4.47 0.64 0.11 0.04 0.00 0.01 B 1.17 0.00 0.00 0.92 0.18 0.04 0.02 0.00 0.00 CCC 0.12 0.00 0.00 0.09 0.02 0.00 0.00 0.00 0.00 Default 0.18 0.00 0.00 0.13 0.04 0.01 0.00 0.00 0.00 J. K. Dietrich - FBE 524 - Fall, 2005 Probability of Default: Two Firms Probability = 1/2% Probability = 1/10% Default Point B Probability = 1/100% Default Point A Value of Firm A J. K. Dietrich - FBE 524 - Fall, 2005 Loss Given Default Seniority Class Mean (%) Standard Deviation (%) Senior Secured 53.8 26.86 Senior Unsecured 51.13 25.45 Senior Subordinated 38.52 23.81 Subordinated 32.74 20.81 Junior Subordinated 17.09 10.9 Source: Carty & Lieberman [96a] -- Moody's Investors Service J. K. Dietrich - FBE 524 - Fall, 2005 Simplified “Road Map” Compute Compute the volatility Compute exposure profile Of value caused by correlations Of each asset Up (down)grades and defaults Portfolio value-at-risk due to credit Source: Introduction to CreditMetrics (1997) J. K. Dietrich - FBE 524 - Fall, 2005 Required Resources Defaultprobabilities (or ratings) Migration probabilities – Historical data requirements – Approaches to estimating correlations Complete data on types of credits and estimations of losses given defaults Exposures to classes of risks Models and simulations of value changes given credit events J. K. Dietrich - FBE 524 - Fall, 2005 Credit Portfolio Risk One Asset Many Assets 0 0 Return Return J. K. Dietrich - FBE 524 - Fall, 2005 Incremental Risk Introduction to CreditMetrics provides good examples (in Section 5) Importance portfolio risk is the marginal risk Marginal risk High risk considers portfolio and large size risk implications $ 10mm J. K. Dietrich - FBE 524 - Fall, 2005 $ Credit Exposure Next Week – October 19, 2005 Take-home midterm examination due; 90- minute examination is open book and open note Examination must be completed without discussion with anyone and a declaration to that effect and time spent turned in with examination Prepare Chapter 9 Arrange a meeting regarding project progress if you have not talked to me J. K. Dietrich - FBE 524 - Fall, 2005