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LECTURE SIX a. Portfolio performance measurement b. Hedge fund risk management c. Credit risk management d. Probability of default 1
Part 1PORTFOLIOPERFORMANCEMEASUREMENT a. Intro. Performance measurement b. Surplus at Risk c. The Market Line (ML) and CAPM d. Several ratios to measure market performance 2
Part 1. Portfolio Performance Measurement 1. Intro. Performance measurement Portfolio management Risk Return Do profits reflect my risk exposure? HOW? • Looking at process/strategies in place, and • Whether outcomes are in line with what was intended or should have been achieved.Lecture 6 • Pure luck? • Good strategy • Separate effect of the market and active management
1. Intro. Performance measurement Some definitions Sell side Buy sidePart 1. Portfolio Performance Measurement Creation, promotion, analysis and Final buyers of financial assets sale of securities. (Large portions of securities) Leverage and speculative Tend to me more conservative No leverage Examples? Examples?Lecture 6
1. Intro. Performance measurement Some definitions Sell side Buy sidePart 1. Portfolio Performance Measurement Creation, promotion, analysis and Final buyers of financial assets sale of securities. (Large portions of securities) Leverage and speculative Tend to me more conservative No leverage Institutions such as Investing institutions such as • Investment bankers • mutual funds, (intermediaries between issuers • pension funds and and public), • insurance firms • Research companies that perform stock research andLecture 6 make ratings. Ig. Roubini • Market makers who provide liquidity in the market.
1. Intro. Performance measurement Absolute and Relative risk Absolute risk Relative RiskPart 1. Portfolio Performance Measurement With respect to the portfolio With respect to a benchmark itself • Tracking error : e = R P - RB • Risk factor: σ • In dollar terms: exP • P: Initial portfolio value • In dollar terms 𝜎 (𝑅 𝑃 − 𝑅 𝐵 ) 𝑃 𝜎 ∆𝑃 ∆𝑃 ∆𝐵 ∆𝑃 𝜎( − ) 𝑃 𝑃 𝐵 𝜎 ∗ 𝑃 𝑃 𝜔 ∗ 𝑃 𝜎 𝑅𝑃 ∗ 𝑃 Tracking Error Volatility Note that there is only WhereLecture 6 the asset or portfolio 2 2 P 2 P B 2 P
1. Intro. Performance measurement Absolute and Relative riskPart 1. Portfolio Performance Measurement Example SPX: 10% return -10% return My trade: 6% return -4% return Absolute risk Relative Risk What would be the difference between absolute and relative risk?Lecture 6
What is my risk in the long term? 2. Surplus at Risk Focused on net profits Performance Measurement Sort of relative risk measurementPart 1. Portfolio Performance Measurement Two assets, long pension assets and short pension liabilities. Assets $ 120,00 Liabilities $ 100,00 Surplus $ 20,00 Volatility 12% Volatility 3% Expected R 8% Expected R 5% Correlation 0,3 Change of assets Change of assets $ 9,60 $ 5,00 (per period) 12% of $120 (per period) 5% of $100 Expected growth of surplus $ 4,60 Change assets - liabilities Expected surplus $ 24,60 Considering the surplus Variance of surplus $ 190,44 variance(a – b) = variance (a) + variance(b) - (2)cov(a,b) Volatility of surplus $ 13,80Lecture 6 Confidence level 95% Normal deviate 1,64 Surplus at Risk $VaR 18,03 –(expected surplus) + (volatility of surplus)*(normal deviate) The complete variance formula is: σ12P12+ σ22P12-2 σ1σ2P1P2ρ
3.The Market Line (ML) and CAPM Small recap Decompose total return into a component due to market risk premia andPart 1. Portfolio Performance Measurement other factors. E(Ri) Overvalued ML M E(RM) RF UndervaluedLecture 6 RiskM Riski Note: Risk is either b or
3.The Market Line (ML) and CAPM Small recap E ( Ri ) rf b [ E ( RM ) rf ] Ri i b i RM eiPart 1. Portfolio Performance Measurement E ( Ri ) rf b [ E ( RM ) rf ] This is the CAPM model E ( Ri ) rf i b i [ E ( RM ) rf ] E(Ri) B ML A M E(RM) C E RFR DLecture 6 RiskM Riski Note: Risk is either b or
3.The Market Line (ML) and CAPM Small recap Capital Market Line (CML) obtained by combining the market portfolio and the riskless assetPart 1. Portfolio Performance Measurement • CML specifies the expected return for a given level of risk • All possible combined portfolios lie on the CML, and all are Mean-Variance efficient portfolios • Here we have a clear relation between the risk of my portfolio and the riskLecture 6 of the market. This is reflected by beta Cov( Ri , RM ) It measures how much an asset’s return bi is driven by the market return 2M
3.The Market Line (ML) and CAPM Small recap Capital Market Line (CML)Part 1. Portfolio Performance Measurement If the stock has a high positive β: • It will have large price swings driven by the market • It will increase the risk of the investor’s portfolio(in fact, will make the entire market more risky …) • The investor will demand a high Er in compensation. If the stock has a negative β : • It moves “against” the market. • It will decrease the risk of the market portfolio • The investor will accept a lower Er Then the SML depicts the relation between β and the Expected Return (Er)Lecture 6 For the risk-free security, b = 0 For the market itself, b=1.
3.The Market Line (ML) and CAPM Small recap Capital Market Line (CML)Part 1. Portfolio Performance Measurement E ( Ri ) rf b [ E ( RM ) rf ] E ( Ri ) rf b [ E ( RM ) rf ] Excess of return of a portfolio is a function of the excess of return of the market W.R. a risk free rateLecture 6
4.Treynor Ratio The Treynor measure calculates the risk premium per unit of risk (bi)Part 1. Portfolio Performance Measurement [ E ( RP ) RF ] TR b ( RP ) Beta measures the investment volatility relative to the market volatility (systematic risk) The Treynor Ratio is negative if • RF > E[RP] AND β > 0 . Manager has performed badly: failing to get performance better than the risk free rate AND manager made a not good election of portfolio • RF < E[RP] AND β > 0 Manger has performed well, managing to reduce risk but getting aLecture 6 return better than the risk free rate Higher Ti generally indicates better performance
4.Treynor Ratio ADVANTAGE: It indicates the volatility a ASSET brings to an entire portfolio. The Treynor Ratio should be used only as a ranking mechanism forPart 1. Portfolio Performance Measurement investments within the same sector. . When presented with investments that have the same return, investments with higher Treynor Ratios are less risky and better managed Cov( Ri , RM ) bi 2MLecture 6
5. Sharpe Ratio Describes how much excess return you are receiving for the extra volatility that you endure for holding a riskier asset.Part 1. Portfolio Performance Measurement [ E ( RP ) RF ] SR ( RP ) The Sharpe measure is exactly the same as the Treynor measure, except that the risk measure is the standard deviation: • Tells us whether a portfolios returns are due to smart investment decisions or a result of excess risk. • The greater a portfolios Sharpe ratio, the better its risk-adjusted performance has been. • A negative Sharpe ratio indicates that a risk-less asset would performLecture 6 better than the security being analysed.
4-5. Sharpe V Treynor Ratio The Sharpe and Treynor measures are similar, but different: • Sharpe uses the standard deviation, Treynor uses betaPart 1. Portfolio Performance Measurement X • Sharpe is more appropriate for well diversified portfolios, Treynor for Portfolio Return 15% RFR 5% Beta Std. Dev. Trenor Sharpe 2.50 20% 0.0400 0.5000 Y 8% individual assets14% 0.0600 0.2143 5% 0.50 Z Market 6% • Sharpe and Treynor: The ranking, not the number itself, is what is most 10% 5% 5% 0.35 1.00 9% 11% 0.0286 0.1111 0.0500 0.4545 important Risk vs Return 15% Portfolio Return RFR Beta Std. Dev. Trenor Sharpe X M X Y 15% 5% 2.50 20% 0.0400 0.5000 Return 10% Portfolio Return RFR Beta Y 8% 5% 0.50 14% 0.0600 Dev. Std. Trenor Sharpe 0.2143 5% X 15% 5% 2.50 20% 0.0400 0.5000 Z Z 6% 5% 0.35 Y 8% 9%5% 0.0286 0.50 14% 0.11110.2143 0.0600 Market 0% 10% 5% 1.00 Z 6% 11% 5% 0.0500 0.35 9% 0.45450.1111 0.0286 0.00 0.50 1.00 1.50 2.00 2.50 Market 10% 5% 1.00 11% 0.0500 0.4545 Beta Risk vs Return Risk vs Return X Risk vs Return 15% 15% 15% M X M X Return 10% Return M 10% YLecture 6 Return 10% Y Y 5% Z 5% Z 0% 5% 0% Z 0% 5% 10% 15% 20% 0.00 0.50 1.00 1.50 2.00 2.50 Std. Dev. Beta 0%
6. Sortino Ratio The Sortino ratio generalizes (focus on the downside) from the Sharpe by using:Part 1. Portfolio Performance Measurement • In the numerator, instead of excess return (above riskfree), Sortino uses excess above hurdle (MAR, minimum acceptable return) • In the denominator, instead of volatility (annualized standard deviation), Sortino uses downside deviation. [ E ( RP ) MAR] SR L ( RP ) • Appears to resolve several of the issues inherent in the Sharpe ratio: • It incorporates a relevant return target, in both the numerator and the denominator; • It quantifies downside volatility without penalizing upside volatility; and because of its focus on downside risk, • It is more applicable to distributions that are negatively skewed thanLecture 6 measures based on standard deviation.
5-6. Sortino Ratio and Sharpe Ratio Example Only consider the returns below the Square difference WR hurdle rate Sq. Difference WR thePart 1. Portfolio Performance Measurement the hurdle rate average of returns Sumation of returns Excess over Hurdle We take a minimun Averag montly return of P 1,821% acceptable return Squared difference Average yearly return 21,851% Times 12 Month Price Returns Hurdle rate R - HUR Hurdle>R (R-Hur)^2 (R-Av)^2 Hurdle rate yield return Y 18,000% 1.5% * 12 1 663,03 -2,539% 1,50% -4,04% -4,04% 0,1631% 0,1901% 2 680,3 -9,834% 1,50% -11,33% -11,33% 1,2847% 1,3585% Rf month 1,80% 3 754,5 10,132% 1,50% 8,63% 0,6907% RF Y 21,60% Times 12 4 685,09 8,234% 1,50% 6,73% 0,4113% Use the formula 5 632,97 9,120% 1,50% 7,62% 0,5327% 6 580,07 -0,136% 1,50% -1,64% -1,64% 0,0268% 0,0383% Volatility 29,06% 7 580,86 -3,966% 1,50% -5,47% -5,47% 0,2988% 0,3349% Sharpe ratio 0,865% 8 604,85 -5,675% 1,50% -7,17% -7,17% 0,5148% 0,5619% 9 641,24 3,719% 1,50% 2,22% 0,0360% Sortino 19,54% 10 618,25 6,575% 1,50% 5,07% 0,2260% Excess return 3,851% P-Hurdle 11 580,11 -10,186% 1,50% -11,69% -11,69% 1,3656% 1,4416% Montly downside VaRianc 19,71% 12 645,9 7,760% 1,50% 6,26% 0,3527% 13 599,39 1,139% 1,50% -0,36% -0,36% 0,0013% 0,0047% 14 592,64 15,067% 1,50% 13,57% 1,7545% 15 515,04 -4,791% 1,50% -6,29% -6,29% 0,3958% 0,4372% 16 540,96 -10,391% 1,50% -11,89% -11,89% 1,4140% 1,4913% 17 603,69 19,217% 1,50% 17,72% 3,0262% 18 506,38 -4,280% 1,50% -5,78% -5,78% 0,3340% 0,3722%Lecture 6 19 529,02 -2,772% 1,50% -4,27% -4,27% 0,1825% 0,2109% 20 544,1 -7,270% 1,50% -8,77% -8,77% 0,7692% 0,8265%
7. Jensen alpha Shows by much the returns of an actively managed portfolio arePart 1. Portfolio Performance Measurement above or below market returns. >0 A positive Alpha means that a portfolio has beaten the market, =0 while a negative value indicates underperformance <0 Risk Premium A fund manager with a negative alpha and a beta greater than one has added risk to the portfolio but has poorer performance than the 0 market Market Risk Premium R i RFR i b i R M RFR iLecture 6 Alpha = Excess of return – (Beta * (Excess of return))
Part 1. Portfolio Performance Measurement 7. Jensen alpha R i RFR i b i R M RFR i Alpha = Excess of return – (Beta * (Excess of return))Lecture 6
7. Jensen alpha Portfolio Portfolio Market P QPart 1. Portfolio Performance Measurement Beta 0.90 1.6 1.0 RM-Rf 11% 19% 10% Alpha 2.0% 3.0% 0% R i RFR i b i R M RFR i Portfolio P Expected Return Portfolio Q 19% SML 16% M 11% M2 PLecture 6 9% 0.9 1.6 Beta
8. Information Ratio Measure of the risk-adjusted return of a portfolio.Part 1. Portfolio Performance Measurement Defined as expected active return divided by tracking error • Active return : difference between the return of portfolio and the return of a benchmark • Tracking error is the standard deviation of the active return E[ R P RB ] Component attributable to the manager’s skill IR VAR( R P RB ) While Sharpe consider the σ of total returns, IF consider σ of alpha • Measures the active return of the managers (abnormal return) portfolio per unit of risk that the manager takes relative to the benchmark. • The higher the information ratio, the higher the active return of the portfolio, given the amount of risk taken, and the better theLecture 6 manager.
8. Information Ratio Returns Date Portfolio Market ExcessPart 1. Portfolio Performance Measurement 01/01/2010 2% 2,06% -0,49% 01/02/2010 1% -5,62% 6,64% 01/03/2010 0,61% -3,42% 4,03% 01/04/2010 0,76% 2,84% -2,08% 01/05/2010 9,69% -5,00% 14,69% 01/06/2010 1,39% 5,30% -3,91% 01/07/2010 3,10% -2,33% 5,44% 01/08/2010 0,46% 8,57% -8,12% 01/09/2010 6,11% 4,77% 1,34% 01/10/2010 9,37% 14,69% -5,32% 01/11/2010 3,88% -6,68% 10,56% 01/12/2010 9,54% 1,38% 8,16% Mean 3,96% 1,38% 2,58% Expected excess of return (Benchmark) Standard Dev 3,73% 6,40% 6,88%Lecture 6 Information Ratio 0,3750 E[ R P RB ] IR VAR( R P RB )
9. Modigliani´s Risk Adjustment Performance • Also known as M2 • Closely related to the Sharpe RatioPart 1. Portfolio Performance Measurement • Focuses on total volatility as a measure of risk, but its risk adjusted measure of performance has the interpretation of a differential return relative to the benchmark index • The idea is to lever or de-lever a portfolio (i.e., shift it up or down the capital market line) so that its standard deviation is identical to that of the market portfolio. • The formula for M2 is: M 2 M R i R f R f i Lecture 6 • The M2 of a portfolio is the return that this adjusted portfolio earned. This return can then be compared directly to the market return for the period.
9. Modigliani´s Risk Adjustment Performance • Suppose that • Return Ri: 35% RM: 28% • Volatility σi: 42% σM: 30%Part 1. Portfolio Performance Measurement • Find a portfolio combination with the same level of risk than the benchmark (market) M 30 0.714 • Portion of the portfolio i 42 • Portion of risk free asset 1 M 0.286 i • The return of this portfolio will be [0.286 * 0.06] [0.714 * 0.35] 0.267 • This portfolio is -1.3% than the market return. This is the M2 Expected Return Market M Portfolio M2 P P*Lecture 6 • Reduce the return of the P • Obtain leSs volatility Volatility
9. Modigliani´s Risk Adjustment Performance M 2 M R i R f R f i SR [ ( RP ) RF ]Part 1. Portfolio Performance Measurement ( RP ) Portfolio Return RFR Beta Std. Dev. Trenor Sharpe X 15% 5% 2.50 20% 0.0400 0.5000 Y 8% 5% 0.50 14% 0.0600 0.2143 Z 6% 5% 0.35 9% 0.0286 0.1111 Market 10% 5% 1.00 11% 0.0500 0.4545 X 0.200.15 0.05 0.05 0.105 M 2 0.11 Risk vs Return 0.11 0.08 0.05 0.05 0.074 15% M2 M X Y 0.14 0.11 0.06 0.05 0.05 0.062 Return 10% Y 2 M 5% Z 0.09 Z • Recall that the market return 0.50 0.10,1.00 only X outperformed. This is the was so 0% 0.00 1.50 2.00 2.50 same result as with the Sharpe Ratio. Beta Risk vs Return X • The M2 of a portfolio is the return that this adjusted portfolio earned. This 15% return can then be compared directly to M market return for the theLecture 6 Return 10% period. Y 5% Z 0% 0% 5% 10% 15% 20% Std. Dev.
10. Marginal Risk • Represents the change in risk due to a small increase in one of the allocations. It is essentially a derivative that measures the rate of change in some measure of interest given a small change in a variable.Part 1. Portfolio Performance Measurement P Cov( Ri , RP ) M arg Risk b i , P P wi P • Beta represents the marginal contribution to the risk of the total portfolio • Large values of beta indicates that a small addition will have a relatively large effect on the portfolio • Positions with large betas should be cut first to reduce risk The portfolio risk/standard deviation is the sum of the risk contributions from each asset. ContributionToRisk wi b i , P PLecture 6
10. Marginal Risk M arg Risk P Cov( Ri , RP ) b i , P P wi P I am running a hedge fundPart 1. Portfolio Performance Measurement Bank of America 25% . Beta=3 σp =10%, Contribution to Risk =.25 x 3 x 10%= 7.5% • 7,5% of my portfolio risk is going to be dictated by what happens to Bank of America • The risk is too concentrated in one stock. In practice, it is desirable to spread out total risk contributions across as many stocks or assets as you can in the most equivalent manner.Lecture 6
Part 1IHEDGE FUND RISKMANAGEMENT a. Introduction b. Strategies 30
1. Introduction What is a H.F.?Part 2. Hedge FundsLecture 6
1. Introduction What is a H.F.?Part 2. Hedge FundsLecture 6
1. Introduction What is a H.F.?Part 2. Hedge FundsLecture 6
Instruments whose prices 2. H.F. Strategies Achieve a beta as close to zero to fluctuate based on the changes in economic policies along protect against systematic risk An heterogeneous group with the flow of capital Long positions in stocks expected to increase. Short positions in stocks expected to decrease Exploit pricing inefficiencies before or after a corporate event:Bankruptcy, Merger, AcquisitionFind “bargains” and accept riskPart 2. Hedge Funds1000 basis points above the risk- free rate of return Exploits pricing differentials between fixed-incomeLecture 6 securities. Long position in convertible securities. AND Holds a portfolio of other investment Short position in the same company’s funds instead of investing directly in common stock. securities
Part IIICREDIT RISKMANAGEMENT a. Intro b. Drivers of Credit Risk c. Settlement risk d. Credit losses 35
1. Introduction Definition The potential for loss due to failure of a borrower to meet its contractual obligation to repay a debt in accordance with the agreed terms • Its effect is measured by the cost of replacing cash flows if the other party defaults • Commonly also referred to as default risk • Credit events includePart 3. Credit Risk Management • bankruptcy, • failure to pay, • loan restructuring • loan moratorium • Example: A homeowner stops making mortgage payments Market Risk Credit Risk Potential loss due to the non Potential loss due to changes in performance of a financialLecture 6 market prices or values contract, or financial aspects of non performance in any contract
2. Drivers of Credit Risk Default: Discrete state for the counterparty (Default or not). It has associated the Probability of Default (PD) defined as the likelihood that the borrower will fail to make full and timely repayment of its financial obligations Exposure At Default (EAD)Part 3. Credit Risk Management The expected value of the loan at the time of default Loss Given Default (LGD) The amount of the loss if there is a default, expressed as a percentage of the EAD Recovery Rate (RR) The proportion of the EAD the bank recoversLecture 6
3. Settlement risk In initial consideration Settlement risk: The risk that one party will fail to deliver the terms of a contract with another party at the time of settlement Foreign exchange (FX) settlement risk is the risk of loss when a bank in a foreign exchange transaction pays the currency it sold but does not receive the currency it bought.Part 3. Credit Risk Management Settlement Risk management: • Real time systems • Bilateral netting agreements (two institutions) • Multilateral netting agreements (two industries) CLS Bank. In foreign exchange and operates the largest multicurrency cash settlement system. It is owned by the worlds leading financial institutionsLecture 6
4. Credit losses (overview) Set up: The credit losses are defined by CL i 1 bi * CEi * (1 f i ) N Where • Random Variable bi is a bernoulli trial that takes values of 1 (Def) or 0 (non Def) • CEi is the Credit Exposure at time of default • fi is the recovery rate (What means 1-fi )Part 3. Credit Risk Management The Expected Credit Loss for a portfolio is: E[CL] i 1 E[bi ] * CEi * (1 f i ) N Default is affected by correlation among i 1 pi * CEi * (1 f i ) N assets: Example Expected Credit Loss Asset Exposure Prob. Def. (5% * 25) (10% * 30) (20% * 45)Lecture 6 A $25 5% $13.5M B $30 10% C $45 20% TT $100
4. Credit losses (overview) Description of the complete distribution Issuer Exposure P. Def P. No Def. A £ 25.00 5% 95% B £ 30.00 10% 90% C £ 45.00 20% 80% Default Loss Probability Cumulative Exp. Loss Variance NonePart 3. Credit Risk Management A B C A,B A,C B,C A,B,CLecture 6 1. How can I find the loss 2. What is the prob. Associated to each scenario? 3. Easy 4. Expected loss of each scenario What could be the VaR of this portfolio? 5. Variance
Part IVPROBABILITY OFDEFAULTLikelihood that the borrower will fail to make full and timelyrepayment of its financial obligations a. Actuarial b. Market prices methods 41
1. Methodologies Actuarial methods • Measure default rates using historical data • Provided by external rating agenciesPart 4. Probability of default Market price methods • Infer default risk from market prices of debt, equity prices, credit derivativesLecture 6
1. Actuarial Methods Corporate Default Probabilities Increase Factor 1 exponentially across Credit Grades Credit Ratings b. a.Part 4. Probability of default • Credit rating is a measure of the firm’s credit risk • External credit rating: Standard & Poor’s, Moody’s, Fitch, etc. Factor 2 Prob. Of default • Probability of staying in the same rating category is given on the diagonal.Lecture 6 • Off-diagonal probabilities present the likelihood that the rating will change within a one-year period.
Part 4. Probability of default 1. Actuarial Methods Factor 3 Transition Matrix • Credit migration or transition matrices use ratings migration histories. • One-year horizon. • Measured using the cohort and the duration method.Lecture 6 • Generally, the transition matrix is affected by the business cycle: downgrades including defaults are higher during recessions
Part 4. Probability of default 1. Actuarial Methods Factor 4 Cumulative Default RatesLecture 6 • How many companies rated ( ) defaulted in each year • This measure is cumulative. It necessarily increases with the horizon
1. Actuarial Methods d1 Default Default 1 - d1 d2 No Default 1 – d2 d3 DefaultPart 4. Probability of default No Default 1 – d3 No Default Cumulative d1 d1+ (1- d1)d2 (1- d1)(1- d2) d3Lecture 6 Compute the cumulative probability of default: • The probability of default in the first year is 5% • The probability of default in the second year is 7%
1. Actuarial Methods Compute the cumulative probability of default: • The probability of default in the first year is 5% • The probability of default in the second year is 7% d1=5% Default Default in 2= 95%*7%=6.65% DefaultPart 4. Probability of default Survival rate = 95% No Default d3 Default Survival rate 2= 95%*97% = 0.883 No Default 1 – d3Lecture 6 No Default Cumulative d1 d1+ (1- d1)d2 (1- d1)(1- d2) d3
Factor 5 1. Actuarial Methods Recovery Rates Recovery Rates Amount recovered through foreclosure or bankruptcy procedures in a credit event (default), expressed as a percentage of face value Are function of • The state of the economy. Higher with expansion • The obligor’s characteristics: Higher when the borrower’s assets are tangible and when previous rating was high • The credit event: distressed debt has higher recovery rate than plainPart 4. Probability of default default • The status of the debtor: Higher seniority has higher recovery rates Credit rating agencies have used two methods to calculate RECOVERY RATES (Moody’s) • Average issuer-weighted trading price on a sovereigns bonds 30 days after its initial missed interest paymentLecture 6 • Ratio of the value of the old securities to the value of the new securities received in exchange,
1. Actuarial Methods Recovery RatesPart 4. Probability of defaultLecture 6 • Average historical sovereign recovery rate: 53% • 67% of recovery rate according to the ratio of value
1. Actuarial Methods Recovery RatesPart 4. Probability of default Senior debt has a higher recovery rate. • According to S&P recovery rates have averaged 51% on a discounted basis and 60% on a nominal basis, based on a sample from 1987 to 2011. • If measured on a dollar-weighted basis, which is the sum of all defaulted debt in the sample divided by the sum of the dollar amount of debt recovered, the averages are slightly lower: 48% • Loans and revolving credit facilities, that have seniority in the capital structure and areLecture 6 often secured: recovered 74% on a discounted basis and when measured on a dollar- weighted basis, the average recovery for loans and facilities is 65% • Bonds have lower average recoveries. The long-run discounted average recovery for bonds is 38%
Next Lecture 2. Market price methods Infer default risk from market prices of debt, equity prices, creditPart 4. Probability of default derivatives • Infer default risk from bonds • Mertons model (Structural Model)Lecture 6