19 19 C h a p t e r Performance Evaluation and R isk Management Performance Evaluation and R isk Management second edition Fundamentals of Investments Valuation & Management Charles J. Corrado Bradford D.Jordan McGraw Hill / Irwin Slides by Yee-Tien (Ted) Fu © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 19 - 2 It is Not the Return On My Investment “It is not the return on my investment that I am concerned about. It is the return of my investment!” – Will Rogers © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 19 - 3 Performance Evaluation & Risk Management Our goal in this chapter is to examine the methods of c evaluating risk- adjusted investment performance, and d assessing and managing the risks involved with specific investment strategies. Goal © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 19 - 4 Performance Evaluation Can anyone consistently earn an “excess” return, thereby “beating” the market? Performance evaluation Concerns the assessment of how well a money manager achieves a balance between high returns and acceptable risks. © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 19 - 5 Performance Evaluation Measures The raw return on a portfolio, R P , is the total % return on the portfolio with no adjustment for risk or comparison to any benchmark. It is a naive measure of performance evaluation that does not reflect any consideration of risk. As such, its usefulness is limited. © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 19 - 6 Performance Evaluation Measures The Sharpe Ratio The Sharpe ratio is a reward-to-risk ratio that focuses on total risk. It is computed as a portfolio’s risk premium divided by the standard deviation for the portfolio’s return. p fp σ RR − =ratio Sharpe © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 19 - 7 Work the Web Visit Professor Sharpe at: http://www.stanford.edu/~wfsharpe © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 19 - 8 Performance Evaluation Measures The Treynor Ratio The Treynor ratio is a reward-to-risk ratio that looks at systematic risk only. It is computed as a portfolio’s risk premium divided by the portfolio’s beta coefficient. p fp RR β ratioTreynor − = © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 19 - 9 Performance Evaluation Measures Jensen’s Alpha Jensen’s alpha is the excess return above or below the security market line. It can be interpreted as a measure of how much the portfolio “beat the market.” It is computed as the raw portfolio return less the expected portfolio return as predicted by the CAPM. ( ) [ ] { } β fMpfpp RRERR − × + − = α © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 19 - 10 Performance Evaluation Measures [...]... McGraw-Hill Companies, Inc All rights reserved 19 - 19 Investment Risk Management Investment risk management Concerns a money manager’s control over investment risks, usually with respect to potential short-run losses We will focus on what is known as the Valueat-Risk approach McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 19 - 20 Value-at-Risk (VaR) Value-at-Risk... McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 19 - 23 More on Computing Value-at-Risk Example: More on VaR For the S&P 500 index fund, what is the probability of a loss of 30% or more over the next two years? 2-year average return = 2×.13 = 26 1-year σ2 = 202 = 04 So, 2-year σ2 = 2×.04 = 08 So, 1-year σ = √.08 ≈ 28 The odds of being within two σ’s are 95 I.e Prob... said to be Sharpe-optimal To find the Sharpe-optimal portfolio, consider the plot of the investment opportunity set of risk-return possibilities for a portfolio Expected Return × × × × ×× × × × ×× ×× × × × Standard deviation McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 19 - 16 Sharpe-Optimal Portfolios The slope of a straight line drawn from the risk-free rate to a... portfolio on the line with the steepest slope is the Sharpe-optimal portfolio McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 19 - 17 Sharpe-Optimal Portfolios McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 19 - 18 Sharpe-Optimal Portfolios Notice that the Sharpe-optimal portfolio is one of the efficient portfolios on the Markowitz efficient... probability of a return of -7 % or worse in a particular year? The odds of being within one σ are about 2/3 or 67 I.e Prob (.13–.20 ≤ RS&P500 ≤ 13+.20) ≈ 67 or Prob (–.07 ≤ RS&P500 ≤ 33) ≈ 67 So, Prob (RS&P500 ≤ –.07) ≈ 1/6 or 17 The VaR statistic is thus a return of –.07 or worse with a probability of 17% McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 19 - 22 Work the... Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 19 - 14 Work the Web The performance measures we have discussed are commonly used in the evaluation of mutual funds See, for example, the Ratings and Risk for various funds at: http://www.morningstar.com McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 19 - 15 Sharpe-Optimal Portfolios A funds allocation... McGraw-Hill Companies, Inc All rights reserved 19 - 24 More on Computing Value-at-Risk In general, if T is the number of years, E (R p ,T ) = E (R p )× T σ p ,T = σ p × T ( Prob(R Prob(R ) So, Prob R p ,T ≤ E (R p )× T − 2.326 ×σ p T = 1% McGraw Hill / Irwin p ,T p ,T ) ≤ E (R p )× T − 1.96 ×σ p T = 2.5% ) ≤ E (R p )× T − 1.645 ×σ p T = 5% © 2002 by The McGraw-Hill Companies, Inc All rights reserved 19. .. 19 - 25 Work the Web Learn about the risk management profession at: http://www.garp.org McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 19 - 26 Chapter Review Performance Evaluation Performance Evaluation Measures • The Sharpe Ratio • The Treynor Ratio • Jensen’s Alpha Comparing Performance Measures Sharpe-Optimal Portfolios McGraw Hill / Irwin © 2002 by The McGraw-Hill... Performance Measures Sharpe-Optimal Portfolios McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 19 - 27 Chapter Review Investment Risk Management Value-at-Risk (VaR) More on Computing Value-at-Risk McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved ... the probability of a loss a portfolio may experience within a fixed time horizon If the returns on an investment follow a normal distribution, we can state the probability that a portfolio’s return will be within a certain range given the mean and standard deviation of the portfolio’s return McGraw Hill / Irwin © 2002 by The McGraw-Hill Companies, Inc All rights reserved 19 - 21 Value-at-Risk (VaR) Example: . / Irwin 19 - 17 Sharpe-Optimal Portfolios © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 19 - 18 Sharpe-Optimal Portfolios Notice that the Sharpe-optimal. McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 19 - 10 Performance Evaluation Measures © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 19 -. return of my investment!” – Will Rogers © 2002 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw Hill / Irwin 19 - 3 Performance Evaluation & Risk Management Our goal in this chapter