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  1. 1. Fundamentals of Investments 19 C h a p t e r Performance Evaluation and Risk Management second edition Valuation & Management Charles J. Corrado Bradford D. Jordan McGraw Hill / Irwin Slides by Yee-Tien (Ted) Fu
  2. 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
  3. 3. Performance Evaluation & Risk Management <ul><li>Our goal in this chapter is to examine the methods of  evaluating risk-adjusted investment performance, and  assessing and managing the risks involved with specific investment strategies. </li></ul>Goal
  4. 4. Performance Evaluation <ul><li>Can anyone consistently earn an “excess” return, thereby “beating” the market? </li></ul>Performance evaluation Concerns the assessment of how well a money manager achieves a balance between high returns and acceptable risks.
  5. 5. Performance Evaluation Measures <ul><li>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. </li></ul><ul><li>It is a naive measure of performance evaluation that does not reflect any consideration of risk. As such, its usefulness is limited. </li></ul>
  6. 6. Performance Evaluation Measures <ul><li>The Sharpe Ratio </li></ul><ul><li>The Sharpe ratio is a reward-to-risk ratio that focuses on total risk. </li></ul><ul><li>It is computed as a portfolio’s risk premium divided by the standard deviation for the portfolio’s return. </li></ul>
  7. 7. Work the Web <ul><li>Visit Professor Sharpe at: </li></ul><ul><ul><li>http://www. stanford . edu /~ wfsharpe </li></ul></ul>
  8. 8. Performance Evaluation Measures <ul><li>The Treynor Ratio </li></ul><ul><li>The Treynor ratio is a reward-to-risk ratio that looks at systematic risk only. </li></ul><ul><li>It is computed as a portfolio’s risk premium divided by the portfolio’s beta coefficient. </li></ul>
  9. 9. Performance Evaluation Measures <ul><li>Jensen’s Alpha </li></ul><ul><li>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.” </li></ul><ul><li>It is computed as the raw portfolio return less the expected portfolio return as predicted by the CAPM. </li></ul>
  10. 10. Performance Evaluation Measures
  11. 11. Comparing Performance Measures
  12. 12. Comparing Performance Measures <ul><li>Sharpe ratio </li></ul><ul><li>Appropriate for the evaluation of an entire portfolio. </li></ul><ul><li>Penalizes a portfolio for being undiversified, since in general, total risk  systematic risk only for relatively well-diversified portfolios. </li></ul>Since the performance rankings may be substantially different, which performance measure should we use?
  13. 13. Comparing Performance Measures <ul><li>Treynor ratio / Jensen’s alpha </li></ul><ul><li>Appropriate for the evaluation of securities or portfolios for possible inclusion in a broader or “master” portfolio. </li></ul><ul><li>Both are similar, the only difference being that the Treynor ratio standardizes everything, including any excess return, relative to beta. </li></ul><ul><li>Both require a beta estimate (and betas from different sources may differ a lot). </li></ul>
  14. 14. Work the Web <ul><li>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: </li></ul><ul><ul><li>http://www. morningstar .com </li></ul></ul>
  15. 15. Sharpe-Optimal Portfolios <ul><li>A funds allocation with the highest possible Sharpe ratio is said to be Sharpe-optimal . </li></ul><ul><li>To find the Sharpe-optimal portfolio, consider the plot of the investment opportunity set of risk-return possibilities for a portfolio. </li></ul>Expected Return Standard deviation × × × × × × × × × × × × × × × ×
  16. 16. Sharpe-Optimal Portfolios <ul><li>The slope of a straight line drawn from the risk-free rate to a portfolio gives the Sharpe ratio for that portfolio. </li></ul><ul><li>Hence, the portfolio on the line with the steepest slope is the Sharpe-optimal portfolio. </li></ul>Expected Return Standard deviation × A R f
  17. 17. Sharpe-Optimal Portfolios
  18. 18. Sharpe-Optimal Portfolios <ul><li>Notice that the Sharpe-optimal portfolio is one of the efficient portfolios on the Markowitz efficient frontier. </li></ul>
  19. 19. Investment Risk Management <ul><li>We will focus on what is known as the Value-at-Risk approach. </li></ul>Investment risk management Concerns a money manager’s control over investment risks, usually with respect to potential short-run losses.
  20. 20. Value-at-Risk (VaR) <ul><li>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. </li></ul>Value-at-Risk (VaR) Assesses risk by stating the probability of a loss a portfolio may experience within a fixed time horizon.
  21. 21. Value-at-Risk (VaR) <ul><li>Example: VaR </li></ul><ul><li>Suppose you own an S&P 500 index fund. Historically, E(R S&P500 )  13% per year, while  S&P500  20%. What is the probability of a return of -7% or worse in a particular year? </li></ul><ul><li>The odds of being within one  are about 2/3 or .67. I.e. Prob (.13–.20  R S&P500  .13+.20)  .67 </li></ul><ul><ul><li>or Prob (–.07  R S&P500  .33)  .67 </li></ul></ul><ul><li>So, Prob ( R S&P500  –.07)  1/6 or .17 </li></ul><ul><li>The VaR statistic is thus a return of –.07 or worse with a probability of 17%. </li></ul>
  22. 22. Work the Web <ul><li>Learn all about VaR at: </li></ul><ul><ul><li>http://www. gloriamundi .org </li></ul></ul>
  23. 23. More on Computing Value-at-Risk <ul><li>Example: More on VaR </li></ul><ul><li>For the S&P 500 index fund, what is the probability of a loss of 30% or more over the next two years? </li></ul><ul><li>2-year average return = 2  .13 = .26 </li></ul><ul><li>1-year  2 = .20 2 = .04. So, 2-year  2 = 2  .04 = .08. </li></ul><ul><ul><li>So, 1-year  =  .08  .28 </li></ul></ul><ul><li>The odds of being within two  ’s are .95. </li></ul><ul><ul><li>I.e. Prob (.26–2  .28  R S&P500  .26+2  .28)  .95 </li></ul></ul><ul><ul><li>or Prob (–.30  R S&P500  .82)  .95 </li></ul></ul><ul><li>So, Prob ( R S&P500  –.30)  2.5% </li></ul>
  24. 24. More on Computing Value-at-Risk <ul><li>In general, if T is the number of years, </li></ul><ul><li>So, </li></ul>
  25. 25. Work the Web <ul><li>Learn about the risk management profession at: </li></ul><ul><ul><li>http://www. garp .org </li></ul></ul>
  26. 26. Chapter Review <ul><li>Performance Evaluation </li></ul><ul><ul><li>Performance Evaluation Measures </li></ul></ul><ul><ul><ul><li>The Sharpe Ratio </li></ul></ul></ul><ul><ul><ul><li>The Treynor Ratio </li></ul></ul></ul><ul><ul><ul><li>Jensen’s Alpha </li></ul></ul></ul><ul><li>Comparing Performance Measures </li></ul><ul><ul><li>Sharpe-Optimal Portfolios </li></ul></ul>
  27. 27. Chapter Review <ul><li>Investment Risk Management </li></ul><ul><ul><li>Value-at-Risk (VaR) </li></ul></ul><ul><li>More on Computing Value-at-Risk </li></ul>