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    Chap19 Chap19 Presentation Transcript

    • 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
    • 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
    • Performance Evaluation & Risk Management
      • 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.
    • 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.
    • 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.
    • 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.
    • Work the Web
      • Visit Professor Sharpe at:
        • http://www. stanford . edu /~ wfsharpe
    • 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.
    • 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.
    • Performance Evaluation Measures
    • Comparing Performance Measures
    • Comparing Performance Measures
      • Sharpe ratio
      • Appropriate for the evaluation of an entire portfolio.
      • Penalizes a portfolio for being undiversified, since in general, total risk  systematic risk only for relatively well-diversified portfolios.
      Since the performance rankings may be substantially different, which performance measure should we use?
    • Comparing Performance Measures
      • Treynor ratio / Jensen’s alpha
      • Appropriate for the evaluation of securities or portfolios for possible inclusion in a broader or “master” portfolio.
      • Both are similar, the only difference being that the Treynor ratio standardizes everything, including any excess return, relative to beta.
      • Both require a beta estimate (and betas from different sources may differ a lot).
    • 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
    • Sharpe-Optimal Portfolios
      • A funds allocation with the highest possible Sharpe ratio is 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 × × × × × × × × × × × × × × × ×
    • Sharpe-Optimal Portfolios
      • The slope of a straight line drawn from the risk-free rate to a portfolio gives the Sharpe ratio for that portfolio.
      • Hence, the portfolio on the line with the steepest slope is the Sharpe-optimal portfolio.
      Expected Return Standard deviation × A R f
    • Sharpe-Optimal Portfolios
    • Sharpe-Optimal Portfolios
      • Notice that the Sharpe-optimal portfolio is one of the efficient portfolios on the Markowitz efficient frontier.
    • Investment Risk Management
      • We will focus on what is known as the Value-at-Risk approach.
      Investment risk management Concerns a money manager’s control over investment risks, usually with respect to potential short-run losses.
    • Value-at-Risk (VaR)
      • 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.
      Value-at-Risk (VaR) Assesses risk by stating the probability of a loss a portfolio may experience within a fixed time horizon.
    • Value-at-Risk (VaR)
      • Example: VaR
      • 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?
      • The odds of being within one  are about 2/3 or .67. I.e. Prob (.13–.20  R S&P500  .13+.20)  .67
        • or Prob (–.07  R S&P500  .33)  .67
      • So, Prob ( R S&P500  –.07)  1/6 or .17
      • The VaR statistic is thus a return of –.07 or worse with a probability of 17%.
    • Work the Web
      • Learn all about VaR at:
        • http://www. gloriamundi .org
    • 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  2 = .20 2 = .04. So, 2-year  2 = 2  .04 = .08.
        • So, 1-year  =  .08  .28
      • The odds of being within two  ’s are .95.
        • I.e. Prob (.26–2  .28  R S&P500  .26+2  .28)  .95
        • or Prob (–.30  R S&P500  .82)  .95
      • So, Prob ( R S&P500  –.30)  2.5%
    • More on Computing Value-at-Risk
      • In general, if T is the number of years,
      • So,
    • Work the Web
      • Learn about the risk management profession at:
        • http://www. garp .org
    • Chapter Review
      • Performance Evaluation
        • Performance Evaluation Measures
          • The Sharpe Ratio
          • The Treynor Ratio
          • Jensen’s Alpha
      • Comparing Performance Measures
        • Sharpe-Optimal Portfolios
    • Chapter Review
      • Investment Risk Management
        • Value-at-Risk (VaR)
      • More on Computing Value-at-Risk