INVESTMENTS 投资学 （博迪BODIE, KANE, MARCUS）Chap024 Portfolio Perance uation.ppt

1、CHAPTER 24,Portfolio Performance Evaluation,2,Two common ways to measure average portfolio return: Time-weighted returns Dollar-weighted returns Returns must be adjusted for risk.,Introduction,3,Time-weighted returns The geometric average is a time-weighted average. Each periods return has equal wei

2、ght.,Dollar- and Time-Weighted Returns,4,Dollar-weighted returns Internal rate of return considering the cash flow from or to investment Returns are weighted by the amount invested in each period:,Dollar- and Time-Weighted Returns,5,Example of Multiperiod Returns,6,Dollar-weighted Return (IRR):,Doll

3、ar-Weighted Return,7,Time-Weighted Return,The dollar-weighted average is less than the time-weighted average in this example because more money is invested in year two, when the return was lower.,rG = (1.1) (1.0566) 1/2 1 = 7.81%,8,The simplest and most popular way to adjust returns for risk is to c

4、ompare the portfolios return with the returns on a comparison universe. The comparison universe is a benchmark composed of a group of funds or portfolios with similar risk characteristics, such as growth stock funds or high-yield bond funds.,Adjusting Returns for Risk,9,Figure 24.1 Universe Comparis

5、on,10,1) Sharpe Index,Risk Adjusted Performance: Sharpe,11,2) Treynor Measure,Risk Adjusted Performance: Treynor,12,Risk Adjusted Performance: Jensen,3) Jensens Measure,p,= Alpha for the portfolio,rp = Average return on the portfolio p = Weighted average Beta rf = Average risk free rate rm = Average

6、 return on market index portfolio,13,Information Ratio,Information Ratio = ap / s(ep),The information ratio divides the alpha of the portfolio by the nonsystematic risk. Nonsystematic risk could, in theory, be eliminated by diversification.,14,M2 Measure,Developed by Modigliani and Modigliani Create

7、 an adjusted portfolio (P*)that has the same standard deviation as the market index. Because the market index and P* have the same standard deviation, their returns are comparable:,15,M2 Measure: Example,Managed Portfolio: return = 35%standard deviation = 42% Market Portfolio: return = 28%standard d

8、eviation = 30% T-bill return = 6% P* Portfolio: 30/42 = .714 in P and (1-.714) or .286 in T-bills The return on P* is (.714) (.35) + (.286) (.06) = 26.7% Since this return is less than the market, the managed portfolio underperformed.,16,Figure 24.2 M2 of Portfolio P,17,It depends on investment assu

9、mptions If the portfolio represents the entire risky investment , then use the Sharpe measure. 2) If the portfolio is one of many combined into a larger investment fund, use the Jensen or the Treynor measure. The Treynor measure is appealing because it weighs excess returns against systematic risk.,

10、Which Measure is Appropriate?,18,Table 24.1 Portfolio Performance,Is Q better than P?,19,Figure 24.3 Treynors Measure,20,Table 24.3 Performance Statistics,21,Interpretation of Table 24.3,If P or Q represents the entire investment, Q is better because of its higher Sharpe measure and better M2. If P

11、and Q are competing for a role as one of a number of subportfolios, Q also dominates because its Treynor measure is higher. If we seek an active portfolio to mix with an index portfolio, P is better due to its higher information ratio.,22,Performance Measurement for Hedge Funds,When the hedge fund i

12、s optimally combined with the baseline portfolio, the improvement in the Sharpe measure will be determined by its information ratio:,23,Performance Measurement with Changing Portfolio Composition,We need a very long observation period to measure performance with any precision, even if the return dis

13、tribution is stable with a constant mean and variance.,What if the mean and variance are not constant? We need to keep track of portfolio changes.,24,Figure 24.4 Portfolio Returns,25,Market Timing,In its pure form, market timing involves shifting funds between a market-index portfolio and a safe ass

14、et. Treynor and Mazuy: Henriksson and Merton:,26,Figure 24.5 : No Market Timing; Beta Increases with Expected Market Excess. Return; Market Timing with Only Two Values of Beta.,27,Figure 24.6 Rate of Return of a Perfect Market Timer,28,Style Analysis,Introduced by William Sharpe Regress fund returns

15、 on indexes representing a range of asset classes. The regression coefficient on each index measures the funds implicit allocation to that “style.” R square measures return variability due to style or asset allocation. The remainder is due either to security selection or to market timing.,29,Table 2

16、4.5 Style Analysis for Fidelitys Magellan Fund,30,Figure 24.7 Fidelity Magellan Fund Cumulative Return Difference,31,Figure 24.8 Average Tracking Error for 636 Mutual Funds, 1985-1989,32,Evaluating Performance Evaluation,Performance evaluation has two key problems: Many observations are needed for s

17、ignificant results. Shifting parameters when portfolios are actively managed makes accurate performance evaluation all the more elusive.,33,A common attribution system decomposes performance into three components: Allocation choices across broad asset classes. Industry or sector choice within each m

18、arket. Security choice within each sector.,Performance Attribution,34,Set up a Benchmark or Bogey portfolio: Select a benchmark index portfolio for each asset class. Choose weights based on market expectations. Choose a portfolio of securities within each class by security analysis.,Attributing Performance to Components,35,Calculate the return on the Bogey and on the managed portfolio. Explain the difference in return based on component weights or selection. Summarize the performance differences i