1、INVESTMENTS | BODIE, KANE, MARCUS Copyright 2011 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin CHAPTER 24 Portfolio Performance Evaluation INVESTMENTS | BODIE, KANE, MARCUS 24-2 Two common ways to measure average portfolio return: 1. Time-weighted returns 2. Dollar-weight
2、ed returns Returns must be adjusted for risk. Introduction INVESTMENTS | BODIE, KANE, MARCUS 24-3 Time-weighted returns The geometric average is a time- weighted average. Each periods return has equal weight. Dollar- and Time-Weighted Returns n n G rrrr1.111 21 INVESTMENTS | BODIE, KANE, MARCUS 24-4
3、 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 n n r C r C r C PV 1 . 11 2 2 1 1 INVESTMENTS | BODIE, KANE, MARCUS 24-5 Example of Multiperiod Returns INVES
4、TMENTS | BODIE, KANE, MARCUS 24-6 %117. 7 )1 ( 112 )1 ( 51 50 21 r rr Dollar-weighted Return (IRR): Dollar-Weighted Return -$50-$53 $2 $4+$108 INVESTMENTS | BODIE, KANE, MARCUS 24-7 Time-Weighted Return %66. 5 53 25354 %10 50 25053 2 1 r r The dollar-weighted average is less than the time-weighted a
5、verage 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% INVESTMENTS | BODIE, KANE, MARCUS 24-8 The simplest and most popular way to adjust returns for risk is to compare the portfolios return with the returns on a comparison uni
6、verse. 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 INVESTMENTS | BODIE, KANE, MARCUS 24-9 Figure 24.1 Universe Comparison INVESTMENTS | BODIE, KANE
7、, MARCUS 24-10 1) Sharpe Index Risk Adjusted Performance: Sharpe rp = Average return on the portfolio rf = Average risk free rate p = Standard deviation of portfolio return () Pf P rr INVESTMENTS | BODIE, KANE, MARCUS 24-11 2) Treynor Measure Risk Adjusted Performance: Treynor rp = Average return on
8、 the portfolio rf = Average risk free rate p = Weighted average beta for portfolio () Pf P rr INVESTMENTS | BODIE, KANE, MARCUS 24-12 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
9、 rate rm = Average return on market index portfolio () PPfPMf rrrr INVESTMENTS | BODIE, KANE, MARCUS 24-13 Information Ratio Information Ratio = p / (ep) The information ratio divides the alpha of the portfolio by the nonsystematic risk. Nonsystematic risk could, in theory, be eliminated by diversif
10、ication. INVESTMENTS | BODIE, KANE, MARCUS 24-14 M2 Measure Developed by Modigliani and Modigliani Create 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: 2 *PM Mrr INVE
11、STMENTS | BODIE, KANE, MARCUS 24-15 M2 Measure: Example Managed Portfolio: return = 35%standard deviation = 42% Market Portfolio: return = 28% standard deviation = 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) =
12、 26.7% Since this return is less than the market, the managed portfolio underperformed. INVESTMENTS | BODIE, KANE, MARCUS 24-16 Figure 24.2 M2 of Portfolio P INVESTMENTS | BODIE, KANE, MARCUS 24-17 It depends on investment assumptions 1)If the portfolio represents the entire risky investment , then
13、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. Which Measure is Appropriate? INVESTMENTS | BODIE, KANE, MARCUS 24-18 T
14、able 24.1 Portfolio Performance Is Q better than P? INVESTMENTS | BODIE, KANE, MARCUS 24-19 Figure 24.3 Treynors Measure INVESTMENTS | BODIE, KANE, MARCUS 24-20 Table 24.3 Performance Statistics INVESTMENTS | BODIE, KANE, MARCUS 24-21 Interpretation of Table 24.3 If P or Q represents the entire inve
15、stment, Q is better because of its higher Sharpe measure and better M2. If P 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 inform
16、ation ratio. INVESTMENTS | BODIE, KANE, MARCUS 24-22 Performance Measurement for Hedge Funds When the hedge fund is optimally combined with the baseline portfolio, the improvement in the Sharpe measure will be determined by its information ratio: 2 22 () H PM H SS e INVESTMENTS | BODIE, KANE, MARCUS
17、 24-23 Performance Measurement with Changing Portfolio Composition We need a very long observation period to measure performance with any precision, even if the return distribution is stable with a constant mean and variance. What if the mean and variance are not constant? We need to keep track of p
18、ortfolio changes. INVESTMENTS | BODIE, KANE, MARCUS 24-24 Figure 24.4 Portfolio Returns INVESTMENTS | BODIE, KANE, MARCUS 24-25 Market Timing In its pure form, market timing involves shifting funds between a market-index portfolio and a safe asset. Treynor and Mazuy: Henriksson and Merton: 2 ()() Pf
19、MfMfP rrab rrc rre ()() PfMfMfP rrab rrc rrDe INVESTMENTS | BODIE, KANE, MARCUS 24-26 Figure 24.5 : No Market Timing; Beta Increases with Expected Market Excess. Return; Market Timing with Only Two Values of Beta. INVESTMENTS | BODIE, KANE, MARCUS 24-27 Figure 24.6 Rate of Return of a Perfect Market
20、 Timer INVESTMENTS | BODIE, KANE, MARCUS 24-28 Style Analysis Introduced by William Sharpe Regress fund returns 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
21、to style or asset allocation. The remainder is due either to security selection or to market timing. INVESTMENTS | BODIE, KANE, MARCUS 24-29 Table 24.5 Style Analysis for Fidelitys Magellan Fund INVESTMENTS | BODIE, KANE, MARCUS 24-30 Figure 24.7 Fidelity Magellan Fund Cumulative Return Difference I
22、NVESTMENTS | BODIE, KANE, MARCUS 24-31 Figure 24.8 Average Tracking Error for 636 Mutual Funds, 1985-1989 INVESTMENTS | BODIE, KANE, MARCUS 24-32 Evaluating Performance Evaluation Performance evaluation has two key problems: 1. Many observations are needed for significant results. 2. Shifting parame
23、ters when portfolios are actively managed makes accurate performance evaluation all the more elusive. INVESTMENTS | BODIE, KANE, MARCUS 24-33 A common attribution system decomposes performance into three components: 1. Allocation choices across broad asset classes. 2. Industry or sector choice withi
24、n each market. 3. Security choice within each sector. Performance Attribution INVESTMENTS | BODIE, KANE, MARCUS 24-34 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 e
25、ach class by security analysis. Attributing Performance to Components INVESTMENTS | BODIE, KANE, MARCUS 24-35 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 into appropria
26、te categories. Attributing Performance to Components INVESTMENTS | BODIE, KANE, MARCUS 24-36 )( & 1 11 11 BiBi n i pipi n i BiBi n i pipiBp n i pipip n i BiBiB rwrw rwrwrr rwrrwr Where B is the bogey portfolio and p is the managed portfolio Formulas for Attribution INVESTMENTS | BODIE, KANE, MARCUS
27、24-37 Figure 24.10 Performance Attribution of ith Asset Class INVESTMENTS | BODIE, KANE, MARCUS 24-38 Performance Attribution Superior performance is achieved by: overweighting assets in markets that perform well underweighting assets in poorly performing markets INVESTMENTS | BODIE, KANE, MARCUS 24-39 Table 24.7 Performance Attribution INVESTMENTS | BODIE, KANE, MARCUS 24-40 Sector and Security Selection Good performance (a positive contribution) derives from overweighting high-performing sectors Good performance also derives from underweighting poorly performing sectors.
