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1、 McGraw-Hill/Irwin 2007 The McGraw-Hill Companies, Inc., All Rights Reserved.Performance Evaluation and Active Portfolio ManagementCHAPTER 1717-2IntroductionComplicated subjectComplicated subjectTheoretically correct measures are difficult to Theoretically correct measures are difficult to construct
2、constructDifferent statistics or measures are appropriate Different statistics or measures are appropriate for different types of investment decisions or for different types of investment decisions or portfoliosportfoliosMany industry and academic measures are Many industry and academic measures are
3、 differentdifferentThe nature of active managements leads to The nature of active managements leads to measurement problemsmeasurement problems17-3Abnormal Performance What is abnormal? Abnormal performance is measured:Comparison groupsMarket adjustedMarket model / index model adjustedReward to risk
4、 measures such as the Sharpe Measure:E (rE (rp p-r -rf f) / ) / s sp p17-4Factors That Lead to Abnormal PerformanceMarket timingSuperior selectionSectors or industriesSectors or industriesIndividual companiesIndividual companies17-5Comparison GroupsSimplest methodMost popularCompare returns to other
5、 funds with similar investment objectives17-6Figure 17-1 Universe Comparison Periods Ending December 31, 200317-7Risk Adjusted Performance: Sharpe 1) Sharpe Indexrp - rfrp = Average return on the portfolio rf = Average risk free ratep p= Standard deviation of portfolio returnp pss17-8Risk Adjusted P
6、erformance: Treynor 2) Treynor Measurerp - rfprp = Average return on the portfolio rf = Average risk free ratep = Weighted average b for portfolio 17-9 = rp - rf + p ( rm - rf) 3) Jensens Measurep pprp = Average return on the portfoliop = Weighted average Betarf = Average risk free raterm = Avg. ret
7、urn on market index port. Risk Adjusted Performance: Jensen= Alpha for the portfolioa aa a17-10M2 MeasureDeveloped by Modigliani and ModiglianiEquates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-bills and the managed portfolioIf the risk
8、is lower than the market, leverage is used and the hypothetical portfolio is compared to the market17-11M2 Measure: ExampleManaged Portfolio Market T-billReturn35% 28% 6%Stan. Dev42% 30% 0%Hypothetical Portfolio: Same Risk as Market30/42 = .714 in P (1-.714) or .286 in T-bills(.714) (.35) + (.286) (
9、.06) = 26.7%Since this return is less than the market, the managed portfolio underperformed17-12Figure 17-2 The M2 of Portfolio P17-13T2 (Treynor Square) MeasureUsed to convert the Treynor Measure into Used to convert the Treynor Measure into percentage return basispercentage return basisMakes it ea
10、sier to interpret and compareMakes it easier to interpret and compareEquates the beta of the managed portfolio with Equates the beta of the managed portfolio with the markets beta of 1 by creating a hypothetical the markets beta of 1 by creating a hypothetical portfolio made up of T-bills and the ma
11、naged portfolio made up of T-bills and the managed portfolioportfolioIf the beta is lower than one, leverage is used If the beta is lower than one, leverage is used and the hypothetical portfolio is compared to the and the hypothetical portfolio is compared to the market market 17-14T2 ExamplePort.
12、P.MarketRisk Prem. (r-rf) 13% 10%Alpha 5% 0%Treynor Measure 16.25 10Weight to match Market w = bM/bPAdjusted Return RP* = w (RP) = 16.25%T2P = RP* - RM = 16.25% - 10% = 6.25%17-15Figure 17-3 Treynor Square Measure17-16Which Measure is Appropriate? It depends on investment assumptions1) If the portfo
13、lio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market.2) If many alternatives are possible, use the Jensen a or the Treynor measureThe Treynor measure is more complete because it adjusts for risk17-17LimitationsAssumptions underlying measure
14、s limit their usefulnessWhen the portfolio is being actively managed, basic stability requirements are not metPractitioners often use benchmark portfolio comparisons to measure performance17-18Figure 17-4 Portfolio Returns17-19Performance AttributionDecomposing overall performance into componentsCom
15、ponents are related to specific elements of performanceExample componentsBroad AllocationBroad AllocationIndustryIndustrySecurity ChoiceSecurity ChoiceUp and Down MarketsUp and Down Markets17-20Process of Attributing Performance to Components Set up a Benchmark or Bogey portfolioUse indexes for each
16、 componentUse target weight structure17-21Calculate the return on the Bogey and on the managed portfolioExplain the difference in return based on component weights or selectionSummarize the performance differences into appropriate categoriesProcess of Attributing Performance to Components17-22Table
17、17-3 Performance of the Managed Portfolio17-23Table 17-4 Performance Attribution17-24Table 17-5 Sector Allocation Within the Equity Market17-25Table 17-6 Portfolio Attribution Summary17-26Lure of Active Management Are markets totally efficient?Some managers outperform the market for Some managers ou
18、tperform the market for extended periodsextended periodsWhile the abnormal performance may not be too While the abnormal performance may not be too large, it is too large to be attributed solely to large, it is too large to be attributed solely to noisenoiseEvidence of anomalies such as the turn of
19、the Evidence of anomalies such as the turn of the year existyear exist The evidence suggests that there is some role for active management17-27Market TimingAdjust the portfolio for movements in the marketShift between stocks and money market instruments or bondsResults: higher returns, lower risk (d
20、ownside is eliminated)With perfect ability to forecast behaves like an option17-28rfrfrMRate of Return of a Perfect Market Timer17-29With Imperfect Ability to ForecastLong horizon to judge the abilityJudge proportions of correct callsBull markets and bear market calls17-30Market Timing & Performance
21、 Measurement Adjusting portfolio for up and down movements in the marketLow Market Return - low etaHigh Market Return - high eta17-31Figure 17-6 Characteristic Lines 17-32Style AnalysisIntroduced by Bill SharpeExplaining percentage returns by allocation to styleStyle Analysis has become popular with
22、 the industry17-33Figure 17-7 Fidelity Magellan Fund Difference Fund versus Style Benchmark 17-34Figure 17-8 Fidelity Magellan Fund Difference Fund versus S&P 50017-35Figure 17-9 Average Tracking Error of 636 Mutual Funds, 1985 - 198917-36Morning Stars Risk Adjusted RatingSimilar to mean Standard De
23、viation rankingsCompanies are put into peer groupsStars are assigned1-lowest1-lowest5-highest5-highestHighly correlated to Sharpe measures17-37Figure 17-10 Rankings Based on Morningstars RARs and Excess Return Sharpe Ratios17-38Superior Selection AbilityConcentrate funds in undervalued stocks or und
24、ervalued sectors or industriesBalance funds in an active portfolio and in a passive portfolioActive selection will mean some unsystematic risk17-39Treynor-Black Model Model used to combine actively managed stocks with a passively managed portfolioUsing a reward-to-risk measure that is similar to the
25、 the Sharpe Measure, the optimal combination of active and passive portfolios can be determined17-40Treynor-Black Model: AssumptionsAnalysts will have a limited ability to find a select Analysts will have a limited ability to find a select number of undervalued securitiesnumber of undervalued securi
26、tiesPortfolio managers can estimate the expected Portfolio managers can estimate the expected return and risk, and the abnormal performance return and risk, and the abnormal performance for the actively-managed portfoliofor the actively-managed portfolioPortfolio managers can estimate the expected P
27、ortfolio managers can estimate the expected risk and return parameters for a broad market risk and return parameters for a broad market (passively managed) portfolio(passively managed) portfolio17-41Reward to Variability MeasuresPassive Portfolio : ( )-=smfmrrESm2217-42 Appraisal RatioA A= Alpha for
28、 the active portfolio( (eA)eA)= Unsystematic standard deviation for activeReward to Variability MeasuressasaeAA217-43Reward to Variability MeasuresCombined Portfolio :( )-+=saseAAmfmrrESP22217-44Summary Points: Treynor-Black ModelSharpe Measure will increase with added ability to pick stocksSlope of CALCML(rp-rf)/sp (rm-rf)/spP is the portfolio that combines the passively managed portfolio with the actively managed portfolioThe combined efficient frontier has a higher return for the same level of risk17-45Figure 17-11 The Optimization Process with Active and Passive Portfolios
