McGraw-Hill/Irwin © 2007 The McGraw-Hill Companies, Inc., All Rights Reserved. Performance Evaluation and Active Portfolio Management CHAPTER 17

17-2 Introduction Complicated subject Theoretically correct measures are difficult to construct Different statistics or measures are appropriate for different types of investment decisions or portfolios Many industry and academic measures are different The nature of active managements leads to measurement problems

17-3 Abnormal Performance What is abnormal? What is abnormal? Abnormal performance is measured: Abnormal performance is measured: Comparison groups Market adjusted Market model / index model adjusted Reward to risk measures such as the Sharpe Measure: E (r p -r f ) /  p

17-4 Factors That Lead to Abnormal Performance Market timing Superior selection –Sectors or industries –Individual companies

17-5 Comparison Groups Simplest method Most popular Compare returns to other funds with similar investment objectives

17-6 Figure 17-1 Universe Comparison Periods Ending December 31, 2003

17-7 Risk Adjusted Performance: Sharpe 1) Sharpe Index 1) Sharpe Index r p - r f r p = Average return on the portfolio r f = Average risk free rate p = Standard deviation of portfolio return p  

17-8 Risk Adjusted Performance: Treynor 2) Treynor Measure 2) Treynor Measure r p - r f ß p r p = Average return on the portfolio r f = Average risk free rate ß p = Weighted average  for portfolio

17-9 = r p - [ r f + ß p ( r m - r f ) ] = r p - [ r f + ß p ( r m - r f ) ] 3) Jensen’s Measure 3) Jensen’s Measure p p r p = Average return on the portfolio ß p = Weighted average Beta r f = Average risk free rate r m = Avg. return on market index port. Risk Adjusted Performance: Jensen = Alpha for the portfolio  

17-10 M 2 Measure Developed by Modigliani and Modigliani Equates the volatility of the managed portfolio with the market by creating a hypothetical portfolio made up of T-bills and the managed portfolio If the risk is lower than the market, leverage is used and the hypothetical portfolio is compared to the market

17-11 M 2 Measure: Example Managed Portfolio Market T-bill Return35% 28% 6% Stan. Dev42% 30% 0% Hypothetical Portfolio: Same Risk as Market 30/42 =.714 in P (1-.714) or.286 in T-bills (.714) (.35) + (.286) (.06) = 26.7% Since this return is less than the market, the managed portfolio underperformed

17-12 Figure 17-2 The M 2 of Portfolio P

17-13 T 2 (Treynor Square) Measure Used to convert the Treynor Measure into percentage return basis Makes it easier to interpret and compare Equates the beta of the managed portfolio with the market’s beta of 1 by creating a hypothetical portfolio made up of T-bills and the managed portfolio If the beta is lower than one, leverage is used and the hypothetical portfolio is compared to the market

17-14 T 2 Example Port. P.Market Risk Prem. (r-r f ) 13% 10% Beta Alpha 5% 0% Treynor Measure Weight to match Market w =  M /  P = 1.0 / 0.8 Adjusted Return R P * = w (R P ) = 16.25% T 2 P = R P * - R M = 16.25% - 10% = 6.25%

17-15 Figure 17-3 Treynor Square Measure

17-16 Which Measure is Appropriate? It depends on investment assumptions It depends on investment assumptions 1) If the portfolio 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  or the Treynor measure The Treynor measure is more complete because it adjusts for risk

17-17 Limitations Assumptions underlying measures limit their usefulness When the portfolio is being actively managed, basic stability requirements are not met Practitioners often use benchmark portfolio comparisons to measure performance

17-18 Figure 17-4 Portfolio Returns

17-19 Performance Attribution Decomposing overall performance into components Components are related to specific elements of performance Example components –Broad Allocation –Industry –Security Choice –Up and Down Markets

17-20 Process of Attributing Performance to Components Set up a ‘Benchmark’ or ‘Bogey’ portfolio Set up a ‘Benchmark’ or ‘Bogey’ portfolio Use indexes for each component Use target weight structure

17-21 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 appropriate categories Process of Attributing Performance to Components

17-22 Table 17-3 Performance of the Managed Portfolio

17-23 Table 17-4 Performance Attribution

17-24 Table 17-5 Sector Allocation Within the Equity Market

17-25 Table 17-6 Portfolio Attribution Summary

17-26 Lure of Active Management Are markets totally efficient? Are markets totally efficient? Some managers outperform the market for extended periods While the abnormal performance may not be too large, it is too large to be attributed solely to noise Evidence of anomalies such as the turn of the year exist The evidence suggests that there is some role for active management The evidence suggests that there is some role for active management

17-27 Market Timing Adjust the portfolio for movements in the market Shift between stocks and money market instruments or bonds Results: higher returns, lower risk (downside is eliminated) With perfect ability to forecast behaves like an option

17-28 rfrfrfrf rfrfrfrf rMrMrMrM Rate of Return of a Perfect Market Timer

17-29 With Imperfect Ability to Forecast Long horizon to judge the ability Judge proportions of correct calls Bull markets and bear market calls

17-30 Market Timing & Performance Measurement Adjusting portfolio for up and down movements in the market Adjusting portfolio for up and down movements in the market Low Market Return - low ßeta High Market Return - high ßeta

17-31 Figure 17-6 Characteristic Lines

17-32 Style Analysis Introduced by Bill Sharpe Explaining percentage returns by allocation to style Style Analysis has become popular with the industry

17-33 Figure 17-7 Fidelity Magellan Fund Difference Fund versus Style Benchmark

17-34 Figure 17-8 Fidelity Magellan Fund Difference Fund versus S&P 500

17-35 Figure 17-9 Average Tracking Error of 636 Mutual Funds,

17-36 Morning Star’s Risk Adjusted Rating Similar to mean Standard Deviation rankings Companies are put into peer groups Stars are assigned –1-lowest –5-highest Highly correlated to Sharpe measures

17-37 Figure Rankings Based on Morningstar’s RARs and Excess Return Sharpe Ratios

17-38 Superior Selection Ability Concentrate funds in undervalued stocks or undervalued sectors or industries Balance funds in an active portfolio and in a passive portfolio Active selection will mean some unsystematic risk

17-39 Treynor-Black Model Model used to combine actively managed stocks with a passively managed portfolio Using a reward-to-risk measure that is similar to the the Sharpe Measure, the optimal combination of active and passive portfolios can be determined

17-40 Treynor-Black Model: Assumptions Analysts will have a limited ability to find a select number of undervalued securities Portfolio managers can estimate the expected return and risk, and the abnormal performance for the actively-managed portfolio Portfolio managers can estimate the expected risk and return parameters for a broad market (passively managed) portfolio

17-41 Reward to Variability Measures Passive Portfolio :           m fm rr E S m 2 2

17-42 Appraisal Ratio Appraisal Ratio A = Alpha for the active portfolio (eA) = Unsystematic standard deviation for active deviation for active Reward to Variability Measures           eA A 2

17-43 Reward to Variability Measures Combined Portfolio :                   eA A m fm rr E S P 22 2

17-44 Summary Points: Treynor-Black Model Sharpe Measure will increase with added ability to pick stocks Slope of CAL>CML (r p -r f )/  p > (r m -r f )/  p P is the portfolio that combines the passively managed portfolio with the actively managed portfolio The combined efficient frontier has a higher return for the same level of risk

17-45 Figure The Optimization Process with Active and Passive Portfolios