Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 1 Chapter 19 Performance Evaluation and Active Portfolio Management

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 3 Abnormal Performance What is abnormal? Abnormal performance is measured: Benchmark portfolio Market adjusted Market model / index model adjusted Reward to risk measures such as the Sharpe Measure: E (r p -r f ) /  p

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 4 Factors That Lead to Abnormal Performance Market timing Superior selection –Sectors or industries –Individual companies

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 5 Risk Adjusted Performance: Sharpe 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  

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 6 Risk Adjusted Performance: Treynor 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 7 = 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  

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 8 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 9 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 10 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 11 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%

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 12 Which Measure is Appropriate? 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 13 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 14 Market Timing Adjusting portfolio for up and down movements in the market Low Market Return - low ßeta High Market Return - high ßeta

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 15 Example of Market Timing * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * r p - r f r m - r f Steadily Increasing the Beta Irwin/McGraw-Hill © The McGraw-Hill Companies, Inc.,

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 16 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 17 Process of Attributing Performance to Components Set up a ‘Benchmark’ or ‘Bogey’ portfolio Use indexes for each component Use target weight structure

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 18 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 19 Lure of Active Management 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 20 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 21 rfrfrfrf rfrfrfrf rMrMrMrM Rate of Return of a Perfect Market Timer

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 22 Numerical Example Year Stock Ret T-Bill Ret Avg. Ret. S.D. Ret Irwin/McGraw-Hill 21-5 © The McGraw-Hill Companies, Inc., 1998

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 23 With Perfect Forecasting Ability Switch to T-Bills in 73, 74, 77, 78 No negative returns or losses Average Ret. =.1724 S.D. Ret. =.1118 Results with perfect timing –70% increase in mean return –46% lower S.D.

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 24 With Imperfect Ability to Forecast Long horizon to judge the ability Judge proportions of correct calls Bull markets and bear market calls Evidence from boxed item: “Market Timing Also Stumps Many Pros”

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 25 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 26 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 27 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

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 28 Reward to Variability Measures Passive Portfolio :

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 29 Appraisal Ratio Appraisal Ratio A = Alpha for the active portfolio (eA) = Unsystematic standard deviation for active deviation for active Reward to Variability Measures  

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 30 Reward to Variability Measures Combined Portfolio :

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 31 M A P E(r)  CML CAL Treynor-Black Allocation RfRf

Essentials of Investments © 2001 The McGraw-Hill Companies, Inc. All rights reserved. Fourth Edition Irwin / McGraw-Hill Bodie Kane Marcus 32 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