 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-1 Portfolio Performance Evaluation Chapter 24

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-2 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 management leads to measurement problems Introduction

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-3 Dollar-weighted returns Internal rate of return considering the cash flow from or to investment Returns are weighted by the amount invested in each stock Time-weighted returns Not weighted by investment amount Equal weighting Dollar- and Time-Weighted Returns

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-4 Text Example of Multiperiod Returns PeriodAction 0Purchase 1 share at $50 1Purchase 1 share at $53 Stock pays a dividend of $2 per share 2Stock pays a dividend of $2 per share Stock is sold at $108 per share

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-5 PeriodCash Flow 0-50 share purchase 1+2 dividend -53 share purchase 2+4 dividend shares sold Internal Rate of Return: Dollar-Weighted Return

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-6 Time-Weighted Return Simple Average Return: (10% %) / 2 = 7.83%

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-7 Averaging Returns Arithmetic Mean: Geometric Mean: Text Example Average: ( ) / 2 = 7.81% [ (1.1) (1.0566) ] 1/2 - 1 = 7.83% Text Example Average:

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-8 Past Performance - generally the geometric mean is preferable to arithmetic Predicting Future Returns- generally the arithmetic average is preferable to geometric - Geometric has downward bias Comparison of Geometric and Arithmetic Means

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-9 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 Abnormal Performance

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Market timing Superior selection - Sectors or industries - Individual companies Factors That Lead to Abnormal Performance

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill ) Sharpe Index r p - r f p r p = Average return on the portfolio r f = Average risk free rate p = Standard deviation of portfolio return   Risk Adjusted Performance: Sharpe

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 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

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill M 2 Measure: Example Managed Portfolio: return = 35%standard deviation = 42% Market Portfolio: return = 28%standard deviation = 30% T-bill return = 6% Hypothetical Portfolio: 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

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill ) 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 Risk Adjusted Performance: Treynor

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Risk Adjusted Performance: Jensen 3) Jensen’s Measure = r p - [ r f + ß p ( r m - r f ) ] p p = Alpha for the portfolio 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.  

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Appraisal Ratio Appraisal Ratio =  p /  (e p ) Appraisal Ratio divides the alpha of the portfolio by the nonsystematic risk Nonsystematic risk could, in theory, be eliminated by diversification

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 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 Which Measure is Appropriate?

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 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 Limitations

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Adjusting portfolio for up and down movements in the market Low Market Return - low ßeta High Market Return - high ßeta Market Timing

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Example of Market Timing * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * r p - r f r m - r f Steadily Increasing the Beta

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Decomposing overall performance into components Components are related to specific elements of performance Example components - Broad Allocation - Industry - Security Choice - Up and Down Markets Performance Attribution

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Set up a ‘Benchmark’ or ‘Bogey’ portfolio Use indexes for each component Use target weight structure Process of Attributing Performance to Components

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 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

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Where B is the bogey portfolio and p is the managed portfolio Formula for Attribution

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Contributions for Performance Contribution for asset allocation (w pi - w Bi ) r Bi +Contribution for security selection w pi (r pi - r Bi ) = Total Contribution from asset class w pi r pi -w Bi r Bi

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill Two major problems - Need many observations even when portfolio mean and variance are constant - Active management leads to shifts in parameters making measurement more difficult To measure well - You need a lot of short intervals - For each period you need to specify the makeup of the portfolio Complications to Measuring Performance