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

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-2 Recent Mutual Fund Data Mutual Funds in Morningstar Database: 17,212 # of funds that have existed over 10 yrs: 2,073 In 10 yrs, 16.69% beatSP500 in avg return and 71% in Sharpe Ratio 10.6% beat the Value-WeightedNYSE index in avg return and 56.73% in Sharpe Ratio. Composite

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-3 Mutual Funds 22% beat the SP 500 in any 5 of the past years. 13.2% beat the Value-Weighted NYSE index in any 5 of the past 10 years

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-4 Hedge Funds? Hedge Funds in TASS database: have existed over 10 years 41% and 31% beat the respective indices in avg return 75% and 69% beat the indices in Sharpe ratio 51% and 41% beat the indices in 5 or more of the past 10 years.

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-5

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-6 What is abnormal? Abnormal performance is measured relative to: 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 or Exceptional Performance

 The McGraw-Hill Companies, Inc., 1999 INVESTMENTS Fourth Edition Bodie Kane Marcus Irwin/McGraw-Hill 24-7 Market timing Superior selection - Sectors or industries - Individual stocks 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 24-9 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 Jensen’s alpha = 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, the Sharpe ratio should be compared to the Sharpe ratio 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 systematic 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 Decomposing overall performance into components Components are related to specific elements of performance Example components - Broad Allocation - Industries - 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 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 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

 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 In Low Market: adopt low ßeta strategy In a High Return Market: load on ßeta! Managing funds against benchmark: Market Timing Example

 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