Bodie Kane INVESTMENTS Marcus Fourth Edition Portfolio Performance Evaluation Irwin/McGraw-Hill 24-1 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition 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% beat SP500 in avg return and 71% in Sharpe Ratio 10.6% beat the Value-Weighted NYSE index in avg return and 56.73% in Sharpe Ratio. Composite Irwin/McGraw-Hill 24-2 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition 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 Irwin/McGraw-Hill 24-3 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition Hedge Funds? Hedge Funds in TASS database: 1512 93 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. Irwin/McGraw-Hill 24-4 The McGraw-Hill Companies, Inc., 1999 Bodie INVESTMENTS Kane Marcus % of Pension Assets in Indices Fourth Edition Calpers ($155.3 billion) NY Common Retirement ($146 billion) NY Teachers' Retirement ($88 billion) Penn Retirement System ($28 billion) Wisconsin Retirement System ($67 billion) 93% 95% 75% 75% 70% 70% 55% 55% 35% 15% -5% Irwin/McGraw-Hill 24-5 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition Abnormal or Exceptional Performance 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 (rp-rf) / p Irwin/McGraw-Hill 24-6 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition Factors That Lead to Abnormal Performance Market timing Superior selection - Sectors or industries - Individual stocks Irwin/McGraw-Hill 24-7 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition Risk Adjusted Performance: Sharpe 1) Sharpe Index rp - rf p rp = Average return on the portfolio rf = Average risk free rate = Standard deviation of portfolio p return Irwin/McGraw-Hill 24-8 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition M2 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 Irwin/McGraw-Hill 24-9 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition M2 Measure: Example Managed Portfolio: return = 35% standard deviation = 42% Market Portfolio: return = 28% T-bill return = 6% standard deviation = 30% 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 Irwin/McGraw-Hill 24-10 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition Risk Adjusted Performance: Treynor rp - rf 2) Treynor Measure ßp rp = Average return on the portfolio rf = Average risk free rate ßp = Weighted average Irwin/McGraw-Hill 24-11 for portfolio The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition Risk Adjusted Performance: Jensen Jensen’s alpha = rp - [ rf + ßp ( rm - rf) ] p p= Alpha for the portfolio rp = Average return on the portfolio ßp = Weighted average Beta rf = Average risk free rate rm = Avg. return on market index port. Irwin/McGraw-Hill 24-12 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition Appraisal Ratio Appraisal Ratio = ap / (ep) Appraisal Ratio divides the alpha of the portfolio by the nonsystematic risk Nonsystematic risk could, in theory, be eliminated by diversification Irwin/McGraw-Hill 24-13 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition Which Measure is Appropriate? 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 aor the Treynor measure The Treynor measure is more complete because it adjusts for systematic risk Irwin/McGraw-Hill 24-14 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition 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 Irwin/McGraw-Hill 24-15 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition Performance Attribution Decomposing overall performance into components Components are related to specific elements of performance Example components - Broad Allocation - Industries - Up and Down Markets Irwin/McGraw-Hill 24-16 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition Process of Attributing Performance to Components Set up a ‘Benchmark’ or ‘Bogey’ portfolio Use indexes for each component Use target weight structure Irwin/McGraw-Hill 24-17 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition Process of Attributing Performance to Components 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 Irwin/McGraw-Hill 24-18 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition Complications to Measuring Performance 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 Irwin/McGraw-Hill 24-19 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition Managing funds against benchmark: Market Timing Example 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! Irwin/McGraw-Hill 24-20 The McGraw-Hill Companies, Inc., 1999 Bodie Kane INVESTMENTS Marcus Fourth Edition Example of Market Timing rp - rf * * * * * * * * * ** * * * * * ** * * * * * rm - rf Steadily Increasing the Beta Irwin/McGraw-Hill 24-21 The McGraw-Hill Companies, Inc., 1999

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