Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-1 Chapter 20

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-2 Chapter Summary  Objective: To introduce the most widespread approaches to risk adjustment for performance evaluation. Introduction The Conventional Theory of Performance Evaluation Market Timing

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-3 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 Objective of Active Management

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-4  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 to Performance Appraisal

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-5 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

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-6  Market timing  Superior selection Sectors or industries Individual companies Factors That Lead to Abnormal Performance

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 20-7 Summary Reminder  Objective: To introduce the most widespread approaches to risk adjustment for performance evaluation. Introduction The Conventional Theory of Performance Evaluation Market Timing

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide ) Sharpe Index r p = Average return on the portfolio r f = Average risk free rate  p = Standard deviation of portfolio return Risk Adjusted Performance: Sharpe

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide ) Treynor Measure Risk Adjusted Performance: Treynor r p = Average return on the portfolio r f = Average risk free rate  p = Weighted average  for portfolio

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide Risk Adjusted Performance: Jensen 3) Jensen’s Measure  p = alpha for the portfolio r p = Average return on the portfolio r f = Average risk free rate  p = Weighted average  for portfolio r m = Average return on market index portfolio

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 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

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 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

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide M 2 Measure: Example Managed Portfolio: return = 35%st dev = 42% Market Portfolio: return = 28%st dev = 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

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide 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?

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide  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

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide Alternative Performance Measures  Mean-variance measures of performance are increasingly challenged  The normality or log-normality of returns is also questioned  Wilfred Vos proposed a new measure that also captures skewness: VVR (Vos Value Ratio)

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide Summary Reminder  Objective: To introduce the most widespread approaches to risk adjustment for performance evaluation. Introduction The Conventional Theory of Performance Evaluation Market Timing

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide  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 Market Timing

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide rfrf rfrf rMrM Rate of Return of a Perfect Market Timer

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide Returns from YearLg StocksT-Bills

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide  Switch to T-Bills in 90 and 94 Mean = 18.94%, Standard Deviation = 12.04%  Invested in large stocks for the entire period: Mean = 17.41% Standard Deviation = 14.11%  The results are clearly related to the period With Perfect Forecasting Ability

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide  Long horizon to judge the ability  Judge proportions of correct calls  Bull markets and bear market calls With Imperfect Ability to Forecast

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide Adjusting portfolio for up and down movements in the market  Low Market Return - low ßeta  High Market Return - high ßeta Identifying Market Timing

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide Example of Market Timing * * * * * * * * * * * * * * * * * * * * * * * r p - r f r m - r f Steadily Increasing the Beta

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide  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 Superior Selection Ability

Bodie Kane Marcus Perrakis RyanINVESTMENTS, Fourth Canadian Edition Copyright © McGraw-Hill Ryerson Limited, 2003 Slide  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