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Chapter 19

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  1. Chapter19 Performance Evaluation and Active Portfolio Management

  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

  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 (rp-rf) / sp

  4. Factors That Lead to Abnormal Performance • Market timing • Superior selection • Sectors or industries • Individual companies

  5. s p • rp = Average return on the portfolio • rf = Average risk free rate = Standard deviation of portfolio return p Risk Adjusted Performance: Sharpe 1) Sharpe Index rp - rf s

  6. rp = Average return on the portfolio • rf = Average risk free rate • ßp = Weighted average b for portfolio Risk Adjusted Performance: Treynor 2) Treynor Measure rp- rf ßp

  7. a = Alpha for the portfolio Risk Adjusted Performance: Jensen 3) Jensen’s Measure = rp - [ rf + ßp ( rm - rf) ] a p p rp = Average return on the portfolio ßp = Weighted average Beta rf = Average risk free rate rm = Avg. return on market index port.

  8. 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

  9. M2 Measure: Example Managed Portfolio Market T-bill Return 35% 28% 6% Stan. Dev 42% 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

  10. T2 (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

  11. T2 Example Port. P. Market Risk Prem. (r-rf) 13% 10% Beta 0.80 1.0 Alpha 5% 0% Treynor Measure 16.25 10 Weight to match Market w = bM/bP = 1.0 / 0.8 Adjusted Return RP* = w (RP) = 16.25% T2P = RP* - RM = 16.25% - 10% = 6.25%

  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 a or the Treynor measure The Treynor measure is more complete because it adjusts for risk

  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

  14. Market Timing Adjusting portfolio for up and down movements in the market • Low Market Return - low ßeta • High Market Return - high ßeta

  15. Example of Market Timing rp - rf * * * * * * * * * * * * * * * * * * * * rm - rf * * * Steadily Increasing the Beta Irwin/McGraw-Hill 19-11 • The McGraw-Hill Companies, Inc., 1998

  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

  17. Process of Attributing Performance to Components Set up a ‘Benchmark’ or ‘Bogey’ portfolio • Use indexes for each component • Use target weight structure

  18. 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 or selection • Summarize the performance differences into appropriate categories

  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

  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

  21. Rate of Return of a Perfect Market Timer rf rM rf

  22. Numerical Example Year 71 72 73 74 75 76 77 78 79 80 Stock Ret. .1431 .1898 -.1466 -.2647 .3720 .2384 -.0718 .0656 .1844 .3242 T-Bill Ret .0439 .0384 .0693 .0800 .0580 .0508 .0512 .0718 .1038 .1124 Avg. Ret. S.D. Ret. .1034 .2068 .0680 .0248 Irwin/McGraw-Hill 21-5 • The McGraw-Hill Companies, Inc., 1998

  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.

  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”

  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

  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

  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

  28. Reward to Variability Measures Passive Portfolio :

  29. Reward to Variability Measures Appraisal Ratio a = Alpha for the active portfolio A s = Unsystematic standard deviation for active (eA)

  30. Reward to Variability Measures Combined Portfolio :

  31. Treynor-Black Allocation CAL E(r) CML P A M Rf s

  32. Summary Points: Treynor-Black Model • Sharpe Measure will increase with added ability to pick stocks • Slope of CAL>CML (rp-rf)/sp > (rm-rf)/sp • 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