100420_11 Portfolio Performance Evaluation

Nonsystematic risk could in theory be eliminated by

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Nonsystematic risk could, in theory, be eliminated by diversification If managers are taking non-systematic risk, presumably they are hoping to achieve a better return.
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Appraisal Ratio/Information Ratio We can find the appraisal ratio using regression output. Appraisal Ratio = p / ( ep ) = 0.554/0.785 = 0.71 Standard Error from the regression is (e p ), needed for calculating the appraisal ratio.
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Which Measure is Appropriate? It depends on investment assumptions If the portfolio represents the entire investment for an individual, Sharpe Index compared to the Sharpe Index for the market. If many investment alternatives are possible, use the Jensen’s  or the Treynor measure.
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Limitations of Performance Measurement 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
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Factors That Lead to Abnormal Performance Market timing Superior selection Sectors or industries Individual companies
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Market Timing Adjusting portfolio for up and down movements in the market Low Market Return - low ßeta High Market Return - high ßeta 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
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Example of Market Timing * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * r p - r f r m - r f
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Market Timing: An Option on the S&P Value of perfect timing is a call option worth C Timing ability measured by P Bull + P Bear -1 Value of timing ability is ( P Bull + P Bear -1) C P = the proportion of correct forecasts r f r f r M
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Returns on Stocks and Bills Year 01 02 03 04 05 06 07 08 09 10 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
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With Perfect Forecasting Ability Switch to T-Bills in ‘03, ‘04, ‘07, ‘08 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.
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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
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Questions?
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