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Ch 24 revised

# Ch 24 revised - CHAPTER 24 PORTFOLIO PERFORMANCE EVALUATION...

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CHAPTER 24: PORTFOLIO PERFORMANCE EVALUATION 1. a. Arithmetic average: % 10 r ABC = ; % 10 r XYZ = b. Dispersion: σ ABC = 7.07%; σ XYZ = 13.91% Stock XYZ has greater dispersion. (Note: We used 5 degrees of freedom in calculating standard deviations.) c. Geometric average: r ABC = (1.20 × 1.12 × 1.14 × 1.03 × 1.01) 1/5 – 1 = 0.0977 = 9.77% r XYZ = (1.30 × 1.12 × 1.18 × 1.00 × 0.90) 1/5 – 1 = 0.0911 = 9.11% Despite the fact that the two stocks have the same arithmetic average, the geometric average for XYZ is less than the geometric average for ABC. The reason for this result is the fact that the greater variance of XYZ drives the geometric average further below the arithmetic average. d. In terms of “forward looking” statistics, the arithmetic average is the better estimate of expected rate of return. Therefore, if the data reflect the probabilities of future returns, 10% is the expected rate of return for both stocks. 5. a. Stock A Stock B (i) Alpha = regression intercept 1.0% 2.0% (ii) Information ratio = α P / σ (e P ) 0.0971 0.1047 (iii) *Sharpe measure = (r P – r f )/ σ P 0.4907 0.3373 (iv) **Treynor measure = (r P – r f )/ β P 8.833 10.500 * To compute the Sharpe measure, note that for each stock, (r P – r f ) can be computed from the right-hand side of the regression equation, using the assumed parameters r M = 14% and r f = 6%. The standard deviation of each stock’s returns is given in the problem. ** The beta to use for the Treynor measure is the slope coefficient of the regression equation presented in the problem. b. (i) If this is the only risky asset held by the investor, then Sharpe’s measure is the appropriate measure. Since the Sharpe measure is higher for Stock A, then A is the best choice.

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Ch 24 revised - CHAPTER 24 PORTFOLIO PERFORMANCE EVALUATION...

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