The beta to use for the treynor measure is the slope

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** 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. (ii) If the stock is mixed with the market index fund, then the contribution to the overall Sharpe measure is determined by the appraisal ratio; therefore, Stock B is preferred. (iii) If the stock is one of many stocks, then Treynor’s measure is the appropriate measure, and Stock B is preferred. 24-3
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6. We need to distinguish between market timing and security selection abilities. The intercept of the scatter diagram is a measure of stock selection ability. If the manager tends to have a positive excess return even when the market’s performance is merely “neutral” (i.e., has zero excess return), then we conclude that the manager has on average made good stock picks. Stock selection must be the source of the positive excess returns. Timing ability is indicated by the curvature of the plotted line. Lines that become steeper as you move to the right along the horizontal axis show good timing ability. The steeper slope shows that the manager maintained higher portfolio sensitivity to market swings (i.e., a higher beta) in periods when the market performed well. This ability to choose more market-sensitive securities in anticipation of market upturns is the essence of good timing. In contrast, a declining slope as you move to the right means that the portfolio was more sensitive to the market when the market did poorly and less sensitive when the market did well. This indicates poor timing. We can therefore classify performance for the four managers as follows: Selection Ability Timing Ability A. Bad Good B. Good Good C. Good Bad D. Bad Bad 7. a. Bogey: (0.60 × 2.5%) + (0.30 × 1.2%) + (0.10 × 0.5%) = 1.91% Actual: (0.70 × 2.0%) + (0.20 × 1.0%) + (0.10 × 0.5%) = 1.65% Under performance: 0.26% b. Security Selection: (1) (2) (3) = (1) × (2) Market Differential return within market (Manager – index) Manager's portfolio weight Contribution to performance Equity –0.5% 0.70 0.35% Bonds –0.2% 0.20 –0.04% Cash 0.0% 0.10 0.00% Contribution of security selection: 0.39% 24-4
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c. Asset Allocation: (1) (2) (3) = (1) × (2) Market Excess weight (Manager – benchmark) Index Return Contribution to performance Equity 0.10% 2.5% 0.25% Bonds –0.10% 1.2% –0.12% Cash 0.00% 0.5% 0.00% Contribution of asset allocation: 0.13% Summary: Security selection –0.39% Asset allocation 0.13% Excess performance –0.26% 8. a. Manager return: (0.30 × 20) + (0.10 × 15) + (0.40 × 10) + (0.20 × 5) = 12.50% Benchmark (bogey): (0.15 × 12) + (0.30 × 15) + (0.45 × 14) + (0.10 × 12) = 13.80% Added value: –1.30% b. Added value from country allocation: (1) (2) (3) = (1) × (2) Country Excess weight (Manager – benchmark) Index Return minus bogey Contribution to performance U.K. 0.15% 1.8% 0.27% Japan –0.20% 1.2% –0.24% U.S. 0.05% 0.2% 0.01% Germany 0.10% 1.8% 0.18% Contribution of country allocation: 0.70% c. Added value from stock selection: (1) (2) (3) = (1) × (2) Country Differential return within country (Manager – Index) Manager’s country weight Contribution to performance U.K. 8% 0.30% 2.4% Japan 0% 0.10% 0.0% U.S. 4% 0.40%
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