# Consider the treynor black model the alpha of an

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44. Consider the Treynor-Black model. The alpha of an active portfolio is 3%. The expected return on the market index is 10%. The variance of the return on the market portfolio is 4%. The nonsystematic variance of the active portfolio is 2%. The risk-free rate of return is 3%. The beta of the active portfolio is 1.15. The optimal proportion to invest in the active portfolio is __________. A. 48.7% B. 98.3% C. 51.3% D. 100.0% E. none of the above w O = [3%/2%]/[(10% - 3%)/4%] = 0.857; w* = 0.857/[1 + (1 - 1.15)0.857] = .983., or 98.3%. Difficulty: Difficult 45. Consider the Treynor-Black model. The alpha of an active portfolio is 2%. The expected return on the market index is 12%. The variance of the return on the market portfolio is 4%. The nonsystematic variance of the active portfolio is 2%. The risk-free rate of return is 3%. The beta of the active portfolio is 1.15. The optimal proportion to invest in the active portfolio is __________. w O = [2%/2%]/[(12% - 3%)/4%] = 0.444; w* = 0.444/[1 + (1 - 1.15) 0.444] = .476., or 47.6%. Difficulty: Difficult 27-24

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Chapter 27 - The Theory of Active Portfolio Management 46. Perfect timing ability is equivalent to having __________ on the market portfolio. Perfect foresight is equivalent to holding a call option on the equity portfolio. Difficulty: Easy 47. Kane, Marcus, and Trippi (1999) show that the annualized fee that investor should be willing to pay for active management, over and above the fee charged by a passive index fund, depends on I) the investor's coefficient of risk aversion II) the value of at-the-money call option on the market portfolio III) the value of out-of-the-money call option on the market portfolio IV) the precision of the security analyst V) the distribution of the squared information ratio of in the universe of securities Kane, Marcus, and Trippi (1999) show that the annualized fee that investor should be willing to pay for active management, over and above the fee charged by a passive index fund, depends on the investor's coefficient of risk aversion, the precision of the security analyst, the distribution of the squared information ratio of in the universe of securities. Difficulty: Moderate 27-25
Chapter 27 - The Theory of Active Portfolio Management 48. Kane, Marcus, and Trippi (1999) show that the annualized fee that investor should be willing to pay for active management, over and above the fee charged by a passive index fund, does not depend on I) the investor's coefficient of risk aversion II) the value of at-the-money call option on the market portfolio III) the value of out-of-the-money call option on the market portfolio IV) the precision of the security analyst V) the distribution of the squared information ratio of in the universe of securities A. I, II, IV B. II, III, V C. II, III D. I, IV, V E. II, IV, V Kane, Marcus, and Trippi (1999) show that the annualized fee that investor should be willing to pay for active management, over and above the fee charged by a passive index fund, depends on the investor's coefficient of risk aversion, the precision of the security analyst, the distribution of the squared information ratio of in the universe of securities.

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• Spring '10
• HAMZA
• Management, Active management, Modern portfolio theory, Active Portfolio Management, active portfolio

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