- Bonus question (0.5): Suppose Tom invest ( 100 % ) of his portfolio in asset ( i ) and he gets some positive alpha under CAPM, (assume that CAPM is true). This means that [ mathbb{E}left[r_{i} ight]-r_{f}=alpha_{i}+eta_{i}left(mathbb{E}left[r_{m} ight]-r_{f} ight) ] for ( alpha_{i}>0 ). People thinks that he has the true ability to choose the right asset as a hedge manager. Now David sees that, and he lever-up by borrowing at the risk free rate (this means shorting the risk-free asset) to achieve the following: he has ( 200 % ) in asset ( i ) and ( -100 % ) in risk free asset. Now calculate the ( eta_{p} ) of his portfolio in terms of ( eta_{i} ). (Check that ( r_{p}=2 r_{i}-r_{f} ).) Next, calculate ( alpha_{p} ) for David's portfolio. Finally, Davids claim that he is a better manager based on how much ( alpha_{p} ) he can generate. Please discuss that. - Because ( alpha ) as a measure of portfolio performance has some fundamental issue, we discuss many other ways to measure performance in class.

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Bonus question (0.5): Suppose Tom invest 100% of his portfolio in asset i and he gets some positive alpha under CAPM, (assume that CAPM is true). This means that Eri] rai+Bi(E[rm] -rf) for a; >0. People thinks that he has the true ability to choose the right asset as a hedge manager. Now David sees that, and he lever-up by borrowing at the risk free rate (this means shorting the risk-free asset) to achieve the following: he has 200% in asset i and -100% in risk free asset. Now calculate the Bp of his portfolio in terms of B. (Check that Tp=2r; -rf.) Next, calculate op for David's portfolio. Finally, Davids claim that he is a better manager based on how much a, he can generate. Please discuss that. Because a as a measure of portfolio performance has some fundamental issue, we discuss many other ways to measure performance in class. Bonus question (0.5): Suppose Tom invest 100% of his portfolio in asset i and he gets some positive alpha under CAPM, (assume that CAPM is true). This means that Eri] rai+Bi(E[rm] -rf) for a; >0. People thinks that he has the true ability to choose the right asset as a hedge manager. Now David sees that, and he lever-up by borrowing at the risk free rate (this means shorting the risk-free asset) to achieve the following: he has 200% in asset i and -100% in risk free asset. Now calculate the Bp of his portfolio in terms of B. (Check that Tp=2r; -rf.) Next, calculate op for David's portfolio. Finally, Davids claim that he is a better manager based on how much a, he can generate. Please discuss that. Because a as a measure of portfolio performance has some fundamental issue, we discuss many other ways to measure performance in class.