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Suppose expected returns of assets can be explained by a two-factor APT model
E[Ri] = Rf + i11 + i22;
where Rf = 0:02 is the risk-free rate, and 1 = 0:08 and 2 = 0:02 are the risk premia associated with Factors I and II, respectively.
You are managing three well-diversi ed portfolios with the following factor risks:
Portfolio Sensitivity to Factor I Sensitivity to Factor II
A 0.85 0
B 0.95 1.5
C 1.1 3
1. One of your investors has chosen a portfolio with weights equal to 20%, 30%, and 50% invested in portfolios A, B, and C respectively. What is the expected return of her portfolio?
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2. Another investor wants a portfolio with Factor II sensitivity of unity and Factor I sensitivity of 0. Show how can you o¤er such a portfolio using portfolios A, B and C. What is the expected return on that portfolio?
3. Suppose the return process of the a fourth portfolio (D) is given by
RD = 0:05 + F1;
where F1 represents the realization of Factor I and it has a mean zero. What
should a trader do with this information? Be speci c about the trade and what
it will do for the investor.
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