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1. You are using a two-factor APT model to find the fair expected return on a well-diversified portfolio P that promises an actual expected return

1. You are using a two-factor APT model to find the fair expected return on a well-diversified portfolio P that promises an actual expected return of 18%. The relevant factor portfolios, their betas in portfolio P, and their factor risk premia are shown in the table below. The risk-free rate is 2.5%.

Factor Factor Beta Factor risk premium
A 1.2 12%
B 0.8 -3.5%

a) According to the APT, what is the fair expected return on the portfolio P?

b) Suppose there exists an additional portfolio Q, which has a beta of 1 on each factor and an expected return of 15.875%. Assuming the risk premium on Factor A is estimated correctly, what must the risk premium on Factor B be to exclude arbitrage opportunities between P and Q?

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