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Consider a single factor APT. Portfolio A has a beta of 2.0 and an expected return...

Consider a single factor APT. Portfolio A has a beta of 2.0 and an expected return of 19%. Portfolio B has a beta of 1.3 and an expected return of 8%. The risk-free rate of return is 3%. You can create a portfolio D which invests ____% in portfolio A and the rest in the risk-free asset so that it has the same beta as portfolio B, and compare the returns to portfolio D and portfolio B to decide the direction of arbitrage trading.

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Answer #1

Portfolio A beta = 2.0

Portfolio B beta = 1.3

Risk Free asset beta = 0

Let w be weight in Portfolio A,

1.3 = w(2) + (1 - w)0

w = 65%

Expected Return of Portfolio D = 0.65(0.19) + 0.35(0.03) = 13.40%

Expected Return of Portfolio B = 8%

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