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Assume that a three-factor APT describes the returns of all well-diversified portfolios, and that the three factors are unexpected changes in production (factor 1), a default spread factor (factor 2), and a Treasury term-spread factor (factor 3). Because of recent adverse events, over the next year, the market expects production to grow only by 1.5%, default spread to be 3.0%, and the term spread to be 1.8%. The pricing relationships for all well diversified portfolios are given by:
E(rA)=0.05+Bi1*0.07+Bi2*0.05-Bi3*0.04
All investors can borrow or lend at the risk free rate of 5%. Sigma(factor1) = Sigma (factor2) = Sigma (factor3) = 0.15. For simplicity, assume that the coefficient of correlation between any two factors is 0. The return process for portfolio A (which is well diversified) over the next year is:
rA=E(rA)+1.2*f1+0.5*f2-0.5*f3
a. What is the expected return portfolio A?
b. What is the standard deviation of portfolio A?
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