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(r_A)=0.05+B_i1*0.07+B_i2*0.05-B_i3*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: 

r_A=E(r_A)+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?