A fund manager determines that the return on his portfolio (with index i-1), and the returns of two other portfolios (i-2.3) satisfy the following factor model: r = a +b+bof+e,. where f, and f, are two factors and e, is an error term with Ele]-0. Cov(f.e)-0. and Cov(f.e)=0 for i=1,2,3. (a) (7 points) Assume that the first portfolio (i-1) has an expected rate of return of 7%, and a standard deviation of 60%. We also know that Cov(r.) 0.22. Cov(r.f)-0.35. var(f)=0.4. var()=0.9, and corr(f.fa)=1/3. What is the variance of the factor model's error term for the first portfolio, i.e. var(e)=? (b) (8 points) Now assume that b=0.1 and b=0.2. Furthermore, if two other portfolios satisfy r = 0.02 +0.25 +0.5f +. r=0.03+0.3f +0.4f + e,. E[r]=0.2, E[r]=0.3, and E[r]=0.1. How can you form a portfolio whose return does not depend on f, or fa? What is the risk-free rate in this economy