KUBS Investments uses the following two factor model for rates of returns, where fB and fC represent the two factors: ri = ai + bifB + cifC + ei Assume that the mean of the error term is zero and that the error term is uncorrelated with both factors and other error terms. Suppose we have the following for the factor model and asset X : var(fB) = 0.16, var(fC) = 0.36, bX = 1, cX = 0.5, E(rX)= 0.18 (a) Find the cov(rX, fB) and cov(rX, fC), assuming the correlation coefficient between the two factors is 0.5 (b) Suppose that the variance of rX is 0.45. What is the variance of eX ? (c) Now suppose Asset X is well diversified, and suppose Assets Y and Z are believed to satisfy the following: rY = aY + 0.5fB + 2fC rZ = aZ + 2fB + fC If E(rY)=0.28, E(rZ)=0.26, what are factor prices B and C? Also find the risk free rate. (Note the APT holds even when the factors are correlated.) (d) Find a Portfolio W of Assets X, Y, Z that immunizes against fluctuations in fB and fC, i.e. the weights of X, Y, Z that make the return of this portfolio independent of the factors. (e) Find the rate of return of Portfolio W. How does your answer relate to your answer in (c) ?