(A) Suppose there are three assets, X,Y, and Z. The covariances of their returns are x,y,y,z,x,z and their variances are x2,y2,z2. Show that if you invest x in asset X,y in Y, and Z in asset Z that the variance of the portfolio return is . That is, write out all of the terms of the variance, and show that is identical. 2 (B) Now suppose we have the same three assets X,Y, Z. If we add a risk-free asset F with return rf, show that the expected portfolio return can be written as: rf+(Rrf), where R is the vector of expected returns for X,Y,Z and is the vector of weights in X,Y,Z, and that this is equivalent to writing the expected return as rf+p(E[rp]rf). (A) Suppose there are three assets, X,Y, and Z. The covariances of their returns are x,y,y,z,x,z and their variances are x2,y2,z2. Show that if you invest x in asset X,y in Y, and Z in asset Z that the variance of the portfolio return is . That is, write out all of the terms of the variance, and show that is identical. 2 (B) Now suppose we have the same three assets X,Y, Z. If we add a risk-free asset F with return rf, show that the expected portfolio return can be written as: rf+(Rrf), where R is the vector of expected returns for X,Y,Z and is the vector of weights in X,Y,Z, and that this is equivalent to writing the expected return as rf+p(E[rp]rf)