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(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
(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. (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. (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)
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