Case zmvp=rf When zmvp=rf, the optimal portfolio (w0,w) is given as w0w=1=(1rrf1e) where =r1rzmvpr1ezrf. - Note that ew=0 - It is optimal to allocate all initial wealth in the risk-free asset, and invest in a self-financing portfolio w 2. Consider the case zmvp=rf in the Markowitz model with a risk-free asset (and follow the notations therein), where the optimal portfolio (with expected return z ) is given on Page 39 of Lecture Notes 2 . Denote a=e1e,c=r1r and denote 2 as the variance of the portfolio. Calculate 2(zrf)2 and express it in terms of a,c, and rf. (Hint: utilize the expression for zmvp. ) Case zmvp=rf When zmvp=rf, the optimal portfolio (w0,w) is given as w0w=1=(1rrf1e) where =r1rzmvpr1ezrf. - Note that ew=0 - It is optimal to allocate all initial wealth in the risk-free asset, and invest in a self-financing portfolio w 2. Consider the case zmvp=rf in the Markowitz model with a risk-free asset (and follow the notations therein), where the optimal portfolio (with expected return z ) is given on Page 39 of Lecture Notes 2 . Denote a=e1e,c=r1r and denote 2 as the variance of the portfolio. Calculate 2(zrf)2 and express it in terms of a,c, and rf. (Hint: utilize the expression for zmvp. )