An interesting property of the global minimum variance portfolio Let Fgmv be the return on the global minimum variance (GMV) portfolio. It can be shown that the covariance between Fgmv and any other portfolio return rp (efficient or not) or individual asset return ; is equal to the variance of the GMV return. Cov [Fgmv.p] = Cov [Fgmv, Fi]= Var[Fgmv] Now it is your task to prove this statement. It is probably easiest to do this (without loss of generality) by considering a portfolio that invests in the global minimum variance portfolio and some other asset (portfolio or individual stock) p. Tcombi = Wpp+(1-Wp)gmv. What weights should you assign to these two assets so that the variance of combi is mini- mized? Calculate the first-order condition for variance minimization (take the derivative of the variance expression with respect to w and put it to zero). Use your logical reasoning to find the variance expression with respect to wp and put it to zero). Use your logical reasoning to find the 3 optimum value for Wp, and see if you can arrive at the claim made in the lecture notes. Voil, you have proved a proposition in financial economics!