The utility of investing in portfolio h is, U(h) = u(h) - var(r(h)) Where u(h) is the expected return of the portfolio; y is the risk-aversion of the investor; and var(r(h)) is the expected variance of the portfolio. We can also write the variance of the portfolio above as, var(htr) = hich Where is the covariance matrix of the assets in the portfolio. Let's define the following scalars, A = 118-11 B = 17u C = ua-14 A = AC B2 > 0 Where 1 is a vector of ones. Furthermore, we have two mutual fund portfolios given by, 2-11 WA =- A WBS- B (1) Rewrite the portfolio h as a function of A, B, C, A, WA, and wg. (2) Use results from part 1 to write h'h as a quadratic function again only using A, B, C, A, WA, and WB (3) Say the investor chooses a target return of Mo. Write the optimal portfolio as a function of previous parameters and y. (4) Show that the above results imply the two-fund separation theorem. The utility of investing in portfolio h is, U(h) = u(h) - var(r(h)) Where u(h) is the expected return of the portfolio; y is the risk-aversion of the investor; and var(r(h)) is the expected variance of the portfolio. We can also write the variance of the portfolio above as, var(htr) = hich Where is the covariance matrix of the assets in the portfolio. Let's define the following scalars, A = 118-11 B = 17u C = ua-14 A = AC B2 > 0 Where 1 is a vector of ones. Furthermore, we have two mutual fund portfolios given by, 2-11 WA =- A WBS- B (1) Rewrite the portfolio h as a function of A, B, C, A, WA, and wg. (2) Use results from part 1 to write h'h as a quadratic function again only using A, B, C, A, WA, and WB (3) Say the investor chooses a target return of Mo. Write the optimal portfolio as a function of previous parameters and y. (4) Show that the above results imply the two-fund separation theorem