Manage A Risky Portfolio With Expected Rate

Solutions to First QuestionData: Risk-free rate (rf) = 5%; Expected rate of return on SP500 [E(rM)] = 13%; Standard deviation of SP500 (σM) = 25%; rate of borrowing (rfB) = 9%; E(rp) = 11%; σp = 15%24. For y to be less than 1.0 (so that the investor is a lender), risk aversion (A) must be large enough such that:y=ErM-rfAσM2<1⟹A>ErM-rfyσM2=13%-5%25%2=1.28For y to be greater than 1.0 (so that the investor is a borrower), risk aversion must be small enough such that:y=ErM-rfAσM2>1⟹A<ErM-rfyσM2=13%-9%25%2=0.64For values of risk aversion within this range, the client will neither borrow nor lend, but instead will hold a complete portfolio comprised only of the optimal risky portfolio:y=1 for 0.64≤A≤1.2825. (i)(ii) Repeat 24 using E(rp) = 11% and σp = 15% instead of values used in question 24.26. The largest percentage fee, denoted as f, depends on the reward-to-variability ratio. For y < 1, the lending rate, 5%, is viewed as the relevant risk-free rate, and we solve for f as follows:Erp-rf-fσp=ErM-rfσM⟹11-5-f15=13-525⟹f=6-15×825=1.2%For y > 1, the borrowing rate, 9%, is the relevant risk-free rate. Then we notice that, even without