1. An investor is considering three mutual funds. The first two are stock fundsA and B the third is a T-bill money market fund that yields a rate of 3%. The probabilitydistribution of the risky funds is as follows:State Probability Return on Stock Fund A Return on Stock Fund B1 0.30 7% -9%2 0.50 11% 20%3 0.20 -10% 26%(a) What are the expected returns and standard deviations of stock fund A and B? What iscoefficient of correlation between A and B?(b) Tabulate and draw the investment opportunity set of the two risky funds. Useinvestment proportions for the stock fund of zero to 100% in increments of 20%.(c) Use your calculation results in part (b) to draw the figure of the opportunity set ofstock fund A and B.(d) What are the investment proportions in the minimum-variance portfolio of the twostock funds and what is the expected value and standard deviation of its rate of return?(e) What are the investment proportions in the optimal risky portfolio (P) of the two stockfunds and what is the expected value and standard deviation of its rate of return?(f) Please draw the CAL of the optimal risky portfolio (P) in the figure you have drawn inpart (c). What is the slope of this CAL(P)?(g) You require that your complete portfolio yield an expected return of 7% and that it isefficient on the CAL(P). What is the standard deviation of your portfolio? What is theproportion invested in the T-bill fund and each of the two stock funds?(h) For an investor with risk aversion coefficient A = 6 what is investorӳ utility if heinvests in the portfolio in part (g)? What is the highest possible utility score that thisinvestor can achieve by investing in the three mutual funds? What is the proportioninvested in the T-bill fund and each of the two stock funds?(i) Draw indifference curves for two complete portfolios in the figure you have drawn inpart (f): one is the portfolio calculated in part (g) the other is the optimal complete portfolio obtained in part (h). Please show graphically why the investor prefers theoptimal complete portfolio.2. Consider two perfectly negatively correlated risky securities K and L. K has anexpected rate of return of 13% and a standard deviation of 19%. L has an expected rate ofreturn of 10% and a standard deviation of 16%.(a) If you invest 25% of your money in K and 75% in L what would be your portfolio’sexpected rate of return and standard deviation?(b) What are the weights of K and L in the global minimum variance portfolio?(c) What must the risk-free rate be in this economy with risky securities K and L?
