1. Investors 1 and 2 allocate their portfolios among stocks, bonds and cash (risk-free). Both investors have the utility functions of the form U(R) = E(R) 22A0%, but they differ as to the value of their risk aversions coefficients. Ai Both investors allocate their portfolios optimally so as to maximize utility. The expected returns and standards deviations of return for the two asset classes are as follows: Securities Expected Return Standard Deviation Stock Fund 0.15 0.30 One Risky Portfolio Bond Fund 0.10 One Risk-free Asset Cash 0.06 This is a combination of one risky portfolio and one risk-free asset. 0.16 We also know that Investor 1 optimally allocated her complete portfolio as follows: 50% Stock Fund, 30% Bond Fund, 20% Cash (1.e., 80% in one risky portfolio and 20% in one risk-free asset) in one The standard deviation of returns (0) on Investorl's complete portfolio is 0.1868. Investor 2, on the other hand, allocates his optimal complete portfolio as follows: 30% Stock Fund, 18% Bond Fund, 52% Cash. (a) Calculate the weights of Stock Fund and Bond Fund in one risky portfolio for both Investor 1 and 2; and calculate the expected returns, E(Tp), for the one risky portfolio of Investor 1 and Investor 2. (5 points) (b) What is the expected return, E(re), on Investor l's complete portfolio? What is Investor l's coefficient of risk aversion, Aj? (15 points) (c) What is the expected return, E(rc), on Investor 2's complete portfolio? What is the standard deviation of returns, Oc on Investor 2's complete portfolio? What is Investor 2's coefficient of risk aversion, A2? (15 points) (d) Given the information above, what must be the correlation of returns between stocks and bonds? (5 points)