Consider a portfolio allocation problem that is a special case of those we studied in class. An investor has initial wealth Y0 = 100. The investor allocates the amount a to stocks, which provide return rG = 0.35 in a good state that occurs with probability 1/2 and return rB = 0.15 in a bad state that occurs with probability 1/2. The investor allocates the remaining Y0 a to a risk-free bond, which provides the return rf = 0.20 in both states. Assuming that the investor has vN-M expected utility, with Bernoulli utility function of the logarithmic form u(Y ) = ln(Y ) calculate the optimal amount a that the investor should allocate to stocks. Re-solve the portfolio allocation problem from question 1, above, assuming that instead of taking the logarithmic form, the investors Bernoulli utility function is u(Y ) = Y 1 1 1 with = 2, or more simply, u(Y ) = Y 1 1 1 = 1 Y + 1 Which investor is more risk averse: the investor from question 1 or the investor from question 2? Which investor allocates more of his or her wealth to stocks? What is your answer if = 0.5?