Consider a portfolio allocation problem that is a special case of those we studied in class. An investor has initial wealth Yo 100. The investor allocates the amount a to stocks, which provide return ra = 0.30 in a good state that occurs with probability 1/2 and return PB = 0.05 in a bad state that occurs with probability 1/2. The investor allocates the remaining Yo a to a risk-free bond, which provides the return rf 0.10 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 investor's Bernoulli utility function is (Y) Yl-y - 1 1-1 with y = 2, or more simply, 1 Cu(Y) = Y-1-1 -1 +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? Consider a portfolio allocation problem that is a special case of those we studied in class. An investor has initial wealth Yo 100. The investor allocates the amount a to stocks, which provide return ra = 0.30 in a good state that occurs with probability 1/2 and return PB = 0.05 in a bad state that occurs with probability 1/2. The investor allocates the remaining Yo a to a risk-free bond, which provides the return rf 0.10 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 investor's Bernoulli utility function is (Y) Yl-y - 1 1-1 with y = 2, or more simply, 1 Cu(Y) = Y-1-1 -1 +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