3.Consider a portfolio allocation problem that is a special case of those we studied in ass. An investor has initial wealth Yo-10000. The investor allocates the amount a to stocks, which provide return rg 0.30 in a good state that occurs with probability 1/2 and return r 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 ri 0.10 in both states. Assuming that the investor has vN-M expected utility, with Bernoulli utility function of the logarithmic form u(Y)-In(Y). Calculate the optimal amount a that the investor should allocate to stocks. (20 points)