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 = 0.3 in good state that occurs with probability 1/2 and return rB = 0.05 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 = 0.1 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

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 rg = 0.3 in good state that occurs with probability 1/2 and return rb = 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 = 0.1 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