Consider the following portfolio allocation problem. An investor has initial wealth w0 = 100: The investor allocates the amount x to stocks, which provide return r = 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 w0 x to a risk-free bond, which provides the return rf = 0:10. Assume that the investor has the following von Neumann-Morgenstern (vNM) expected utility function:

Consider the following portfolio allocation problem. An investor has initial wealth w0 = 100: The investor allocates the amount x to stocks, which provide return r = 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 w0 x to a risk-free bond, which provides the return rf = 0:10. Assume that the investor has the following von Neumann-Morgenstern (vNM) expected utility function:

u(w) = lnw where w is wealth. Calculate the optimal amount x that the investor should

allocate to stocks.

u(w) = lnw where w is wealth. Calculate the optimal amount x that the investor should

allocate to stocks.

Which investor is more risk averse, the investor in (a) or in (b)? Which investor allocates more of his or her wealth to stocks?