Suppose that the average investor in a hedge fund exhibits mild risk aversion with a utility function for wealth (x) of the form

U(x) = 3x^4/5

The average investor has an amount X invested in the fund, where 70% of X is invested in risky capital assets and the remaining 30% is invested in risk-free money-market assets. Assume that due to a recent crisis within the capital markets there is now a 35% chance that the value of the risky capital assets held by the average investor will decrease by 40% during the next few months.

(a) Verify both graphically and mathematically that the average investor exhibits risk aversion.

(b) Calculate the risk-neutral value of the portfolio held by the average investor.