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) = 3x4/5 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. (c) Calculate the certainty equivalent of this portfolio and compare it with part (b). (d) Calculate the risk-premium on this portfolio and provide a brief interpretation of it. (e) Calculate the minimum sale price of the capital assets for the average investor. 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) = 3x4/5 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. (c) Calculate the certainty equivalent of this portfolio and compare it with part (b). (d) Calculate the risk-premium on this portfolio and provide a brief interpretation of it. (e) Calculate the minimum sale price of the capital assets for the average investor