J ohn has a utility function given by the expression U(x) = E(r) -A(s). Where E(r) is the expected return on an asset and s

John has a utility function given by the expression U(x) = E(r) -½A(s²). Where E(r) is the expected return on an asset and s is the standard deviation of returns on that asset.John has the opportunity to purchase the XJKsecurity that returns 25.9% with 23% probability and returns 8.6% the remainder of the time.

The security has a price of $33 and A=11

a) What is the risk-neutral valuation of the XJK security? Recall the risk-neutral value is simply the expected value.

b) Using the utility function above, find John's risk-averse valuation of XJK security. Hint: Find John's certainty equivalent (CEQ) for this security's payoff.

c) If the expected annual return on the market is 6.575%, the standard deviation of the market return is 8.9% and the risk-free rate for the next year is 1.22% then what is John's optimal percent of funds that he'll invest in the market?

d) Use the rates given in part c to answer this question. If a stock had a Beta of 2.92 what would be the expected return for that stock in the coming year?