John has a utility function given by the expression U(x) = E(r) - A(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 XJK security that returns 22.8% with 23% probability and returns 7.6% the remainder of the time. The security has a price of $33 and A=3

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 6.67%, the standard deviation of the market return is 10.4% and the risk-free rate for the next year is 1.24% 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 1.45 what would be the expected return for that stock in the coming year?