Question: John 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) - A(s). 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 24.5% with 31% probability and returns 8.2% the remainder of the time. The security has a price of $33 and A=6

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 9.1575%, the standard deviation of the market return is 16.4% and the risk-free rate for the next year is 1.38% 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 1.88 what would be the expected return for that stock in the coming year?

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