Expected Utility Assignment

You are lucky enough to have a million dollars in the bank. You have decided that there are only three serious investment options: putting it under your mattress, investing in stock, and investing in bonds. Your utility function over total (or gross) wealth is U(x) = (x) (ie utility of wealth is the square root of x).

Answer the following questions:

A) If you stick your money under the mattress, how much utility will you have at the end of one year? Show your calculations.

B) Bonds in general are very dependable, but markets have been jittery as of late. You estimate that there is a 90% chance that you will gain 4%, but there is a 10% chance that you will gain nothing (zero percent). What is the expected utility of investing the $1,000,000 in bonds?

C) Stocks have recently been extremely volatile. If you invest in stocks, there is a 40% chance that you will gain 21%, 40% chance that you will gain nothing, and a 20% chance that you will lose 10%. What is the expected utility of investing the $1,000,000 in stocks?

D) Given that you are an expected utility maximizer, what course of action would you choose? What is the smallest amount someone would have to offer you in order to get you to change your mind assuming the amount they offer you is certain?

E) If, instead of maximizing expected utility, you were exceedingly loss averse, what would you do?