Nick is an investor who likes to hedge his bets. His wealth is $5,760,000, but in the case of a stock market crash (which oceurs with a probability of 1/6), his wealth will be reduced to $360,000. His utility is U(W ) = W1/2, (a) Find Nick's expected utility and expected wealth. (b) Which amount of money would Nick need to have for sure to be at least as well off as with the uncertainty? How much would Nick at most be willing to pay to get rid of the uncertainty? () What is the expected loss? What is the most that Nick would be willing to pay to completely insure himself? (d) Nick can buy options from a large bank which pay off one dollar in the case of a crash and cost 20 cents (whether there is a crash or not). How many of these options should Nick buy? [Round to the nearest integer.] (e) What is the expected profit of the bank from selling the options to Nick