1.) Consider an investor with the following utility function U = W=14 facing a gamble that costs $10,000 to play. With probability x, the $10,000 will turn into $15,000, and with probability (1¬x), the $10,000 will turn into $5000.
a. Assume a fair coin. Characterize the investor as either risk averse, risk neutral, or risk loving. Will this investor participate in the gamble? How much does the investor require above in the form of a risk premium to participate in the gamble?
b. Compute the absolute and relative risk aversion. Are they increasing, decreasing, or constant?
c. Now suppose we are not using a fair coin. Find the level of x that would make the investor act as if they were risk neutral.
2.) Assume the following and use attached Excel sheet.
a. Assume a standard two moment utility function U = E (r) - 0.5Acr,.
b. Use historical averages as proxies for population counterparts. See attached.
c. Use daily data for IVV and EWG for the year 2012. This can be found at finance.yahoo.com under Historical prices. I have provided them for you in attached.
d. Use log returns. Scale everything into percent ja(pt / Pt.$) x 100 for ease of interpretation.
Create an indifference curve that runs through the IVV and EWG. Show work and print it out using Excel.
3.) Suppose an investor has the following utility function: 11,(W) = In(W) Suppose there are two possible payouts Cu and CL which denote the upper and lower payouts respectively. The probability of obtaining the lower payout is O.
a. Come up with an analytic expression for the certainty equivalent amount of wealth in this gamble.
b. Derive the analytic expression for the sensitivity of the certainty equivalent to cy.., Interpret the sign.