Homework 11: Decision Making under Uncertainty You are considering an investment
ID: 2495977 • Letter: H
Question
Homework 11: Decision Making under Uncertainty You are considering an investment in the fast food industry and have narrowed your choices down to Ferocious Chicken and Benign Buffalo. Ferocious Chicken has the potential to return long-run profits of dollar 10 million with probability 0.25, dollar 5 million with potential to return dollar 30 million with probability 0.05, dollar 5 million with probability 0.90, and lose (-dollar 30 million) with probability 0.05. What are the means and standard deviations of the profit distributions of the two investments? What is the coefficient of variation for the two investments? Which investment would a risk lover choose? Which would a risk neutral choose? Suppose the investor has utility function U = Squarerootof 30 + x, where x is the amount of money (in millions; don't write all the zeroes). Which investment will this investor choose? Mr. Trembly owns a house (H) in St. Johns wood, a remote location far from the nearest fire hydrant. The current assessed value of his house is dollar 250, 000. The risk of fire in this location is estimated to be 2 percentage (0.02), and in such an eventuality the house will be a total loss; that is, worth dollar 0. What is the expected value of Mr. Trembly's asset, E(H)? What is a "fair premium" that will ensure that whatever happens, Mr. Trembly will have the expected value of the house? Now assume that Mr. Trembly has utility function U = squareroot of dollar. What is the expected utility of Mr. Trembly's risky asser? Now, given Mr. Trembly's expected utility, what is Certainty Equivalent to the house? And what is the Risk Premium for the house? How much will Mr. Trembly be willing to pay in total to insure the house?Explanation / Answer
1.
a.
For investment in Ferocious Chicken
Mean Profit (X1) = Profit1*Probability1 + Profit2*Probability2 + Profit3*Probability3
Mean Profit (X1) = 10*.25 + 5*.5 - 1*.25 = $4.75 Million
Standard Deviation (SD1) = (P1*(Mean – Profit1)^2 + P2*(Mean – Profit2)^2 + P3*(Mean- Profit3)^2)^ .5
Standard Deviation (SD1) = (.25*(4.75 -10)^2 + .5*(4.75 - 5)^2 + .25*(4.75+1)^2)^ .5
Standard Deviation (SD1) = 3.897
For Investment in Benign Buffalo
Mean Profit (X2) = Profit1*Probability1 + Profit2*Probability2 + Profit3*Probability3
Mean Profit (X2) = 30*.05 + 5*.90 -30*.05 = $4.5 Million
Standard Deviation (SD2) = (P1*(Mean – Profit1)^2 + P2*(Mean – Profit2)^2 + P3*(Mean- Profit3)^2)^ .5
Standard Deviation (SD1) = (.05*(4.5 -30)^2 + .9*(4.5 - 5)^2 + .05*(4.5+30)^2)^ .5
Standard Deviation (SD1) = 9.604
b.
Coefficient of variation = (Standard Deviation / Mean)*100
For Ferocious Chicken, Coefficient of variation = (4.75 / 3.897)*100 = 121.888%
For Benign Buffalo, Coefficient of variation = (4.5 / 9.604)*100 = 46.855%
b.
Risk lover will choose the investment that comes up with high risk. Thus, investment in Benign Buffalo is the option, risk lover will go for. Risk neutral will choose Ferocious chicken that offers lowest risk and better mean return.
c.
U = (30 + X)^.5
Utility derived from Ferocious Chicken investment = (30+4.75)^.5 = 5.89
Utility derived from Benign Buffalo investment = (30+4.5)^.5 = 5.87
Utility derived from Ferocious Chicken investment is bigger than the utility derived from Benign Buffalo investment. Thus, investor will choose Ferocious Chicken investment.
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