Jonathan invested $20,000 in exchange-traded funds (ETFs) for one year, with the
ID: 1108465 • Letter: J
Question
Jonathan invested $20,000 in exchange-traded funds (ETFs) for one year, with the following possible end-of-year values:
Probability
End-of –year Value
0.8
24000
0.2
18000
Jonathan’s preferences can be best described by the utility function w2, where w is Jonathan’s wealth. Jonathan does not have any wealth other than the $20,000. (For simplicity, assume zero discounting. Carry two decimal places in your calculations.
a) Calculate Jonathan’s certainty equivalent (CE) and his risk premium (RP) for his investment in ETFs.
b) Briefly explain the economic meaning of Jonathan’s certainty equivalent and his risk premium that you derived in part (a). What can you infer about Jonathan’s preferences towards risk? (Hint: In your answer refer to the actual numbers).
Probability
End-of –year Value
0.8
24000
0.2
18000
Explanation / Answer
a) Expected utility = 0.8*(24000^2) + 0.2*(18000^2) = 525600000
CE is W* where W*^2 = E(U)
W = (E(U))^0.5 = (525600000)^0.5 = 22926
Hence CE is 22926. Expected loss = 0.2*(2000) = 400. There is no risk premium because his certainty equivalent is more than what he has invested.
b) Here the certainty equivalent income is the certain amount of income that gives the same expected utility to the insurer as his uncertain income. Risk premium is the amount given to consumer to take risk. It is the consumer surplus if the consumer is able to buy actuarially fair insurance. His utility function is U = W^2 which implies he is risk-seeking.
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.