# Maps Oversatt Gmail D YouTube 08:16 Ga till intamning WISEflow STNG PNA 41A/FEA41A NEK/F... Flowet slutar kl. 12:15:0 Titel: 9- Min inlmning Tid kvar: 03:58: Av: Charbel Halef Arbetet ir sparats i WISEN 1 Nsta 2 of 4 Q1 1. Utility and risk preferences (9p) Assume there is an investment opportunity which pays with equal chances either 50,000 or 150,000 SEK a. What is the expected payoff? What is the standard deviation? b. The mean-variance utility function can be specified as: U = E(w) - A02. Compute the certainty-equivalent payoff (wealth) and the risk premium for an investor with A-4. C. Use power-utility with A-4 to compute the certainty equivalent payoff (wealth) and the risk premium for an investor with A-4. Compare with b). d. Use power-utility as above and compare expected utility E[u(w)] with the utility of the expected payoff U(E[w]). Comment. e. illustrate c) and d) in a figure and explain how the concavity of the utility function is related to the size of the risk premium. f. For the utility function U = 1 -e-aw, what is the measure of absolute and relative risk aversion (generally, not for the numbers above)? Comment about whether this is realistic for an utility function. B 1 U e en 0 / 10000 Ordgrns att ska G = # Maps Oversatt Gmail D YouTube 08:16 Ga till intamning WISEflow STNG PNA 41A/FEA41A NEK/F... Flowet slutar kl. 12:15:0 Titel: 9- Min inlmning Tid kvar: 03:58: Av: Charbel Halef Arbetet ir sparats i WISEN 1 Nsta 2 of 4 Q1 1. Utility and risk preferences (9p) Assume there is an investment opportunity which pays with equal chances either 50,000 or 150,000 SEK a. What is the expected payoff? What is the standard deviation? b. The mean-variance utility function can be specified as: U = E(w) - A02. Compute the certainty-equivalent payoff (wealth) and the risk premium for an investor with A-4. C. Use power-utility with A-4 to compute the certainty equivalent payoff (wealth) and the risk premium for an investor with A-4. Compare with b). d. Use power-utility as above and compare expected utility E[u(w)] with the utility of the expected payoff U(E[w]). Comment. e. illustrate c) and d) in a figure and explain how the concavity of the utility function is related to the size of the risk premium. f. For the utility function U = 1 -e-aw, what is the measure of absolute and relative risk aversion (generally, not for the numbers above)? Comment about whether this is realistic for an utility function. B 1 U e en 0 / 10000 Ordgrns att ska G =