2. Certainty Equivalent and Risk Premium for a Power Utility (30 points) An investor whose initial...

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2. Certainty Equivalent and Risk Premium for a Power Utility (30 points) An investor whose initial wealth is $1,000 is offered an opportunity to play a gamble with 2 possible outcomes: winning $250 with a probability of 2/3 or losing $400 with a probability of 1/3. The investor utility function is given by u(W) = Wk, where k is a real number. Compute the absolute risk aversion coefficient and describe the risk attitude of the investor (Risk-averse or Risk-taker) as a function of k. Justify your answer. Assume that k = 1/2. What is the Certainty equivalent of this risky game? What is the exact risk premium of this risky game? How good is the approximation obtained by using a Taylor series expansion and absolute Risk-aversion coefficient? Assume that k = 2. What is the Certainty equivalent of this risky game? What is the exact risk premium of this risky game? How good is the approximation obtained by using a Taylor series expansion and absolute Risk-aversion coefficient? 2. Certainty Equivalent and Risk Premium for a Power Utility (30 points) An investor whose initial wealth is $1,000 is offered an opportunity to play a gamble with 2 possible outcomes: winning $250 with a probability of 2/3 or losing $400 with a probability of 1/3. The investor utility function is given by u(W) = Wk, where k is a real number. Compute the absolute risk aversion coefficient and describe the risk attitude of the investor (Risk-averse or Risk-taker) as a function of k. Justify your answer. Assume that k = 1/2. What is the Certainty equivalent of this risky game? What is the exact risk premium of this risky game? How good is the approximation obtained by using a Taylor series expansion and absolute Risk-aversion coefficient? Assume that k = 2. What is the Certainty equivalent of this risky game? What is the exact risk premium of this risky game? How good is the approximation obtained by using a Taylor series expansion and absolute Risk-aversion coefficient?

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To compute the absolute risk aversion coefficient and analyze the risk attitude of the investor well first calculate the expected utility and then der... View the full answer