Using the Utility Function in Portfolio Management, where the utility function is the constant relative risk aversion utility of wealth function U(W) = W^(gamma)/gamma, set gamma to 0.5 and consider a 50-50 bet on winning 50,000 or getting nothing. What is the certainty equivalent wealth for this bet under these assumptions? Group of answer choices 30,000 10,000 25,000 12,500

Using the Utility Function in Portfolio Management, where the utility function is the constant relative risk aversion utility of wealth function U(W) = W^(gamma)/gamma, set gamma to 0.5 and consider a 50-50 bet on winning 50,000 or getting nothing. What is the certainty equivalent wealth for this bet under these assumptions? Group of answer choices 30,000 10,000 25,000 12,500

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.14P

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Buying and selling prices for risky investments obviously are related to certain equivalents. This problem, however, shows that the prices depend on exactly what is owned in the first place. Suppose that your utility for wealth (A) can be represented by the utility function u(A) = In [(A)] You currently have R1000 in cash. A business deal of interest to you yields a reward of R100 with probability 0,5 and RO with probability 0,5. 2.1 If you own this business deal in addition to the R1000, what is the smallest amount for which you would sell the deal? 2.2 Suppose you do not own the deal. Formulate an appropriate equation and solve with algebra to find the largest amount you would be willing to pay for the deal. 2.3 Explain why the amounts in 2.1 and 2.2 are slightly different.
Suppose you visit with a financial adviser, and you are considering investing some of your wealth in one of three investment portfolios stocks, bonds, or commodities. Your financial adviser provides you with the following table, which gives the probabilities of possible returns from each investment To maximize your expected return, you should choose: Stocks Bonds Probability Return Probability Return 0.15 20% 0.15 16.7% 06 10% T 04 7.5% 0.25 8% 0.45 3.3% OA bonds OB stocks OC. commodities OD. All of the portfolios have the same expected return. If you are risk-averse and had to choose between the stock or the bond investments, you would choose OA the stock portfolio because there is less uncertainty over the outcome OB. the bond portfolio because there is less uncertainty over the outcome. OC. the stock portfolio because of greater expected return. OD. the bond portfolio because of greater expected return. Commodities Probability Return 02 20% 0.2 15% 0.2 8% 02 02 5% 0%
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Use the utility function u = E (r,) – 0.5 A o, where A is the risk aversion parameter and A = 3.5. Use the average annual return on the S&P 500 as E(r,). Use the average annual interest rate on the US Government 10-year treasury bond over the past decade as r Solve for the investor's optimal allocation between the risky and the risk-free asset.
(a) Calculate the risk-premium on this portfolio and provide a brief interpretation of it (b) Calculate the minimum sale price of the capital assets for the average investor.
Suppose Investor A has a power utility function with γ = 1, whilst Investor B has a power utility function with γ = 0.5 (i) Which investor is more risk-averse(assuming that w > 0)? (ii) Suppose that Investor B has an initial wealth of 100 and is offered the opportunity to buy Investment X for 100, which offers an equal chance of a payout of 110 or 92. Will she choose to buy Investment X?
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