A risk averse investor with utility function: u(w) = (w)1/2 where w represents wealth, He has $200 (wo) available to invest in the financial market. He has two alternatives. One is a risk-free asset with interest rate ofr 2%; and the other alternative is to invest in a risky asset whose return is represented by a discrete probability distribution: = (1%, 5%; 1/2, 1/2). %3D Consider the following two portfolios (P1 an P2): P1 consists in investing $50 in che risky asset, and P2 in investing $150 in the risky asset. Calculate the expected utility of every portfolio: u(P1) = (use two decimals) (P2) = (use two decimals). %3D

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
Publisher:NICHOLSON
Chapter7: Uncertainty
Section: Chapter Questions
Problem 7.10P
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A risk averse investor with utility function: u(w) = (w)1/2 where w represents
wealth, He has $200 (wo) available to invest in the financial market. He has two
alternatives. One is a risk-free asset with interest rate of r 2%; and the other
alternative is to invest in a risky asset whose return is represented by a discrete
probability distribution:
(1%, 5%; 1/2, 1/2).
%3D
Consider the following two portfolios (P1 an P2): P1 consists in investing $50 in
the risky asset, and P2 in investing $150 in the risky asset.
Calculate the expected utility of every portfolio:
Eu(P1) =
(use two decimals)
%3D
Eu(P2) =
(use two decimals).
%3D
Based on your calculations, the investor will prefer the portfolio
(1/2]
Transcribed Image Text:A risk averse investor with utility function: u(w) = (w)1/2 where w represents wealth, He has $200 (wo) available to invest in the financial market. He has two alternatives. One is a risk-free asset with interest rate of r 2%; and the other alternative is to invest in a risky asset whose return is represented by a discrete probability distribution: (1%, 5%; 1/2, 1/2). %3D Consider the following two portfolios (P1 an P2): P1 consists in investing $50 in the risky asset, and P2 in investing $150 in the risky asset. Calculate the expected utility of every portfolio: Eu(P1) = (use two decimals) %3D Eu(P2) = (use two decimals). %3D Based on your calculations, the investor will prefer the portfolio (1/2]
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