Consider the Arrow's portfolio model with one risky asset and one risk-free asset. The von Newmann-Morgenstern utility functions of an investor is: u(w) = In w, where w represents wealth, and In natural log. Denote as a the amount invested in the risky asset. Let the initial wealth be $10,000, the interest rate of the risk-free asset 5%, and the probability distribution of the return of the risky asset X = (1%, 5%; 0.55, 0.45). 1.1 Write the equation of the expected utility of final wealth 1.2 Take the first derivative of the expected utility with respect to a. 1.3 Now evaluate the first derivative, that you found in 1.2 above, at a = 0. What can you conclude about the optimal value of a? Why is that so?

Consider the Arrow's portfolio model with one risky asset and one risk-free asset. The von Newmann-Morgenstern utility functions of an investor is: u(w) = In w, where w represents wealth, and In natural log. Denote as a the amount invested in the risky asset. Let the initial wealth be $10,000, the interest rate of the risk-free asset 5%, and the probability distribution of the return of the risky asset X = (1%, 5%; 0.55, 0.45). 1.1 Write the equation of the expected utility of final wealth 1.2 Take the first derivative of the expected utility with respect to a. 1.3 Now evaluate the first derivative, that you found in 1.2 above, at a = 0. What can you conclude about the optimal value of a? Why is that so?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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