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An investor has a utility function of U(m,s,l)-lª(m-1/2 A s2)1-a, where A>0 and 0

An investor has a utility function of U(m,s,l)-lª(m-1/2 A s2)1-a, where A>0 and 0

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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An investor has a utility function of U(m,s,l)=lª(m-1/2*A*s<)1-a , where A>0 and 0<a<1 are preference parameters. m and s represent the expected return and standard deviation of the investor's complete portfolio, respectively. The investor can invest in a risk-free bond with the return of Rf, in a risky security with the expected return of E[RM] and the standard deviation of sM, and in a non-interest-paying liquid security (such as cash). I refers to the weight of the liquid security inside the investor's portfolio. Assume it is possible to short any security apart from the liquid security. Which of the following statements about this investor's optimal portfolio is the most inaccurate? As a increases, she invests a larger fraction of her wealth in the liquid asset. O a. All of the statements are accurate. Ob. The fraction of wealth invested in the risky asset decreases as a increases. O c. As E[RM] increases, she invests a larger fraction of her wealth in the liquid asset. d. A more risk averse investor (higher A) invests less in the liquid asset.
Transcribed Image Text:An investor has a utility function of U(m,s,l)=lª(m-1/2*A*s<)1-a , where A>0 and 0<a<1 are preference parameters. m and s represent the expected return and standard deviation of the investor's complete portfolio, respectively. The investor can invest in a risk-free bond with the return of Rf, in a risky security with the expected return of E[RM] and the standard deviation of sM, and in a non-interest-paying liquid security (such as cash). I refers to the weight of the liquid security inside the investor's portfolio. Assume it is possible to short any security apart from the liquid security. Which of the following statements about this investor's optimal portfolio is the most inaccurate? As a increases, she invests a larger fraction of her wealth in the liquid asset. O a. All of the statements are accurate. Ob. The fraction of wealth invested in the risky asset decreases as a increases. O c. As E[RM] increases, she invests a larger fraction of her wealth in the liquid asset. d. A more risk averse investor (higher A) invests less in the liquid asset.
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