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Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = -e-". There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1- q and Ro with probability q. We assume R1 < 0, Ro > 0. Let a be the share of wealth w invested in the risky asset, so that 1 - a share of wealth is invested in the safe asset. (a) Find a as a function of w. How does a change with wealth? Explain the intuition. (b) Another investor has the utility function u(x) = In(x). How does a change with wealth? Explain the intuition. (c) Calculate relative risk aversion for two investors using the utility functions in (a) and (b). How do they depend on wealth? How does this account for the qualitative difference in the answers you obtain in parts (a) and (b)

Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = -e-". There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1- q and Ro with probability q. We assume R1 < 0, Ro > 0. Let a be the share of wealth w invested in the risky asset, so that 1 - a share of wealth is invested in the safe asset. (a) Find a as a function of w. How does a change with wealth? Explain the intuition. (b) Another investor has the utility function u(x) = In(x). How does a change with wealth? Explain the intuition. (c) Calculate relative risk aversion for two investors using the utility functions in (a) and (b). How do they depend on wealth? How does this account for the qualitative difference in the answers you obtain in parts (a) and (b)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = -e-ª. There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1 - q and Ro with probability q. We assume R1 < 0, Ro > 0. Let a be the share of wealth w invested in the risky asset, so that 1 – a share of wealth is invested in the safe asset. (a) Find a as a function of w. How does a change with wealth? Explain the intuition. (b) Another investor has the utility function u(x) = wealth? Explain the intuition. In(x). How does a change with (c) Calculate relative risk aversion for two investors using the utility functions in (a) and (b). How do they depend on wealth? How does this account for the qualitative difference in the answers youu obtain in parts (a) and (b)!
Transcribed Image Text:Consider the following portfolio choice problem. The investor has initial wealth w and utility u(x) = -e-ª. There is a safe asset (such as a US government bond) that has net real return of zero. There is also a risky asset with a random net return that has only two possible returns, R1 with probability 1 - q and Ro with probability q. We assume R1 < 0, Ro > 0. Let a be the share of wealth w invested in the risky asset, so that 1 – a share of wealth is invested in the safe asset. (a) Find a as a function of w. How does a change with wealth? Explain the intuition. (b) Another investor has the utility function u(x) = wealth? Explain the intuition. In(x). How does a change with (c) Calculate relative risk aversion for two investors using the utility functions in (a) and (b). How do they depend on wealth? How does this account for the qualitative difference in the answers youu obtain in parts (a) and (b)!
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