Consider an investor with initial wealth yo, who maximizes his expected utility from final wealth, Eu()]. This investor can invest in two a risky securities, 1 and 2, with random return 1 and 2. Those risky returns are two binomial variables, perfectly correlated. More specifically, with probability p we have ₁ = r and 2 =r+6, and with probability 1-p we have ₁ = 0 and ₂ = -8, where r > 0 and 6 > 0. We assume that this investor has log preferences, that is u(y) = log(y). 1. For a given fraction, a, of the initial wealth, invested in risky security 2, what is the distribution of final wealth, i? 2. Determine the expression of E[u(1)] as a function of a. 3. Explain why there is an upper bound and a lower bound for a, and determine those bounds. 4. Determine the optimal fraction a*. 5. When p = 0.5, describe qualitatively the optimal investment strategy. Does it make sense?

Consider an investor with initial wealth yo, who maximizes his expected utility from final wealth, Eu()]. This investor can invest in two a risky securities, 1 and 2, with random return 1 and 2. Those risky returns are two binomial variables, perfectly correlated. More specifically, with probability p we have ₁ = r and 2 =r+6, and with probability 1-p we have ₁ = 0 and ₂ = -8, where r > 0 and 6 > 0. We assume that this investor has log preferences, that is u(y) = log(y). 1. For a given fraction, a, of the initial wealth, invested in risky security 2, what is the distribution of final wealth, i? 2. Determine the expression of E[u(1)] as a function of a. 3. Explain why there is an upper bound and a lower bound for a, and determine those bounds. 4. Determine the optimal fraction a*. 5. When p = 0.5, describe qualitatively the optimal investment strategy. Does it make sense?

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.9P

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