Consider an investor with initial wealth yo, who maximizes his expected utility from final wealth, E[u(₁)]. This investor can invest in two a risky securities, 1 and 2, with random return f₁ and ₂. Those risky returns are two binomial variables, perfectly correlated. More specifically, with probability p we have r₁ = r and ₂ = r + 6, and with probability 1 - p we have ₁ = 0 and ₂ = -6, 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, ₁? 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, E[u(₁)]. This investor can invest in two a risky securities, 1 and 2, with random return f₁ and ₂. Those risky returns are two binomial variables, perfectly correlated. More specifically, with probability p we have r₁ = r and ₂ = r + 6, and with probability 1 - p we have ₁ = 0 and ₂ = -6, 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, ₁? 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?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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