Answered: optimal fraction of wealth that the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1 Question 2. Suppose that there is one risk free asset with return rf and one risky asset with normally distributed returns, r ∼ N(µ, σ2). The investor has an expected utility maximizer with the CARA utility u(r) = −e −Ar. Write down the investor’s maximization problem of choosing α fraction of his wealth will be invested in the risky asset Find the optimal fraction of wealth that the investor will invest in the risky asset α∗Hint: Use the fact that if a random variable x is distributed normally with mean µx and variance σ2x , then for any constant α, What happens to the optimal fraction of wealth that the investor will invest in the risky asset as the risk aversion A increases? Explain the intuition behind your result.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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