Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Using the random variables X and Y from Table 2.2, consider two new random variables W = 4 + 8X and V = 11 - 2Y. Compute (a) E(W) and E(V); (b) J2W and J2V; and (c) JWV and corr(W, V).
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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.
Suppose that an individual is just willing to accept a gamble to win or lose $1000 if the probability ofwinning is 0.6. Suppose that the utility gained if the individual wins is 100 utils. What is expected gains/loss.
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