Reference no: EM132541926
Risky investment An individual with wealth w is deciding how much to invest in the stock market. Denote the investment by z. With probability π the price of this stock will go up by r X 100%, and with probability (1-π) the price of this stock will go down by r X 100%. The current price of the stock is $1.
(a) What is her total wealth when she makes a profit on her investment? What is her total wealth when she makes a loss on her investment?
Her Bernoulli utility function is given by u(x) = xa , a ∈ (0, 1)
(b) What is her expected utility from the investment level z? [Hint: Each lottery in this case is denoted by a different level of z because nothing else varies across lotteries. So we can think of the expected utility as a function of z.]
(c) What is her expected utility maximizing level of investment in terms of π, w and r ?
(d) If = 0.5, how much does she invest? What if = 1?
(e) Suppose the parameter values are = 0.5, π = 4/5 and r = 1. How much does she invest?
(f) What is the certainty equivalent and risk premium for the lottery corresponding to z? What is the risk premium?
(g) What happens to the risk premium as a -> 1? Provide an intuition for this result?
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