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Behavioral Finance: Expected Value of Wealth

Consider a person with the following utility function over wealth: u(w) = ew, where e is the exponential function (approximately equal to 2.7183) and w = wealth in hundreds of thousands of dollars. Suppose that this person has
a 40% chance of wealth of $50,000 and a 60% chance of wealth of $1,000,000 as summarized by P(0.40, $50,000, $1,000,000).

a. What is the expected value of wealth?
b. Construct a graph of this utility
function.
c. Is this person risk averse, risk neutral, or
a risk seeker?
d. What is this personĂ¢??s certainty equivalent
for the prospect?
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An individual has the following utility function:
u(w) = w.5 where w = wealth.

a. Using expected utility, order the following
prospects in terms of preference,
from the most to the least preferred:
P1(.8, 1,000, 600)
P2(.7, 1,200, 600)
P3(.5, 2,000, 300)
b. What is the certainty equivalent for
prospect P2?
c. Without doing any calculations, would
the certainty equivalent for prospect P1
be larger or smaller? Why?

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A stock has a beta of 1.2 and the standard deviation
of its returns is 25%. The market risk
premium is 5% and the risk-free rate is 4%.

a. What is the expected return for the
stock?
b. What are the expected return and standard
deviation for a portfolio that is
equally invested in the stock and the
risk-free asset?
c. A financial analyst forecasts a return of
12% for the stock. Would you buy it?
Why or why not?

Solution Summary

The solution determines the expected value of wealth.

$2.19