This document presents a table showing the payoffs and probabilities for two investments, Investment A and Investment B. It asks the reader to calculate the expected return and standard deviation for each investment, and determine which investment would be preferred by three individuals - Bob, Sarah, and Cathy - based on their different utility functions for the given payoffs.

1. Question 4. Suppose that two investments have the same three payoffs, but the probability
associated with each payoff differs, as illustrated in the table below:
Payoff
Probabilities for Investment A
Probabilities for Investment B
$600
0.1
0.3
$500
0.8
0.4
$400
0.1
0.3
(5 points) Find the expected return of each investment.
(5 points) Find the standard deviation of each investment.
(5 points) Bob has the utility function , where I denoted the payoff. Which investment will Bob
choose?
(5 points) Sarah has the utility function . Which investment will Sarah choose?
(5 points) Cathy has the utility function U = 2I. Which investment will Cathy choose?
Payoff Probabilities for Investment A Probabilities for Investment B
$600 0.1 0.3
$500 0.8 0.4
$400 0.1 0.3