9.25. Suppose you are considering two investments, and the critical issues

are the rates of return (R₁ and R₂). For Investment 1, the expected rate

of return (₂) is 10%, and the standard deviation (₁) is 3%. For the

second investment, the expected rate of return (₂) is 20%, and the

standard deviation (₂) is 12%.

a. Does it make sense to decide between these two investments on the

basis of expected value alone? Why or why not?

b. Does it make sense to represent the uncertainty surrounding the

rates of return with normal distributions? What conditions do we

need for the normal distribution to provide a good fit?

earning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part.

Probability Models

c. Suppose you have decided to use normal distributions (either

because of or in spite of your answer to part b). Use @RISK to

find the following probabilities:

P(R₁ <0%)

P(R₂ <0%)

P(R₁>20%)

P(R₂ <10%)

d. Suppose R₁ and R₂ are correlated (as they would be if, say, both

of the investments were stocks). Then the random variable AR =

R₁-R₂ is normal with mean ₁-₂ and variance of +-

2po2 where p is the correlation between R₁ and R₂. If

p=0.5, find P(R₁ >R₂). Find the probability that R₁ > R₂.

e. How could you use the information from the various probabilities

developed in this problem to choose between the two investments?