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 (μ1) is 10%, and the standard deviation (σ1) is 3%. For the second investment, the expected rate of return (μ2) is 20%, and the standard deviation (σ2) 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?
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 DR = R1 – R2 is normal with mean μ1 – μ2 and variance σ21 + σ22 – 2 ρσ1 σ2 where ρ is the correlation between R1 and R2. If σ = 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?