The managing partner for Westwood One Investment Managers, Inc., gave a public seminar in which she discussed a number of issues, including investment risk analysis. In that seminar, she reminded people that the coefficient of variation often can be used as a measure of risk of an investment. (See Chapter 3 for a review of the coefficient of variation.) To demonstrate her point, she used two hypothetical stocks as examples. She let x equal the change in assets for a $1,000.00 investment in stock 1 and y reflect the change in assets for a

$1,000.00 investment in stock 2. She showed the seminar participants the following probability distributions:

x P(x) y P(y)

$1,000.00 0.10 $1,000.00 0.20 0.00 0.10 0.00 0.40 500.00 0.30 500.00 0.30 1,000.00 0.30 1,000.00 0.05 2,000.00 0.20 2,000.00 0.05

a. Compute the expected values for random variables x and y.

b. Compute the standard deviations for random variables x and y.

c. Recalling that the coefficient of variation is determined by the ratio of the standard deviation over the mean, compute the coefficient of variation for each random variable.

d. Referring to part

c, suppose the seminar director said that the first stock was riskier since its standard deviation was greater than the standard deviation of the second stock. How would you respond? (Hint:

What do the coefficients of variation imply?)