Investing: Stocks and Bonds Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data (Reference: Morningstar Research Group, Chicago).

x: 11 0 36 21 31 23 24 y: 10 29 14 22 18 14

(a) Compute , and .

(b) Use the results of part

(a) to compute the sample mean, variance, and standard deviation for x and for y.

(c) Compute a 75% Chebyshev interval around the mean for x values and also for y values. Use the intervals to compare the two funds.

(d) Interpretation: Compute the coefficient of variation for each fund. Use the coefficients of variation to compare the two funds. If s represents risks and represents expected return, then can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better?

Explain. LO.1