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 −11 −11 −21 y: 10 −2 29 14 22 18 14 −2 −3 −10

(a) Compute Sx, Sx2, Sy, and Sy2.

(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 x represents expected return, then s/x can be thought of as a measure of risk per unit of expected return. In this case, why is a smaller CV better? Explain.

AppendixLO1