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

(a) Compute ˆ‘x, ˆ‘x2, ˆ‘y, and ˆ‘y2.
(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 and also for y. Use the intervals to compare the two funds.
(d) Compute the coefficient of variation for each fund. Use the coefficients of variation to compare the two funds. If s represents risk 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.

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