Question: 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

1. Compute \[\sum{x},{{\sum{x}}^{2}},\sum{y},\sum{{{y}^{2}}}\] .
2. Use the results of part (a) to compute the sample mean, variance, and standard deviation for x and for y.
3. Compute a 75% Chebyshev interval around the mean for x values and also for y values. Use the intervals to compare the two funds.
4. Compute the coefficient of variation for each fund. Use the coefficients of vari-ation to compare the two funds. If s represents risks and z represents expected return, then s/z 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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