Understanding Basic Statistics 6th Edition by Charles Henry Brase,Corrinne Pellillo Brase

Exercise 33

Investing: Stocks and Bonds Do bonds reduce the overall risk or 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).

(a) Compute x , x 2 , y , and y 2.
(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 belter Explain.