Do Bonds Reduce the Overall Risk of an Investment Portfolio

Multiple Choice

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 Index (all Stocks) . Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond) . For the past several years, assume the following data. The sample means for x and y are 10.40 and 9.20, respectively.
$$\begin{array} { l l l l l l l l l l l } x : & 13 & 0 & 36 & 22 & 32 & 24 & 25 & - 13 & - 13 & - 22 \\y : & 7 & - 2 & 27 & 16 & 23 & 17 & 16 & - 2 & - 3 & - 7\end{array}$$ Compute a 75% Chebyshev interval around the mean for x-values and also for y-values. Round your answers to the nearest hundredth.

A) for x-values: -10.16 to 51.52 and for y-values: -2.95 to 33.50
B) for x-values: -30.72 to 22.55 and for y-values: -15.10 to 21.35
C) for x-values: -15.10 to 33.50 and for y-values: -30.72 to 51.52
D) for x-values: -30.72 to 22.55 and for y-values: -2.95 to -13.90
E) for x-values: -30.72 to 51.52 and for y-values: -15.10 to 33.50