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.

x:

$16$

$0$

$27$

$16$

$21$

$32$

$36$

$15$

$17$

$13$

y:

$28$

$8$

$18$

$17$

$23$

$24$

$10$

$7$

$4$

$8$

A button hyperlink to the SALT program that reads: Use SALT.

$($a$)$ Compute $\backslash$Sigma x$,\backslash$Sigma x$2,\backslash$Sigma y$,\backslash$Sigma y$2.$

$\backslash$Sigma x

$\backslash$Sigma x$2$

$\backslash$Sigma y

$\backslash$Sigma y$2$

$($b$)$ Use the results of part $($a$)$ to compute the sample mean, variance, and standard deviation for x and for y$.($Round your answers to four decimal places.$)$

x y

x

s$2$

s

$($c$)$ Compute the coefficient of variation for each fund. $($Round your answers to the nearest whole number.$)$

x y

CV

$\%$

$\%$

Use the coefficients of variation to compare the two funds.

For each unit of return, the stock fund $($x$)$ has lower risk.

For each unit of return, the balanced fund $($y$)$ has lower risk.

For each unit of return, the funds have equal risk.

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.

A smaller CV is better because it indicates a higher risk per unit of expected return.

A smaller CV is better because it indicates a lower risk per unit of expected return.