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.

$($a$)$ Compute $x,x^2,y,y^2.$

$($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.$)$

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

CV

$x,\%$

$y,\%$

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 $\stackrel{}{x}$ represents expected return, then $\frac{s}{\stackrel{}{x}}$ 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.