Do bonds reduce the overall risk of an investment portfolio? Let $x$ be a random variable representing annual percent return for a certain stock index $($all stocks$).$ Let annual return for a balanced index $(60\%$ stock and $40\%$ bond$).$ For the past several years, we have the following data.

$x$:$,11,0,38,18,31,23,26,-13,-15,-20$

$y$:$,8,-3,29,14,22,21,13,-1,-2,-11$

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

$x=$

$x^2=$

$y=$

$y^2=$

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

$($c$)$ Compute a $75\%$ Chebyshev interval around the mean for $x$ values and also for $y$ values. $($Round your answers to two decimal places.$)$

Use the intervals to compare the two funds.

$75\%$ of the returns for the balanced fund fall within a narrower range than those of the stock fund.

$75\%$ of the returns for the stock fund fall within a narrower range than those of the balanced fund.

$25\%$ of the returns for the balanced fund fall within a narrower range than those of the stock fund.

$25\%$ of the returns for the stock fund fall within a wider range than those of the balanced fund.

$($d$)$ Compute the coefficient of variation for each fund. $($Round your answers to the nearest integer.$)$

For each unit of return, the stock fund has lower risk.

For each unit of return, the balanced fund 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.