Fund $A$ is a highly respected, socially responsible mutual fund of stocks and bonds. Fund B is another highly regarded fund that represents the entire stock and bond market $($an index fund$).$

The mean and standard deviation of annualized percent returns are shown below. The annualized mean and standard deviation are for a recent.

Fund A: $\stackrel{}{x}=9\mathrm{.}46\%$;$s=13\mathrm{.}80\%$ Fund B: $\stackrel{}{x}=9\mathrm{.}12\%$;$s=12\mathrm{.}62\%$

$($a$)$ Compute the coefficient of variation $($in percent$)$ for Fund A$.($Round your answer to one decimal places.$)$

$\%$

Compute the coefficient of variation $($in percent$)$ for Fund B$.($Round your answer to one decimal places.$)$

$\%$

If $\stackrel{}{x}$ represents return and $s$ represents risk, then explain why the coefficient of variation can be taken to represent risk per unit of return. From this point of view, which fund appears

to be better? Explain.

Since the $CV$ is $\frac{s}{s^2}$ we can say that the $CV$ represents the risk per unit of return; Fund A appears to be better because the $CV$ is smaller.

Since the $CV$ is $\frac{s}{s^2}$ we can say that the $CV$ represents the risk per unit of return; Fund $B$ appears to be better because the $CV$ is smaller.

Since the $CV$ is $\frac{s}{\stackrel{}{x}}$ we can say that the $CV$ represents the risk per unit of return; Fund A appears to be better because the $CV$ is smaller.

Since the $CV$ is $\frac{s}{\stackrel{}{x}}$ we can say that the $CV$ represents the risk per unit of return; Fund $B$ appears to be better because the $CV$ is smaller.

Since the $CV$ is $\frac{s}{\stackrel{}{x}}$ we can say that the $CV$ represents the risk per unit of return; neither fund is better because the $CV$ s are equal.

Since the $CV$ is $\frac{s}{s^2}$ we can say that the $CV$ represents the risk per unit of return; neither fund is better because the $CV\text{'}$s are equal.

$($b$)$ Compute a $75\%$ Chebyshev interval around the mean for Fund A$.($Enter your answer in the form: lower limit to upper limit$.$ Include the word $"$to$.")$

Compute a $75\%$ Chebyshev interval around the mean for Fund B$.($Enter your answer in the form: lower limit to upper limit$.$ Include the word $"$to$.")$

Use the intervals to compare the two funds. As usual, past performance does not guarantee future performance.

Fund $B$ has a wider range of returns, with less downside, but also less upside.

Fund $B$ has a narrower range of returns, with more downside, but also more upside.

Fund $B$ has a narrower range of returns, with less downside, but also less upside.

Fund $B$ has a wider range of returns, with more downside, but also more upside.