$A$

$\mathrm{.}3$

$.$

$$ Equity Risk Premium Assessment

$[2$

$points$

$]$

$As$ a mutual fund portfolio manager, you have informed your client that the equity risk premium

$($

the excess return $of$ the market over the risk

$-$

free rate

$)$

$is$ normally distributed with a population mean $of$

$6$

$percent$ and a population standard deviation $of$

$18$

$percent.$ However, over the past year, your mutual fund has delivered $an$ average return $of$

$-2\mathrm{.}0$

$percent$ relative $to$ the risk

$-$

free rate. Your client $is$ very upset, claiming that such poor performance should $be$ exceptionally rare and questioning the viability $of$ your fund's strategy.

Evaluate the client's concerns $by$ calculating the probability $of$ experiencing $an$ average return $of$

$-2\mathrm{.}0$

$percentor$ lower over a one

$-$

year period. Should the client $be$ worried about the performance based $on$ the historical risk and return characteristics?