$In$ the middle $of2021,$ Emily had been working for a year $asan$ analyst for $an$ investment company

that specialises $in$ serving very wealthy clients. These clients often purchase shares $in$ closely held

investment funds with very $limited$ numbers $of$ shareholders. $On20$ February $2020,$ stock markets

across the world suddenly crashed after growing instability due $to$ the COVID$-19$ pandemic. Emily$s$

firm, however, saw this market collapse $asan$ opportunity $to$ put together a fund that purchases

some $of$ the $securities$ that investors shunned $by$ acquiring them $at$ bargain prices and holding them

until the market for those $securities$ recovers.

The investment company began putting together sales information concerning the possible

performance $of$ the new fund and made the following predictions regarding the possible

performance $of$ the fund over the ensuing year $as$ a function $of$ the performance $of$ the economy:

State $of$ the economy Probability Fund return

Rapid expansion $10\%50\%$

Modest growth $55\%30\%$

$No$ growth $30\%5\%$

Recession $5\%-90\%$

Emilys boss asked her $to$ perform a preliminary analysis $of$ the new fund$s$ performance potential for

the coming year. Specifically, $he$ asked that Emily addresses each $of$ the following issues:

Questions:

$1.$ What $is$ the expected rate $of$ return?

$2.$ What $is$ the standard deviation $of$ the fund$s$ return?

$3.$ What $is$ the reward $to$ risk ratio for the fund based $on$ the fund$s$ standard deviation $asa$

measure $of$ risk?

$4.$ What $is$ the expected rate $of$ return for the fund based $on$ the Capital Asset Pricing Model

CAPM?

$5.$ Based $on$ your analysis, $do$ you think the proposed fund offered a fair return given its risk?

Explain why $or$ why not.

$In$ addition $to$ the information provided above, Emily observed that the risk$-$free rate $of$ interest for

the following year was $4\%,$ the market risk premium was $5\mathrm{.}5\%$ and the beta for the new investment was $3\mathrm{.}55.$