Global Wealth Advisors recently published the following statistics for three of their top$-$performing mutual funds:

$$

Funds

Average Return

Standard Deviation

Beta

Horizon Global Fund

$18\%$

$2\mathrm{.}50\%$

$0\mathrm{.}9$

Stellar Growth Fund

$20\%$

$3\mathrm{.}00\%$

$1\mathrm{.}1$

Apex Value Fund

$23\%$

$3\mathrm{.}80\%$

$1\mathrm{.}3$

$$

The current risk$-$free rate is $5\%,$ and the average market return is $17\%.$

$($a$)$ Emily Wang, a portfolio manager for a large superannuation fund, is considering adding one of the above three mutual funds to her existing well$-$diversified portfolio.

$($i$)$ Recommend a suitable risk$-$adjusted performance measure that Emily could use to rank these funds for her investment needs. Explain why this measure is appropriate for her investment scenario.

$($ii$)$ Using the recommended measure, determine the best$-$ranked fund among the three listed. Provide calculations to justify your answer.

$($b$)$ David Lee, an individual investor, plans to create a complete portfolio by combining risk$-$free assets with one of the above three mutual funds.

$($i$)$ Suggest a suitable risk$-$adjusted performance measure that David could use to rank these funds for his investment objectives. Explain why this measure is suitable for his situation.

$($ii$)$ Using the suggested measure, identify the best$-$ranked fund from the list. Provide your calculations to support the answer