John, Rani and Prince were batchmates in their B$-$School. All three graduated and started working in the mutual funds industry. At present, John is the fund manager at ABC Capital and manages Rs$\mathrm{.}500$ crore fund $($Fund A$).$ He follows an active investment strategy. His fund primarily invests in IT and auto sector. Rani is the fund manager at Great Union Capital and she manages Rs$\mathrm{.}350$ crore fund $($Fund B$).$ She is also an active fund manager. Her fund invests in pharma and energy sectors$.$ Prince is the fund manager at Steadygrowth funds. He manages Rs$\mathrm{.}250$ crores $($Fund C$).$ His sectors of interest are FMCG and green energy stocks. They

wanted to compare their funds performance and see who is the best fund manager. All three of them keep Nifty $50$ as their benchmark index. Risk free rate is $7\%.$ The following details are given:

Average Return

Standard Deviation

Beta

Fund A

$13\%$

$19\%$

$25\%$

$10\%$

$0\mathrm{.}5$

Fund B

$20\%$

$1$

Fund C

$30\%$

$1\mathrm{.}5$

Nifty $50$

$18\%$

$16\%$

$1$

a$.$ Compare the funds' performance using Jensen's Alpha $(2\mathrm{.}5$ marks$)$

b$.$ Compare the funds' performance using Sharpe ratio $(2\mathrm{.}5$ marks$)$

c$.$ Compare the funds' performance using Treynor ratio

$(2\mathrm{.}5$ marks$)$ d$.$ Which fund manager's performance is best $(2\mathrm{.}5$ marks$)$