A$\mathrm{.}1.$ Analysis of Mutual Fund Returns $[2$ points $]$

Given the return series for two mutual funds, answer the subsequent questions:

Year Fund Alpha Fund Beta

$201412\mathrm{.}73\mathrm{.}7$

$201513\mathrm{.}23\mathrm{.}7$

$201612\mathrm{.}83\mathrm{.}2$

$201711\mathrm{.}75\mathrm{.}2$

$201813\mathrm{.}23\mathrm{.}2$

$201910\mathrm{.}27\mathrm{.}2$

$2020-2\mathrm{.}252\mathrm{.}0$

$1.$ Which fund, Alpha or Beta, displays a greater dispersion in returns as measured by variance, standard deviation, and range?

$2.$ Given a risk$-$free rate of $3\%,$ which fund, on average, demonstrates a superior risk$-$adjusted performance, using the Sharpe ratio? $[$Sharpe ratio $=($Asset Return $-$ Risk Free Return$)/$standard deviation$]$

$3.$ Compare the geometric mean of the two funds. How does the geometric mean differentiate from the arithmetic mean?