Consider the following returns:

$\backslash$table$[[$Year End,$\backslash$table$[[$Stock X$],[$Realized$],[$Return$]],\backslash$table$[[$Stock Y$],[$Realized$],[$Return$]],\backslash$table$[[$Stock Z$],[$Realized$],[$Return$]]],[2004,20\mathrm{.}1\%,-14\mathrm{.}6\%,0\mathrm{.}2\%],[2005,65\mathrm{.}7\%,4\mathrm{.}3\%,-3\mathrm{.}2\%],[2006,-25\mathrm{.}7\%,-52\mathrm{.}1\%,-27\mathrm{.}0\%],[2007,56\mathrm{.}9\%,71\mathrm{.}1\%,24\mathrm{.}9\%],[2008,6\mathrm{.}7\%,17\mathrm{.}3\%,-5\mathrm{.}1\%],[2009,17\mathrm{.}9\%,0\mathrm{.}9\%,-11\mathrm{.}3\%]]$

a$.$ Calculate the variances of Stock X$\text{'}$s$,$ Stock Y$\text{'}$s$,$ and Stock Z$\text{'}$s returns respectively.

b$.$ Calculate covariance and correlation between Stock X$\text{'}$s and Stock Y$\text{'}$s returns.

c$.$ Given that the risk$-$free rate is $4\%,$ calculate the Sharpe ratio of a portfolio that is made up with $45\%$ of Stock X$,25\%$ of Stock Y$,$ and $30\%$ of Stock Z$.$