Assume that $($i$)$ the expected return on the stock market is $10\%$ with a standard deviation of $20\%,($ii$)$ the expected return on gold is $5\%$ with a standard deviation of $25\%,$ and $($iii$)$ the risk$-$free rate is $2\%.$ Further assume the correlation between returns on stocks and those on gold is $-0\mathrm{.}5.$ Which of the following is closest to the volatility $($standard deviation of returns$)$ of a portfolio that is $80\%$ stocks and $20\%$ gold?

$($a$)10\mathrm{.}2\%$

$($b$)15\mathrm{.}0\%$

$($c$)21\mathrm{.}0\%$

$($d$)14\mathrm{.}2\%$

$($e$)2\mathrm{.}01\%$

Which of the following is closest to the Sharpe ratio of each stocks and gold in $24?$

$($a$)$ Sharpe ratio of Stocks $=0\mathrm{.}40,$ of gold $=0\mathrm{.}20$

$($b$)$ Sharpe ratio of Stocks $=0\mathrm{.}50,$ of gold $=0\mathrm{.}12$

$($c$)$ Sharpe ratio of Stocks $=0\mathrm{.}50,$ of gold $=0\mathrm{.}20$

$($d$)$ Sharpe ratio of Stocks $=0\mathrm{.}40,$ of gold $=0\mathrm{.}12$