A portfolio has an expected annual return of $12\mathrm{.}2\%$ and a standard deviation of $18\mathrm{.}2\%.$ What is the smallest expected loss over the next calendar quarter given a probability of $1\%?$

$17\mathrm{.}49\%$

$17\mathrm{.}25\%$

$18\mathrm{.}87\%$

$18\mathrm{.}12\%$

$16\mathrm{.}55\%$A portfolio has an expected annual return of $12\mathrm{.}2\%$ and a standard deviation of $18\mathrm{.}2\%.$ What is the smallest expected loss over

Show image transcript

Here$$s the best way to solve it$.$

Expert$-$verified

$100\%(3$ ratings$)$

Hello

YOUR REQUIRED ANSWER IS OPTION D : $18\mathrm{.}12\%$

Given that annual expected return $=12\mathrm{.}2\%$ and annual S$.$D$.=18\mathrm{.}2\%$

Converting them into quarterly numbers:

Quarterly expected return $=12\mathrm{.}2\%/4=3\mathrm{.}05\%$

Quarterly S$.$D$.=18\mathrm{.}2\%/(4^0\mathrm{.}5)=9\mathrm{.}1\%$

z$-$score for $1\%$ VaR $=2\mathrm{.}33$

Hence,

$1\%$ VaR $=3\mathrm{.}05\%-(9\mathrm{.}1\%*2\mathrm{.}33)=21\mathrm{.}17\%-3\mathrm{.}05\%=18\mathrm{.}12\%$ my question is how did he calculate the $2\mathrm{.}33$