Consider two asset classes: Stocks and Bonds. You estimate the following parameters for these two asset class funds.

correlation matrix b$/$n Stocks and Bonds

E$($r$)$ sd$($r$)$ Stocks Bonds

Stocks $11\%33\%10\mathrm{.}6$

Bonds $6\%12\%0\mathrm{.}61$

Consider a $$100,000$ portfolio consisting of $$40,000$ in Stocks and $$60,000$ in Bonds. So$,$ the portfolio is $40\%$ in Stocks and $60\%$ in Bonds. Given the expected return on the portfolio is $8\%,$ and the standard deviation of the portfolio return is $18\mathrm{.}44\%,$ what is the lower limit on the portfolio value in a year if we use a $95\%$ probability level $($note: the loss at the lower limit is known as the $2\mathrm{.}5\%$ value$-$at$-$risk$)?($use $2$ decimals without $$,$ so $$10\mathrm{.}00$ is $10\mathrm{.}00)$