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Suppose you have invested $25\%$ of your portfolio in each of four different stocks. The mean and standard deviation of the annual return on each stock are shown in the file P$16\_38.$xlsx$.$ The correlations between the annual returns on the four stocks are also shown in this file.

If necessary, round your answers to a whole percentage value.

a$.$ What is the probability that your portfolio's annual return will exceed $20\%?$

$\%$

b$.$ What is the probability that your portfolio will lose money during the year?

$\%$

$1$ Distributions of returns $($assumed normal$)$

$\backslash$table$[[,$Mean,Stdev,,$],[$Stock $1,15\%,20\%,,],[$Stock $2,10\%,12\%,,],[$Stock $3,25\%,40\%,,],[$Stock $4,16\%,20\%,,],[,,,,],[$Correlation matrix$],[,$Stock $1,$Stock $2,$Stock $3,$Stock $4],[$Stock $1,1\mathrm{.}00,0\mathrm{.}80,0\mathrm{.}70,0\mathrm{.}60],[$Stock $2,0\mathrm{.}80,1\mathrm{.}00,0\mathrm{.}75,0\mathrm{.}55],[$Stock $3,0\mathrm{.}70,0\mathrm{.}75,1\mathrm{.}00,0\mathrm{.}65],[$Stock $4,0\mathrm{.}60,0\mathrm{.}55,0\mathrm{.}65,1\mathrm{.}00]]$