Suppose each stock in Andre$$s portfolio has a correlation coefficient of $0\mathrm{.}40(\backslash$rho $=0\mathrm{.}40)$ with each of the other stocks. The market$$s average standard deviation is approximately $20\%,$ and the weighted average of the risk of the individual securities in the partially diversified four$-$stock portfolio is $37\%.$

If $40$ additional, randomly selected stocks with a correlation coefficient of $0\mathrm{.}30$ with the other stocks in the portfolio were added to the portfolio, what effect would this have on the portfolio$$s standard deviation $(\backslash$sigma p

$)?$