Darnell is an amateur investor who holds a small portfolio consisting of only four stocks. The stock holdings in his portfolio are shown in the following table:

Stock

Percentage of Portfolio

Expected Return

Standard Deviation

Artemis Inc. $20\%8\mathrm{.}00\%28\mathrm{.}00\%$

Babish & Co$.30\%14\mathrm{.}00\%32\mathrm{.}00\%$

Cornell Industries $35\%13\mathrm{.}00\%35\mathrm{.}00\%$

Danforth Motors $15\%3\mathrm{.}00\%37\mathrm{.}00\%$

The expected return on Darnell$$s stock portfolio is $.$

Suppose each stock in the preceding portfolio has a correlation coefficient of $0\mathrm{.}4(\backslash$rho $=0\mathrm{.}4)$ with each of the other stocks. The market$$s average standard deviation is around $20\%,$ and the weighted average of the risk of the individual securities in the partially diversified portfolio of four stocks is $33\%.$

If $40$ additional, randomly selected stocks with a correlation coefficient of $0\mathrm{.}3$ 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

$)?$

It would gradually settle at about $35\%.$

It would gradually settle at about $50\%.$

It would stay constant at $33\%.$

It would gradually settle at about $20\%.$