I need some help picking the correct response for this question please.?
ID: 2673951 • Letter: I
Question
Suppose each stock in the preceding portfolio has a correlation coefficient of 0.4 (p = 0.4) 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 diverse portfolio of four stocks is 28%.It 40 additional, randomly selected stocks with a correlation coefficient of 0.3 were added to the portfolio, what effect would this have on the portfolio standard deviation?
A) it would gradually settled at about 35%
B) it would gradually settle at about 20%
C) it would stay constant at 28%
D) it would decrease gradually, settling at about 0% Suppose each stock in the preceding portfolio has a correlation coefficient of 0.4 (p = 0.4) 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 diverse portfolio of four stocks is 28%.
It 40 additional, randomly selected stocks with a correlation coefficient of 0.3 were added to the portfolio, what effect would this have on the portfolio standard deviation?
A) it would gradually settled at about 35%
B) it would gradually settle at about 20%
C) it would stay constant at 28%
D) it would decrease gradually, settling at about 0%
Explanation / Answer
In the existing portfolio, the risk or standard deviation is 28% The Correlation Coefficients(CorC) of the 4 stocks in the portfolio is 0.4 Higher the CorC higher the risk of the portfolio. The market standard deviation is 20%, which is below the current portfolio SD The 40 stocks being added to the portfolio have a lower CorC of 0.3 (than the 0.4 of the existing stocks). Since we are adding stocks with lower SD (20% market average) and lower CorC, this would bring down the risk of the portfolio. This would narrow down to the options B and D. But since no stock being added has a negative CorC, the possibility of the risk being cancelled (to 0%) is not present. So the correct option is B. Other way to look at it would be adding more and more stock from the market to the portfolio will bring the portfolio itself more and more closer to the market itself aligning the SD of portfolio equal to the market which is 20%