If 40 additional, randomly selected stocks with a correlation coefficient of 0.3 with the other stocks in the portfolio were added to the portfolio, what effect would this have on the portfolio’s standard deviation ( σpσp )?

Consider the following explanation and calculation

Explanation:

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%

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