# portoflio problem from Qbank

A portfolio manager adds a new stock that has the same standard deviation of returns as the existing portfolio but has a correlation coefficient with the existing portfolio that is less than +1. Adding this stock will have what effect on the standard deviation of the revised portfolio’s returns? The standard deviation will: A) increase. B) decrease. C) remain unchanged. D) decrease only if the correlation is negative. *************************************************** the answer is B. As given in the question the co-relation coefficient is less than +1 then why would it always decrease the new overall SD of the portfolio. I think the new SD can increase or decrease if correlation coeff is non-negative and will always decrease if correlation coeff is negative. Please help!!

but how could stdev increase in this situation? this question illustrates the point of portfolio diversification. As long as the new asset (with the same sdev) is not 100% correlated with the portfolio then adding it will decrease the portfolio’s variance. Just think about the equation for a two assets portfolio: SP^2 = w1^2 S1^2 + w2^2 S2^2 + 2 W1 W2 rho S1 S2 as long as rho is anything less then +1 the portfolio variance will decrease since the asset’s sdev is equal (or even less) then the portfolio’s stdev

Agreed, the key is that the new stock has the SAME std deviation as the existing portfolio but is not perfectly correlated (less than +1) with it, resulting in diversification benefits.

thank you charlee and shabadoo. I missed the “same std dev” part, it makes sense now