# Portfolio variance Q.

In portfoilio management, there is this equation: S_p^2 = Portfolio variance = S^2 ( (1-p)/n + p) So, if n=1 (only one stock in portfolio), then S_p^2 = S^2 (variance of that single stock). If correlation =+1.0, then: S_p^2 = S^2, thats all fine. What if correlation =-1.0, what’s S_p^2? Plugging in p=-1.0, I get: S_p^2 = S^2 ( (1-p)/n + p) = S^2 (2/n -1), which is a negative number for n>= 3. What am I missing?

I’m beginning to see the answer (although not completely satisfied), but I’ll give others the chance to give it a try.

anyone who has gone through PM?

You are using an unrealistic assumption of correlation. Show me three variables that have average correlation of -1 with each other (each pairwise correlation would have to be -1 which is impossible for more than 2 variables). Positive aveage correlation is a reasonable assumption, especially for large portfolios.

You’re right, but I expected that they would put some constraints on p and n to make the equation universally valid…something like n <= (1-P)/P, which covers the negative correlation part, but still.