# negative potfolio variance?

Please refer to P393 of V6. If n is very large, and the average correlation among stocks is negative, will we have a negative portfolio variance?

Yep. Odd isn’t it? This is for the folllowing formula: *portfolio variance = average variance(1 - correlation/ n + correlation) Now, plug in -0.75 for correlation, and 100 for n. The average variance can be any number. You will have a negative number in the end, which is your portfolio variance.

maybe by the formula. However, by definition, variance can never be negative. Variation is the squared deviation of a value from its mean. Not possible for a squared value to be negative. Maybe I am missing something.

n large and negative correlatiion? is this possible at all? I think that the formula says it is not possible because variance cannot be negative.

Yeah, I didnt even run through davidyoung’s example before responding. it cant happen with that formula. even if you had a corr of -1 and a n of 1000, the answer would be a positive (very very small pos).