Portfolio Variance vs. Statistical Variance

Why isnt the data set divided by n or n-1 when doing portfolio variance? Is it because of the fact that each return has an expected probability of occurrence? And if so, if on the CFA when they dont give use expected probability of a return, do we divide by N when we know all the inputs if since knowing every return of a portfolio would be a populations versus a sample? Pg. 234 of CFAI consfuses you some more in saynig how a previous example is divided by (N-1). Did they type the formula incorrectly? Thanks!

I think your assumption is right. I think you might be mixing up Expected returns and its Variances with actual sample data returns. The expected probabilities for the expected return of an asset sum to 1.0, meaning that you basically have a population of returns. (notice you use the probability in the calculation for both the expected return and the variance page 231) When you are given a sample of returns and are required to find the mean return and its variance, that is were you would use the n or n-1 (usually n-1 unless they give you over 30 sample data points) notice though when you calculate the COV of returns of two assets in a portfolio, you are using sample data of returns and you are required to use the (n-1) (COV = Sum(errors of x * errors of y)/n-1. I hope this helps. Hard to explain i guess.