Correlation-Portfolio Management

Corelation 101 states that the lower the correlation between two assets the greater the diversification benefits. On page 394-395 portfolio management section, it says the lower the correlation the more stocks are required to reach your minimum variance portfolio.

Shouldnt it be the lower the correlation the less stocks needed for greater diversificiation, since you get more diversification? Im finding this concept a bit confusing, anyone care to explain?

Without having the book to look at what’s going on, my first guess is that the minimum variance portfolio is easy to construct with two highly correlated stocks: take a long position in one and a short position in the other. However, the optimum portfolio is not the minimum variance portfolio; it’s the portfolio that has the best return for a given variance. You need lots of stocks to build the optimum portfolio, but you only need a handful for the minimum variance portfolio, and only the top expected return stock to build the maximum return portfolio.

there is a formula in the book

Portfolio Variance = n-1/n * Mean covariance + 1/n AvgVariance.

and there is proof of this concept as well.

Since covariance is a pairwise concept - as there is lower covariance btween 2 pairs of stocks - you need more stocks in order to have a big enough effect on the variance of the portfolio.