Mean-Variance analysis help

According to page 351 in the portfolio managment book, “the lower the average correlation [between stocks] the greater the number of stocks needed [to reduce portfolio variance].” Does that make sense. I figure the lower the correlation, the less stocks needed to reduce variance.

The original statement in the book is right. Think about what correlation means. Correlation * Std Stock 1 * Std Stock 2 = Covariance 1,2 and 2 * Covariance 1,2 is the one that adds on to the Portfolio Variance. If correlation is lower – this means the term getting added on to the Portfolio variance is going to be smaller. So you would need more stocks to reduce the Portfolio variance significantly. CP

yanke10, All the book is really saying is that if your average correlation is already low, it will be that much harder to reduce it by adding further stocks to the portfolio. If the average correlation was high it wouldn’t take much to reduce it - think “diminishing marginal returns”. Start with a portfolio with a high average correlation. Add one stock - average correlation drops, say, by 50%. Start with a portfolio with a low average correlation. Add one stock - average correlation would only drop by 5%. Therefore in a portfolio with low average correlation you need more stocks to achieve the same amount of “diversification”. Good question!

i understand now. thanks for the help

but if you already have low correlation in the PF, why would you want to diversify?. arent you already diversified?