# correlation- portfolio mgt

hi, can someone explain please why the lower the correlation between stocks in a portfolio, the higher the number of stocks needed to achieve the same reducing benefits of diversification? i thought the higher the correlation the more stocks you need in a portfolio…

Was thinking about that for a moment, too, especially since CFAI doesn’t give an explicit explanation (not even in the footnotes they seem to love so much…). I don’t have the books in front of me and will not mathematically prove it, but instead post what my gut feeling tells me. Which of course may be total nonsense. Think about it this way: if the stocks in your universe are highly correlated, there is not much diversification benefits you can generate with a portfolio in the first place, which in turn means that a “handful” of stocks would probably do it. Assuming correlations are close to but not perfectly positive, portfolio standard deviation will likely be very close to just the weighted sum of the individual stock standard deviations, i.e. there are no “significant” diversification benefits by adding more stocks. Picture the portfolio st. dev. formula. On the other hand, if your universe consists of stocks with low correlations the diversification benefits of a portfolio are definitely greater compared to the above situation. The “right” or “optimal” number of stocks to fully enjoy those benefits will probably be higher, however. Because given their low correlations, holding an increasing number of stocks will keep reducing the st. dev. of your portfolio until maximum diversification is reached. The question is when do we reach that point…they say at about 30 stocks. Maybe someone has a more “technical” explanation?