Diversification by omission

From Fama/French Forum

Can investors build a better portfolio by combining asset classes that have low correlations? It is possible, explains Ken French, but not in the way that most investors attempt it. Some think they can enhance diversification by eliminating mid caps and concentrating on only large and small cap stocks because these asset classes are less correlated. Ken explains that portfolio variance is determined not only by correlation, but also by variance of the individual asset classes and, critically, by their weighting in the portfolio. He emphasizes that throwing out mid caps is equivalent to doubling up on the risk of large and small caps, which is the opposite of diversification.

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