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Limits of diversification

The point past which adding names barely reduces portfolio dispersion: issuer-specific risk has already been cancelled and what is common to all of them remains in full.

Formula

\sigma_p^2 = \frac{\bar{\sigma}^2}{n} + \frac{n-1}{n}\,\overline{\mathrm{Cov}}

As the number of holdings grows the first term tends to zero and the second to the average covariance. That average is the risk a longer list cannot remove.

How to read the number

The value of a new holding is decided by how weakly it is related to what is already there, not by the length of the list.

When the metric lies

A basket of many names from one sector or one country looks diversified and is not: the average covariance inside such a group is high.

Also known as: diversification limit

Related terms