Diversification In A Multi-Factor World

Our guest blogger this week is Dr. Richard Roll from UCLA. Dr. Roll has published more than 100 articles and is perhaps most famous for stating that CAPM would never be tested in his lifetime as CAPM holds theoretically but is almost impossible to test empirically. Originally an aeronautical engineer, Dr. Roll wrote the operating manual for NASA's Saturn V rocket. Here, he discusses how correlation does not affect diversification in a multi-factor world.

In a multi-factor world, diversification benefits do not generally depend on correlation. This is because correlation, say between two investment portfolios, is a very poor measure of whether the portfolios are explained by the same underlying factors. If the factor loading (betas) are disparate, two portfolios can be perfectly explained by the same factors, yet their simple correlation can be zero or even negative.

In general, the individual assets in two portfolios can be re-weighted to make portfolio betas congruent. This implies that true diversification benefits depend only on the idiosyncratic volatility that remains after re-weighting to align betas. Similarly, the risk reduction from adding an asset to an existing portfolio does not depend on the asset’s correlation with the portfolio, contrary to the prescription in many investment textbooks.

These implications evince the fundamental importance of measuring the underlying factors and estimating factor sensitivities for every asset. Several methods for measuring factors have been investigated in previous literature, but an easy-to-implement general method is simply to specify a group of heterogeneous indexes or traded portfolios. Exchange Traded Funds (ETFs) could be well-suited for this purpose.