Just like Deion Sanders on the field, diversification goes both ways. Most investors intuit the benefit of defensive diversification, but diversification can play offense, too. The defensive ability of diversification to protect capital is a function of the non-correlation and is available to all investors in any strategy. Diversification as a proactive strategy is comparable to a rebalancing bonus. The sum of the defensive and offensive performance capabilities of diversification is what we call the Diversification Alpha™.
Let us look at the offensive side of it. The offensive capabilities of diversification can be substantial. This diversification ratchet is not available to all investors, as passive, buy and hold strategies such as capitalization or price-weighted indices cannot collect the alpha.
The alpha is made possible by exploiting diversification, volatility and some sort of trading activity, such as rebalancing but it can be other activity such as reconstitution or reoptimization. This trilogy of portfolio variables combines the idiosyncratic asset volatility to produce alpha.
More rebalancing, more diversification (non-correlation) and, contrary to MPT, more volatility, are all catalysts to increase this level of alpha. The affect is a veritable profits ratchet, which relates to Parrondo’s paradox (see Stutzer, The Paradox of Diversification (Stutzer, Spring, 2010)). This strategy is implemented at some large investment managers such as Parametric and Janus Intech. Our index construction technique enables a more efficient capture of the Diversification ratchet due to the optimization’s direct focus on diversification, and the unbundling of diversification from risk measurement.
The diversification ratchet is very similar to a rebalancing bonus; however, the ratchet is a more appropriate moniker because the alpha is available to investors without rebalancing at all. Other forms of portfolio activity produce the alpha; reconstitution, reoptimization, profit taking, stop loss, trimming, even dollar cost averaging. In all cases, the alpha requires diversification.
Portfolio managers get the defensive contribution of diversification whether or not they try to. The driver is the amount of non-correlation exploited. Diversification Returns and Asset Contributions (David Booth, June 1992) coined the term diversification returns and represents an additive portfolio return attributed to diversification. Booth & Fama approximated this as ½ the variance reduction in the portfolio given by diversification. The weighted average asset variance would be the portfolio variance if the correlations were all 1. For the most recent Diversification Weighted® 500, the weighted average asset variance is 9.35, corresponding to a standard deviation of 30.57%. The portfolio variance is 3.41%, corresponding to a standard deviation of 11.64%. The difference in variances, 5.94% when halved, provides a 2.97% annual diversification defensive return. Not bad.
As this shows, the incremental return is a function of the amount of variance reduction. It is not a function of the actual level of the portfolio variance. For example, if you start with low volatility assets, say having a weighted average standard deviation of 9% and the covariances of the portfolio serve to further reduce the portfolio standard deviation to 8%. The diversification return is . While the portfolio may claim a low variance the diversification return of 86 basis points is a fraction of the 297 basis point diversification return obtained by the DW 500. If your focus is variance and not correlation, it limits the amount of variance reduction and thus the Diversification Alpha.
The Diversification Alpha is the sum of the diversification return and the rebalancing bonus, or diversification ratchet. Gravity Capital Partners has Diversification Weighted separately managed accounts that are optimized around the production of the alpha.