Intuitively, we would expect pronounced allocation benefits across factors that have low correlation with each other. As shown in Figure 1, the correlation of the relative returns of the four smart-factor indexes over the cap-weighted benchmark is far below 1. This entails in particular that a combination of these indexes would lower the overall tracking error of the portfolio significantly. On a side note, the same analysis done conditionally for either bull or bear market regimes leads to similar results. More generally, in an asset allocation context, Ilmanen and Kizer  have showed that factor diversification was more effective than the traditional asset-class diversification method, and that the benefits of factor diversification are still very meaningful for long-only investors.
Moreover, investors may benefit from allocating across factors in terms of implementation. Some of the trades necessary to pursue exposure to different factors may actually cancel each other out. Consider the example of an investor who pursues an allocation across a value and a momentum tilt. If some of the low-valuation stocks with high weights in the value strategy start to rally, their weight in the momentum-tilted portfolio will tend to increase at the same time as their weight in the value-tilted portfolio will tend to decrease. The effects will not cancel out completely, but some reduction in turnover can be expected through such natural crossing effects.
We now turn to a detailed analysis of the two key benefits of multifactor allocations; namely, the performance benefits and the implementation benefits.
Performance Benefits Of Allocating Across Factors
Investors may use allocation across factor tilts to target an absolute (Sharpe ratio, volatility) or relative (information ratio, tracking error with respect to broad cap-weighted index) risk objective. We show in Figure 2 the performance and risk characteristics of two multi-beta allocations in the U.S. stock market over a 40-year track record and in the developed excluding U.S. universe over the last 10 years. The first one is an equal-weight allocation of the four smart-factor indexes (low volatility; midcap; value; and momentum). This allocation is an example of a simple and robust allocation to smart factors, which is efficient in terms of absolute risk. The second one combines the four smart-factor indexes so as to obtain equal contributions (see Maillard et al. ) to the tracking error risk from each component index. This approach is an example allocation with a relative risk objective consistent with risk-parity investing.4 Both multi-beta allocations are rebalanced quarterly. Of course, the multi-beta multi-strategy equal weight (EW) and equal risk contribution (ERC) indexes are starting points in smart-factor allocation. More sophisticated allocation approaches (e.g., conditional strategies, or strategies that are not agnostic on the rewards of the different smart-factor indexes) can be deployed using smart-factor indexes as ingredients to reach more specific investment objectives (see Amenc et al. [2014b]).