**Felix Goltz** and** Antoine Thabault** assess the performance and implementation benefits of multi-factor allocations.

Many investors are seeking to improve the performance of their equity portfolios by capturing exposure to rewarded factors. In this article, we analyse the potential benefit of combining factor tilts.

Combinations of tilts to different factors may be of interest for two reasons. First, multi-factor allocations are expected to result in improved risk-adjusted performance. In fact, even if the factors to which the factor indices are exposed are all positively rewarded over the long term, there is extensive evidence that they may each encounter prolonged periods of underperformance.

More generally, the reward for exposure to these factors has been shown to vary over time. If this time variation in returns is not completely in sync for different factors, allocating across factors allows investors to diversify the sources of their outperformance and smooth their performance across market conditions.

Intuitively, we would expect pronounced allocation benefits across factors which have low correlation with each other. Our research has shown that the correlation of the relative returns of four smart factor indices (low volatility, mid-cap, value and momentum) over the cap-weighted benchmark is well below one. This entails in particular that a combination of these indices would lower the overall tracking error of the portfolio significantly. The same analysis done conditionally for either bull or bear market regimes leads to similar results.

Second, 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.

**PERFORMANCE BENEFITS**In a nutshell, our results suggest that multi-beta indices present new opportunities for active managers and multi-managers to enhance their performance at very low marginal cost.

Investors may use allocation across factor tilts to target an absolute or relative risk objective. We looked at two multi-beta allocations in the US stock market over a 40-year track record. The first is an equal-weight allocation of the four smart factor indices. This allocation is an example of a simple and robust allocation to smart factors, which is efficient in terms of absolute risk.

The second combines the four smart factor indices so as to obtain equal contributions to the tracking error risk from each component index. This approach is an example allocation with a relative risk objective. Both multi-beta allocations are rebalanced quarterly. Of course, the multi-beta multi-strategy equal weight (EW) and equal risk contribution (ERC) indices are starting points in smart factor allocation. More sophisticated allocation approaches can be deployed using smart factor indices as ingredients to reach more specific investment objectives.

The research shows that both the multi-beta multi-strategy EW and ERC indices present returns that are close to the average performance of the constituents but lower absolute and relative risk than the average constituent index. Both allocations thus deliver improvements in the Sharpe ratio compared to the average constituent index.

The most impressive gains compared to the average of components are witnessed in relative risk, where the reduction in the tracking error is around 0.70% for the EW allocation and 1% for the ERC allocation (which represent a risk reduction of about 11.5% for the EW allocation and more than 16% for the ERC allocation relative to the average tracking error of the component indices). Such improvements in the information ratio, of 11.9% and 14.9% for the EW and ERC allocations respectively, are significant and support the idea of diversification between smart factors. Moreover, compared to the average of their constituent indices, the multi-beta multi-strategy indices also exhibit significantly lower extreme relative risk (95% tracking error) and maximum relative drawdown.

It is noteworthy that – due to its focus on balancing relative risk contributions of constituents – the ERC allocation provides greater reductions in the relative risk measures such as the tracking error and the extreme tracking error risk.

Additionally, the benefits of allocation across different factors can be seen in the probability of outperformance, which is the historical frequency with which the index will outperform its cap-weighted reference index for a given investment horizon. The probability of outperformance increases considerably for the multi-beta indices compared to the component indices, especially at short horizons. The higher probabilities of outperformance reflect the smoother and more robust outperformance resulting from the combination of different rewarded factors within a multi-beta index.

**SMART FACTOR**The multi-beta indices we analysed were designed not only to provide efficient management of risk and return but also for genuine investability. Each of the smart factor indices has a target of 30% annual one-way turnover which is set through optimal control of rebalancing (with the notable exception of the momentum tilt, which allows for a 60% turnover). In addition, the stock selections used to tilt the indices implement buffer rules in order to reduce unproductive turnover due to small changes in stock characteristics. The component indices also apply weight and trading constraints relative to market-cap weights so as to ensure high capacity.

Finally, these indices offer an optional high liquidity feature which allows investors to reduce the application of the smart factor index methodology to the most liquid stocks in the reference universe.

In addition to these implementation rules, which are applied at the level of each smart factor index, the multi-beta allocations provide a reduction in turnover (and hence of transaction costs) compared to separate investment in each of the smart factor indices.

**DIFFERENT SOURCES**

This reduction in turnover arises from different sources. First, when the renewal of the underlying stock selections takes place, it can happen that a stock being dropped from the universe of one smart factor index is being simultaneously added to the universe of another smart factor index. Second, for constituents that are common to several smart factor indices, the trades to rebalance the weight of a stock in the different indices to the respective target weight may partly offset each other.

In our research we see that the turnover of multi-beta indices is very reasonable. In fact, managing a mandate on each smart factor index separately would yield a turnover which is higher than the average turnover across the smart factor indices. This is due to the fact that rebalancing each component index to the allocation target would induce extra turnover. However, implementing the multi-beta index in a single mandate exploits the benefits of natural crossing arising across the different component indices and actually reduces the turnover below the average level observed for component indices.

**HIGHLY LIQUID**

In addition to turnover, our research shows the average capacity of the indices in terms of the weighted average market-cap of stocks in the portfolio. The capacity measure indicates decent capacity levels with an average market-cap of around $10 billion for the multi-beta index, while the highly liquid version further increases capacity to levels exceeding $15 billion.

It should be noted that the highly liquid multi-beta index also maintains the level of performance (information ratio) of the standard multi-beta index.

Finally, even when assuming unrealistically high levels of transaction costs, all the smart factor indices deliver significant outperformance net of costs. Compared to the average stand-alone investment in a smart factor index, the multi-beta index results in higher average returns net of costs due to the turnover reduction through natural crossing effects across its component smart factor indices.

*Felix Goltz is head of applied research at Edhec-Risk Institute and research director, ERI Scientific Beta. Antoine Thabault is quantitative equity analyst, ERI Scientific Beta.*

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