Bottom-up vs. top-down approaches

Category: Asia, Global
By Felix Goltz*

Improving multi-factor equity exposure

With increasing investor interest in multi-factor solutions, product providers have been debating the respective merits of the “top-down” and “bottom-up” approaches to multi-factor portfolio construction. Top-down approaches assemble multi-factor portfolios by combining distinct sleeves for each factor, while the bottom-up methods build multi-factor portfolios in a single pass by choosing and/or weighting securities by a composite measure of multi-factor exposures. In this article, we discuss the results of recent research assessing the merits of both the approaches.

Top-down approach

Top-down multi-factor portfolios blend single factor portfolios to draw on differentiated sources of returns while reducing the conditionality of performance. The approach is simple and transparent and affords flexible factor-by-factor control of multi-factor allocation, which makes it possible to serve diverse needs through different combinations of the same building blocks and allows for dynamic strategies. Its tractability and granularity also facilitate performance analysis, attribution and reporting. Typically assembled from reasonably diversified factor sleeves, top-down multi-factor portfolios tend to result in portfolios with large effective numbers of stocks and thus good diversification of idiosyncratic risk.

Bottom-up portfolio construction seeks to concentrate portfolios to offer higher scores across targeted factors with a view to reaping the higher rewards expected from higher exposures. Under reasonable assumptions about the mapping of factor scores by securities, direct selection and/or weighting of securities on the basis of their characteristics across the targeted factors will result in higher factor scores than the combination of specialised sleeves. The difference in potential scores between the two approaches increases with the targeted, concentration of the portfolio and the number of factors targeted and decreases with factor correlations. While this is a general problem, the superiority of bottom-up over top-down approaches in achieving high scores across multiple factors is typically illustrated by examples involving a pair of factors with low correlation such as valuation and momentum. Mixing stand-alone portfolios targeting a high score for one factor in isolation leads to holding securities with low or negative scores in respect of the other targeted tilt. These securities that cause accelerated dilution of the scores of targeted tilts within the total portfolio can be avoided altogether when the two-factor portfolio is built directly by choosing securities that score highly in respect of each factor or on average across the two factors.

Performance enhancing

Proponents of bottom-up approaches argue that their higher factor exposures produce additional performance that makes it worthwhile for most investors to forsake the simplicity, transparency and flexibility of top-down approaches. However, while studies of bottom-up approaches document increased long-term returns, they typically fail to discuss short-term risks, and implementation issues such as heightened turnover.

More generally, the question of the superiority of the bottom-up approach should be addressed from the perspective of the robustness and investability of the performance displayed in-sample. Ultimately, investors are interested not in attractive-looking simulated track records but in true performance that is replicable out-of-sample. For ERI Scientific Beta, one of the keys to this robustness is the support of consensual, non-vested academic research.

It is understandable that computational technicians will tend to try to account for stock level exposures to multiple factors with the highest possible precision; and in this case, it is worth considering insights from finance. Empirical evidence on factor premia overwhelmingly suggest that the relationships between factor exposures and expected returns – which have been validated for diversified test portfolios – do not hold with a high level of precision at the individual stock level. This suggests that overexploiting information in factor exposure is not likely to improve performance. In addition, while there is ample evidence that portfolios sorted on a single characteristic are related to robust patterns in expected returns, such patterns may break down when simultaneously incorporating many different exposures.

Ultimately, the bottom-up versus top-down debate relates to two factor investing approaches. The first, which supports the bottom-up approach, is where the objective of maximising factor exposure justifies renouncing all other dimensions of portfolio construction and notably diversification. The second – which supports the top-down approach – considers that the right way to obtain improved risk-adjusted returns associated with factor investing is to reconcile exposure to the rewarded factors with excellent diversification of the non-rewarded specific risks.

Factor investing

In a recent white paper1, we show that factor concentration alone does not provide solutions that have reasonable levels of extreme relative risk and correspond ultimately to solutions with a strong level of turnover, which at an equivalent level of factor intensity (and therefore of variation in relation to the cap-weighted benchmark) have risk-adjusted performances that are lower than factor investing approaches, even naively diversified (equal-weight deconcentration).

In order to reconcile the benefits of strong factor intensity, notably by taking into account the risks of dilution of the factor exposures linked to the negative interactions between factor indices with those of diversification, Scientific Beta has evolved its smart-factor indices offering through the application of a high factor exposure filter. This development is consistent with the smart factor 2.0 approach advocated by EDHEC-Risk Institute since 2012.

The smart beta 2.0 index construction approach distinguishes two steps in the construction of smart-beta strategies, first, tilting towards the targeted risks by way of transparent security selection, and second, diversifying away the undesired and unrewarded risks by applying a diversification weighting scheme. We use this approach to construct individual smart-factor indices tilting towards documented factors, and to assemble top-down multi-factor portfolios. A basic smart-factor index is constructed by making a (broad) stock selection on the basis of a single and consensual metric related to the targeted factor (such as the book-to-market ratio for value vs. growth selections) and then applying a deconcentration or diversification weighting scheme to the selection. The approach reconciles factor investing with diversification and deals with each in separate steps. Once smart factor indices for different targeted factors have been put together, it is straightforward to implement any multi-factor allocation by blending these indices.

Whatever the methodologies used, the bottom-up approach is based on the idea of selecting factor champions, i.e. stocks with the highest multi-factor scores. However, in a long-only context, it may be less important to identify factor champions than to avoid factor losers, as the market tends to penalise the losers more than it rewards the winners. We find that the absolute value of underperformance for the factor loser portfolios is greater than the outperformance of the factor champion portfolios. In our research, we test the elimination of stocks with the lowest multi-factor scores within each of six single-factor stock selections prior to applying the diversification weighting schemes. The objective is to obtain smart factor indices with higher factor exposures in multi-factor combinations and we thus term these filtered indices “diversified high factor exposure smart-factor indices”.

The multi-factor metric chosen is the arithmetic average of the normalised rank scores for five of the six targeted factors (valuation, momentum, volatility, investment and profitability); the size factor is omitted as any diversification weighting scheme induces a tilt away from the largest capitalisations that is not diluted by blending smart-factor indices targeting different factors.

Diversified high factor exposure smart-factor indices – in addition to achieving the desired factor tilt by way of the initial selection – thus also have aggregate exposure to the other rewarded factors that are higher than that of their unfiltered counterparts. This mitigates dilution when indices targeting different factors are blended.

Conclusion

By focussing solely on increasing factor score intensity and by assuming strong relationships between security-level scores and performance, score-weighted approaches expose investors to risks that are unrelated to factors and for which no reward should be expected. Focussing solely on increasing factor intensity leads to inefficiency in capturing factor premia, as exposure to unrewarded risks more than offsets the benefits of increased factor scores. High factor scores in bottom-up approaches also come with high instability and high turnover. We introduce an approach that considers cross-factor interactions in top-down portfolios through an adjustment at the stock selection level. This approach, while producing lower factor intensity than bottom-up methods, leads to higher levels of diversification and produces higher returns per unit of factor intensity. It dominates bottom-up approaches in terms of relative performance, while considerably reducing extreme relative losses and turnover.         

* Felix Goltz is head of applied research, EDHEC-Risk Institute, research director, ERI Scientific Beta


1 Amenc, N., F. Ducoulombier, M. Esakia, F. Goltz and S. Sivasubramanian. February 2017. Accounting for Cross-Factor Interactions in Multi-Factor Portfolios: The Case for Multi-Beta Multi-Strategy High Factor Exposure Indices. ERI Scientific Beta white paper.