Top-down versus bottom-up multi-factor approaches

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Noël Amenc, Frédéric Ducoulombier, Felix Goltz and Sivagaminathan Sivasubramanian look at the pros and cons of top-down and  bottom-up strategies for factor investing 

At a glance

• Academic studies have paid relatively little attention to the variability of these factor premia over time and to the short and medium-term risks of investment along factor lines.
• Critics of the traditional top-down approach observe that there is a downside to assembling indices that have been designed to independently target distinct factors.
• The most flexible way to produce portfolios that score highly across the characteristics that proxy for exposure to a set of targeted factors is to build multi-factor portfolios from the bottom-up.
• Modifying smart-factor index selections to take cross-factor exposures into consideration allows exposures to be improved while preserving the transparency, flexibility and efficiency of the top-down approach.

Factor investing has been one of the most hotly-discussed topics among institutional investors for several years. The underlying reason for this fascination with factor investing is simple. It has been widely established by the academic literature, and more recently by studies commissioned by large institutional investors, that the bulk and the more reliable elements of the performance of active management could be captured by exposure to a small set of systematic risk factors documented in academic studies.

It is also the case that the remaining contribution of idiosyncratic security selection is negative for most investors and non-persistent. It then follows that instead of seeking outperformance through the expensive search for the elusive managers who would exhibit persistent success in traditional stock-picking – which requires forecasting the future value of individual securities with high precision – end-investors would better engage in beta picking by selecting equity portfolios exposed to the right factors. That such portfolios have been increasingly available as low-cost and transparent systematic strategies also goes a long way in explaining the new-found popularity of factor investing.

Launched at the beginning of the decade, the first explicit factor indices were designed to independently target individual factors by selecting, and sometimes weighting, securities on the basis of characteristics proxying for factor exposure (such as market capitalisation for exposure to the size factor, or the book-to-market ratio for the value factor).

Such single-factor indices dominate the indexed smart beta holdings of institutional investors and with the latter typically holding several instruments tracking different single-factor indices, the dominant multi-factor approach is, in practice, one based on the aggregation of single-factor portfolios. This approach is referred to as a top-down, building-block, portfolio mix, combination or composite portfolio. Naturally, growing investor interest in multi-factor investing has prompted providers to offer one-stop multi-factor products.

This investor appetite was whetted by studies illustrating the relevance of multi-factor diversification and the benefits of top-down multi-factor indices. Multi-factor portfolios are justified by their ability to tap into differentiated sources of factor returns and reduce conditionality risk such as regime dependency or factor cycles, which are associated with a risk of under-performance.

Indeed, while academic studies have highlighted the existence of statistically and economically significant premia over the long term (factor portfolio by factor portfolio), they have devoted less attention to the variability of these premia over time and to the short and medium-term risks of investment along factor lines. Investment practitioners, however, recognise that investing in any factor comes with the risk of prolonged underperformance relative to the broad equity market. They also realise that factor premia are less than perfectly correlated, owing to differentiated sensitivities to macroeconomic and market risks.

In a long-only context, this decorrelation between time variations in risk premia translates into low correlations between the relative returns of factor indices (see figure 1), which indicates strong potential for reducing relative risk (that is tracking error) in a multi-factor context.

All of these are strong arguments in favour of the traditional top-down approach to building multi-factor indices. However, there is an alternative approach, which has been heavily promoted in the recent past. Critics of the traditional top-down approach observe that there is a downside to assembling indices that have been designed to independently target distinct factors, since a lack of consideration for cross-index factor interactions will generally lead to an accelerated dilution of portfolio-level factor exposures when these distinct factor sleeves are combined. Indeed, practitioners have underlined that any stock that displays a favourable tilt relative to a rewarded factor can simultaneously exhibit detrimental tilts towards other rewarded factors. Naturally, the more attractive the correlation between two factor indices, the likelier it is that their constituent securities exhibit such traits, on average.

Correlations of relative returns across factor tilted cap weighted indices

A casual comparison of figures 1 and 2 confirms that the pairs of factor indices with the most attractive correlations have the most dilutive factor exposures. While this is to be expected from pursuing differentiated sources of returns, critics of the top-down approach claim this decrease in the overall level of factor intensity represents an avoidable loss of opportunity. 

This decrease may not be problematic if the objective of the multi-factor portfolio is to diversify one’s benchmark through a double layer of factor and specific risk diversification. However, if the investor’s objective is to achieve strong factor intensity, this interaction between indices should be taken into consideration.

The most flexible way to produce portfolios that score highly across the characteristics that proxy for exposure to a set of targeted factors is to build multi-factor portfolios from the bottom-up. This can be achieved by selecting and combining securities on the basis of a composite score of their factor characteristics, an approach also known as the composite-score approach.

Top-down multi-factor portfolios blend single-factor portfolios with a view to drawing on differentiated sources of returns while reducing the conditionality of performance. The approach is simple, 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. More importantly, it allows dynamic strategies, notably allocation strategies that recognise variations in risk parameters (particularly at the level of single-factor indices), to deliver risk-controlled payoffs. Its tractability and granularity also facilitate performance analysis, attribution and reporting. Being 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.

On the contrary, practitioners seeking to concentrate portfolios have favoured bottom-up portfolio construction to offer higher scores across targeted factors with a view to reaping the higher rewards expected from higher proxied exposures. Indeed, under reasonable assumptions about the mapping of factor scores by securities, the 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 can achieve (with the difference in potential scores increasing with the targeted concentration of the portfolio and the number of factors targeted, and decreasing with factor correlations). While this is a general problem, the superiority of bottom-up over top-down approaches for the achievement of high scores across multiple factors is typically illustrated by examples involving a pair of factors with low correlation such as value and momentum.

Mixing stand-alone portfolios that target 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 an 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.

Factor investment practitioners agree that the bottom-up approach involves the sacrifice of the flexibility, transparency and tractability of the top-down approach and many also admit that popular bottom-up approaches offer less control over unrewarded risks or turnover than their top-down counterparts. Proponents of bottom-up approaches however argue that their higher factor exposures produce additional performance that makes it worthwhile for many, if not most, investors to forsake the many benefits 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.

In this context, a recent paper of ours entitled ‘Accounting for Cross-Factor Interactions in Multi-Factor Portfolios: the Case for Multi-Beta Multi-Strategy High Factor Exposure Indices’ shows how a smart beta index construction framework and smart factor indices can be seamlessly adapted to integrate stock-level cross-factor interactions. This is applied to the design of indices that can serve as building blocks for top-down multi-factor portfolios yielding higher exposures across targeted factors. We then compare various multi-factor portfolios built with these diversified high-factor exposure smart-factor indices to score weighted bottom-up approaches. To provide an acid test, a six-factor portfolio is targeted and the top-down approaches are compared against the bottom-up strategies with both broad and narrow stock selections.

Unsurprisingly, it does not pay off to forego what has been described as ‘the only free lunch in investing’. In multi-factor investing, diversification of non-rewarded risk is as relevant as anywhere else and score weighting is not only an inefficient way to harvest long-term factor premia, but also exposes investors to sizeable absolute and relative extreme risks. We also find that the higher multi-factor scores achieved by score weighting come with more instability in individual factor exposures and overall intensity.

Our results show that filtering securities with poor multi-factor scores within single-factor selections increases the composite factor scores, absolute performance and Sharpe ratios of ‘top-down’ approaches based on smart factor indices, without compromising the diversification of unrewarded risks. Compared with concentrated bottom-up strategies, these top-down approaches post comparable absolute performances but superior relative performances, they produce higher returns per unit of factor intensity, and they enjoy considerably lower turnover.

All in all, our results suggest that the long-term performance benefits found in back-tests of score-weighted approaches come at a significant cost in terms of efficiency, short-term risks and implementation costs. Meanwhile, modifying smart factor index selections to take cross-factor exposures into consideration allows exposures to be improved while preserving the transparency, flexibility and efficiency of the top-down approach. This modification thus promises to further improve the performance of risk-based dynamic multi-factor allocation strategies.

Noël Amenc is professor of finance, EDHEC-Risk Institute and CEO, ERI Scientific Beta; Frédéric Ducoulombier is director of risk and compliance, ERI Scientific Beta; Mikheil Esakia is quantitative research analyst, ERI Scientific Beta; Felix Goltz is head of applied research, EDHEC-Risk Institute and research director, ERI Scientific Beta; and Sivagaminathan Sivasubramanian is quantitative research analyst, ERI Scientific Beta

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