The mixed vs the integrated approach to style investing: Much ado about nothing?

Date01 November 2018
Published date01 November 2018
DOI: 10.1111/eufm.12139
The mixed vs the integrated approach to style
investing: Much ado about nothing?
Markus Leippold
Roger Rueegg
Department of Banking and Finance,
University of Zurich, Plattenstrasse 14,
8032 Zurich, Switzerland
Department of Banking and Finance,
University of Zurich and Zurich Cantonal
Bank, Hardstrasse 201, 8005 Zurich,
We study the difference between the returns to the
integrated approach to style investing and those to the
mixed approach. Unlike the mixed approach, the integrated
approach aggregates factor characteristics at security level.
Recent literature finds that the integrated approach
dominates the mixed approach. Using statistical tools for
robust performance testing, we demystify these findings as a
statistical fluke. We do not find any evidence favouring the
integrated approach. What we do find is that the integrated
approach exhibits a higher sensitivity to the low-risk
anomaly. However, this reduction in risk does not lead to an
improvement in performance.
factor investing, integrated and mixed approach, value, momentum, low
G11, G12, G14
Style investing is the investment process that aims to harvest risk premia through exposure to factors.
Factors are the foundation of all portfolios: they are the persistent forces driving the returns of stocks,
bonds and other assets. There are diverging views on how to build multi-factor portfolios. The current
The authors thank Michael Wolf for insightful comments and Fabian Ackermann, Michael Bretscher, Andreas Kappler,
Florian Arnold and Andri Silberschmidt for helpful discussions. Finally, the authors would like to thank the anonymous
referees for valuable comments and suggestions that helped to significantly improve the paper.
Eur Financ Manag. 2018;24:829855. © 2017 John Wiley & Sons, Ltd.
debate is centred around two approaches. The first approach is to mix where a portfolio is built by
combining stand-alone factor portfolios. The second approach is to integrate where a portfolio is built
by selecting securities that have simultaneously strong exposure to multiple factors at once. Recent
research suggests that a bottom-up or integrated approach provides higher returns and lower risks than
a mixed approach.
Hence, it seems that the debate about mixing or integrating has been concluded.
However, such a finding clearly must invite suspicion, as it contradicts the standard paradigm in
finance. Higher returns can only be achieved by taking higher risks.
We contribute to the recent
literature on style investing by providing a thorough analysis of the differences in the returns and risk of
the mixed and integrated approaches to long-only style investing. We find that the integrated approach
shows superior returns to risk characteristics in only a few combinations of styles. When we adjust for
multiple hypothesis testing, we can no longer reject the hypothesis that the two approaches are the
same. Hence, our findings present a challenge to the previous literature that promotes the integrated
An early contribution that analyzes an integrated (or bottom-up) approach to style investing is
Haugen & Baker (1996). With a selected set of factors, they show that factor models are surprisingly
accurate in forecasting the future relative returns of stocks. They find high abnormal returns together
with lower risk numbers in stocks with high predicted returns and argue that their result reveals a major
failure in the efficient markets hypothesis. Subsequent contributions on style investing turned their
focus on how to optimally combine individual factor portfolios. Of interest was in not whether to mix or
integrate, but in how to derive optimal factor exposures.
Factor portfolios were regarded as given
building blocks.
Only recently, the integrated approach regained attention with two publications. Clarke et al.
(2016) argue that the mixed approach captures only one-half of the potential improvement over the
market Sharpe ratio. They show that when the group constraint is released and the securities are
viewed as a bundle of styles instead of the styles being regarded as a bundle of securities, one can
capture much more of the excess returns of the factors. The second work promoting the integrated
approach is Bender & Wang (2016). They assert that integration leads to a superior riskreturn
trade-off due to the fact that it captures nonlinear cross-sectional interaction effects between
Interestingly, the ETF industry has yet to make up its mind whether mixing or integrating is the
right approach. Table 1 summarizes the most well-known multi-factor ETFs. While the largest ETF,
managed by Goldman Sachs, pursues a mixed approach to factor investing, we find FlexShares, JP
Morgan and iShares implementing an integrated approach to factor investing. Moreover, AQR, one of
the largest global investment managers with US$ 159.2 billion assets under management as of
August 2016, maintain in Fitzgibbons et al. (2016) that a long-only portfolio is more profitable if based
on an integrated approach. Indeed, it is the general tenet of the financial industry that the integrated
approach is superior to the mixed approach. To our best knowledge, the only contrary view that we are
aware of is the white paper by Fraser-Jenkins et al. (2016). They find that the integrated and mixed
approaches lie on the same return to risk line.
See Bender & Wang (2016), Clarke et al. (2016), and Fitzgibbons et al. (2016).
In addition, it contradicts the risk based explanation of why style premia exist. To clarify this point, consider a
combination of value and momentum stocks. Strictly speaking, we thereby avoid overvalued momentum stocks that are
threatened by a sudden market crash. However, bearing the risk of a sudden crash is the most rational explanation of why
the momentum premium exists (see Daniel & Moskowitz, 2016). Hence, we would expect lower returns in the integrated
approach, contrary to what recent publications suggest.
See, for example, Blitz (2015) for an overview.

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