Feeling the factors: how to represent factor exposures

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Please note that this article may contain technical language. For this reason, it is not recommended to readers without professional investment experience.

One of the challenges with factor investing is to show that a given portfolio invested in a given universe of stocks is indeed exposed to the desired factors. Here we look at how to represent factor exposures in portfolios and some of the limitations of the exercise.

Traditionally, portfolio managers provide explanatory commentary on the rationale for the main stock holdings in their portfolio. For any investor, the fact that Apple*, for instance, is a highly profitable US company in the IT sector is quite obvious. So such comments are usually quite easy to follow and intuitive in nature. Even a global overweight in US or IT stocks is easy to picture, in terms of the actual stocks that are overweight in the portfolio, as we tend to know the stocks classified in these categories and these do not change sector or country that often. However, academic research tells us that systematically overweighting a sector or a country are mostly sources of non-remunerated tracking error risk against a given market capitalisation index.

Stocks can change style rapidly

Factor investing is much more challenging to picture. The concepts that distinguish some factors can still be easily understood in general terms. For example, ‘we favour cheap stocks’ for Value, or ‘we prefer stocks that have recently outperformed’ for Momentum, or ‘we favour the most profitable stocks’ for Quality. When however it comes to low vol the picture starts to become more complicated as not many of us have in mind the volatility of returns of a stock that would allow us to easily arrive at a list of stocks corresponding to the idea that ‘we favour the least volatile stocks’. A second difficulty is that what today is a cheap stock can tomorrow be an expensive stock and what today is a profitable stock can tomorrow be unprofitable. Stocks change style more rapidly than they change sector or country.

When it comes to multi-factor investing, intuition becomes a poor guide. For example, when looking for the stocks that are the cheapest (Value) and outperforming (Momentum), the two ideas tend to point in different directions: if the price goes up, it outperforms, but then is also likely to become more expensive, and vice versa. Of course a stock might still be cheap, and already be outperforming, but such a subtle situation is harder to visualise. And when there are four factors in play, the exercise of conceptualising those stocks that should be overweight in a multi-factor portfolio becomes virtually impossible.

Quantitative strategies better adapted to large stock universes

Another feature of factor investing that challenges our ability to envisage how a portfolio will be positioned is the number of stocks held in portfolios. Quantitative strategies are better adapted to large universes of stocks and typically use more stocks than those held by a manager running money on a traditional, judgemental basis. An opportunity set composed of a bigger universe of stocks ensures that the behaviour of the strategy remains statistically significant and is explained by exposures to systematic factors rather than the idiosyncratic risk of individual stocks.

Let’s take our Diversified Equity Factor Investing (DEFI) strategy as an example. DEFI is an equity multi-factor strategy that builds portfolios invested in value, quality, momentum and low vol stocks. When applied to the MSCI World index stock universe, DEFI portfolios hold more than 100 stocks of the 1 600 or so stocks in the benchmark index. If fewer stocks than this were held, stock idiosyncratic risk would dominate the portfolio and the strategy would behave significantly differently if only 20 stocks were held.

Switch to all-stock representations with factor-related measures

A way out of this conundrum is to change the type of representation that we use when looking at the composition of portfolios, to switch to representations that encompass all the stocks, and via measures related to the factors.

For instance, the DEFI world portfolio can be illustrated as shown below in Exhibit 1. Each grey dot represents a stock in the MSCI World universe, while each red dot represents a stock in the portfolio. Value, momentum and quality metrics in the graphs are based on an average of several factors for each stock and each is normalised across the universe so that stocks rank from the worst (0%) to the best (100%).

Exhibit 1: Representation of the DEFI world portfolio with grey dots representing stocks in the MSCI World index and red dots stocks held in the portfolio. The extent of momentum/low volatility increases along the x axis and value/quality increases up the y axis.factor investing

Source: THEAM, BNP Paribas Investment Partners. For illustrative purposes only.

With such a representation, it is more obvious that the portfolio is more exposed to each of these four factors (value, momentum, quality and low vol) than the benchmark index. This is the result of the global stock selection produced by the strategy. Note, however, that even if some stocks picked in the portfolio may be below average for one factor they score well on other factors. Conversely, some stocks scoring well on some factors may be absent from the portfolio because their absence frees some risk budget to hold stocks with more consistently high scores across all four factors. It is clear from the representation in the two graphs that the portfolio produced by the strategy tends to avoid buying stocks in the bottom left quadrant where the most expensive stocks, with weakest momentum, lower quality and higher risk are found.

With the development of factor investing, more and more investors require analysis of these factor exposures. Some data providers like Style Research propose ‘skylines’ of factor reports to illustrate the different factor exposures of any fund, calculated based on their holdings and sized in order to show the extent to which the deviation of the exposure to one factor in the portfolio relative to the benchmark index is significant.

In Exhibit 2 below we show an example for our DEFI Europe strategy, broken down by Style Research. Positive bars show a positive exposure to a factor in the portfolio relative to the benchmark index. The DEFI Europe portfolio is exposed to value, momentum, quality and low-risk factors by construction. Interestingly, the Style Research report is not picking this up because we do not necessarily always use the same factor definitions. The blue bars do not pick up a positive exposure to the value factors that Style Research uses as standard. The quality exposure appears in the green bars, generally above benchmark. The low-volatility exposure is the second red bar and is, as expected, negative, while the momentum exposure appears in the two black bars, indicating, as we would expect, a positive exposure to medium-term (MT) momentum. The style of the fund can therefore be globally understood just from this one representation, and compared with other funds, whatever their strategy.

Exhibit 2: Analysis of the DEFI Europe strategy by Style Research with representation of factor exposurefactor investing

Source: THEAM, BNP Paribas Investment Partners and Style Research. For illustrative purposes only.

The main advantage of such a breakdown is that it means portfolios managed using quantitative and judgemental strategies can be represented in the same way, enabling comparisons between exposures and a closing of the cultural gap between the two approaches.

The main difficulty for the investor is that relying on standard style reporting like this can be misleading when less conventional factor definitions are used in multi-factor strategies, i.e. when quantitative managers add more of their proprietary colour with the objective of outperforming benchmark indices more consistently. This is the case for our DEFI Europe strategies.

Quantifying factor exposures is important – but not easy

All in all, with the growing importance of factor investing, it is clear that quantifying factor exposures is important. This is not necessarily an easy or intuitive task, for a number of reasons. Firstly, stocks tend to migrate from one style to another over time and cannot necessarily be classified permanently as value, low vol, quality or momentum stocks.

Secondly, while some market standards are in place, e.g. Style Research, when it comes to factor definitions to allow for the comparison of factor exposures across funds, they do not provide the complete story and can even be misleading when applied to multi-factor strategies that incorporate a higher dose of proprietary improvements over the plain vanilla factors used by the industry.

Written on 5 December 2016 in Paris

*The above mentioned securities are for illustrative purpose only and do not constitute any investment recommendation

Etienne Vincent

Head of Global Quantitative Management, THEAM

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