Optimal factor index design?

EDHEC-Risk Institute suggests that investors should be wary when implementing factor tilts to ensure diversification still reigns, and that factor index design does not lead to concentration, which in turn leads to high turnover and investability hurdles. By Felix Goltz, ERI Scientific Beta.

With recent developments in risk factor-based investing, many investment product providers offer strategies that help investors to gain exposure to various identified risk factors, such as value, momentum, and size.

While there is consensus on the factors that are rewarded over the long term, implementation of factor investing, notably in the long-only universe, is not subject to the same consensus.

Concentrated factor indices identify stocks that have a pronounced factor tilt for a given factor, and aim to obtain strong exposure to this factor through stock selection that is often restrictive, resulting in relatively few securities in the portfolio in terms of the nominal number of stocks.

Moreover, the weighting scheme applied to the stock selection is either market-cap weighting or score-based weighting, resulting in a very uneven distribution of weights. Therefore, the effective number of stocks in the portfolio will also be low.

The idea behind this approach is to maximise over the long term the return associated with the strongest exposure possible to the rewarded risk factor.

Smart factor indices implement a relatively mild stock selection, where stocks with above-average exposure for a given factor are retained.

In a second step, these stocks are weighted by a combination of diversification-based methods that aim to create a well-balanced portfolio in terms of weights and risks. The idea behind this approach is to reconcile the exposure to the right factor with avoidance of excessive portfolio concentration. Poor portfolio diversification exposes the investment to risks of excessive volatility over the short and medium term.

Our recent research, presented in a 2015 EDHEC Risk Institute working paper, has compared the results of smart factor indices with several stylised examples of concentrated factor indices. Before turning to the empirical comparison, a number of conceptual considerations are in order.


Conceptual issues

Products that aim to capture explicit risk-factor tilts through concentrated portfolios effectively neglect adequate diversification. This is a serious issue because diversification has been described as the only “free lunch” in finance. It allows a given exposure to be captured with the lowest level of risk required.

In contrast, gaining factor exposures exposes investors to risk factors, and therefore, such exposures do not constitute a “free lunch.” They instead constitute compensation for risk in the form of systematic factor exposures. Such capturing of risk premia associated with systematic factors is attractive for investors who can accept the systematic risk exposure in return for commensurate compensation.

However, factor-tilted strategies, when they are very concentrated, may also take on other, non-rewarded, risks. Non-rewarded risks come in the form of idiosyncratic or firm-level risk, as well as potential risk of sector concentration. Financial theory does not provide any reason why such risk should be rewarded. Therefore, a sensible approach to factor investing should not only look to obtain a factor tilt, but also at achieving proper diversification within that factor tilt. To illustrate this point, we focus on the value factor as an example below, but the discussion carries over to other factors too.

In fact, if the objective was to obtain the most pronounced value tilt, the only unleveraged long-only strategy that corresponds to this objective is to hold 100% in a single stock – the one with the largest value tilt, as measured, for example, by its estimated sensitivity to the value factor or its book-to-market ratio.

This thought experiment clearly shows that the objective of maximising the strength of a factor tilt is not reasonable. Moreover, this extreme case of a strong factor tilt indicates what the potential issues with highly concentrated factor indices are.

First, such an extreme strategy will allow the highest possible amount of return to be captured from the value premium, but it will necessarily come with a large amount of idiosyncratic risk, which is not rewarded and therefore should not be expected to lead to an attractive risk-adjusted return.

Second, it is not likely that the same stock will persistently have the highest value exposure within a given investment universe. Therefore, a periodically rebalanced factor index with such an extreme level of concentration is likely to generate 100% one-way turnover at each rebalancing date, as the stock held previously in the strategy is replaced with a new stock that displays the highest current value exposure at the rebalancing date.

While practical implementations of concentrated factor-tilted indices will be less extreme than this example, we can expect problems with high levels of idiosyncratic risk and high levels of turnover whenever index construction focuses too much on concentration and pays too little attention to diversification.

Interestingly, the importance of diversification for a given factor tilt was outlined more than 40 years ago in Benjamin Graham’s famous book on value investing: “In the investor’s list of common stocks there are bound to be some that prove disappointing … But the diversified list itself, based on the above principles of selection […] should perform well enough across the years. At least, long experience tells us so.”

Aiming at a highly concentrated value portfolio would be completely inconsistent not only with financial theory, but also with the principles put forth by the early advocates of value investing.

Cap-weighted portfolios of value stock selections may at first seem to be more neutral implementations than score-weighted portfolios. However, it is well known that cap weighting has a tendency to lead to very high concentration given the heavy tailed nature of the distribution of market cap across stocks in the same universe.

It is well documented in the academic literature that simple cap-weighted value-tilted portfolios have not led to attractive performance. In fact across different studies, empirical results show that a value strategy needs to be well-diversified to deliver a significant premium.

For example, the standard Fama and French value factor includes a broad selection of stocks, and uses a two-tiered weighting approach to obtain better diversification. In particular, the value factor is an equal-weighted combination of sub-portfolios for different market-cap ranges, effectively overweighting smaller size stocks and increasing the effective number of stocks.

The fact that the most widely cited research documenting the relevance of the value factor does not use simple cap-weighted factors, but rather constructs more balanced portfolios, shows the lack of support for industry practices using simple cap-weighted factor indices. For completeness, we may add that the literature does not use any score-weighted approaches either.

Overall, it thus appears that neither of the approaches that propose to construct concentrated factor indices is supported by the academic literature, or for that matter, by common sense.


Testing different approaches


Turnover and investability

As discussed in our thought experiment in the introduction, it is clear that high levels of concentration potentially lead to severe turnover. Turnover will be high especially when the stock-selection criteria move fast, leading to pronounced changes in eligible stocks for a given factor tilt from one rebalancing date to the next. Of course, intuition suggests that the turnover will depend on the severity of the stock selection screen.

Our research reports the increase in turnover for concentrated portfolios compared to the well-diversified equal-weighted indices created for six different factors (value, size, momentum, low vol, profitability and investment). Narrowing down the stock universe to obtain strong factor tilts severely increases turnover, thus leading to strategies that are more difficult and costly to implement than strategies based on broader selections.

Turnover for the factor-tilted strategies reaches levels close to 50% when selecting only the one-fifth of stocks with the strongest factor score, while turnover is close to 30% for the strategies based on broader indices selecting half the stocks.

The implementation hurdles that are apparent from the analysis of turnover are confirmed when analysing tradability metrics such as the days to trade the necessary positions for the strategy. This measure, which considers the available trading volume in stocks whose rebalancing generates this turnover, confirms the implementation problems of concentrated approaches compared to more diversified approaches.


Idiosyncratic risk

Increasing concentration is also expected to lead to an increase in unrewarded, idiosyncratic risk. We assess this issue by regressing returns of the factor strategies onto the standard Carhart factors including the market, size, value and momentum factors. The idiosyncratic risk is then measured as the standard deviation of the residual return relative to the systematic return component which results from the factor exposures.

In order to estimate diversification benefits, we compute the ratio of unexplained return with respect to the Carhart factors (or “Carhart alpha”) to the residual standard deviation.

Our results provide strong evidence that diversification benefits are sizeable when moving from concentrated approaches to better-diversified approaches. A key issue with concentrated approaches is that idiosyncratic volatility increases with higher concentration. Note that financial common sense suggests that idiosyncratic risk should be diversified away! This confirms that many concentrated indices are often exposed to risks which are not only unrelated to the factor tilts that they are intended to capture but also likely to be unrewarded over the long term.

A recent example of how idiosyncratic risk materialised in factor indices is the emissions scandal related to car maker Volkswagen. Clearly, if a company cheats on emissions testing, this is a purely idiosyncratic event from which investors can diversify away by spreading their portfolio weights across multiple firms and industries.

The table below presents the weights and performance attribution to Volkswagen AG and other automobile stocks in various multi-factor indices, for the period surrounding the diesel scandal in 2015.

The SciBeta Extended Europe Multi-Beta Multi-Strategy EW index, a well-diversified multi-factor index only allocated a 0.05 per cent weight to Volkswagen, while the cap-weighted Stoxx 600 index allocated 0.35 per cent to this single stock. It should be noted that the SciBeta Extended Europe Multi-Beta Multi-Strategy EW index follows a methodology which explicitly targets good diversification of specific risk through a diversification-based weighting scheme, in addition to targeting factor exposures to multiple factors.

If we now examine other forms of multi-factor indices that have marketed the performance that can be achieved through strong exposure to factors, and have been less concerned about diversification of specific risk, we note that the exposure to Volkswagen AG risk is considerable.

We observed, for example, that the Lyxor J.P. Morgan Europe Multi-Factor index was very strongly exposed to the risk of the Volkswagen AG stock, as was the MSCI Europe Diversified Multiple-Factor index. As such, these indices respectively contained almost 1.5 and more than 2 times more Volkswagen AG stock than the Stoxx Europe 600, and almost 10 times and 16 times more Volkswagen AG stock than the SciBeta Extended Europe Multi-Beta Multi-Strategy EW index. Since they contain a low effective number of stocks, these indices do not benefit from a deconcentration effect.