Myths about fundamental indexing¹

1. An earlier version of this paper was called ‘An anatomy of fundamental indexing’.

ABSTRACT

Fundamental indexing starts from the observation that in a value-weighted portfolio, any overpricing affects the stock’s portfolio weight upward and its typical return downward, and vice versa; but on average the ‘drag’ on the portfolio’s expected return caused by this negative interaction is avoided if weights are based instead on accounting-based instruments for true value. We find that the drag effect is statistically and economically unimportant. Our empirical work avoids regression-based alphas, which are flawed by demonstrable instabilities in the exposures.

KEYWORDS:

• portfolio management
• drag
• pricing errors

JEL CLASSIFICATION:

• G11
• G12
• G14

Acknowledgements

We thank Anup Basu, Gaël Imad Eddine, Aurobindo Ghosh, Hening Liu, Vestman Roine, and Martina Vandebroek, and participants in presentations at the authors’ home institutions and at the Indian Finance Conference (Bangalore), the BRForum (Antwerp), a Paris Finance Meeting, a Symposium on Banking and Finance (Shanghai), and the Inquire Europe Conference (Munich). Any remaining errors are the authors’ sole responsibility.

ORCID

Lieven De Moor http://orcid.org/0000-0002-1290-2971

Notes

1. An earlier version of this paper was called ‘An anatomy of fundamental indexing’.

2. See, e.g. Arnott, Hsu and Moore (2005), Hemminki and Puttonen (2008), Stotz, Döhnert and Wanzenfried (2007), Neukirch (2008), Jun and Malkiel (2008), Asness (2006), Walkhäusl and Lobe (2010), Houwer and Plantinga (2009), Peltomäki (2010), and Mihm and Locarek-Junge (2010, Ferreira and Krige (2011), Forbes and Basu (2011), Balatti, Brooks and Kappou (2017). Less satisfactory results are reported by e.g. Blitz, Van de Grient and Van Vliet (2010), Boudt, Darras, Nguyen and Peeters (2015), Miziolek and Zaremba (2017), Piljak and Swinkels (2017), Chen et al. (2007), Graham (2012).

3. See, e.g. Arnott, Hsu and Moore (2005), Hemminki and Puttonen (2008), Stotz, Döhnert and Wanzenfried (2007), Neukirch (2008), Jun and Malkiel (2008), Asness (2006), Walkhäusl and Lobe (2010), Houwer and Plantinga (2009), Peltomäki (2010), and Mihm and Locarek-Junge (2010, Ferreira and Krige (2011), Forbes and Basu (2011), Balatti, Brooks and Kappou (2017). Less satisfactory results are reported by e.g. Blitz, Van de Grient and Van Vliet (2010), Boudt, Darras, Nguyen and Peeters (2015), Miziolek and Zaremba (2017), Piljak and Swinkels (2017), Chen et al. (2007), Graham (2012).

4. The error may conditionally exhibit autocorrelation, but at this stage we are after the links between and .

5. This is to eliminate tiny, illiquid and penny stocks which are reasonably more likely to contain data errors. Penny stocks are often fallen angels (Chan & Chen, 1991) which are highly speculative and illiquid. Tiny companies likewise have limited liquidity; can be subject to high price pressure or price manipulation, and often represent too little value to warrant attention.

When a stock falls below a floor on date t, both the return before and after that date are removed. That is, we do not remove the entire return series of a firm that does badly at one point, as this would have introduced a classical survivorship bias. Our way of filtering may still affect returns to some extent, but (i) it cannot have a serious effect on the difference between EW and VW returns, which is what matters to us; and (ii) it occurs only for very small firms, whose impact on total portfolio performance is too minute to matter.

6. Negative and zero book values and sales are almost surely mistakes. Negative free cash flows, in contrast, make more sense and are much more prevalent.

7. With a faster correction chances of capturing that correction within the horizon are better; and even if all corrections do happen inside the horizon, a sudden correction produces a higher mean monthly return than a gradual one. For instance, if a price goes from 50 to 100 in five equal percentage steps, the average per period return is 0.15. In contrast, if it jumps from 50 to 100 in period 1 and then pays for zero returns, the average return is 0.20. Note that the reversal we document here relies on hindsight; we observe a group of small stocks (or, in the next paragraph, a high BtM stock) and then check whether they went down recently, on average.

8. The fallen-angel effect is documented by, e.g. Chan and Chen (1991), Chen and Zhang (1998), Lakonishok and Vermaelen (1990), Ikenberry, Lakonishok and Vermaelen (2002) or Peyer and Vermaelen (2009). Bearing in mind their own resume, the story goes, professional portfolio managers are reluctant to invest in stocks that did quite badly recently, so prices are depressed and expected returns high.

9. This does not yet mean that the style is constant: the adjustment is nonlinear, being proportional to the market weight and its interaction with BtM’s deviation from the average:

10. The annual return is calculated as , with N the number of months, 360. The reminder of the analysis is done in terms of arithmetic average monthly returns. These mean monthly returns could be poor indicators of long-term cumulative returns if there are serious autocorrelation patterns that differ across strategies. But the geometric average annual returns do not bear this out. Across the seven strategies, there is a 0.997 correlation between simple monthly average and geometric annual averages. Thus, it looks correct to study just the mean monthly returns.

11. We always weight by market cap across buckets. Weighting in proportion to BtM across cells would not make sense: we do know that BtM matters. What FI claims to beat is VW, and we want to know why that happens.

12. This consideration also implies that our findings cannot be due to our reliance on Thomson Reuters Datastream. Our dataset does differ from the usual CRSP or Compustat files, used in this kind of research, with respect to the presence of more tiny stocks. This does load the dice in favor of FI in the sense that these smallest stocks, being traded in illiquid markets and lacking analyst attention, are prime candidates for pricing errors; in that sense, our conclusion that the drag effect is trivial is conservative. Adding such an idiosyncratic group of stocks does create a risk that the overall picture may be obscured by noise. But the value weight of those smallest vigintiles is tiny, so the aggregate estimate is essentially unaffected.

13. By construction, the VW market portfolio has a value exposure of 0 and the HML fund has value exposure 1.