AgPa #69: Rebalancing Luck

Fundamental Indexation: Rebalancing Assumptions and Performance (2010)
David Blitz, Bart van der Grient, Pim van Vliet
The Journal of Index Investing Fall 2010, 1(2), URL/SSRN

This week’s AGNOSTIC Paper is already more than 10 years old, but still carries a very important message. The core idea is very simple. If you design an investment strategy, you must make decisions about rebalancing. There are two aspects to consider. How much and when. This week’s authors examine the when at the example of fundamental indices. They show that choosing arbitrary rebalancing date(s) introduces substantial luck or bad luck to a strategy. Even more important, this luck or bad luck doesn’t seem to cancel out over time and thus permanently affects real-world returns. Fortunately, however, there are ways to make yourself less dependent from rebalancing luck…

Before I continue with the paper, let me briefly mention that I got the idea for this post from this episode of the outstanding Flirting with Models Podcast. They discuss rebalancing luck around minute 34:50.

Everything that follows is only my summary of the original paper. So unless indicated otherwise, all tables and charts belong to the authors of the paper and I am just quoting them. The authors deserve full credit for creating this material, so please always cite the original source.

Setup and Idea

Some background for those who aren’t familiar with the idea behind fundamental indices. To the best of my knowledge, Rob Arnott and his company Research Affiliates originally published the concept of fundamental indexation back in 2005.1Arnott, Hsu, Moore, “Fundamental Indexation”, 2005, Financial Analysts Journal 61(2), URL The core idea is pretty simple. Why not weight stocks by some fundamental metric of the underlying business instead of market capitalization as passive strategies do? For example, Walmart would receive a higher weight than Apple in a fundamental index that weights stocks according to sales instead of market capitalization. One might argue that this is closer to the economic reality than market capitalization.

In the 18 years since this 2005-paper, the literature and practitioners mostly concluded that fundamental indices are pretty similar to strategies that attempt to capture the well-known value factor. Given the evidence for value investing, this of course doesn’t question fundamental indexation. According to today’s general view, however, fundamental indexation is just a differently branded variant of a systematic value strategy.

Anyway, the important information to understand this week’s paper ist the original rebalancing assumption of Arnott et al. (2005). The first versions of Research Affiliates’ fundamental indices rebalanced annually at the end of March.2Meanwhile, they shifted to quarterly rebalancing. But more on that below. And this is the point that this week’s authors examine in more detail. They argue that “[…] the choice of the annual rebalancing date of a fundamental index introduces a significant degree of arbitrariness that is undesirable for an objective benchmark index.”

Note that it is not about how much turnover, it is only about when. I really like this quote because it is essentially just common-sense. Unless you have specific ideas why a particular date is the best one, it doesn’t seem right to just randomly pick one. As we will see, this intuition fits the empirical data as the choice of the rebalancing date has significant and permanent impacts on the returns of fundamental indices.

Data and Methodology

The authors replicate the fundamental indices from Research Affiliates (now RAFI Indices) using the original methodology of Arnott et al. (2005). For this purpose, they examine the 1,000 largest US stocks by both market capitalization and various fundamentals (book value, sales, cash flow, dividends) between 1991 and 2009. They obtain the data from Compustat, a standard high-quality vendor.

To isolate the effect of rebalancing luck (or bad luck), the authors backtest their fundamental index with four different rebalancing dates. At the end of March (original methodology), and at the end of the remaining three quarters (June, September, December). Once again, they only change the rebalancing dates. All four indices rebalance just once a year and all differences should therefore come from rebalancing luck or bad luck. Together with the market-cap weighted benchmark, this analysis is the basis for the following results.

Important Results and Takeaways

Different rebalancing dates lead to different outcomes

To start with, the authors show in the table below that all four fundamental indices outperform the market-cap weighted benchmark over the sample period. So far so good.3This is in-line with the results of Arnott et al. (2005) which they attempt to replicate. Obviously, this is a good sign. As I mentioned before, fundamental indices are nowadays seen as variant of systematic value strategies. We can therefore relate this outperformance to the historic evidence for the value premium. The authors further note that all fundamental indexes have roughly the same tracking error of about 5% to the benchmark.

Table 1 of Blitz et al. (2010).

In danger of stating the obvious, the four different rebalancing dates lead to different return statistics. While all four fundamental indices outperform the benchmark by roughly 2%-points per year, Panel B shows that the four indices do have non-negligible tracking errors among each other. They range between 0.9 and 2.1% which is low, but not zero. No matter how we frame it, the (somewhat obvious) message of this table remains that rebalancing dates matter and different choices produce slightly different strategies. As we will see next, however, these aggregate statistics hide a lot of intermediate swings that investors experience over shorter horizons.

Rebalancing luck (or bad luck) is relevant and persistent

The chart below shows returns by calendar years for each of the four fundamental indices from 2002 to 2009. If rebalancing dates were irrelevant, all bars would be exactly the same for each year. They are not. While returns are admittedly quite similar in most years, there are clear differences in 2002, 2003, and 2009. For example, the March index returned 10% in 2009 while the September index was slightly negative. A 10% spread between two strategies that follow the same process and are supposed to do the same thing. For 2003, the spread between the best and worst index amounts to 5%, which is also sizable.

Figure 1 of Blitz et al. (2010).

The authors further apply some time series econometrics and conclude that those differences are not recovered over time. They find no statistical evidence for mean-reversion in the differences among fundamental indexes with different rebalancing dates. In English: the effect of rebalancing luck or bad luck seems to be permanent and doesn‘t cancel out over time. I think this makes intuitive sense. If you are lucky and catch the trough of a crisis with rebalancing in March, the other rebalancing dates simply don‘t have a lot of opportunities to do the same thing and catch up.

There is a solution: stretch rebalancing over the year

Assuming that there are no fundamental reasons that favor rebalancing at one date over the other, having that much luck or bad luck in your portfolio is not desirable. Before we come to the rather obvious solution, however, let‘s first explore the mechanics behind those patterns.

The idea of the fundamental index is to invest in the largest companies by some fundamental metric. The theoretical dream is therefore a strategy that rebalances continuously as new fundamental data of companies becomes available. You want to have a portfolio of the fundamentally largest companies at each point in time, and as soon as your portfolio deviates from that, you rebalance. Since this is almost certainly too costly in practice, you need to make compromises. There is nothing wrong with that, but any restriction regarding the timing and amount of turnover moves us away from our theoretical dream. The only question is how much.

Rebalancing just once a year at a rather arbitrary date seems to be a pretty strong restriction. The authors therefore argue in favor of a very simple alternative. Instead of counting on (rebalancing) luck, which is always a bad strategy, invest in a blended fundamental index. The blended fundamental index is simply an equal weighted portfolio of the four indices that rebalance at the end of March, June, September, and December. Importantly, this again doesn’t increase turnover. It just stretches it equally over the year and therefore reduces the impact of timing luck or bad luck at individual dates.4It is of course also possible to do it monthly or at any other frequency. The authors‘ blended fundamental index is just an illustration to make the point. Interestingly, Research Affiliates actually adapted this methodology. They still reconstitute their fundamental indices annually, but now stretch the rebalancing over all four quarters.

Conclusions and Further Ideas

Most of the results in this paper are pretty straight-forward and they may even seem obvious from today‘s perspective. I haven‘t been in the asset management industry back in 2010, so I cannot tell how big of an issue those fundamental indices and their methodology were. And to be honest, this is not at all important for me. I picked this paper because I believe the results are as relevant today as they were 13 years ago.

More and more people (including me) try to capture the major factors via systematic index funds or ETFs. I think it is generally great that such products make basic implementations of those strategies available to everyone. However, many of them come with strange rebalancing assumptions such that investors effectively end up with a lot of rebalancing randomness. For example, the MSCI Momentum indices rebalance for whatever reason only two times per year at the end of May and November. While it is already very unfortunate that MSCI implements a dynamic strategy like momentum with such slow turnover, concentrating all of it on two arbitrary dates is in my opinion even worse.5See this post for more about that problem. Given the results above, I think investors should definitely consider such methodological details in their fund selection.

The practical takeaways from this week‘s paper are thus twofold. First, unless there are plausible reasons why rebalancing at one date should be systematically better than on another, we should stretch it over the year. This is the best we can do to reduce the impact of rebalancing luck or bad luck in our portfolio. Remember that the impact tends to be permanent. This is of course nice when we are lucky and easily confused with skill. On the other hand, losing money through unlucky rebalancing in an otherwise sound strategy is very unfortunate and should be avoided.

Second, if you are in a position like me and want to have exposure to value, momentum, low risk, or quality via index funds or ETFs, check the rebalancing methodology of the underlying strategy. If it seems arbitrary or concentrated to a few days, a composite of similar strategies with different rebalancing dates should help to make yourself less dependent from luck or bad luck.6Unfortunately, this is difficult to implement for EU-based investors. Virtually all available factor ETFs track MSCI indices which follow a variant of the same general methodology.

Finally, as you probably noted, I strongly generalize the results of this paper. I do believe that the problem of rebalancing luck is quite universal and applies to a lot of investment strategies. Nonetheless, this week‘s paper only examines US fundamental indices from 1991 to 2009. Any statement about rebalancing luck beyond this is therefore some kind of speculation on my part. But I think we can agree that putting all your turnover in one or two arbitrary days doesn’t seem to be a very robust approach. On the other hand, it would be interesting if there are strategies which actually have some optimal rebalancing dates. But this is something for another AGNOSTIC Paper…

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1 Arnott, Hsu, Moore, “Fundamental Indexation”, 2005, Financial Analysts Journal 61(2), URL
2 Meanwhile, they shifted to quarterly rebalancing. But more on that below.
3 This is in-line with the results of Arnott et al. (2005) which they attempt to replicate. Obviously, this is a good sign.
4 It is of course also possible to do it monthly or at any other frequency. The authors‘ blended fundamental index is just an illustration to make the point.
5 See this post for more about that problem.
6 Unfortunately, this is difficult to implement for EU-based investors. Virtually all available factor ETFs track MSCI indices which follow a variant of the same general methodology.