Keeping it Simple: The Disappearance of Premia for Standard Non-Market Factors (2023)
Avanidhar Subrahmanyam
SSRN Working Paper, URL
This week’s AGNOSTIC Paper is almost a cheat as it is only 3 pages long. I found the paper in the newsletter (URL) of a German journalist and thought it is so unconventional that I have to write about it. The author, Avanidhar Subrahmanyam, is a well-known financial economist at the UCLA School of Management and articulates a very simple statistical critique on factor investing. I believe it is important to seek disconfirming evidence, so I regard it as duty to look at this paper with an open mind.
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
Factor investing (URL) has often been criticized for data mining and a lack of causality (URL). Rightly so! There are a lot of pitfalls that can lead to data mining problems and we humans are prone to see patterns in things that are actually random. I also agree that most research on financial markets is very hypothetical and has little chance to ever become a profitable investment process. All of this highlights the need for robust processes, out-of-sample tests, and intellectually-honest researchers.
Regular readers of this blog know that I put high emphasis on such issues (see for example AgPa #49 and #55) and only believe in a handful of thoroughly tested strategies. Also note that many successful asset management firms wouldn’t exist without strategies like momentum (URL), value (URL), or quality (URL).
Now, I promised to approach the paper with an open mind and so will I do. The critique of Subrahmanyam aims at the lacking statistical significance of the five Fama & French (2015) factor premiums over time. In addition, he finds the same lack of significance for the momentum, short-term reversal, and long-term reversal factor.
Before we go into the results, I want to say that I generally agree with the author. You can do as much fancy research as you want. In the end, factors should deliver a meaningful premium to investors and you want to have sufficient conviction (statistical significance) that those premiums are not just random. At the same time, I believe there are more details in this question than the paper suggests.
Data and Methodology
The data and methodology are very simple. The author downloads factor data from Kenneth French’s website (URL) and calculates average monthly factor premiums. Just to get everyone on the same page, factor premiums are the long-short returns for each factor. For Kenneth French’s data, that means going long (short) portfolios with the highest (lowest) factor signals.
The author is very open with his simple methodology and mentions that “[…] all that is needed for this project is Excel […]”. His spreadsheet of data is indeed available for download (URL). All he does is calculating monthly averages, standard deviations, and the according t-statistics of factor returns for the sample period from 1996 to July 2023.
Important Results and Takeaways
Only two factors are significant over the last 27+ years
The table below summarizes the results for the US stock market (MKT, URL), size (SMB, URL), value (HML, URL), profitability (RMW, URL), investment (CMA), momentum (MOM, URL), short-term reversal (STREV), and long-term reversal (LTREV).
Except for the overall stock market (MKT) and the profitability factor (RMW), t-statistics do not exceed the common significance threshold of 1.96. The author therefore concludes that “[…] using a defensible sample size and method, most standard factors other than the excess market return do not yield a first moment reliably different from zero, leave alone a Sharpe ratio different from zero.” In English: although average factor returns are positive, we cannot say with satisfying confidence that this wasn’t just luck or randomness.
The author also relates those results to a quite famous study by McLean & Pontiff (2016) which shows that factor premiums decrease by about 32% after the academics started to write about them.1An annual 10% factor premium would turn into a 6.8% factor premium, for example. Subrahmanyam even links the lone significance of the profitability factor (RMW) to the fact that it only emerged in the academic community in the early 2010s. All other factors are considerably older and investors had thus more time to arbitrage them away.2Older here refers to the time of the first meaningful academic publications. That has nothing to do with reality. Warren Buffett, for example, knows since the 1970s that quality investing works (URL)…
He further builds on this argument and “cautiously assert[s] here that what is really going on is that momentum, reversals, value, real investment, and size represented genuine anomalies that simply got arbitraged away via scale expansion of anomaly-based trading. As time goes on, I would expect much the same to happen to the profitability anomaly, and perhaps […] we will be back to the CAPM (if anything at all).”
In English: unless you are an arbitrageur, forget about all the insignificant factors. Keep it simple, and go with the overall stock market. As I mentioned above, I cannot deny the data and generally agree with the author here. For most people and probably a surprisingly large number of institutions, the statement above is very good advice. On his way, however, the author touches a lot of issues which I believe are worth discussing in more detail.
Conclusions and Further Ideas
First, it is not a new insight that factor premiums are very difficult to measure over time. Fama & French (2020), for example, also mention that we cannot answer the question about a declining value premium with any reasonable statistical confidence. From a totally different corner of the finance world, Aswath Damodaran (2024) also argues that it is even impossible to estimate the historical equity risk premium with reasonable precision.
So that factor premiums are extremely noisy and often statistically insignificant is true, but was probably never really different. In fact, I would argue that the great majority of real-world investing involves uncertainty beyond what scholars are used to from statistics. Have you ever seen an entrepreneur who makes capital expenditure decisions on the basis of t-statistics? Don’t get me wrong. Approaching markets with scientific and statistical rigor is important and I am a big believer in that. But in my view, we should also accept that we are dealing with a problem that lacks the precision of natural sciences.
Second, it is also right and important to mention that factors become weaker after publication. This is a fundamental feature of markets. If you are crazy enough to publish a profitable strategy, I want to have the profits and start trading. When enough people do that, the anomaly eventually disappears. Few people debate that and quantitative asset managers frequently highlight the importance of constant innovation. Let me also once again quote Cliff Asness who gets not tired to “[…] point out for the 1000th time that 50% of a back test out of sample across many factors is a freaking home run” (URL).
My point is, we all know about the arbitrageurs and the arguments of the author sound very reasonable. At no point, however, he provides any empirical analysis to test his arguments. I cannot say he is wrong and theoretically agree with his reasoning. But I think it is far from clear that arbitrageurs alone lead to the insignificance of factor premiums in this particular sample. Take the value factor as counter example. It went through a very difficult period after the 2008 crisis and became much cheaper over time. This is quite the opposite of arbitrage or crowding and the factor still delivered no premium.
Finally, factors are more than just expected premiums and few serious factor-investors look at single factors anyway. The real beauty comes from multi-factor combinations. If you combine five factors with mildly positive premiums and low or even negative correlations to each other, the resulting portfolio will be pretty good. Of course, you still need a positive premium to make money over the long-term. But the statistical significance of any single factor premium is considerably less relevant in a portfolio context. Asness et al. (2014), for example, mention that a Sharpe ratio optimizer would still add momentum to a multi-factor portfolio with value at a negative premium of down to -3% per year.
Bottom line: I think the author is both right and wrong with his critique. He is of course objectively right in his calculations and he is also right to remind us to not forget the basics. At the same time, I think he is wrong in the sense that his critique does not cover all nuances of factor investing. In addition to that, I believe serious factor-investors and researchers are aware of his issue for quite some time anyway.
- AgPa #82: Equity Risk Premiums and Interest Rates (2/2)
- AgPa #81: Equity Risk Premiums and Interest Rates (1/2)
- AgPa #80: Forget Factors and Keep it Simple?
- AgPa #79: The Momentum OGs – 30 Years Later
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