There was over $2 trillion in factor investing funds worldwide in March 2024 according to data from LSEG Lipper, one fifth in ETFs. (Financial Times, March 9, 2024). See the UBS Global Investment Returns Yearbook by Dimson, Marsh, and Staunton for a history of factor returns.
A factor model projects the expected return from holding a stock by multiplying the expected return for a set of “factors” by the stock’s sensitivity to that factor return and summing for all factors:
The ellipse (…) indicates their can be additional factors, 4, 5, 6, and so on. The factors are usually seen as risk factors with the the sensitivity of the given investment to that risk. For a factor model to be legitimate, Alpha is zero if the market is efficiently pricing factors or non-zero if mispricing risk. So a factor model is both a model to capture the risk of investing but also for identifying abnormal returns (alphas).
The Capital Asset Pricing Model (CAPM) is such a model (with only one factor):
where the sole Factor1 is the expected return on the market. That model was shown to not work2M“beta is dead”2Mthus an attempt to identify additional factors in a “multifactor model.”
Now, what are these additional factors? There have been attempts to identify them with theory but the main approach has been empirical: Search in the data for measures that predict returns, then form factors with these measures. This is data mining with no theory or even explanation of why these are the factors we want. At last count, over 400 potential factors have been “discovered” by dredging data! When factors are “discovered,” there remains the additional task to get the expected return to the factors. The tricky matter of getting the expected return on the CAPM is compounded with additional factors. Then there remains the problem of estimating the betas on the factors.
The book has been quite skeptical about the CAPM, and your authors are more so with multifactor models. They appear to work well in explaining returns in the cross section. However, applying them out of sample (in real time) they don’t work and it’s in real time that the investor works. So, when you see an investment firm touting returns from factor investing, remain skeptical. They are probably working with doubtful models or doubtful estimates of factor returns. They may be reporting in-sample correlations or reporting real-time returns in periods when the strategy just got lucky Or, if the model happens to capture some aspect of risk, the returns are just reward for risk exposures.
The most ubiquitous model is the Fama and French model in its various forms. Here is an excerpt from an interview with Fama:
WALKER: In your opinion, what’s the current best asset pricing model? Is it the five-factor model?
FAMA: I don’t know. I wouldn’t claim that. It does well on the things it was designed to explain, both nationally and internationally. But there are contradictions of it. So it’s like every other model. There are things that it can’t explain. So I would say it explains the things it was designed to explain, and they’re really important. A lot of money is managed based on those things. But is it the best model? I hope not.
I would like to see… I don’t want more factors. I want less. I want simpler models that work, not more complicated models. So I’m still hoping that it’ll last—I will last—to the point where something good comes along that says, “I don’t need five; here are two that’ll do the trick.”
WALKER: Yeah. More parsimonious.
FAMA: Yeah, right, exactly.
WALKER: Because the models with more factors feel like you’re just overfitting to the data.
FAMA: Right. You’re just data dredging.
WALKER: Data dredging, yeah. Have you developed any theories behind any of the factors that you added to the CAPM?
FAMA: Well, so the three-factor model basically added a size factor, small stocks versus big stocks, and a value-growth factor, value versus growth being the second factor. And there was a little bit of intuition in those, in the sense that everybody would think that small stocks are more risky than big stocks. Everybody would kind of agree that value stocks tend to be poorly performing companies. Maybe the market requires higher expected returns for those.
But multifactor asset pricing requires something in people’s tastes that make them have negative attitudes that will persist. So if you tell me that after this discovery of these things, value factor, small stock factor, people pile into them because they’re really not concerned that the stocks are small or that they’re poorly performing companies, they only care about the expected return. Well, then I get a problem because I think that will erase it. I think that’ll nullify the model on its own.
The problem is you won’t know if that happened or not. So those models have not done as well in the last 15 to 20 years of data. But that’s a drop in the bucket as far as model testing goes. That’s the reality of it. You basically need a lifetime of data to test an asset pricing model
https://josephnoelwalker.com/eugene-fama-156/?ref=the-joe-walker-podcast-newsletter
For reasons why factor investing fails, see
Arnott, R., C. Harvey, V. Kalesnik, and J. Linnainmaa. 2019. Alices’s Adventures in Factorland: Three Blunders that Plague Factor Investing. Journal of Portfolio Management 45 (4), 18-36.
