The Value Effect in Stock Returns

/u/BainCapitalist asked about the "value effect" - the observation that stocks with high book-to-market ratios outperform stocks with low book-to-market ratios (in general we find this effect in any fundamental-to-price ratio). He asked how it squares with the EMH - something I am not going to answer here because, truth be told, no one knows the answer to that yet. cc//u/QuesnayJr, /u/FinancialEconomist

What I do want to do is illustrate precisely what the "value effect" is and the "puzzle" the value effect presents in financial economics. I will give a brief background on the value effect then will illustrate some of the issues with the value effect and its puzzle in the context of John Cochrane's fantastic paper Discount Rates. See pages 14 and 53 of the PDF.

The Theory

Economic theory tells us that returns to assets should be commensurate in risk - the higher the risk, the higher the return. The Capital Asset Pricing Model (CAPM) relates returns to a single risk factor - the excess return to the market-cap weighted portfolio. In practice, the beta-hat of a regression of returns on the market factor tells you how much of a portfolio's return is generated by the market risk factor and the constant tells you how much of the returns were abnormal returns - returns unexplained by market risk (for instance, perhaps idiosyncratic risk in the instance of a single asset).

The Value Effect

Many authors have documented the value effect in finance and accounting literature. I use data available on Kenneth French's website to replicate the graphs that Cochrane created for his AFA address (Cochrane and I are using the same data sets). The value effect is studied using book-to-market (B/M) ratios (the most commonly used value factor used in asset pricing).

Cochrane notes that from 1963 through 2010, we see the "value effect" and the puzzle" it presents. This is the replicated graph. (Note: the numbers will be off slightly, especially with the Y axis; I believe Cochrane uses average excess returns despite saying "average returns" while I use average gross returns of the portfolios.)

Market beta - the measurement of risk - on these portfolios don't vary that much. Indeed, both the highest B/M stocks (value) and lowest B/M stocks (growth) have nearly the same beta but vastly different returns! What this graphs tells us is that if we owned the value portfolio we'd get higher returns for the same amount of risk as the growth portfolio - the "value effect". But, if the CAPM is correct in saying that higher returns should be reflected in risk, then why do these portfolios have non-monotonically increasing returns? This is the "puzzle" that financial economists have studied for quite some time, one that has no clear answer.

Cochrane notes, however, that prior to 1963, the graph doesn't look the same. This is the return-beta relationship for B/M sorted portfolios from 1926-1963. Here, we still see that value commands a higher return than growth and is sorta-kinda monotonically increasing, but the returns are commensurate in risk. There is a "value effect" but no puzzle! The CAPM prices the portfolios quite well.

The fact that the puzzle of the value effect doesn't exist in pre-1963 data should give us pause. Why is this the case? We generally assume that we're capturing the true data generating process when testing for asset pricing anomalies (the more commonly used word for these "puzzles") so when we look out-of-sample to other periods of time, we should see the relationship still hold (given enough data; 34 years is a decent amount of time for out-of-sample testing).

He's dead Gene

Cochrane's graphs end at 2009 - Discount Rates is a nine year old paper at this point! Ever since the Great Financial Crisis, we've seen growth stocks outperform value stocks. Many people in the financial industry and especially financial journalism have proclaimed that value is dead (though prominent factor-based quantitative asset management firms believe differently). While the data set is much smaller than either of the two previous graphs, we can still look to see if the value effect still exists. I have updated the graph for 2009-2020 data.

Here, we see that not only is growth outperforming value, but we see the same sort of relationship we see in the 1963-2009 data in reverse (kind of - value has a really high beta while the rest of the portfolios have similar betas). The CAPM doesn't quite price all the portfolios jointly (I'm eye-balling a GRS test, forgive me for my sins), however, there's no value effect here - growth outperforms value with similar amounts of risk.

121 data points isn't much to go off of. So what if we do one, big, in sample test of the B/M deciles? This is what ~94 years of data looks like. After including both the 1926-1963 and the 2009-2020 data, we see that the puzzle disappears - value earns more than growth, (roughly) monotonically, but is commensurate in higher betas.

Conclusion

Is the value effect real? We probably will never know, but, through rough exploratory analysis, we can see here that the value effect exists but the observation that the returns aren't commensurate with risk - the "puzzle" - is sensitive to choice of time periods. As n grows larger, the puzzle of the value effect seems to be going away and the CAPM does a decent job at explaining returns for value stocks.