### Multifactor Explanations of Asset Pricing Anomalies

- Fama and French (1996)
- A version of the paper can be found here.
- Want a summary of academic papers with alpha? Check out our Academic Research Recap Category.

### Abstract:

Previous work shows that average returns on common stocks are related to firm characteristics like size, earnings/price, cash flow/price, book-to-market equity, past sales growth, long-term past return, and short-term past return. Because these patterns in average returns apparently are not explained by the CAPM, they are called anomalies. We find that,

except for the continuation of short-term returns, the anomalies largely disappear in a three-factor model. Our results are consistent with rational ICAPM or APT asset pricing, but we also consider irrational pricing and data problems as possible explanations.

### Core Idea:

In 1993, Fama and French argued that value stocks with high B/M ratios have higher premiums, and such premiums cannot be explained by the traditional CAPM model. Fama and French defined a three-factor model to help better explain the cross-section of stock returns, or why some stocks earn higher returns than others.

However, asset pricing researchers continued to flood the academic journals with new anomalies that challenged the Fama and French 3-factor model. For example, as we have discussed recently on the blog, DeBondt and Thaler (1985) find a reversal in long-term returns and Jegadeesh and Titman (1993) find intermediate-term momentum.

In this paper, Fama and French (1996) defend their 3-factor model by showing that many anomalies from previous literature disappear in the context of their 3-factor model.

The anomalies that lack robustness are as follows:

**Earnings/Price, Cash Flow/Price, and past sales growth:**

Table III in the paper shows that the 3-factor model can capture the returns to portfolios formed on E/P, C/P, and sales growth. Specifically, low E/P, low C/P, and high sales growth are typical of strong firms that have negative slopes on HML, and they have lower expected returns. Conversely, high E/P, high C/P, and low sales growth are typical of weak firms that have positive slopes on HML, and they have higher expected returns. As HML returns are positive, loading positively on this factor, which E/P, C/P and sales growth do, leads to higher expected returns. The 3-factor model would seem to explain these anomalies, which Fama and French argue simply load on HML.

**Long-term past return anomalies**

Panel B and C of Table VII below shows that 3-factor model can also capture the reversal of long-term returns documented by DeBondt and Thaler (1985).

DeBondt and Thaler noted that extreme price movements over long formation periods were followed by movements in the opposite direction. (If you are curious about the details, we wrote a post about this)

Once again, Fama and French say the 3-factor model can account for this. In another word, long-term losers tend to have positive HML slopes and higher future average returns. Conversely, long-term winners tend to be strong stocks that have negative slopes on HML and low future returns. Panel C demonstrates this especially clearly. Again, Fama and French argue that DeBondt and Thaler are just loading on the HML factor.

But what happens if we examine shorter formation periods for momentum?

### “Main Embarrassment” of the 3-factor Model

Here Fama and French run into problems. Fama and French (1996) admit that the “main embarrassment” of the three-factor model is its ** failure** to capture the continuation of short-term momentum anomalies.

The first panel in Table VII below shows that in the three-factor regressions, the intercepts are strongly negative for short-term-losers and strongly positive for short-term winners. So there is something going on here that is not explained by the 3-factor model.

The problem is that losers load more on SMB and HML than winners. Thus, as for the portfolios formed on long-term past returns, the three-factor model predicts reversal for the post-formation returns of short-term losers and winners, and so missed the observed continuation. — FF(1996)

While many anomalies disappear under robust tests, shorter term momentum anomalies (formation periods ~1 year) are robust. These could not be explained by existing risk factors. This is a significant admission from Fama French:

We have saved until last the discussion of the main embarassment of the three-factor model, its failure to capture the continuation of short-term returns documented by Jegadeesh and Titman (1993) and Asness (1994). There are at least three possible stories.

- “Spurious result of data snooping.”
- “Asset pricing is irrational.”
- “Asset pricing is rational, but our three-factor model is (alas!) just a model, and the continuation anomaly exposes one of its shortcomings.”

### Carhart 4-factor Model: MOM Factor Formally Added

Carhart (1997) constructs his 4-factor model by using FF 3-factor model **plus** **an additional momentum factor**. He shows that his 4-factor model with MOM substantially improves the average pricing errors of the CAPM and the 3-factor model.

After his work, the standard factors of asset pricing model are now commonly recognized as Value, Size and Momentum.

- The views and opinions expressed herein are those of the author and do not necessarily reflect the views of Alpha Architect, its affiliates or its employees. Our full disclosures are available here. Definitions of common statistics used in our analysis are available here (towards the bottom).
- Join thousands of other readers and subscribe to our blog.
- This site provides
**NO**information on our value ETFs or our momentum ETFs. Please refer to this site.

GuestMarch 25, 2015 at 2:04 pmIs it safe to say that an “investment factor” is on its way to being a new standard?

jimhsuMay 19, 2015 at 3:43 pmInteresting and informative. However, Carhart (1997) claims that “Jegadeesh and Titman’s (1993) spread in mean

return among last-year’s winning and losing stocks is not an investable strategy at the individual security level”, and that the performance of momentum funds is coincidental. Now more recent research seems to question that assumption, but is momentum a stronger effect on the sector/asset class level vs individual securities, or vice versa, and does the rise of simplified asset class exposure (ETFs) support the former?

Jack Vogel, PhDMay 20, 2015 at 11:18 amWhere in the Carhart (1997) paper does it say this?

jimhsuMay 20, 2015 at 5:35 pmCarhart 1997 (this link, the link above didn’t work for me: http://onlinelibrary.wiley.com/doi/10.1111/j.1540-6261.1997.tb03808.x/abstract )

Page 73, 2nd paragraph.

I’m pretty sure momentum works (doing some reading, and also my own backtesting), just curious about that statement.

Jack Vogel, PhDMay 20, 2015 at 9:10 pmThanks for pointing this out. The paper comes to this conclusion by looking at funds with the highest loading on Momentum. However, this does not mean that the funds are momentum strategies, only that compared to other funds, they are the closest to momentum. These are most likely growth funds, which is not the same as a momentum strategy.

Here is a study we did on the distribution of momentum returns:

http://blog.alphaarchitect.com/2014/07/16/ride-winners-and-cut-losers-period/

zhenMay 22, 2016 at 2:31 pmHi Dr Vogel,

This is a good article, and it would be help for my paper. Can I ask you a question which me for a long time.

Do you know how many times to construct the portfolio? I read some paper, all of them just construct the portfolio one time (or do not mention the time them divide portfolios), like if they want to check the the avaliebility of fama model for stocks from 2005-2010, they just check the accounting data from 2003-2004 Dec of stocks they need, then construct portfolio just base on data from 2003-2004 Dec.

but I just confused, if base on 2003-2004, a compay is regarded as s/h, but we have 6 years time series to test fama model, it is very possible that in 2008, this company actually become a b/m company, so it should category into a b/m pofortlio.

but if we construct portfolio several or many times(like once a month or a week), the model testing would become very complicated, a lot of regression result we have, and paper cannot contain all of them.

Any idea for my question?

Zhen

Jack Vogel, PhDMay 23, 2016 at 9:42 amIn the paper above, Value portfolios (formed on fundamentals) are formed once a year on 6/30. The momentum portfolios are formed monthly.

We have two articles highlighting how portfolio construction affects momentum and value portfolios:

http://blog.alphaarchitect.com/2015/11/16/how-portfolio-construction-affects-momentum-funds/#gs.ceBML2Q

http://blog.alphaarchitect.com/2016/05/13/how-portfolio-construction-affects-value-funds/#gs.9nxDQIs

I hope that helps.