How to use the Fama French Model

/How to use the Fama French Model

How to use the Fama French Model

The CAPM is prolific, but doesn’t appear to work! (Note: see here for our epic post on the history of factor investing.)

For example, in the figures below I’ve plotted the Fama-French 25 (portfolios ranked on size and book-to-market) against beta.

In the first figure, I plot the average excess return to the FF 25 against the average excess return one would expect, given beta.

ff 25 plotted

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

Sure doesn’t look like the CAPM does a very good job: empirically observed excess returns have no visible relationship to their CAPM predicted excess returns.

Next, I plot the actual excess returns and CAPM expected excess returns against estimated betas for the FF 25:

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

Again, the CAPM doesn’t do a good job of explaining returns. Moreover, a closer inspection indicates that the small-value and the small-growth portfolios are really out of wack.

If you’d like to see how I calculated the charts above, please reference the excel file here.

Given such a poor track record, is anyone still using the CAPM?

Lot’s of people, apparently…

Welch (2008) finds that ~75% of professors recommend the use of the model when estimating the cost of capital, and Graham and Harvey (2001) find that ~74% of CFOs use the CAPM in their work.

A few quotes from Graham and Harvey 2001 sum up common sentiment regarding the CAPM:

“While the CAPM is popular, we show later that it is not clear that the model is applied properly in practice. Of course, even if it is applied properly, it is not clear that the CAPM is a very good model [see Fama and French (1992)].

“…practitioners might not apply the CAPM or NPV rule correctly. It is also interesting that CFOs pay very little attentionto risk factors based on momentum and book-to-market-value.”

Of course, there are lots of arguments to consider before throwing out the CAPM. Here are a few:

  • Everyone learns about it and knows how to use it (although, Graham and Harvey suggest that many practitioners don’t even apply the CAPM theory correctly)
  • Data is easy to obtain on betas.
  • Roll’s critique–maybe the CAPM isn’t a junk theory, rather, the empirical tests showing the CAPM doesn’t work are bogus.

Regardless, being that this blog is dedicated to empirical data and evidence, and not about ‘mentally masturbating about theoretical finance models,’ we’ll operate under the assumption that the CAPM is dead until new data comes available.

The Fama French 3-Factor Alternative?

Given the CAPM doesn’t work that well in practice, perhaps we should look into the Fama French model (which isn’t perfect or cutting edge, but a solid workhorse nonetheless). And while the FF model inputs are highly controversial, one thing is clear: the FF 3-factor model does a great job explaining the variability of returns. For example, according to Fama French 1993, the 3-factor model explains over 90% of the variability in returns, whereas the CAPM can only explain ~70%!

The 3-factor model is great, but how the heck does one estimate the FF factors?

Dartmouth Professor Ken French comes in for the rescue!

Prof. Ken French houses one of the richest data resources on the web–I like to call it “MSCI Barra for broke people.”

Here’s the link:

Prof. French provides all the data you’ll ever need.

The Fama and French 3-factor Model

First, here are the links to the 3-factor model source documents if you enjoy reading archaic academic finance journals: Fama French 1992 and Fama French 1993.

I also recommend reading the CAPM chapter from Ivo Welch’s finance book to “freshen up” on your quantitative factor model knowledge (admit it, upon graduation from your MBA program you threw all that knowledge out the window!)

In words, the Fama French model claims that all market returns can roughly be explained by three factors: 1) exposure to the broad market (mkt-rf), 2) exposure to value stocks (HML), and 3) exposure to small stocks (SMB).

For a full recap of exactly how the factors are created, here is a link.

How to use the Fama and French 3-factor model

I went ahead and built a simple spreadsheet model so blog readers can calculate some alphas and betas associated with the 3-factor model and get some ‘hands-on’ experience.

A link to a spreadsheet and more details is here.

I have posted data from French’s website into the excel document. Returns are from 1950–2010. The user can enter in data for their favorite index/mutual fund into column “I” and see how the returns stack up against the CAPM and the FF model.

For fun, I went ahead and plugged in the equal-weight CRSP universe (consists of all NYSE/AMEX/NASDAQ stocks–imagine Wilshire 5000). And here are the results:

The results are hypothetical results and are NOT an indicator of future results and do NOT represent returns that any investor actually attained. Indexes are unmanaged, do not reflect management or trading fees, and one cannot invest directly in an index. Additional information regarding the construction of these results is available upon request.

According to the CAPM, the EW CRSP index has alpha of roughly 2.5%/year. However, when the FF model is used, the alpha drops to a mere 25bp a year, or essentially zero.

This brief analysis of the equal-weight CRSP index is a prime example of why the FF model is better than the CAPM–the FF model can actually tell you what is driving the returns (you’ll notice the .84 SMB estimate associated with the EW CRSP index). And knowing what drives returns is important: We’ve all heard the tales of magical performance from the 1.5% and 20% “mini-Warren-Buffett-crowd”  who run small value funds and continuously pound the table that they “beat the market.” Before FF, an allocator might look at these small-cap managers and think, “Wow, this manager has some secret sauce at their disposal and deserves a 1.5% management fee and 20% performance allocation.” Now, an allocator can use the FF model and quickly determine that the manager has little “alpha,”  and can switch their allocation into a vanguard small-cap index fund that charges 25bp.

If you’re curious, go ahead and drag and drop returns of your favorite ‘active manager’ into the spreadsheet. In many cases, the CAPM will show that they have alpha, but when you examine their returns using the FF model you will quickly see that they don’t have “alpha,” merely an ability to invest in small caps and/or value stocks. Luckily, gaining exposure to small caps and/or value stocks is very cheap these days.

“Alpha” versus genuine “Value-add”

There is a great controversy over whether or not small stocks and value stocks are actually ‘riskier’ than other stocks in the universe. The arguments fall on two sides of the fence:

  • size and value represent “risk,” and therefore SHOULD earn higher average excess returns.
  • size and value represent “alpha,” and therefore provide investors with an opportunity to earn outsized risk adjusted returns.

The evidence, seems to suggest that value stocks in particular, are actually a better deal than growth stocks. But regardless, getting back to the point mentioned earlier, be it risk or alpha, the empirical evidence is still the same: the FF model EXPLAINS returns.

Why does explaining returns matter?

In the grand scheme of things, the “alpha” vs “risk” argument is irrelevant for performance benchmarking because there are firms in the marketplace (e.g., DFA, Vanguard, ETFs, etc.) that give investors access to small-caps and value stocks at extremely low costs.

The key lesson is that one shouldn’t be asking whether or not their active manager can outperform the market, rather, they should be asking, given my active manager’s exposures to the market, size, and value, can he beat alternative products in the marketplace that charge ‘index’ fees and not ‘active’ fees.

Have fun.

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About the Author:

Wes Gray
After serving as a Captain in the United States Marine Corps, Dr. Gray earned a PhD, and worked as a finance professor at Drexel University. Dr. Gray’s interest in bridging the research gap between academia and industry led him to found Alpha Architect, an asset management that delivers affordable active exposures for tax-sensitive investors. Dr. Gray has published four books and a number of academic articles. Wes is a regular contributor to multiple industry outlets, to include the following: Wall Street Journal, Forbes,, and the CFA Institute. Dr. Gray earned an MBA and a PhD in finance from the University of Chicago and graduated magna cum laude with a BS from The Wharton School of the University of Pennsylvania.
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  • Will

    I would be interested in your thoughts on the following question.

    The CAPM and the FF Model are positive models of stock prices; i.e. they purport to predict the price of an individual stock today. Why wouldn’t the most appropriate and direct test of the models be to actually input the relevant parameters (Rf, Rm, Betas and expected cashflows) and estimate the price of a stock today, and then compare that to actual observed price of the individual stock?

    In averaging over long periods ex post they are open to accusation of curve fitting? And in doing so don’t they lose the information that is most interesting to someone who tries to employ the model for capital budgeting/investment decisions: how good is the model at the level of the individual transaction, where I need to apply it? (Although I also wonder its possible to reconcile the change of the models from positive to normative in this respect?)

  • Geoff Willis

    The Fama & French models work because they are measuring the liquidity of the markets. Both size and book to market ratios are surrogates for liquidity. See the liquidity section of the paper below for a discussion:

  • wes

    Liquidity is definitely another factor to consider when analyzing performance. It is easy to “outperform” the market when you are loaded up on illiquid stocks. The real question is whether or not there are ‘index-like’ alternatives out there which allow an investor to get exposure to illiquid stocks on the cheap. If there are low-cost alternatives, it makes sense to take a hard look at managers who take on liquidity risk, if there are no low-cost alternatives and the “alpha” from illiquid stocks is high enough, then paying a manager to journey into the illiquid unknown might make sense.

  • wes

    Hi Will,

    There is always a worry that these models are purely data-mining exercises and will not work out of sample. I think there is also a focus on trying to limit the number of pricing factors to 3 or 4, in order to avoid ‘curve-fitting’. In general, when asset pricing models are proposed, the academic community spends a lot of time analyzing the data and the statistics associated with the results. In the case of the FF model, the possibility of the observations fitting as well as they did, are very low, hence the reason people think there is some ‘bite’ to the model. That said, nobody can be 100% sure that a model will actually work in the future, just because it has worked in the past. A more elegant 3 factor model that might appeal to your intuition is the Chen Zhang Marx Model . check it out. If you think you have a model that works better than these 3-factor beauties, go for it!

    Regarding the use of the model in the context of capital budgeting: you can certainly use the model to estimate the stock price/project today. Fill out your DCF model, but when you get to the section where you need to input a cost of capital, instead of inputting RF+marketbeta*(broad market return-RF), input RF+marketbeta*(broad market average return-RF)+SMBbeta*(SMB average return)+HMLbeta*(HML average return). Of course, who the heck can estimate a beta for SMB and HML on a project if there is no data on the matter? Well, nobody, but that isn’t the point. Perhaps you recognize that the project has risk associated with being small (SMB) and/or capital intensive (HML), so maybe you add 3-5% to the overall cost of capital. A lot of practitioners already do this sort of analysis without the use of a formal model–add a few points for ‘size discount’, for example.

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  • Sorry, this complete BS. Stock prices are not normally distributed, as Mandelbrot showed. They form a stable Paretian distribution with characteristic exponent less than 2, which is to say they exhibit fat tails. Least-squares regression does not work on this non-normal distribution. Beta is crap. Alpha is crap. You can use bad math to write academic papers and win a Nobel Prize, but if you try to use it to run money, you will suffer the fat-tail fate of Long Term Capital Management.

  • wes

    Everything you mentioned is true, however, there are other asset pricing models that account for skewness, kurtosis, ‘extreme’ moves, ‘option-like payoffs’, etc…some work, some don’t.
    Nonetheless, there is still no denying the empirical fact that the easy to use, ‘out-of-the-box’ 3 factor model does a great job explaining the cross section of returns.

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  • George

    Wes, do we know if the FF 3-factor model also explains stock returns in international markets?

  • wes

    Hey George,
    Fama and French (and Davis?) have done this analysis–I haven’t reviewed that literature in quite a while, but it is definitely out there. In general, the answer is “Yes.” I think Japan might be an anomaly.

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  • Mindaugas

    Hi Wes,

    Just wanted to thank you a lot for the explanation and the excel spreadsheet! It helped me understand the FF model quicker and apply it in my thesis! Really appreciate!

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