In the Fama-French 3-factor model the portfolio returns are explained by

  • the market
  • the SMB factor (Small [market capitalization] Minus Big) and
  • the HML factor (High [book-to-market ratio] Minus Low) thus "value" minus "growth" stocks.

I know that the factor world has grown by much more factors but for some reason Fama and French have started with these

What is the intuition to use exactly those factors? Which behaviour do we usually expect from these factor? Doesn't small often go hand in hand with growth - would this mean that SMB and HML are (sometimes) negatively correlated?

In (some) booming markets (dot.com bubble) we can expect small companies to outperform large ones - thus SMB should perform positive. In difficult markets companies with a sound basis (high book to market - value) could outperform those with rather high price compared to its book assets (growth) then HML could outperform.

Do these thoughts make sense?

EDIT: 1) Note that factor-investing where portfolios are invested trying to track the factors became popular in recent years. 2) What about the FF-model is true after 2008?


5 Answers 5


It is just partial answer to your question.

The Fama and French three factor model can be written as: $$R_{it}=\beta_{im}R_{Mt}+ \beta_{iSMB}SMB_t+\beta_{iHML}HML_t + e_{it}$$ In this model the market index is supposed to capture systematic risk originating from macroeconomic factors. Whereas, SMB and HML are firm specific variables and are chosen because of empirical findings that firm size and book to market ratio predict deviations of average stock returns from levels predicted by CAPM.

Fama and French justified their model on empirical grounds. FF found historical-average returns on stocks of small firms and on stocks with high ratios of book equity to market equity (B/M) are higher than predicted by the security market line of the CAPM. The reason pointed out by FF that firms with high ratios of book-to-market value are more likely to be in financial distress and small stocks may be more sensitive to changes in business conditions and thus provide higher historical-average return than predicted by CAPM.

Beside this you can read paper of Goyal(2012) where author compare the performance of CAPM from FF model. Goyal found clear improvement of FF model over CAPM.


Your intuition is not exactly right. To start with often the facts that small minus big or high minus low explain the cross-section of returns is called a puzzle. It is called a puzzle precisely because there is no unifying explanation for them.

It is fairly agreed among academics that the Size effect is most likely a January effect, or probably it even disappeared. On the other hand there have been several explanations for the HML: most of them rely on supply side frictions. An example is Lettau and Wachter (2007) and another example is Zhang (2005).

Edit after comment below: if you are looking for factor investment strategies, there are better factors to use such as the one on Adrian, Etula, and Muir (2014), among many others. Take a look at figure 1 of their paper and Table III (where you can also check that the size factor is insignificant).

  • $\begingroup$ Right, I understand ... I don't believe in CAPM .. I wonder whether I should believe in FF ... could you please amplify a bit more as you claim that SMB does not exist anymore (I wonder whether this is "true") .. and you cite papers pre 2008 - could you reference to something more recent (with a link)? I know I ask for a lot but as factor investing became popular I wonder about the factors ... $\endgroup$
    – Richi Wa
    Feb 12, 2016 at 9:19
  • $\begingroup$ There are better factors... I have edited my answer above. $\endgroup$
    – phdstudent
    Feb 12, 2016 at 9:34
  • $\begingroup$ I will read the paper, Figure 1 looks interesting indeed .. $\endgroup$
    – Richi Wa
    Feb 12, 2016 at 12:35
  • $\begingroup$ @phdstudent very interesting paper. $\endgroup$ Jan 30, 2018 at 18:04
  • $\begingroup$ I realize this is pretty old now, but I fail to see what's interesting in the Adrian, et al. paper. Their LMP factor is just a full-sample linear combination of FF and Momentum that does worse than the MVO solution. $\endgroup$ Feb 2, 2018 at 2:10

Evans and Schmitz (2015) might give an answer to your question if the Fama-French factors are indeed working or not.

Value, size and momentum have a long history as stock price predictors, and similar indicators have been applied to stock indices in order to predict the performance of one national index against another. Published back tests of trading systems based on these ideas have shown impressive performance, but in this paper we find that this performance does not continue past the publication dates.

We argue that selection bias at the time of publication has a part to play in the disappointing out‐of‐sample performance of these indicators. We show how the combination of estimation uncertainty and selective reporting can readily explain the observed deterioration in performance. Importantly, with a fuller understanding of these effects, the long‐term poor performance of the indicators could have been anticipated at the time.



Fama-French's factor selection for the 3 and 5 factor models is premised on the idea that systemic returns above or below a benchmark are due only to the assumption of risk (i.e., investors who overweight risky (e.g., under-regarded and out of favor) securities only do so in anticipation of greater rewards).

The history of this core intuition dates back to Modigliani Miller (I or II) in which the authors proposed a) leverage does not change the value of a firm (or its expected returns on capital), and b) excess returns could be explained by a beta coefficient which represented risk. The CAPM then proposed that this beta could be directly observed from market returns and covariances. FF then retorted with the FF 3 factor model (1992) to demonstrate that such a simple explanation for risk misrepresented the core beliefs about market efficiency.

Under the Chicago School, market efficiency is not a belief that market prices are right, but rather than it is exceedingly difficult to determine if they are wrong. In an Chicagoan efficient market, in which investors allocate capital according to their beliefs and tolerance for risk, beliefs are still fallible. Therefore, I don't actually think FF intended their factor models for use in tactical asset allocation or to explain all variation in returns, but rather to demonstrate the shortcomings of CAPM.

As such, it is important to note there is no such thing as "cheap" in the FF universe. For example, the B/M factor (HML) is not meant to convey "cheapness", but rather investors' expectations regarding a firm's future ability to pay investors. This intuition, in turn, comes from the dividend discount model (DDM) in which the net present value is defined by the discounted future cash flows which investors receive from holding a particular security or basket of securities.

FF (2015) elaborate:

There is much evidence that average stock returns are related to the book-to-market equity ratio, B/M. There is also evidence that profitability and investment add to the description of average returns provided by B/M. The logic for why these variables are related to average returns can be explained via the dividend discount model. The model says that the market value of a share of stock is the present value of expected dividends per share,

(1) $$ m_t = \sum_{\tau=1}^{\infty} E \left(d_{t+1} \right)\frac{1}{1+r^\tau} $$

In this equation $m_t$ is the share price at time $t$, $E(dt+τ)$ is the expected dividend per share in period $t+τ$, and $r$ is (approximately) the long-term average expected stock return or, more precisely, the internal rate of return on expected dividends.

Therefore, firms with relative low book values relative to market values imply a) high future earnings and/or, b) low risk. Likewise, firm with relatively high book values relative to market values imply a) low future earnings, and/or b) high risk.

The profitability factor (i.e., operating return on equity) is related to the DDM. Incorporating a proxy measure for net present value which is distinct from book value helps to differentiate between marginal and robust firms. On first appearance, the profitability does not fit FF's theme on risk. However, it can be seen as a proxy for book value's sensitivity to risk.

Likewise, the intuitions for the selecting size (SMB) and investment (i.e., asset growth) factors relate back to risk. With size, it is generally regarded that smaller business are riskier than large ones. With investment, firms which invest are generally as safe, while firms which underinvest are generally regarded as risky.

Notably, momentum does not fit into the broader framework. Although, FF continue to track portfolios constructed by sorts of prior returns, momentum is not formally considered as evidence for or against the EMH. Rather, it is an anomaly which might be better explained by the behavioral economists. Mean reversion, on the other hand, is not as problematic since it is presumably caused by timing issues in supply/demand and is expensive to trade.


I can't tell your intuition is right or wrong, but i can give you a partial answer to your question: What is the intuition to use exactly those factors?

In fact, Fama-French Three-Factor Model is just one kind of The Principal Component Analysis(PCA). In PCA analysis, you can choose any explaining variables, say 10 or 50 variables of regression. Each of the selected variables may explain the dependent variable well or not. Next, you choose Principal component among the variables which explain best(which has the largest variance). Selecting Top 3 PCs is known to be sufficient.

It depends on the data that Which of the variables are best. But Fama French Model is well known because this model's 3 Principal factors-market return, SMB and HML- have been found significant for many statistical research.

  • $\begingroup$ Sorry, but PCAs are independent or at least uncorrelated .. Fama-French fractors are not uncorrelated ... this is just wrong ... $\endgroup$
    – Richi Wa
    Feb 16, 2016 at 13:09
  • $\begingroup$ Sorry for the -1 ... wanted to correct it to 0 which is impossible ... $\endgroup$
    – Richi Wa
    Feb 16, 2016 at 13:20
  • $\begingroup$ @Seung-hoonHan Good attempt but FF factor model is nothing to do with PCA. Variables in FF models are very specific and you do not need to run PCA to find factor in FF model. $\endgroup$
    – Neeraj
    Feb 16, 2016 at 14:53
  • $\begingroup$ Thanks for your comments. i misunderstood the difference between two modes. I admit that my guess is absolutely wrong. $\endgroup$
    – hansh
    Feb 18, 2016 at 9:32

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