The Factor Zoo - Fama-French 1993
Eugene Fama and Kenneth French, Founders of the Fama-French Pricing Model.
As we have explored previously, the Capital Asset Pricing Model is one of the most seductive ideas in finance. Arguably, one of the most elegant ways to visualize potential returns. It states that the expected return on any stock, fund, or portfolio is just the risk-free rate plus the number beta, multiplied by the premium the whole market earns for bearing risk. In that sense, nothing else is relevant to pricing the asset - company, sector and manager data is irrelevant. With diversifying away and approaching the mathematical floor of idiosyncratic risk what remains is priced by a single sensitivity to the market. William Sharpe published this idea in 1964, Lintner independently a year later and in the end earned a Nobel Prize in 1990. For nearly two decades in finance, it wasn’t just a model for asset pricing, it was asset pricing itself.
Where the issue lies is that the model does not describe the data. Substantial cracks in CAPM appeared in the late 1970s and 1980s. In an empirical study conducted in 1977, Sanjoy Basu found that stocks with low price-to-earnings ratios earned more than their betas said they should. Four years later, Banz came to the same conclusion about small companies, and with a margin too large to be noise. Rosenberg, Reid and Lanstein showed in 1985 that book-to-market did it too. So, each of these findings could be considered an anomaly to the model - a return that beta did not explain therefore shouldn’t exist.
And in 1992, the stars of this research Kenneth French and Eugene Fama gave the explanation. When we sort the entire US stock market on beta, we find that high-beta stocks did not earn more for their holders compared to low beta stocks. So, the so important beta variable, supposed to solve the pricing of the stock market, explained almost nothing. Size and book-to-market, on the other hand, explained a great deal. And as we will see below, any characteristic that predicts returns gives us the same picture.
And the above figure illustrates the shape of the failure. We have taken nine portfolios and sorted them by size and past twelve-month return - with a time frame from 1963-2017. From there we plotted what CAPM predicted against what actually happened. If the model was correct, every dot would sit on the dashed line, and you wouldn’t be reading this now. Small sized past winners were predicted to earn 7.5%/annum over the risk-free rate, but in practice we saw a 16.1% return. Small sized past losers were predicted 8.5% above the risk-free rate, and they performed with a near zero return of 0.4%. The gap between these two portfolios is sixteen percentage points per year, and beta indicates no difference whatsoever. Both have betas above 1.2; the model thinks they are roughly the same asset.
A little note from us: Under CAPM the vertical distance from the point to the dashed line on our graph is known as alpha. From the model’s standpoint we can view this as kind of a residual return, the part of the return you paid a manager to find. But by 1992, there was clear indication that the residual return wasn’t a residual at all. It was an anomaly that was structured, persistent, and in the cases of size and value, quite large. If beta was not the price of the risk we pay to hold a stock, something else must be.
Well, instead of arguing about what the extra risks were, in 1993 Fama and French decided to simply build factors to account for them. We take every stock on the market, again. We sort each one into small and big by their market capitalization. Next, we sort them into cheap, middle and expensive considering their book-to-market. From the intersections we form six big portfolios and then we define two new factors to add to CAPM. The first factor is SMB (Small minus Big), the return on the small portfolios minus the return on the big ones. HML (High minus Low), would be the cheap portfolios minus the expensive ones. We build on CAPM by adding the market itself, and a stock’s expected return is now the risk-free rate plus three betas times three premiums.
But we raise attention to the construction more than the looks. SMB and HML are not just some obscure statistical abstractions, they are long-short portfolios that are physically holdable. That means the factor premium is a return a real investor could have earned, and it means a fund's exposure to the factor is something the fund could have bought without any skill at all. Well, shall we check if that is the case? Let’s move from a theory debate to an empirical test with data.
The legacy Fama-French Model explained the size and value anomalies by definition, since it was derived from them, and it also explained a lot around them too. The R-squared on diversified portfolios rose from the 70s under CAPM to the 90s. So this became the standard benchmark in academic finance for the next twenty years and is what most people understand when we say “Fama-French”.
More than twenty years later, in 2015 the authors also added two more factors. A study in 2013 by Robert Novy-Marx showed that profitable firms earn more than unprofitable ones at the same valuation, and a separate sidenote suggested that firms which invest aggressively tend to earn less than firms who employ a more conservative approach to investing. So, another two factors were born: RMW (Robust minus Weak) and CMA (Conservative minus Aggressive Investment). The three-factor model turned into a five factor one. And the truth is that once profitability and investment are included, the value factor gives us almost nothing in terms of information. HML, the factor that started the whole enterprise, was redundant in its own successor. Fama and French kept it anyway, partly for continuity and partly because it still helps in some samples.
And to sweeten the deal even further, there is another very popular, sixth factor that the founders of the three-factor model have never adopted, but it is very widely used. In 1993 scholars Narasimhan Jegadeesh and Sheridan Titman gave us even more valuable insight on how the infamous random walk does not really exist. Stocks which rose over the past year kept rising for a few months, and therefore Carhart bolted a factor onto the legacy Fama-French model. Named UMD for up minus down, it accounted for said momentum phenomenon. Even more intriguingly, Fama and French publish this momentum factor in their own data library, which we have used for this research, yet they have declined to include it in their model since they cannot tell the story of risk. A strategy that buys what went up is hard to describe as compensation for bearing anything and even the creators refer to it as “the premier anomaly”. And that is the whole reason why there is an error in this approach to pricing risk: a factor is supposed to be a price of risk, and the momentum factor, which is by far the most robust one in the data does not even remotely resemble risk. (For more information refer to EMH Cracks and Momentum Effect Publication on TFR)
In figure 2 we have shown what a dollar in each of the long-short factors became between July 1963 and July 2026 - on a logarithmic scale. It’s clear that momentum is the standout in our experiment: from $1 to $48. The market itself, which is not a long-short bet but simply the equity premium over cash, became $43. If we were to utilize the value factor, we get $7. By profitability we have $6, by investment $5 and size gave us the lowest outcome of $2.9. What is interesting to look at here is the shape of the line for size. As we can see it started well in the 1970s and 1980s and then it practically averaged a plateau for forty years. If we recall the original story of the model the size factor (SMB) was the first to be named, and then the first to stop giving us a premium.
Which ultimately raises the question that we are going to explore next. If a factor is a real price of risk, it should persist. If it is a pattern that people noticed, it should fade once enough of them notice.
And this is the part where the story gets messy. By 2011 John Cochrane, in his address to the American Finance Association was describing the literature for Fama-French model factors as a “factor zoo”, hence the iconic name. Every year we observe new factors like accruals, asset growth, net share issuance, idiosyncratic volatility, illiquidity, distress, tens of accounting ratios presented in different ways. Each factor presented itself with a t-statistic of above 2. A t-statistic is a measure of how far your estimate sits from what you would expect under the null hypothesis, in units of its own uncertainty. With a value of 2 being two standard errors away from the null, the conventional threshold for statistical significance. Harvey, Liu and Zhu counted 316 published factors by 2016 and made a point that should have been obvious: if hundreds of researchers test thousands of candidate variables against the same fifty years of returns, some will pass a 5% significance test by accident. The three argued that the new threshold for deeming a factor relevant should be t-statistic of 3, instead of 2, claiming that most of the “zoo” would not clear it.
Remember how crowding removes the effect of an idea. Well, McLean and Pontiff took on this practical approach and asked what happens to a published anomaly after it is public for everyone. They tested 97 of them, and the average return fell by about a quarter between the end of the original sample and the paper’s publication. Subsequently, by more than half once the paper was in full circulation. Of course, the average returns didn’t fall to an absolute zero, but in most cases whatever edge was left was simply either data mining or an inefficiency eliminated by trading.
So how do we explain the fact that most factors almost fade away when more investors are introduced. Well, two explanations are on the table, and they have different implications. The first version of the crowding on factors is a story of risk premium, publicizing the factors caused capital to crowd in until the price of bearing the risk itself fell. In that case “almost fading away” is inaccurate for the majority of them: they are alive, just cheaper, with a diminished premium. The exact response that you would expect from an efficient market absorbing new information.
The second idea is that some of these factors were never risk premiums at all. They were just irregularities in a particular fifty-year span that had no reason to recur. The investment factor, negative for over a decade, looks more like the second. Momentum, halved but still enormous, looks more like the first. Size, the founding factor, is the hard case: a premium that has been zero or negative for forty years is difficult to refer to as a price for anything.
In any case, from a practical standpoint the conclusion is the same. The factors that Eugene Fama and Kenneth French coined in the beginning are not stable constants by nature. They have a tendency to decay, cycle and the simple act of naming them changed their behavior. Which leads to the next logical question, if even the factors can be influenced, what happens to a manager’s alpha when you measure it against all of the established factors at once?
Turns out that the test we devised isn’t very difficult and we can repeat it easily. We create a regression of a fund’s monthly return over cash on the factors. The slopes we get are the fund’s exposures to the market, or as we call them the betas. The intercept itself is the alpha: the part of the return that none of the exposures explain. We run the regression a total of four times. Once with one factor, once with three, five then six. Now let’s see what happens to the intercept.
We did this test for five track records. Buffett’s Berkshire Hathaway from 1990, the longest record of any investment vehicle with a single decision-maker. From its launch in 2014 ARKK has been the most cherished active fund in the last decade and then transitioned into the most criticized. SCHD and USMV both launched in 2011 with one being a dividend strategy and the other a low-volatility holder. Both funds marketed themselves on the premise that one rule can beat the market. SPY, the S&P 500 itself, as a control that should show no alpha at all.
Ordinary least squares on monthly returns over the one-month Treasury bill rate, run four times per fund: one factor, three, five, then six. The slopes are the exposures; the intercept is alpha, annualised by multiplying by twelve. Standard errors are Newey-West with six lags.
Factors from the Kenneth R. French Data Library, July 1963 to July 2026; fund prices are dividend-adjusted monthly closes from Stooq. Figure 3 splits each factor’s history at the year its paper appeared: 1992 for size and value, 1993 for momentum, 2015 for profitability and investment. Figure 1 uses nine value-weighted portfolios sorted on size and prior twelve-month return, 1963 to 2017.
Now let’s discuss the results from our investigation. Berkshire is the case which matters the most. Through the lenses of CAPM, Buffett’s alpha since 1990 is almost 7% per annum, with a t-statistic of 2.5. Indeed, a great performance for such a long period of time, and the reason why media hails him as the greatest investor alive. If we add factors to the equation: with size and value, alpha falls to 5.1%, with profitability and investment it falls to 4.3% with a t-statistic of 1.76, below the set threshold of 2. Momentum changes nothing. The loadings tell you where the 2.6 points went: Berkshire has a market beta of only 0.72, a value loading of 0.52, a profitability loading of 0.22 and a size loading of minus 0.37, with the value tilt alone accounting for about 1.1 of those points. Basically, Buffett’s strategy is very simple: he buys large, cheap and profitable companies with less market exposure than the index. And to be fair he has been advertising his methods for sixty years now.
Roughly a third of his edge over the market is tilt, something that an investor can now acquire through exposure in an ETF. But the remaining two thirds have been unexplained. In 2018 Frazzini, Kabiller and Pedersen showed that when we add a quality factor and a betting-against-beta factor, and include Berkshire’s cheap insurance-float leverage, most of the remainder is absorbed. So, we take a stop at six factors and let’s face the facts: an alpha of 4.3% over 436 months is not statistically distinguishable from zero, while on a track record that nobody else has matched. Thus, can we say that Buffett’s firm has more information than we do, therefore he outperforms every regular investor? Well, not really. Frazzini, Kabiller and Pedersen gave us insight that Buffett’s edge is a strategy: buying cheap, safe, big firms on 1.6x insurance-float leverage and holding on during downturns.
With ARKK we see the opposite pattern to Berkshire Hathaway, under CAPM we observe an alpha of -5.4% a year, the mark of a fund that rose with the disruption trade in 2020 and fell with it in 2022. Add the same factors as with Berkshire and the alpha goes to +1.6%, with a t-statistic of 0.4. With such numbers we can comfortably claim that the edge is indistinguishable from zero. But what the regression found is a market beta of 1.52, a size loading of 0.69, a value loading of -0.8, and a profitability loading of -0.98. In essence the last number is the entire fund. Word for word ARKK did the exact opposite of Warren Buffett’s strategy, they held small, expensive, unprofitable companies, with one and a half times the market risk. Every dollar of its spectacular rise and fall is accounted for by that same description above. There was no thesis in the returns, only exposure. Anyone who wanted the ride could have had it with some leverage and a bet on small, unprofitable growth stocks.
SCHD and USMV give the same version of the story just with a quieter whisper. SCHD’s CAPM alpha is 1% a year and under our six-factor principle it turns into -0.3%. USMV’s CAPM alpha is 1.2% and with factors accounted turns into -0.8%. Both funds show meaningful loading on profitability and investment with 0.37 and 0.28 for SCHD and 0.30 with 0.21 for the latter. In other words, the dividend strategy is essentially a profitability screen with a marketing budget. A strategy that employs low portfolio volatility is a profitability and conservative-investment screen with a different marketing budget, plus a beta of 0.72 that none of the six factors gives any credit for. Neither of these two options is a bad way to own equities. But neither is what their names suggest, and the small positive alpha a naïve comparison to the S&P 500 would show is fully explained by exposures that cost a few basis points elsewhere.
If we look at SPY it is what a control should be doing. It has a negative alpha of 1.0%/year, which is not the expense ratio of 0.09% but the gap between the S&P 500 and the broader market portfolio used by French, whose mid and small caps did better over the early part of our sample (10.2% a year for SPY against 11.1% for the French market), and its R-squared is 0.99. Therefore, this method finds nothing because there is nothing to find, which by itself is a positive sign for the validity of the method.
In this figure we draw the same result but just the opposite way around. For each of the funds we chose, we take the share of monthly variation which the six factors account for, and we get the following numbers. 0.99 for SPY, 0.86 for SCHD, 0.79 for both ARKK and USMV, and 0.36 for Berkshire. The three ETFs here are four fifths factor exposure. And Berkshire is the only one of our testing subjects that the model cannot mostly explain. But Berkshire is one stock and the other four are diversified portfolios, and a single stock always carries noise of its own that no factor model will absorb. So the remaining 64% is mostly that, not alpha. Alpha is the intercept, and we have already seen what happened to it.
Which leaves the question a buyer of any of these funds should be asking. If four fifths of what these funds do can be had by holding an index ETF, what is the manager's fee paying for?
Hence, we established that four fifths of what said funds do month to month is factor exposure you can get when holding an ETF, and that once the factors are in, their alpha is roughly zero. So how do we explain what is left? The industry’s historical answer would be skill. The main characters of our story Fama and French tested this theory on the entire universe of US equity mutual funds from 1984 to 2006. What they found was that before fees, the aggregate alpha of the active funds against the three-factor model they created was roughly zero. When we apply the high industry fees, we get that the alpha was negative. Some funds did have positive alpha, but considering the population size, that would mean we could attribute their performance to luck rather than statistical significance. The result has been replicated many times with more factors and more years, and it does not move.
What we saw moving was the product itself. If a fund outperformed the market and the reason for that was really exposure, then the exposure could be sold on its own, without the manager, at a fraction of the cost. And now we arrive at the concept of smart beta. Value ETFs, quality ETFs, low-volatility ETFs, momentum ETFs are essentially all Fama-French factors, or some close relative to said factors in a different wrapper. When the industry took the academic finding that alpha was mostly beta wearing a disguise, it turned this finding into products that are now worth roughly two trillion dollars by Morningstar’s count, which sell beta openly. The fee for a factor tilt fell from a percentage point to a handful of basis points in a decade.
And there is great irony in this piece, and Section III explains it well. Selling a factor at a scale is the most efficient known way to reduce its premium. Introduce more people and the phenomenon disappears. The value premium spent the 2010s below zero while value ETFs gathered assets. The size premium has not recovered since it became a product. What happens here is that smart beta monetized the factors by making them cheaper to own, and making them cheaper to own is the same mechanism that makes them pay out less. When we come back to our zoo analogy, the zoo isn’t empty because the animals inside are fake, but because the visitors keep feeding the animals.
The consequence for paying a manager to find the extra edge is arithmetic. A fund that charges 0.7% in fees, whose factor exposure by itself costs 0.05%, is charging its customer 0.65% for whatever edge is left after the factors. That same remaining edge is, on the evidence of Section IV, indistinguishable from noise for every fund but Berkshire. And we want to make a clear point here that we do not condemn active fund managers, but the marketing behind them. The price should be set by the part of the edge that is not factor exposure.
As a result, the Fama-French model is mostly a pricing tool. It tells you what portion of any return could have been bought and at what cost. What it cannot do is buy the rest. Is there any of the rest?
Eugene Fama and Kenneth French did not close the book on beating the market. They moved the goalposts, and with every evolution of their model the goal has moved further away. With CAPM you had to beat just one beta to be skilled. In today’s world to be a successful manager you must beat at least six, and in the wider aspect of the zoo, many more. The bar that we should set for alpha is not how much it clears the market average, but that you earned more than any combination of exposures a passive investor could have assembled. And under these criteria, pretty much no manager does so.
What seems to have an edge are two things. Firstly information - a return that comes from knowing something before the market has time to react cannot be considered a factor exposure, because it simply isn’t systematic risk anyone else is bearing.
The second edge is Berkshire’s residual, and we should not overstate its effects. Buffett’s 4.3% a year over 36 years is a significant number that the six-factor model cannot really account for and is produced by a strategy its author has described for nearly six decades. But the problem here is that the strategy is very capital intensive and with the rise of outrageous AI IPOs and modern finance harder and harder to execute. Statistically, it is indistinguishable from zero, and studies that explore the topic further explain Berkshire’s success with two more factors to the model and the famous insurance-float leverage. The honest position is that the best-documented investor in history has an unexplained return that is large in economic terms and marginal in statistical ones. If that is what skill looks like after the factors are taken out, skill is rarer and quieter than the industry that sells it.
