Three Wasn't Enough: the Fama-French Five-Factor Model

There is a special kind of scientific honesty in updating your own famous model. In 1993, Eugene Fama and Kenneth French published the three-factor model, market, size and value, and it became the standard yardstick of academic finance for two decades. Then in 2015, the same two authors published a paper that essentially said: our own model has a hole in it, and here is the patch.

The result was the five-factor model, which keeps the original three ingredients and adds two more: profitability and investment. It is one of the most-used models in finance today, and the story of why they added those two factors tells you a lot about how asset pricing actually works.

The problem: the three-factor model kept leaving residue

A good asset pricing model should soak up all the predictable patterns in returns. If your model is complete, then after you account for a stock's exposure to your factors, nothing else about the company should systematically predict how it does. Any leftover, any "alpha," should be noise.

By the late 2000s, researchers had found that the three-factor model was leaving a lot of non-noise residue behind. Two patterns kept showing up in the leftovers:

• Highly profitable companies beat unprofitable ones, even after adjusting for market, size and value. Robert Novy-Marx had made this case forcefully in 2013.
• Companies that grow their asset base aggressively underperform companies that grow slowly or not at all. Firms on an expansion spree, buying, building, issuing shares, tended to disappoint.

Neither pattern was explained by the three factors. That is a model failing at its job.

The key idea via analogy: reading the company's plumbing, not just its price tag

The original three-factor model looked mostly at the price of a company relative to its book value. It asked "is this stock cheap?" but not much else.

Think of buying a rental property. Price-to-book is like asking "am I paying below the assessed value of the building?" That is useful. But you would obviously also want to ask two more questions: how much rent does it actually bring in (profitability), and is the owner constantly pouring cash into renovations and extensions (investment). Two buildings with the same price tag can look very different once you know their rent roll and their capital spending.

That is essentially what Fama and French added:

1. Market, the original CAPM idea, how much a stock rides the overall market.
2. Size, the small-company premium.
3. Value, the cheap-versus-expensive premium.
4. Profitability, the extra return from owning companies with strong operating earnings relative to their book value, rather than weak ones. They build it the usual way, an imaginary portfolio that buys robust-earnings companies and shorts weak-earnings ones. The nickname is RMW, "robust minus weak."
5. Investment, the extra return from owning companies that grow their assets slowly rather than aggressively. Buy the conservative growers, short the aggressive ones. The nickname is CMA, "conservative minus aggressive."

Why should these two work? Fama and French appeal to a simple valuation identity. If you hold a company's price and its book value fixed, then a company expected to earn more profit must be being discounted at a higher rate, which means investors expect a higher return from it. And a company expected to plough more of that profit back into the business (rather than paying it out) must, holding everything else the same, be being discounted at a lower rate. So profitability should predict higher returns and heavy investment should predict lower returns. It is not a behavioral story: it falls out of the arithmetic of what a price means.

Why it mattered

• It became the new default benchmark. Just as the three-factor model raised the bar for proving skill in 1993, the five-factor model raised it again. A fund manager who was quietly loading up on profitable, capital-disciplined companies had, after 2015, a harder time calling that alpha.
• It absorbed the "quality" idea into the mainstream. Profitability and conservative investment are close cousins of what practitioners had long called quality investing. The paper gave the idea an academic seal.
• It made a provocative claim about value. In their tests, once you add profitability and investment, the value factor became largely redundant in explaining average US returns. That is a striking thing for the co-inventors of the value factor to report, and it kicked off a long argument about whether value is a real independent premium or a noisy blend of the other factors.
• It sharpened a rivalry. Hou, Xue and Zhang had proposed a very similar four-factor "q-factor" model built on profitability and investment. The two camps have argued ever since about who got there first and whose version fits better, which has been genuinely productive for the field.

The honest limitations

• It still can't explain everything. Fama and French are candid that the five-factor model fails on certain groups of stocks, particularly small companies whose returns look like those of firms that invest heavily despite being unprofitable. That is a real, acknowledged hole.
• It drops momentum. The single most stubborn anomaly in finance, momentum, is simply not in the model. Fama and French have never been comfortable including it, but leaving it out means the model provably fails to price momentum-sorted portfolios.
• The factors overlap. Profitability, investment and value are all built from the same accounting statements and are correlated with each other. Untangling which one is "really" doing the work is hard, and different construction choices give noticeably different answers.
• More factors is not automatically more truth. Every extra factor gives a model more freedom to fit historical data. The five-factor model fits better than three, but part of that is simply because five knobs bend more than three. This is exactly the worry that motivates the multiple-testing critiques of the factor literature.

The one-line takeaway

Fama and French updated their own famous model to admit that two things they had left out, how profitable a company is and how aggressively it grows its asset base, systematically predict returns, and in doing so they made quality-style investing part of the academic canon.