Risk compensation does not come from the market as a whole alone. Long-term returns can be decomposed into compensation for a few kinds of systematic risk, and these sources of risk are called factors: market, size, value, profitability, investment and momentum. The part of a portfolio's return that seems to beat the market is often just the result of bearing the risk of these factors. A credible factor needs an economic explanation and must hold up in out-of-sample tests. Even a credible factor can underperform for more than ten years in a row, and that is precisely why it earns compensation.
Under the capital asset pricing model, a stock's expected return depends only on how much it moves with the market. Researchers soon found patterns the model could not explain. Basu found in 1977 that stocks with low price-to-earnings ratios had higher average returns; Banz found in 1981 that companies with small market capitalization had higher average returns; Rosenberg and colleagues found in 1985 that stocks with high book value relative to market value had higher average returns. Using long-run data on US stocks, Fama and French confirmed in 1992 that once market capitalization and the book-to-market ratio are controlled for, beta has almost no power to explain returns.
Average returns sorted by size and book-to-market ratio
Stocks are sorted into five groups by market capitalization (small to large) and five by book-to-market ratio (low to high), giving the average annual returns of 25 portfolios. Tap any cell for a description.
Tap any cell.
A factor is a source of risk borne in common by a group of stocks. Researchers capture it with a simple method: sort stocks by some characteristic, buy the group with the strongest characteristic and sell the group with the weakest, and the return of this "long-short portfolio" is the factor return. For example, buying the 30% of stocks with the highest book-to-market ratio and selling the lowest 30% gives the value factor; buying the group with the smallest market capitalization and selling the largest gives the size factor.
In 1993 Fama and French proposed the three-factor model: market, size and value. In 1997 Carhart added momentum, the tendency of stocks that rose most over the past year to keep outperforming. In 2015 Fama and French added two more factors, profitability and investment: companies with strong profitability, and companies that expand their investment conservatively, have higher average returns.
With factors, a portfolio's return can be taken apart: how much comes from bearing market risk, how much from bearing the risk of size, value and other factors, and only what remains is the manager's true excess return, usually called "alpha". For many funds that seem to beat the market, the excess return shrinks sharply or even disappears once a multi-factor decomposition is applied: they simply held more small-cap or value stocks.
Where does a “market-beating” fund’s return come from?
Over the past ten years a fund earned 9% a year above the risk-free rate, while the market earned 6% above it. Switch the explanation and see how much true excess return is left.
This matters directly for evaluating products: returns earned by bearing factor risk can be replicated with low-cost factor products; only the part that remains after the factors are removed is worth paying active management fees for.
There are two explanations for factor returns. Fama and French lean towards a risk explanation: value stocks are often companies in operating difficulty that are more likely to deteriorate further when the economy is bad, so investors demand a higher return to hold them. In 1994 Lakonishok, Shleifer and Vishny proposed a behavioural explanation: investors extrapolate companies' past performance too far, becoming too pessimistic about companies with dim prospects and too optimistic about popular companies, so value stocks end up undervalued.
Why value stocks earn more: two explanations
The two explanations rest on different mechanisms and have different implications. Tap a question to see how each explanation answers it.
Value stocks are often companies in operating difficulty that are more likely to deteriorate further when the economy is bad. Holding them means bearing the risk of “doing worse in bad times”, so investors demand a higher return.
Proponents: Fama and FrenchInvestors extrapolate past performance too far: they are too pessimistic about companies with dim prospects and too optimistic about popular ones, so value stocks are undervalued and growth stocks overvalued.
Proponents: Lakonishok, Shleifer and Vishny (1994)The two explanations have different implications. If it is risk compensation, it will persist over the long run, at the cost of losses in bad times; if it is mispricing, it may weaken once it becomes widely known. In practice both components may be present at the same time.
Academics have reported hundreds of "factors". In 2011 Cochrane called this situation the "factor zoo". In 2016 Harvey, Liu and Zhu counted 316 published factors and pointed out that with so many attempts, some will appear significant by luck alone; they proposed raising the bar for statistical tests from the usual t-statistic of 2 to at least 3.
Test enough factors and some will look “significant” by luck
Suppose researchers test 300 candidate factors, of which only 10 are real and the other 290 do nothing. Adjust the test threshold and see how many of those that pass are real.
Beyond the statistical bar, a credible factor needs two more conditions: a clear economic explanation, and continued validity in periods and markets outside the original study.
Even factors that pass the tests do not deliver positive returns every year. Under Fama and French's definition, the value factor lagged growth for a long stretch from 2007, and by mid-2020 its cumulative drawdown was about 55% (Arnott et al., 2021); many people concluded that value investing no longer worked. From the standpoint of risk compensation, this is exactly why the compensation exists: if bearing factor risk produced a steady profit every year, it would no longer be risk, and competition would erode the compensation.
A compensated factor can still lag for years on end
Suppose a factor earns an average compensation of 3% a year over the long run, with annual volatility of 12%. Choose a holding period to see the probability that the cumulative return over that period is negative; below are three possible 40-year paths.
Factors break the question "where does the return come from" out of a vague "good stock picking" into a few sources that can be identified and priced.
Tell users how much of the return comes from market, size, value and other factors, and how much is true excess return.
Only the part that remains after the factors are removed is worth paying active management fees for.
New factors produced by AI or backtests need an economic explanation, a higher statistical threshold and out-of-sample tests.
Show users the longest historical period of underperformance before they buy, so they are not forced to give up during a slump.