Factor investing: understanding the Fama-French factors

In depth10 min read · updated 19 September 2026 · 20 sources

The Fama-French factors explain why equity portfolios perform differently: not only because of the overall market, but because they are invested to a greater or lesser extent in small, cheap, profitable or conservatively investing companies. Eugene Fama and Kenneth French presented the three-factor model in 1993 and extended it to five factors in 2015. A factor regression shows you which of these characteristics a fund contains and whether any genuine skill remains once the factors are stripped out.

The factors at a glance

Every factor apart from the market is a long-short portfolio: the return on SMB is the return on small stocks minus the return on large ones. A positive factor premium means that the characteristic has paid off historically: on average over many years, not in every year. Because the long side and the short side are the same size, such a portfolio requires no capital in arithmetic terms; its “return” is the premium itself.

How SMB and HML are constructed

Every year at the end of June, Fama and French sort all US stocks twice: by size (the breakpoint is the median NYSE market capitalisation) and by the ratio of book value to market value (breakpoints at the 30th and 70th NYSE percentiles). The intersections produce six value-weighted portfolios. SMB is the average of the three small portfolios minus the average of the three big ones, and HML is the average of the two cheap portfolios (value) minus the two expensive ones (growth). In this way, each factor measures one characteristic while the other is largely balanced out. Profitability and investment are constructed along the same lines in the five-factor model.

Carhart (1997) introduced the momentum factor into fund research. It goes back to Jegadeesh and Titman (1993): stocks that had done well over the past 3 to 12 months performed better in the following months than the losers of the same period.

Factor regression: which factors are in the fund?

The estimated coefficients are called factor loadings. A loading of 0.3 on SMB means that the fund behaves as if, in addition to the market, it had invested 30% in a long-short “small minus big” portfolio. A negative HML loading indicates a growth style, a positive one a value style. R² indicates what share of the fluctuations the factors explain. For broad equity funds, it is usually well above 0.9.

Alpha from monthly data is scaled up to a year. A monthly alpha of 0.15% gives (1 + 0.0015)¹² − 1 = 1.81% a year. Whether this is more than chance is shown by the t-statistic: with a standard error of 0.10% a month, t = 0.15 / 0.10 = 1.5. That is too little to speak of genuine skill.

How reliable are factor premiums?

Factor premiums are small relative to their volatility. That is why very long time series are needed to distinguish them from zero. The t-statistic of a premium is its mean divided by its standard error, i.e. by the monthly volatility divided by the square root of the number of months.

For the US, the factor data go back to July 1926. Our own analysis up to August 2026 gives an average excess return of around 8.4% a year for the market (t-statistic 4.6), around 4.2% for value (HML) (t-statistic 3.4) and around 2.0% a year for size (SMB), with a t-statistic of only 1.8. For the other regions, the data only start in 1990. That is too short for reliable statements about individual premiums.

What the research shows

Factor research begins with the critique of the CAPM. Sharpe (1964) had shown that, in equilibrium, only market risk should be rewarded. Banz (1981), by contrast, found that small companies delivered higher returns than their beta would suggest. Fama and French (1992) summarised the findings and reached a sobering conclusion for the CAPM:

Size and the book-to-market ratio, on the other hand, explained the differences between stocks well. From this, Fama and French (1993) built the three-factor model, which also includes term and default factors for bonds. Fama and French (2015) added profitability and investment behaviour to create the five-factor model. In parallel, Novy-Marx (2013) showed that profitable companies do about as well as cheap ones: the “other side” of value. Asness et al. (2019) combine profitability, growth and safety into quality and find a premium in the US and 24 other countries; Hou et al. (2015) derive a similar model from investment theory.

Beyond equities, Asness et al. (2013) found value and momentum premiums in eight markets and asset classes, from equity indices through bonds and currencies to commodities. The two premiums are negatively correlated with each other, which makes them particularly interesting as a pair. Fama and French (2012) examined size, value and momentum in North America, Europe, Japan and Asia Pacific.

Risk or mispricing?

Why factor premiums exist is disputed. The risk explanation says that small and cheap companies are more vulnerable in bad times, so investors demand compensation. This fits the arbitrage pricing theory of Ross (1976) with several risk factors. The behavioural explanation says that investors extrapolate too much and overpay for glamorous growth stocks. For momentum, Daniel and Moskowitz (2016) show that the strategy crashes abruptly in panic phases after market slumps, when the market recovers; managing it by expected return and variance roughly doubled alpha and Sharpe ratio in their data.

For advanced readers: the factor zoo and statistics

Since 1993, hundreds of further “factors” have been published. In his presidential address, Cochrane (2011) spoke of a zoo of new factors. Harvey et al. (2016) show that with so many tests, a t-statistic of 2 is no longer enough; a new factor should reach a t-statistic above 3.0. McLean and Pontiff (2016) examined 97 published return predictors: outside the original sample they delivered 26% less return, and after publication 58% less.

• Time-series or cross-sectional regression: a fund's factor regression is a time-series regression. To test whether a characteristic is priced across many stocks, research uses monthly cross-sectional regressions following Fama and MacBeth (1973).
• Autocorrelated residuals: if periods overlap or the residuals are autocorrelated, ordinary standard errors underestimate the uncertainty; Newey and West (1987) provide robust standard errors.
• Correlated factors: HML, RMW and CMA are related. If you put all of them into one regression, the loadings are redistributed and become less certain. The sum of the factor contributions, however, remains stable.
• Luck or skill: Fama and French (2010) compare the alphas of active US funds with simulated alphas without skill: after costs, only a few funds produce enough excess return to cover their costs.

What you learn from this in practice

• Is an active fund really better? If the alpha disappears as soon as size and value are in the regression, a cheap factor ETF would have delivered the same. This is exactly how Carhart (1997) explained the apparent persistence of successful funds.
• What is in your own portfolio? A world portfolio with a small-cap ETF has a positive SMB loading; a technology ETF usually has a negative HML loading (growth).
• Targeted composition: factor exposures can be replicated with ETFs, with the smallest possible tracking error. Style analysis provides the right mix of indices for this.
• Setting expectations: a factor loading is not a promise of returns. If you buy a value fund, you have to be able to endure long dry spells.

Limitations and common mistakes

Factor premiums fluctuate strongly and can fail to appear for a long time. In the US, value (HML) lost around 56% cumulatively against growth from the beginning of 2007 to the end of 2020. That was fourteen years in which a value investor had every reason to doubt their strategy. In the US, size has delivered only around 0.3% a year on average since 1981. On top of that, there are practical limits:

• Not directly investable: the short side of the factors requires short selling; long-only factor ETFs capture only part of the premium, and there are costs on top.
• Currency: the factor data are calculated in US dollars. A regression with euro returns mixes factor and currency effects.
• Short periods: with 36 months, loadings and alpha are very uncertain; the t-statistic shows how uncertain.
• Data snooping: the more factors and periods you try out, the more likely you are to find a combination that looks good by chance (see backtest overfitting).

How Portfolio Lab calculates it

Under Factors, Portfolio Lab estimates the regression by ordinary least squares with an intercept: the fund's monthly return minus the risk-free rate against the factors. You can choose three- and five-factor models for the US, North America, Europe, Japan, Asia Pacific ex Japan, developed markets with and without the US, and a five-factor model for emerging markets, optionally with momentum and two bond factors (term: long government bonds minus money market; credit: long corporate bonds minus long government bonds). Because the factors are in US dollars, the page calculates all returns in US dollars. It reports loadings, t- and p-values (ordinary standard errors), R², alpha as (1 + α)¹² − 1 per year, a rolling regression over 36 months and an exact decomposition of the average return into interest, factor contributions and alpha. The factor methodology also describes factor allocation, replication and factor statistics.

This article explains a method; it is not investment or tax advice. Worked examples are simplified and rounded. All terms in the glossary.