Common Risk Factors in the Returns on Stocks and Bonds

Source: Fama, E. F. & French, K. R. (1993). Journal of Financial Economics 33(1), 3–56.

TL;DR

The paper that operationalized the three-factor model. It introduces the tradable SMB (small

minus big) and HML (high minus low book-to-market) factors alongside the market, and shows that

together they explain most of the common variation in diversified stock returns — capturing the size

and value premia that the CAPM cannot. These factors became the workhorse benchmark of empirical finance.

What it documents

Building the actual long-short factor portfolios (from 2×3 sorts on size and book-to-market) and

demonstrating, via time-series regressions, that market + SMB + HML price a wide cross-section of

stock (and, in part, bond) portfolios.

How it is constructed

SMB: average return of small-cap portfolios minus large-cap portfolios.

HML: average return of high-book-to-market (value) minus low-book-to-market (growth) portfolios.

Both from independent 2×3 size / book-to-market sorts of NYSE/AMEX/NASDAQ stocks, rebalanced annually.

Evidence

Market, SMB, and HML jointly produce high R² and small intercepts (alphas) across 25 size-BM

portfolios — the size and value effects are systematic, factor-like risks.

Why it matters

Defines HML and SMB, the factors used (and extended) by virtually all subsequent cross-sectional

research; the executable value and size strategies on this platform are built from these series.

The empirical foundation for factor investing and for measuring "alpha" beyond size and value.

Limitations and risks

Whether size/value are risk premia or mispricing is unresolved; the size effect later weakened.

The model misses momentum (added by Carhart) and profitability/investment (added in FF5).

Key references

Fama, E. & French, K. (1993) — Common Risk Factors in the Returns on Stocks and Bonds — Journal of Financial Economics

Fama, E. & French, K. (1992) — The Cross-Section of Expected Stock Returns — Journal of Finance

Carhart, M. (1997) — On Persistence in Mutual Fund Performance — Journal of Finance

Reference replication on ConvexPi

An open, verified replication of this strategy is maintained at convexpi/replications. It recomputes the strategy from underlying building blocks and scores it out of sample (the McLean & Pontiff test):

Period	Annualized Sharpe
In-sample (pre-1993)	+0.49
Out-of-sample (≥ 1993)	+0.21
Last 10 years	+0.01

Verdict: decayed. Run it on live data in Colab · view the code