Model explainer — theory, significance, and formulas.

A model that decomposes "where stock returns come from" into three drivers: the broad market + the small-firm effect + the value effect. Since its 1993 publication it has become the de facto standard in asset-pricing research, and Eugene Fama received the 2013 Nobel Memorial Prize in Economics.

The previous standard, the Capital Asset Pricing Model (CAPM), held that "all return is explained by market risk (β)." In reality, however, even at the same market beta — meaning the same CAPM-implied market risk — small companies tended to outperform large ones, and undervalued value stocks tended to outperform expensive growth stocks. CAPM could not explain this gap.

Fama and French argued that this was not because the market was inefficient, but because those names carry additional, distinct risks beyond market risk. They expanded the notion of "risk" from one dimension (market) to three (market, size, value), which was a paradigm shift in asset-pricing theory.

The most easily misread part — saying a beta is "positive" does NOT mean "my portfolio is made of those kinds of stocks." It means "my portfolio's returns moved together with that factor's returns." A positive β_S does not imply your portfolio contains lots of small-caps — it means "during periods when small-caps did well, my portfolio also rose, and during weak periods it fell with them." Even an SPY-only portfolio can show a positive β_S if its returns happened to co-move with small-caps over the window.

Each of the three factors is defined as follows — read them all in terms of "return exposure".

• MKT (Market factor) — the equity market's return in excess of the risk-free rate. β_M tells you "on average, how many percent does my portfolio move when the market moves 1%?" 1.0 means lockstep with the market; 1.5 means a 1.5× amplification; 0.5 means you only capture half of market moves.
• SMB (Small Minus Big · size factor) — the average return of small-caps minus the average return of large-caps. A positive β_S means your portfolio tends to rise during small-cap leadership. It does not mean you actually hold small-caps — it means your price movements co-move with the small-cap stream. A negative β_S means you tend to rise during large-cap leadership instead.
• HML (High Minus Low · value factor) — value-stock (low-P/B) returns minus growth-stock (high-P/B) returns. A positive β_H means your portfolio tends to rise when value outperforms; a negative β_H means it rises when growth leads — again, this is co-movement of returns, not what is in the basket.

In short — betas describe "return co-movement strength", not "holdings composition." Example: a portfolio holding only SPY (a large-cap ETF) can still show a positive β_S if its returns co-moved with small-caps over the analysis window. Always read a factor beta as "how much does my portfolio move when that factor's return moves by one unit?"

Alpha is "the return that remains" after the three factors are accounted for. In the regression R_p − R_f = α + β_M·MKT + β_S·SMB + β_H·HML + ε, the first term on the right is α. If alpha is statistically significantly positive — that is, if there is a genuine extra return not explained by market, size, or value exposure that cannot be attributed to luck — the manager of that portfolio may have genuine security-selection skill or exposure to a previously unmeasured risk.

The diagram above splits a hypothetical portfolio return into five pieces. On top of the risk-free reward (R_f), the contributions of the three factors stack up, and finally unexplained alpha (α) is added to give the total return. The point of the chart is that even when the total is +1.0%, you can see where it came from. If only α is zero, "this return is entirely a result of factor exposure"; if α is positive, whether that "unexplained extra return" reflects real skill or chance is decided by the t / p value (typically significant when |t| > 2, p < 0.05).

• Verifying whether an active fund's "excess return" is real skill or just heavier exposure to the size / value factors
• The theoretical foundation for smart-beta and factor ETFs
• Diagnosing which style (small / large, value / growth) your portfolio is tilted toward
• Risk-adjusted performance evaluation (far more accurate than raw return alone)

As phenomena that the three factors could not explain — profitability (quality), conservative investment style, and momentum — were discovered, the same authors extended their own model, producing the 5-factor model.

• Kenneth R. French — Data Library (Tuck School of Business) · The raw FF factor data (MKT/SMB/HML) — this tool's US-stock factor source (Korean stocks use factors we compute in-house)
• Wikipedia — Fama–French three-factor model · Overview of the model definition, history and extensions
• Nobel Prize — Eugene F. Fama (2013 Sveriges Riksbank Prize) · Official citation — empirical analysis of asset prices