Guide · Fama-French 3 Factor Model

Do you know where your returns came from?

01 · Introduction

Beyond the market, two more forces

In 1992, Eugene Fama and Kenneth French uncovered two systematic patterns in decades of US stock data that market risk alone couldn't explain — small beat large, and value beat growth over the long run. They then built a model that decomposes return into four sources.

Your excess return = β₁ × Market (MKT) + β₂ × Size (SMB) + β₃ × Value (HML) + Alpha (α)

Beta (β) tells how much you're exposed to each factor; alpha (α) is the residual the three factors can't explain. To honestly claim "I did well," α must be statistically significant and positive. Otherwise, your return is just compensation for some risk you took.

"Comparing returns leads to wrong conclusions.
Only comparisons after controlling for risk factors are meaningful."

— Common Risk Factors in the Returns on Stocks and Bonds, Fama & French (1993)

02 · Position

Where did your return come from?

The beta (β) values and alpha (α) on your analysis page show where your portfolio's return flowed in from. Below is a sample decomposition of a portfolio that earned +15.4% annually.

Example · Source decomposition of a +15.4% annual return

In this example, the market pulled the most weight at +9.2%p of the +15.4%. About 60% of the return came simply because "the market was good." Alpha is +2.3%p, roughly 15% of the total. If that alpha is statistically significant, it's "real skill"; if not, it's likely just luck.

Which of the three shapes does your own result resemble?

A · Alpha significant

Possibly real skill

α is positive with p-value below 0.05. There's statistically meaningful excess return the three factors can't explain. Still, verify the analysis window is long enough (36 months minimum) and that trading costs are accounted for.

B · Factor-exposure

α ≈ 0, beta does the work

If α is near zero, your return is actually the result of exposure to some factor. Neither good nor bad — just that the accurate phrasing becomes "I took on a certain risk," not "I did well."

C · Negative alpha

Underperforming the factors

Negative α means you're underperforming a plain ETF with the same factor exposure. Stock selection isn't adding value — it's destroying it. Switching to an index ETF may be the rational move.

03 · Playbook

Five things you can do with the result

Don't stop at reading the betas and alpha. You can actually use these numbers to do the following five things.

Hidden Tilt · check your intent

Are unintended bets hiding inside?

You thought you diversified well, but the regression spits out an SMB β of 0.7. That means you've been unknowingly betting big on small caps — an exposure that bleeds in large-cap rallies, and you didn't even know it. Betting knowingly and being exposed unknowingly are two completely different things.

How toCheck β·SMB and β·HML against a |0.3| threshold → ask whether each exposure was intentional → if not, rework holdings or hedge with names exposed to the opposite factor.

Factor Rotation · business-cycle play

Rotate factors with the business cycle?

It's true that different phases seem to favor different factors. In recovery · expansion, small caps (SMB+) and high-β names are more sensitive to the upside; in peak · contraction, defensive large caps (SMB−) and low-β tend to cushion the drawdown. But higher β doesn't earn you more — it amplifies both gains and losses, and the evidence that you can time the cycle by rotating factors to capture excess return is weak. So use this to align your exposure with your risk tolerance, not as a timing bet for extra return. Where Markowitz shows the total amount of risk, 3-Factor shows what kind of risk lives inside it.

How toIdentify the current phase (recovery · expansion · peak · contraction) → in recovery/expansion tilt to β·SMB +, β·MKT ≥ 1 → at peak/contraction tilt to β·SMB ≤ 0, β·MKT < 1 → adjust weights in the Equalizer and re-check the resulting betas.

Personality · keep the character

Swap holdings without changing the portfolio's personality

You're swapping stock A out for stock B. Pick any random name and your "cautious sentinel" portfolio might quietly mutate into something more aggressive. If the two stocks share similar 3-Factor betas, the holdings change but the portfolio's risk structure and expected-return composition stay the same — diversification, volatility, VaR all hold steady. Change the names, keep the character.

How toRun a 3-Factor regression on candidate B alone → compare β·MKT, β·SMB, β·HML against stock A → if each pair is within ±0.2, the swap is safe → otherwise find another candidate, or confirm the character change is intentional.

Skill vs Luck · separating the two

Is this fund actually skilled?

Don't take "beats the market by +5%" advertising at face value. The question is whether that +5% is alpha or just factor exposure. If a fund with β·MKT 1.2 and β·SMB 0.3 outperformed by +5% last year, that may simply be "more market exposure plus a small-cap tilt," not manager skill. Only α and its p-value give the honest verdict.

How toRun a 3-Factor regression on the fund's monthly returns → check α and its p-value → if α > 0 and p-value < 0.05, the skill is statistically meaningful → otherwise it's luck or factor exposure.

Smart Beta · prescription for negative alpha

Negative alpha? Trade stocks for ETFs

If your α came out clearly negative, there's an uncomfortable truth to accept: your stock picking is underperforming a plain ETF with the same factor exposure. There's no reason to keep insisting on individual names. Keep the factor exposure you want (say HML value), but let the market handle selection. You collect the same factor reward, drop the idiosyncratic risk, and pay less in fees.

How toIdentify your current factor exposure (e.g. β·HML +0.4) → look up ETFs tracking that factor (Korea: KODEX/TIGER value or equal-weight series; US: VTV, IWN, etc.) → match the ETF's factor exposure → factor in trading costs and taxes before switching.

04 · Limitations

What 3-Factor doesn't tell you

The better a model is, the more clearly you need to know its boundaries. Four things to remember before trusting the output blindly.

Factors were discovered, not legislated. SMB and HML are patterns spotted statistically in past data. There's no guarantee they will keep working. Treat the model's output as a hypothesis, not a fact.

Limitation 01

Premiums are averages, not guarantees

The size and value premiums were discovered in US data from 1926–1990. Yet in the 2010s, the US value premium disappeared for a stretch. "Positive on average" and "positive over the next decade" are not the same statement.

Limitation 02

Markets are not interchangeable

Applying effects discovered in the US directly to Korea, Japan, or emerging markets can mislead. There were periods in Korea where SMB wasn't consistently positive, and stretches where HML even flipped sign. That's why this tool analyzes Korean stocks with Korea-specific factors of its own.

Limitation 03

The definition of "value" lags the times

HML usually defines value via P/B ratio. But the real worth of modern companies — heavy in intangibles like brands, software, and data — doesn't hit the books. The "high P/B = expensive" equation is breaking down. Where you draw the line for "value" can move the result.

Limitation 04

Three factors aren't the whole story

Since the 3-Factor model, more factors have been discovered — momentum (WML), profitability (RMW), investment (CMA), low-volatility, quality, and others. Decomposing with only three makes "whatever's left is alpha" look clean, but other factors may actually be hiding inside that residual.

05 · Next Step

If 3-Factor isn't enough

The 3-Factor model is a starting point, not the finish line. In 2015, Fama and French published the 5-Factor model — adding profitability (RMW) and investment (CMA) to capture the extra pattern that "profitable firms" and "firms that invest conservatively" earn higher returns.

What looked like alpha under 3-Factor may turn out to be RMW or CMA under 5-Factor. In other words, "hidden alpha" shrinks and the evaluation becomes more honest.

Recommended Next

Fama-French 5-Factor analysis

Adds profitability (RMW) and investment (CMA) for a finer decomposition. You can see whether what looked like alpha in 3-Factor was actually exposure to another factor. The tool that takes "is my alpha real?" one level deeper.