Concepts / Factor Decomposition

Factor Decomposition

5 min read · Concept

Most strategies that look like alpha are tilts to factors with names. Factor decomposition tells you which factors and how much is left over.

What it is

A factor regression decomposes your strategy's return stream into a sum of known risk premia plus an unexplained residual. The known premia are the Fama-French factors (market, size, value), the Carhart momentum factor, and the quality and investment factors from the Fama-French 5-factor extension.

Run an OLS regression of strategy returns on these factor returns. The coefficients are your factor exposures (betas). The intercept is your alpha — the part of the return that the factors don't explain. If you're trying to claim genuine edge over and above known premia, that intercept needs to be (a) economically meaningful and (b) statistically significant.

The formula

# Fama-French 5 + momentum (FF5+UMD)
strategy_return = alpha
                + beta_mkt   * mkt_excess_return
                + beta_smb   * size_factor
                + beta_hml   * value_factor
                + beta_rmw   * profitability_factor
                + beta_cma   * investment_factor
                + beta_umd   * momentum_factor
                + epsilon

# Annualised alpha = 12 * monthly_intercept (or 252 * daily_intercept)
# t-statistic = coefficient / standard_error

Quantis runs two separate regressions and shows both betas. The simpler single-factor OLS-vs-benchmark gives you the market beta. The full FF5+momentum gives you the per-factor breakdown, the alpha intercept, and the per-coefficient t-stats.

Reading the betas

beta_mkt: sensitivity to broad market returns. Long-only equity strategies cluster around 0.7–1.1. A long-short market-neutral strategy should land near 0.
beta_smb (size): positive means you're tilted to small caps; negative means large caps. Most retail strategies on liquid universes have beta_smb near 0.
beta_hml (value): positive means you hold cheap stocks; negative means expensive ones. Quality strategies often have negative beta_hml — they hold profitable, expensive names.
beta_rmw (profitability): positive for quality strategies. Loading on this factor explains most of what people call “quality alpha.”
beta_umd (momentum): positive for momentum strategies (obviously) and for strategies that accidentally pick up momentum from the way they screen — e.g. high-recent-FCF-growth screens often have hidden momentum tilt.

Reading the alpha

The alpha intercept is the headline. Annualised, it's the return your strategy delivers after stripping out everything the known factors would have given you anyway.

|t-stat| > 2: the alpha is statistically significant at the 5% level. This is the bar — without it, the alpha is just sample noise.
Annualised alpha > 3% with t > 2: a strategy that's genuinely doing something the factors don't explain. Rare.
Annualised alpha 1–3%, t-stat marginal: probably genuine but small. Whether it survives transaction costs and slippage is a separate question.
Annualised alpha negative or near zero: all your return is factor exposure. You're not adding edge over a long-only factor ETF mix that costs 5bps. This isn't necessarily bad — factor exposure is fine — but don't call it alpha.

R-squared: how much does factors explain?

R² tells you what fraction of the strategy's return variance is explained by the factor model.

R² > 0.80: the strategy is essentially a factor cocktail. The named factors explain almost everything; whatever residual exists is small. Common for index-tracker-adjacent strategies.
R² 0.4–0.7: meaningful factor exposure plus genuine idiosyncratic content. Most active strategies live here.
R² < 0.2: the strategy's returns are mostly idiosyncratic — neither well-explained nor well-rejected by the factors. Treat the alpha number with extra caution; the regression has limited statistical power.

What to watch in the result card

Two betas, agree. If the single-factor OLS beta and the FF beta_mkt are wildly different, the decomposition is unstable. They should usually be within 0.1 of each other.
Alpha t-stat shown. The number without the t-stat is meaningless. Quantis always shows both.
Sign of factor loadings makes sense. A “quality” backtest with negative beta_rmw is internally inconsistent — your construction isn't doing what its label says.

Common mistakes

Reporting alpha without the t-stat. Annualised alpha of 4% sounds great until you see the t-stat is 0.6 — meaning the result is consistent with no edge at all.
Using only CAPM (one factor). Single-factor regression overstates alpha because it lumps every other factor into the residual. Use at least FF3, ideally FF5+momentum.
Comparing alphas across different factor models. Alpha vs CAPM and alpha vs FF5+UMD are not the same number. Always state which model.