Transparency is a feature. This page explains what the multi-factor regression measures and why we compute it — in plain terms. The precise formulas and numeric conventions are documented in our internal methodology; the summary here is deliberate, not an omission.
This tool generalizes the single-benchmark market model to any set of named factors — for example the classic Fama–French factors covering the broad market, company size, value, profitability, investment, and momentum. It explains a portfolio's excess return as a blend of exposures to those factors plus an unexplained leftover called "alpha" — the part of the return the factors do not account for.
The method fits the portfolio's excess return (its return above the risk-free rate) to the supplied factors using ordinary least squares — the standard best-fit regression. Each factor earns an estimated exposure (its "beta") describing how strongly the portfolio moves with that factor, and the intercept is the alpha. Because published factor series such as Fama–French are already stated as excess or long-short returns, only the portfolio's own return has the risk-free rate removed; the factors are used exactly as supplied.
Alongside each exposure, the tool reports how statistically reliable it is. It uses the classical constant-variance regression standard errors and turns each into a t-statistic — a measure of how large an exposure is relative to its own uncertainty, where a larger magnitude signals a more dependable estimate. It also reports the R-squared and adjusted R-squared, which describe the share of the portfolio's variation the factors explain (between 0 and 1, higher meaning the factors capture more), with the adjusted version penalizing the use of extra factors. Alpha and the residual (idiosyncratic) volatility — the size of the return swings the factors leave unexplained — are both annualized so they read on a yearly scale.
Factors are taken as the providers publish them, without re-centering or rescaling, and are expected as decimal fractions rather than percents. The reported t-statistics are the classical constant-variance kind; heteroskedasticity- and autocorrelation-robust variants are a possible later refinement rather than what is shown today.
