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Return-fit intercept from the centroid

The OLS intercept is a=ȳ−b x̄, so the fitted line passes through the paired means.

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Identify the two sample means

The observation centroid is (x̄,ȳ). With an intercept, the fitted line’s value at x̄ equals ȳ. This identity connects the slope estimate and intercept rather than estimating them independently.

Recover the intercept

a=yˉ−bxˉ,y^(xˉ)=yˉa=\bar{y}-b\bar{x},\qquad\widehat{y}(\bar{x})=\bar{y}

a is in response-return units per supplied period.

Use the original means

Benchmark mean is zero, asset mean 1.2% and slope 2.1, giving intercept 1.2%. That equality between intercept and asset mean occurs here because benchmark mean is zero; it is not a universal shortcut.

Keep the zero-X meaning in context

The intercept describes the fitted Y value at X=0. If zero lies outside the observed explanatory range, that interpretation involves extrapolation. A raw-return intercept is not automatically CAPM-relative Jensen alpha.

Further references