Fit a return line from centered sums

Start from paired means

For the original record, benchmark mean is zero and asset mean 1.2%. Center each observation around its own series mean before constructing the cross-product and benchmark squared sum.

Keep units consistent

Recover the line

Slope is 21/10=2.1. Intercept is 1.2%−2.1×0%=1.2%. These are fitted sample coefficients in the supplied record, not population parameters established by five observations.

Check the fitting identities

With an intercept, residuals sum to zero and their benchmark-weighted sum is zero, up to numerical rounding. The line minimises the sum of squared residuals for the supplied equal-weight pairs. This arithmetic does not validate a particular error distribution.