Menchero's Optimised Linking

Single-period performance attribution splits a portfolio's excess return over a benchmark into pieces — how much came from picking the right sectors, how much from picking the right stocks within them. That works cleanly for one period. The trouble starts when you try to chain many periods together into a total, because returns compound multiplicatively while the attribution effects were computed additively, so simply adding up each period's allocation effect and each period's selection effect across the year does not reconstruct the true total excess return; a leftover "interaction" or "linking" residual appears that has no clean story attached to it.

Menchero's optimised linking solves this by adjusting each period's individual effects with a small, mathematically derived correction factor before summing them, chosen specifically so that the corrected effects add up exactly to the true multi-period excess return with no leftover residual. The adjustment is smallest when returns are small and volatility is low, and grows as the compounding effect becomes more pronounced.

It has become close to an industry standard in attribution software specifically because clients find an unexplained residual line more alarming than a technical footnote about how the linking was done.