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The Menchero arithmetic algorithm extends a single-period attribution analysis to multiple-periods by noting that the returns of the portfolio geometrically compound over T periods for the portfolio single-time period return, 
, as follows: 
The benchmark multiple-period return,
, is as follows:
For small single-period returns, the relative performance is approximately as follows:
As the single-period returns become larger this breaks down due to the characteristic scaling arising from geometric compounding. The Menchero algorithm compensates for this by introducing the following scaling factor, , in the previous approximation equation:
The Menchero algorithm then deduces the correct scaling law that ensures any residual will be small. It is simply the ratio of the average arithmetic excess return to the average geometric excess return:
Next, the Menchero algorithm introduces corrective terms, , that distribute the small residual among the time periods so that the following holds exactly:
The coefficients are the final optimized linking coefficients:
Finally, the Menchero algorithm derives optimal values for the small values:
Where is a dummy index of summation.
The following sections summarize the required calculations.
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