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Geometric sector effects for a single period natively sum to the effect at the total level. This property is not preserved after compounding single periods over time. There are various industry approaches to handling Geometric Attribution over time. The Geometric Method uses an approach published by Bacon (Carl R. Bacon, Practical Portfolio Performance Measurement and Attribution [Chichester: John Wiley & Sons, Ltd., 2004]). A small adjustment is made to each sector effect so that the sector effects compound to match the effect at the total level. This new relationship is preserved in the multi-period results that are calculated by compounding single period effects.
The sector adjustment is to multiply each sector effect by the ratio of the effect at the total level over the compounded sector effects. This ratio is then raised to the ratio of the absolute value of the sector effect over the sum of the absolute values of all the sector effects.
In standard notation, the unadjusted Geometric effects (shown with superscript GU) have the property:
The Geometric Method effects (shown with superscript GM) have the property:
The allocation effect (A) is shown above, but the same relationships are true for all the attribution effects.
The Geometric Method allocation adjustment is:
Similarly, the Geometric Method selection adjustment is:
The single currency Geometric Method allocation and selection effects compound to the geometric excess return. This is true at the sector and total levels for single periods and combined periods:
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