5

Smoothing algorithms

5.1 Why returns do not combine neatly over time

5.2 The importance of internally consistent return contributions

5.3 Path-independence

5.4 Carino smoothing

5.5 Geometric smoothing

5.6 Foreign exchange return and smoothing

5.7 Summary

5.1 WHY RETURNS DO NOT COMBINE NEATLY OVER TIME

Whether they arise from individual securities, sectors or portfolio risks, a fundamental property of return contributions is that they compound additively over markets, but geometrically over time. One outcome of this is that, for a portfolio where return is calculated over more than one time period, cross terms or compounding will distort the results and potentially obscure the true sources of return in a portfolio.

5.1.1 Cross terms

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