Separating Local-Currency and FX Returns in Portfolio Attribution

Summary

The document asks how performance attribution can separate an asset’s local-currency return from the foreign-exchange return when reporting in a base currency. It presents the continuous-compounding identity that expresses the base-currency return as the sum of those components, then describes viewing a multi-currency portfolio as security positions measured in local currencies alongside separate FX positions. This setup is intended to distinguish value added by security selection from the effect of currency moves.

The author’s central question is how that separation works when portfolio returns are combined using weights. The post does not provide an answer, derivation, worked portfolio example, or empirical evidence, so it leaves unresolved whether and under what conventions weighted contributions add cleanly. The discussion is useful as a framing of an attribution problem, but readers would need additional material to understand the role of simple versus continuously compounded returns, weight definitions, and rebalancing over time.

Key ideas

• Continuous compounding allows an asset’s base-currency return to be decomposed into local return and FX return.
• A multi-currency portfolio can be represented as local-currency security holdings plus FX exposures.
• The post raises, but does not resolve, how weighted return contributions combine under this decomposition.
• Attribution results depend on return conventions and portfolio weights, topics the post leaves unexplored.

Tags

# Performance Attribution and FX positions


# Performance Attribution and FX positions












I'm currently reading the book "Mastering Attribution" from Andrew Colin.

He first explains that you can separate the FX returns from the security return if the returns are continous compounding:

> Assuming continuous compounding, the base currency return $r_{BASE}$ of an asset is given by $$r_{BASE}=r_{LOCAL}+r_{FX}$$ where $r_{LOCAL}$ is its local currency return, and $r_{FX}$ is the foreign exchange return due to changes in the exchange rate between the local and base currencies.

Then he explains that we can separate a portfolio in two subportfolios:

> For a clearer view of the effects of the manager’s investment decisions, one should treat this multi-currency portfolio as two subportfolios, one containing securities with returns measured in local currency and one containing FX positions. This allows the value added by local currency investment decisions to be separated from the value added by exchange rate movements.

From what I understand the fact that you can separate the effects is a consequence from the fact that the returns are compounded. If so, why he can add the returns multiplied by the weights if the returns are not arithmetical?

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.