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Why Averaged FX Rates Do Not Reverse Symmetrically in Consolidation

Article Quant Q&A · Author: Scott
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Summary

The document describes a multinational consolidation path from a USD functional currency in El Salvador through GBP books in the UK and back to USD books in the US. It reports that USD transactions can return at a different amount after translation, giving USD 15.00 becoming USD 15.12 as an example. The stated cause is using monthly averages of daily exchange rates: the average USD-to-GBP rate is generally not the reciprocal of the average GBP-to-USD rate.

The author questions whether recording this difference as a translation gain or loss is appropriate, distinguishing it from a transaction gain or loss caused by exchange-rate movement between conversion dates. They suggest consistently translating a currency pair in one direction, but say accounting rejected that proposal. The document presents the issue and asks for standard treatment; it does not establish the applicable accounting rules or provide a remedy, so the example should not be read as guidance on accounting standards.

Key ideas

  • Averaging daily rates in each direction can produce rates that are not reciprocals.
  • Sequential translation through an intermediate currency can change an amount even when the period is the same.
  • The author distinguishes this effect from gains or losses caused by rates changing over time.
  • The document asks whether the difference is properly treated as a translation gain or loss but gives no authoritative resolution.

Tags

ForexMulti-assetStatistics
Full text
# Average monthly exchange rates causes translation error in consolidated books


# Average monthly exchange rates causes translation error in consolidated books












I newly work for a multinational company with a corporate structure such that during consolidation, the books need to be translated multiple times and sometimes back to the original currency. I've come across a curious issue - transactions occurring in USD are translated back to USD with a change. USD15.00 becomes USD15.12, for example.

The relevant structure of the company is like this: El Salvador - SV (USD) -> UK (GBP) -> US (USD)

My expectation is that expenses in SV denominated in USD will show up in the consolidated US books exactly as they appeared in the SV books. However that's not the case. What I discovered is that our accounting group is averaging daily exchange rates over the month and using that - which is fine. But mathematically, if you average USD-GBP, it does not equal to the inverse of the average of GBP-USD.

My accounting group is booking the difference as a translation gain/loss. But I believe that's incorrect because a transaction gain/loss is caused by differing rates over time (USD-GBP at one rate, then the USD drops and it is converted back at a different time). This change is due to differing rates over the exact same time period.

My proposed solution to accounting was to only ever translate a currency pair in one direction. For example alphabetically (aways GBP-USD or HKD-SGD, never USD-GBP or SGD-HKD) to avoid this problem, but it was rejected and I was told this is standard in accounting.

This just seems intuitively wrong. Am I correct? What's the standard remedy for this?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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