Skip to content
All library documents

Converting International Equity Returns to USD for Replication

Article Quant Q&A · Author: Mike Haye
Read the original

Summary

The document addresses how to reproduce an international equity analysis that reports returns in US dollars and measures excess returns over US Treasury bills. Its example concerns Danish stocks and a local-currency index, both denominated in Danish kroner. The accepted answer says that reproducing the paper requires returns in USD terms, so currency conversion must be included in the return series used for the analysis.

One suggested workflow is to construct the stock and index returns in their local currency first, then convert the resulting index series into USD. The answer also points to an existing dataset from the research provider, whose excess returns are already expressed in USD and above US Treasury bill returns. The document offers no conversion formula, exchange-rate convention, or tests comparing workflows. Its guidance is specific to matching the stated currency basis of the cited research and does not establish that USD returns are appropriate for every analysis of foreign equities.

Key ideas

  • Replicating a study with USD returns requires accounting for currency conversion in international equity returns.
  • The example compares Danish stocks and an index denominated in kroner.
  • The suggested workflow builds local-currency indices before converting the result to USD.
  • An existing dataset is described as providing USD excess returns above US Treasury bills.
  • The document does not specify exchange-rate timing or a detailed conversion formula.

Tags

EquitiesForexFactor investingBacktesting
Full text
# Converting international equity returns to USD


# Converting international equity returns to USD












Background: I am trying to replicate some results from the Betting Against Beta paper by Frazzini & Pedersen (FP). (http://www.econ.yale.edu/~af227/pdf/Betting%20Against%20Beta%20-%20Frazzini%20and%20Pedersen.pdf)

Specifically, I am trying to recreate the results for the Danish equity market, which has the local currency DKK.

In section 3 of the paper, FP state:

> All returns are in US dollars, and excess returns are above the US Treasury bill rate.

This follows a paragraph about the international equities analysis, so I assume it specifically applies to international equities.

Betas are calculated against the MSCI Denmark index, which, like the stocks I am analysing, is listed in DKK.

My question is two-fold:

- Does the statement from the paper imply that I need to convert all daily returns for every stock and the index to USD?

- If so, do I then need to get the USD/DKK exchange rate for every day (data point) I have stock/index returns for, multiply this by the individual daily stock prices, and then calculate returns anew?

Cheers!

## Answer by Helin (score 2, accepted)

https://quant.stackexchange.com/a/33709

If your purpose is to reproduce the result in the paper, then yes, all returns should be converted into USD terms, using the proper exchange rate. To simplify things, you could build your indices in local currency terms, and only convert the final index into USD terms.

Also, I believe AQR publishes these datasets already, which can be downloaded here. Note that AQR's excess returns are already in USD terms and over US T-bills (exactly what you need).

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.