# 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:

1. Does the statement from the paper imply that I need to convert all daily returns for every stock and the index to USD?
2. 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!

## 1 Answer

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).

• Would the following be a correct way to do it?: Multiply all the daily prices of my stocks by the daily USD/DKK rate, to get daily prices in USD terms, and then calculate returns as I normally would. Thanks! Commented Apr 17, 2017 at 9:19
• @MikeHaye Yes, that works. Commented Apr 20, 2017 at 2:11
• [This answer](quant.stackexchange.com/a/68079/548380 to a related question has a simple example. Commented Sep 25, 2021 at 21:10