# Computing FX forward returns using spot returns and an existing term structure

Sorry for the naive question, I am new to the area. I have YTD spot returns on the USD/GBP pair and a forward yield curve. How would one go about computing the forward returns in 2 years using this information? I've scanned google for the right formulae but most of them relate to roll rates on commodities and I don't see how that would be transferable information to the problem I'm trying to solve.

I am going to make some assumptions here. I assume you will be buying GBP Spot and Selling GBP forward 2 Yrs. Currently 1 GBP is 1.30 USD. If you sell this 1 GBP forward 2Yrs at the current 2 Yr forward GBP/USD of say 1.34 USD and you do nothing else, you will earn the carry for two years.

The return would be $$(1.34/1.3 - 1)(360/Act)$$ assuming you are calculating return on a LIBOR equivalent basis. This would be approximately 1.538% annualized.

The calculation of the 1.34 USD per GBP 2 Yr forward would be as follows:

$$(1 GBP * (1+2Y_{GBP Rate} *Act/365))/(1.30 USD * (1+2Y_{USD Rate} *Act/360)$$ again assuming you are using LIBOR rates.

• How would the spot return play a role in this? I understand that the spot return is the log ratio of the spot price today vs the spot price yesterday. Wouldn't you need to incorporate this information somehow into the forward return calculation? Apr 20, 2019 at 7:47
• @lowentropy It would not enter into the above strategy described. Perhaps my assumptions are not what your strategy. What data do you have? USD yield curve? GBP Yield curve? Perhaps you can elaborate on the trade for which you are calculating the return. Apr 22, 2019 at 14:27
• Certainly, I have the USD/GBP forward yield curve, the trade is for a 3Y forward contract buying GBP using USD. Apr 22, 2019 at 16:00
• In your case the return calculation will be just adding the returns for two years. Alternatively, if you have the spot rate two years after the trade is put on, you only need to take ln(spot fx rate in 2yrs/ current spot fx rate). Apr 22, 2019 at 17:58
• @lowentropy. Also you would have to add the return from the 1 Yr forward at year 2 from the 3 Yr forward price at which you initiated the position. Apr 23, 2019 at 0:04