Estimating FX Forward Carry from Spot and Interest Rates

Summary

The document explains how to estimate the two-year forward exchange rate and the annualized carry return for a GBP position using spot and forward quotes. It assumes a position that buys GBP at spot and sells it forward, then compares the forward price with the current spot price to express the return on a LIBOR-equivalent basis.

It also gives an interest-rate-parity calculation for deriving the forward price from GBP and USD rates, with separate day-count conventions for the two currencies. The example uses illustrative spot and forward prices and rate inputs. The calculation depends on the stated trade direction, rate conventions, and day counts; it does not explain how to forecast future spot returns or account for transaction costs and changing market rates.

Key ideas

• A forward price relative to spot can express the carry on a currency position held to the forward date.
• The example assumes buying GBP at spot and selling it forward against USD.
• The forward exchange rate can be estimated from the two currencies’ interest rates and the spot rate.
• The calculation’s result depends on the trade direction, rate basis, and day-count conventions.

Tags

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


# 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.

## Answer by AlRacoon (score 3)

https://quant.stackexchange.com/a/45200

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.

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