Guide

# What is an FX forward curve?

### Summary

An FX forward curve is a curve that shows FX forward pricing for all the different dates in the future. FX forward pricing is determined by the current exchange rate, the interest rate differentials between the two currencies, and the length of the FX forward.

#### What does the FX forward curve represent?

Unlike an interest rate forward curve, which can be interpreted as the market’s expectations for future SOFR, SONIA, or EURIBOR settings, an FX forward curve denotes FX forward pricing for all the corresponding future dates agreed today. FX forward pricing is calculated based on the spot rate and the interest rate differentials between the two currencies for the tenor of the forward. It does not include any market sentiments or forecasts of where future exchange rates will be. It is simply an arithmetic calculation.

#### How is an FX forward curve constructed?

The main component of forward pricing is the interest rate differential between the two currencies, which is added to the pricing such that there cannot be any arbitrage, no matter which currency you hold.

Let’s assume you are planning to sell EUR in 12 months receiving USD in return. The forward pricing for such a transaction ensures that there is no arbitrage between the following two scenarios: (i) exchanging the EUR into USD today and holding the USD for 12 months, or (ii) holding the EUR for 12 months and converting it into USD in 12 months’ time.

Let’s start with EUR 1,000,000. Using a spot rate of 1.20001, that will give us USD 1,200,000. If we keep the EUR, in a year’s time with interest rate being -0.5%, we will have EUR 995,000. If we keep the money in USD, with interest rate 0.2%, it will become USD 1,202,400. Dividing USD 1,202,400 by EUR 995,000 gives us an implied forward rate of 1.2084. The implied forward points based on interest rate differential are 0.0084 (or 84 pips). A pip refers to the last decimal place quoted for a currency pair. Most currency pairs are priced to 4 decimal places, so a pip will be the same as 0.01%, or a basis point, in those cases. The exact value of a pip depends on the currency pair and the quoting convention. For example, a pip in USD-JPY denotes the second decimal place, whereas a pip in EUR-CZK denotes the third decimal place.

Using interest rate differential only, we have the following formula for forward rate:

Forward rate = current spot rate + forward points deduced from interest rate differential

However, we often find market forward points to be slightly different to the theoretical implied forward points. In this example, the current market tradeable forward point is 86 pips. The difference is called cross currency basis and it is driven by relative supply and demand between currencies. As an example, many non-U.S. financial institutions seek to maintain USD reserves today. To do so they purchase USD in the spot market while selling USD in the forward market to return the USD to their native currency. This dynamic – excess demand to buy USD today but also to sell USD in the future – pushes USD forward rates down below levels implied from interest rate differentials.

We can now refine the forward rate formula to:

Forward rate = current spot rate + forward points deduced from interest rate differential + cross currency basis

#### How should an FX forward curve be used?

FX forward curves are the basis for pricing FX derivatives. The interest carry shows whether entering into an FX forward for that currency pair will be a cost or a gain compared to the current spot rate. For example, an investor whose fund currency is EUR has a cross-border deal in USD and is looking to hedge the FX of profit repatriation (from USD back to EUR). FX hedging will be a cost to the investor because USD is the higher yielding currency. EUR is the lower yielding currency and the investor will be “penalized” by the interest rate differential. The forward rate will be worse than the current spot rate. An FX forward curve will give a good indication of what this cost/gain is.

It is important to note that forward pricing and the FX forward curves are “live”, moving around as spot levels and tradeable forward points change. The real-time forward curve is used for locking in new FX forwards, unwinding existing forwards, and calculating the mark-to-market of existing forwards, and is one of the key drivers of option pricing.

Many funds, investors, and corporates engage Chatham to see how forward curves are evolving and for live execution of their FX hedging needs.

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1 This is a rounded rate from August 6, 2020 and is used for illustrative purposes only.

### Disclaimers

Chatham Hedging Advisors, LLC (CHA) is a subsidiary of Chatham Financial Corp. and provides hedge advisory, accounting and execution services related to swap transactions in the United States. CHA is registered with the Commodity Futures Trading Commission (CFTC) as a commodity trading advisor and is a member of the National Futures Association (NFA); however, neither the CFTC nor the NFA have passed upon the merits of participating in any advisory services offered by CHA. For further information, please visit chathamfinancial.com/legal-notices.

Transactions in over-the-counter derivatives (or “swaps”) have significant risks, including, but not limited to, substantial risk of loss. You should consult your own business, legal, tax and accounting advisers with respect to proposed swap transaction and you should refrain from entering into any swap transaction unless you have fully understood the terms and risks of the transaction, including the extent of your potential risk of loss. This material has been prepared by a sales or trading employee or agent of Chatham Hedging Advisors and could be deemed a solicitation for entering into a derivatives transaction. This material is not a research report prepared by Chatham Hedging Advisors. If you are not an experienced user of the derivatives markets, capable of making independent trading decisions, then you should not rely solely on this communication in making trading decisions. All rights reserved.

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