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.
