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Currency forwards and interest rates

M

Mayowa Okulate

Member
Hi

I'm trying to work out if we can infer anything from the relative level of interest rates in terms of how they will affect forward vs spot rate of a currency. For example, looking at Mock exam question 5ii, where we are asked to calculate the forward rate. Since interest rates are higher in $ compared to £, can we expect $ to get stronger since there will be higher demand for $? This would lead me to the conclusion that since the dollar is expected to be more valuable, the forward rate would be less than $1.2 per £.

In fact, the answer shows the opposite, which means that my logic doesn't work? Any ideas please? Thanks
 
Your logic has a flaw. The spot transaction and the forward transaction basically get you the same thing in the end, therefore they are just different ways of doing the same trade. If $ rates are higher and a UK investor is buying dollars, then the spot trade would get the dollars and benefit from the higher dollar interest rate sooner. On the other hand the forward trade leaves the funds for longer in pounds (at a lower interest rate). So if the forward was the same rate as the spot, no-one would take that route. The forward has to be more attractively priced (a more favourable exchange rate) to create a free market.
It is best to avoid thinking of a forward as an "expectation of where a spot rate is headed". If most traders think an asset is heading upwards, it will move upwards immediately - both the spot market for the asset and the forward market. The spot and forward are just two ways to buy (or sell) the asset.
 
Thanks Colin, that makes sense.

Just to be clear, if $ interest rates are higher than £, would the forward rate always be priced cheaper than the spot rate (due to the 'convenience' derived from holding $)? Presumably there are other factors affecting demand for the currency other than interest rates. I'm just trying to work out general rules but appreciate there might be none!
 
In theory - yes. SP5 gives you the formula for the "no arbitrage" fair price for a forward on an asset paying interest.
F = S * exp(r-q)T
So if the dollar is the "underlying asset" and q = "interest rate on the underlying asset" which is higher than "r". Then F should be lower than S. It is complicated a bit by the fact that people talk about the conversion rate of a currency, rather than the price of the currency (ie the cost of a dollar in pounds), but the basic concept is fine. The forward price of a dollar would have to be less (cheaper) than the spot, because otherwise you could by the spot cheaper, then benefit from the high dollar interest as well. win / win - and there are no free lunches in the market.
There are relatively few other factors, as you mention above. The only things is the cost of doing the arbitrage to bring the prices back to fair price. If the cost is high, then the actual price can deviate from the fair by a larger margin, and there is no arbitrage profit available. So it stays there. The other thing would be the assumptions, the obvious one being the assumed rate of interest you will get on pounds and on dollars over the period. If that is uncertain, there will be a range of fair values.
 
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