When Textbooks Are Wrong (Or How to Lower Your EUR Interest Rate)

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March 21, 2012 – Pick up any textbook on derivatives, turn to the chapter on currency forwards, and you will see that the value of a currency in the future is simply a matter of interest rate differentials.

Chris Danielian
Chris Danielian

I just did this with the (generally accepted) bible of basic derivatives, John C. Hull’s Fundamentals of Futures and Options Markets, and I see this formula:

Forward = Spot*e^((r2-r1)t),

where r2 and r1 are the local rates in the respective currencies.  The direct implication of this formula is that the currency with the higher local interest rate will be worth less (i.e., weaker) in the forward market.

To understand this logically let’s go through a transaction from USD to AUD.  An investor could take USD and convert to AUD today at spot prices, and then invest the money at local AUD interest rates which are currently much higher than USD local rates.  If they want to have no risk of translating back to USD in the future they must re-convert in the forward markets today.  Assume they could convert in the forward markets at the same level as spot, every investor in the world would convert USD to AUD, invest locally in AUD, and at the same time re-convert to USD in the forward market at the same level as spot.  They would do this because the interest rates in AUD are higher, but they have no currency loss to re-convert.  Of course, that arbitrage cannot happen, in practice as everyone tries to do this trade it has the effect of strengthening AUD in the spot market (as everyone buys AUD spot), and weakening AUD in the forward market (as everyone sells AUD to re-convert to USD).  Hence the currency with the higher local interest rates is always weaker in the forward markets – so says the textbooks.

Let us look at EUR/USD currency at the present moment, EUR 1yr local rates (Euro LIBOR) are roughly 1.45% and USD 1yr local rates (LIBOR) are roughly 1.05%.  As per our discussion above, the EUR must be a weaker currency in the forward markets.  So then what to make of this data:

EUR/USD Forward Curve (2012 March21)

The chart above is telling you that spot EUR = 1.3191 while one year forward EUR = 1.3226, so the EUR currency is stronger versus USD in the one year forward market.  But hold on: rates are higher in local EUR and therefore, according to an accredited source such as Hull, this cannot be possible.  However, we are staring at a bloomberg screen which says it is so – have we gone down the rabbit hole?

What does all this mean?

First let’s discuss the practical implications before we discuss why it exists.  The stronger EUR currency in the forward market means that the interest rate on a cross currency swap will be lower for EUR than USD (I will not go in to detail as to why, call to discuss).  Now assume one can borrow EUR in two different ways: 1) borrow locally in EUR, or 2) borrow locally in USD and swap that to EUR via a cross currency swap.  If you do #1, you will borrow in EUR at 1.45% for one year.  If you do #2, then you will borrow in EUR at 0.63% for one year!  Congratulations, by understanding the nuances of the currency and interest rates markets you have magically lowered your local EUR borrowing rate.

Now, why does it exist?  Let us think through how to take advantage of this “arbitrage,” the devil is always in the details.  One clear way to take advantage of this situation is to take physical USD, convert them to EUR, invest them locally in EUR, and at the same time convert them in the forward markets back to USD.  This roundabout trade will net you a larger interest rate than just investing locally in USD.  But what have you done?  You have effectively lent EUR to a European financial institution – are you prepared to do that?  The market has obviously already made up its mind.  So, at its core, this anomaly arises because of the credit condition of European institutions.

Textbooks would have you believe that the only consideration in the forward price of a currency is the interest rate differential, but the realities of the market are far more subtle and complex.    Understanding this, and potentially using it to your advantage, can allow your firm and its investors to benefit from this particular market nuance.

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