# FX Swap pricing and the mystery of Covered Interest Parity

### Juan Martínez

#### 07/10/2020

Sometimes described as a sort of physical law in international finance [1], Covered Interest Parity (CIP) has failed to hold after the Global Financial Crisis (GFC) of 2008. This has given rise to an interesting debate during the last decade that has resulted in relevant insights regarding international financial markets in general and FX Swaps in particular.

This post will be the first of a series. It is, thus, centered on introducing the basics of CIP trying to assume as little background as possible. Soon another post will follow discussing the recent debate around CIP in more depth.

## What is CIP for?

CIP allows to come up with a fair price for FX Swaps/Forwards, which constitute the most fundamental instruments for hedging currency risk. If you don’t find currency risk particularly interesting or relevant, you may want to take a look at this post or this other one. Anyway, how does an FX Swap hedge currency risk?

Imagine you want to enter a 5 year long investment in a foreign country. You will need foreign currency (FOR) to finance your investment, thus you exchange some of your domestic currency (DOM) at the current rate (Spot). At the same time, you want the guarantee that you’ll be able to exchange your FOR back to DOM once the investment has ended, so you agree a rate (Forward) for the transaction which will take place in 5 years.

These two transactions with opposite directions at different times comprise an FX Swap. Note that by setting the Forward rate in advance, we avoid the uncertainty of being exposed to the FORDOM currency pair, effectively hedging currency risk.

The question now is, what is a fair Forward rate? We will see that this is easily answered by asking instead, what is an unfair Forward rate?

## An example of CIP arbitrage

Let’s make a quick example to show how a mispriced Forward rate looks like. Imagine both Spot and Forward rates are 1 FORDOM. Just to clarify, 40 FORDOM would mean the price of 1 unit of FOR is 40 units of DOM, it’s as if the price of one barrel of oil was quoted as 40 OILUSD for instance. Back to the example, interest rates are 0% and 10% for DOM and FOR respectively. This means you could borrow 1 million DOM at 0%, and exchange it through a Swap to obtain 1 million FOR which you lend at 10%.

At the end of the period, you are returned the 1 million FOR notional of your foreign deposit, which you exchange at the previously agreed Forward rate of 1, to obtain 1 million DOM and return your domestic loan. During the process you haven’t been exposed to any currency risk and nonetheless you receive 0.1 million FOR in interests, apparently for free. Note that these profits could also had been hedged in advance with an FX Forward withouth incurring in additional costs.

In summary, the current setup leads to the possibility of obtaining riskless profits, also known as arbitrage. Anyone with market access would try to replicate this strategy, buying FOR at Spot rate to lend it and selling it back at Forward rate. The Spot market wouldn’t be affected by this change in offer/demand since it’s comparatively much more liquid than the Forward market; so the result would be a depreciation of the FORDOM Forward rate (i.e. the price of FOR in DOM units), which will continue until no profits can be made. In our case this would result in a Forward rate of 1/1.1=0.91 FORDOM. This way when converting your 1.1 million FOR at the end of the period you obtain 1 million DOM in exchange, with no profits or losses.

## CIP formally expressed

Going through a couple examples like the one above with different interest rates one can intuitively reach the following conclusion. The equilibrium is reached when the forward rate equals the spot rate discounting foreign interests and incorporating domestic interests:


$F = S \cdot \frac{ 1 + \text{ir}_{DOM} }{ 1 + \text{ir}_{FOR} }$

Another way to look at this is by considering the Spot (S) and Forward (F) as a ratio between two cashflows, S or F units of DOM for each unit of FOR.


$S = F \cdot \frac{ 1 + \text{ir}_{FOR} }{ 1 + \text{ir}_{DOM} } = \frac{ \frac{F \; \text{DOM} }{ 1 + \text{ir}_{DOM} } }{ \frac{1 \; \text{FOR} }{ 1 + \text{ir}_{FOR} } }$

Therefore the Spot is the ratio between the Forward cashflows brought to present value. In other words, the present value of the Spot and the Forward rates are equal. In an FX Swap, they have opposite directions so they cancel each other resulting in no expectation of profit. Whenever market rates deviate from CIP, market participants are encouraged to arbitrage it, sustaining the equilibrium.

If the formula doesn’t make complete sense, we recommend you work through a couple examples like the one above with different interest rates, hopefully you’ll see things eventually fit in. You may also want to refer to other alternative explanations to get better intuition. Wikipedia provides a nice visual example made by John Shandy showing how the interest earned by an american investor should be the same either if he lends locally, or abroad hedging currency risk with an FX Swap. Hence the name Covered Interest Parity.

## 2008 and the lost of CIP

Finally we will see how CIP estimations of fair Forward rates relate to actual market data. To better compare the two, we will plot Swap prices, i.e. we will substract the Spot rate from the Forward rate. Below we can see the data in the two most liquid currency pairs, namely EURUSD and USDJPY.

We can see that real Swap prices are more noisy but generally approximate very well the CIP estimation up until 2008. From then on, we see small but systematic deviations. Is there an opportunity for arbitrage? Why has the CIP stopped holding? Why was precisely 2008 the turning point?

To deal with these questions we will have to return to some of the simplifications we’ve made earlier for the sake of clarity and delve into the details. Nonetheless, the debate is still ongoing and there are no clear answers, which only makes the topic more interesting.

## Conclusion

We have introduced Covered Interest Parity as a no arbitrage condition that allows the pricing of FX Swaps. The model derived is reasonably valid until 2008, when systematic deviations arise. Explaining this phenomenon will be the objective of our next post.

## References

[1] Borio, Claudio EV, et al. “Covered interest parity lost: understanding the cross-currency basis.” BIS Quarterly Review September (2016).