# In Search of Lost Covered Interest Parity

### Juan Martínez

#### 24/03/2021

The puzzle of Covered Interest Parity (CIP) began in 2008 and has remained as such for many years. There have been multiple attempts to solve the mystery but none of them has reached a complete consensus and the debate is still ongoing. Nevertheless, the discussion has lead to a fair amount of interesting insights.

CIP is one of the backbones of international finance and the basic tool for FX Swaps (and Forwards) pricing. Here we will discuss some of the changes and nuances that have turned a previously straightforward model into something more interesting and worthy of detailed analysis.

## CIP recap

Briefly, CIP states that the interest rates earned on a local currency should equal the interest rates earned on foreign currencies once currency risk has been hedged with an FX Swap. Thus, taking interest rates as given we can come up with a fair price for an FX Swap. Here we are assuming some familiarity with the concept of CIP, if that’s not the case you might find this post useful.

Mathematically it’s often expressed as follows:

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

Where F is the forward exchange rate, S the spot rate, and
$$\text{ir}_\text{DOM}$$ and $$\text{ir}_\text{FOR}$$ the interest rates on domestic and foreign currency respectively.
Recall that the relationship between swap and forward rates is: $$\text{Swap} = F – S$$.

We can rearrange the CIP formula to align it with the definition given in the first paragraph:

$$1 + \text{ir}_\text{DOM} = \frac{F}{S} \left( 1 + \text{ir}_\text{FOR} \right)$$

Any deviation from this equality should apparently lead to arbitrage and riskless profits.

## The non-zero basis

These deviations are usually measured in terms of the FX basis, which is the difference between the interest earned with local rates ($$\text{ir}_\text{DOM}^\text{Local}$$) and foreign rates hedging currency risk with an FX Swap ($$\text{ir}_\text{DOM}^\text{Swap}$$). In other words, the difference between the two sides of the equation above:

$$b = \frac{F}{S} \left( 1 + \text{ir}_\text{FOR} \right) – \left( 1 + \text{ir}_\text{DOM}^\text{Local} \right) = 1 + \text{ir}_\text{DOM}^\text{Swap} – \left( 1 + \text{ir}_\text{DOM}^\text{Local} \right) = \text{ir}^\text{Swap} – \text{ir}^\text{Local}$$

Where we have dropped the subscript since both rates are denominated in domestic currency.

As a side note, the reason CIP deviations are often expressed in terms of the basis is that it eases interpretability. For instance, a US company seeking funds may look at the EURUSD basis and if it’s negative ($$\text{ir}^\text{Swap} < \text{ir}^\text{Local}$$), as it is now, might decide to borrow in Europe to pay a lower interest than in the US money markets. In fact, this is what many companies have been doing in the last decade as Borio et al.  report.

Back to the topic, the figure below, extracted from Hong et al.  provides a nice overview of the recent evolution of the basis seen from the USD perspective.

First, the fact that the turning point is 2008 is not casual as you might have imagined, but we will have to leave that for another post. Hint: it has to do with the widening of the OIS-LIBOR spread.

Second, the magnitude of the CIP deviations is considerable enough for the BIS (Bank of International Settlements) to pose the question: is money being left on the table? in a symposium on CIP.

A common theme in finance is to see apparently free money turn into a well-priced reward for previously unknown risk. So first we will try to address the question above by deepening our understanding of the risk mechanics behind the CIP arbitrage and the FX Swap.

## Revising CIP

So far we’ve talked as if there were a single type of interest rate to consider, namely LIBOR (London Inter-Bank Offered Rate). This represents the rate at which a panel of well-established banks is willing to lend to each other on an unsecured basis. Unsecured meaning that if the borrower were to default, the lender would not get their money back.

LIBOR rates were industry-standard pre-2008 and the most commonly used in the CIP literature. However, using LIBOR rates (or any type of unsecured lending rates) in the CIP model does not lead to riskless arbitrage as we will see.

Unsecured lending rates can be decomposed into three components, namely: risk-free rate, liquidity premium, and credit risk premium.

$$ir = r + lp + cp$$

The liquidity premium is the reward for holding a less liquid asset: the promise of getting back the loan instead of the lent cash. A credit risk premium is a reward for holding the risk that the borrower may default on the loan.

Then we can reframe CIP as:

$$F = S \frac{1 + r_{\text{DOM}} + lp _{\text{DOM}} + cp _{\text{DOM}} }{1 + r_{\text{FOR}} + lp_{\text{FOR}} + cp_{\text{FOR}} }$$

This means that the swap price should reflect the relative risk-free rate, liquidity and credit risk between the two currencies. But is this correct?

In order to answer that question, we need to take a look at the risk profile of the FX Swap. Spoiler alert: as Wong et al.  point out, the credit risk differential should not be there.

## Redefining FX Swaps. Repos or collateralized loans

The real voyage of discovery consists not in seeking new lands but in having new eyes.

Marcel Proust

So let’s take a look at FX Swaps with new eyes.

An FX Swap can be seen as a repo, which is short for a repurchase agreement. Repos originated in the Middle Ages when usury law banned charging interests on loans. As a workaround, people seeking funding would sell any item and compromise to buy it back later at a higher price. In this way, pawnshops acted as banks providing liquidity at an interest rate implicit in the higher repurchase price.

The item exchanged acts as collateral that the lender can keep in case of a counterparty default, limiting credit risk. On the other hand, there’s a liquidity differential between the two assets involved (cash and collateral) that the borrower needs to pay for.

In an FX Swap, the collateral happens to be cash too but denominated in a different currency. In summary, an FX Swap transaction involves being exposed to a liquidity differential but to no credit risk differential (note that apart from the notional being covered with collateral, the unrealized PnL is limited due to marking-to-market procedures ). Thus an accurate CIP model should look more like this:

$$F = S \frac{1 + r_{\text{DOM}} + lp_{\text{DOM}} }{1 + r_{\text{FOR}} + lp_{\text{FOR}} }$$

So no wonder there were CIP deviations when using LIBOR rates. The model was right but the inputs were wrong. Mystery solved!

Well, not so quickly.

In short, no interest rate has been able to replace LIBOR rates successfully. Rates from other types of repo contracts were a good candidate, since they don’t incorporate credit risk either, but they still lead to significant CIP deviations. We will address this in more detail in another post.

## Concluding remarks

So back to the starting point! Is money being left on the table? Can we come up with a fair price for FX Swaps? The questions remain the same, but I hope you have gained some interesting insights in the process. We will continue with this discussion in the future and hopefully, come back with some comforting answers. See you then!

## References

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

 Hong, Gee Hee, et al. “What Do Deviations from Covered Interest Parity and Higher FX Hedging Costs Mean for Asia?.” Open Economies Review (2020): 1-34.APA

 Wong, Alfred, and Jiayue Zhang. Breakdown of covered interest parity: mystery or myth?. Vol. 96. Bank for International Settlements, 2018.

 Kohler, Daniel, and Benjamin Müller. Covered interest rate parity, relative funding liquidity, and cross-currency repos. No. 2019-05. Swiss National Bank, 2019.