## Wednesday, March 4, 2015

### Primer: Understanding Covered Interest Rate Parity

Covered interest rate parity is the relationship that determines the fair value of forward currency levels. It is easily understood from the perspective of an international bond investor or issuer, and these entities ensure that it holds in practice.

The most concise statement of the relationship is as follows. If a foreign currency bond is trading at a spread of x basis points relative to that foreign currency LIBOR curve, and if it is hedged into the local currency, the hedged bond will have a yield that is a spread of x+y basis points (approximately) versus the local currency LIBOR curve (all prices being mid-market quotes), where y is the "basis". (The basis has a fair value of zero.)

The error term (y) is determined in the cross-currency basis swap market. The fair value for these cross-currency basis swap spreads is zero, but cross-currency funding pressures can cause the spread to move, which moves the level of the hedged yield. I explain this in further detail within this article, but without dragging in mathematical formulae.

Within some of the economic literature, the explanation of the covered interest rate parity relationship can be confusing, mainly because the explanations do not take account of the cross-currency basis swap market. But the real disputes within economics revolve around uncovered interest rate parity: do forward rates predict future spot rates? That is a larger question, but I want to discuss it after pinning down the proper understanding of covered interest rate parity. In my view, once you understand covered interest rate parity, there is no mystery about the uncovered interest rate parity concept.

### Technical Digression On "LIBOR"

Within this article, I refer to the "LIBOR curve", which is a generic yield curve that is defined from overnight out to 50 years. This is a term used by analysts who build modern fixed income pricers (which used to be part of my previous job description). It is the primary yield curve used to price private sector instruments within a currency.*

I abstract from two annoying semantic issues.
1. LIBOR also refers to a specific set of interest rate fixes which are the London Interbank Offer Rate. The LIBOR fixes are critical for determining the valuation of the "generic LIBOR" curve, which is why the generic curve was named in this fashion. The generic curve is fitted based on interest rate fixes (such as LIBOR itself), short rate rate futures, and swaps. For simplicity, you can think of this as a yield curve for default risk free generic bank deposits**, which acts in a similar fashion to a Treasury fitted yield curve.
2. In some currencies, the short rate fixings used are not LIBOR. I will refer to LIBOR as a generic term, rather than drag in these less well known (amongst non-fixed income specialists) fixings.

### A Bond Investor's View Of Covered Interest Rate Parity

Imagine that you are a bond investor in the United States in a parallel universe where various financial prices are at convenient levels. In particular, it is 10 am Eastern Standard Time, and markets are quiet. You have \$10 million which you need to invest. (Note: all prices here are mid-market; you would expect to lose out to the dealer on bid-offer spreads relative to these prices.)

You observe that a large multinational issuer has a U.S. dollar (USD) denominated 1-year bond that trades with a spread of 0 versus 1-year LIBOR that is 4%. You would like to buy this bond, but you would like to get a higher yield, because 4% is an unsustainably low yield (or something like that).

You look at a euro (EUR)-denominated bond from the same issuer, and it is also trading at a spread of 0 to 1-year  EUR "LIBOR", which happens to be 5%. That looks attractive, except your pesky risk officer will not let you take any foreign exchange risk. The spot EUR-USD exchange rate is a very convenient 1:1 relationship.

So, you think about the following transactions:
• buy 10 million EUR, exchanging the \$10 million USD you have in hand;
• buy 10 million EUR of the bond at 5%;
• enter into a forward exchange rate agreement that exchanges the 10.5 million EUR you will receive in one year*** back to USD.
For the sake of argument, we assume the EUR-USD basis over 1-year is zero. (I discuss this later.) What will happen is that the forward exchange rate will be chosen such that your proceeds when converted back to USD will be USD 10.4 million. (The forward exchange rate is 1 USD = 1.0096 EUR; that is, you need more EUR to buy 1 USD than is the case at the spot exchange rate.)

In other words, you end up exactly where you started from, with a USD-denominated return of 4%. If we ignore the "costs" of entering into derivative contracts, you are indifferent between buying the USD or EUR bond. The relationship between a forward exchange rate and the spot rate is determined by "LIBOR" differentials. (1.0096 = 1.05/1.04)

If the forward rate was appreciably different, you would have a "free lunch". Imagine that the foreign exchange desk at the bank was filled with drunken rookies that set forward rates to equal the spot rate. The EUR bond would then yield 5% in USD terms after hedging. You would dump all of your existing holdings, and buy the EUR-denominated bond, picking up a "free" 100 basis points in yield. The major banks who dominate foreign exchange trading tend not to let incidents like that happen.

It is not just bond investors, issuers look at this relationship. Issuer spreads relative to "LIBOR" roughly reflect default risk, which is independent of the currency the bond is issued in. If forwards were set out of line with this relationship, issuers would just issue in the most advantageous currency, and hedge back into the desired currency. This adds to the balance sheet weight that pins down the arbitrage relationship.

Importantly, this has nothing to do with foreign exchange ("forex") traders. If some foreign exchange traders came up with some wacky theory that the forward rate should trade somewhere else relative to spot, they would crushed by the arbitrage trades of bond investors and issuers. In order to counteract those arbitrage trades, the forex traders would have to make big trades on the slope of the currency forward curve. Risk managers would diagnose them as taking interest rate risk, and they would be forced out of those positions (in the same way that bond investors are not allowed to take foreign exchange risk).

The "basis" between the market forward and what is implied by LIBOR differentials is the spread on cross-currency basis swaps. A basis swap is essentially an exchange of funding: one party lends at "LIBOR" in one currency versus receiving a loan at "LIBOR" in the other. A spread is added to one side of this funding swap, and this spread drives the deviation of forwards from what is implied by domestic interest rate differentials.

A basis swap looks like making an exchange of currencies spot, and then reversing the transaction forward. But there are intermediate floating rate cash flows during the transaction (at the LIBOR fix rate), which compensates for the interest rate differential between the two currencies. This allows the future exchange rate used within the swap to equal the spot rate. A standard currency forward, such as the transaction I described in the example above, is determined by swapping the floating rates within a basis swap for fixed rates. The deviation of the forward from spot is determined by the difference between the two embedded long-term swap rates,

If markets are non-stressed, large institutions should be able to borrow near LIBOR in all currencies, and so the spread should be near zero. However, divergences can occur.
• During the financial crisis, it became clear that European banks had large USD-denominated asset exposures which they were funding in wholesale markets. When the USD commercial paper markets shut out many EUR banks, those banks had a funding currency mismatch. They could easily find cheap EUR funding from deposits or the ECB, but not USD funding. They turned to the cross-currency basis swap market to exchange EUR funding for USD. Since the flow was one way - nobody in the U.S. was particularly attracted to EUR fixed income assets - spreads on the basis swap moved significantly. This spread move was often interpreted as being like a default risk premium, but this is not exactly true. It just reflects a spread of funding costs in different regions, which at most reflects a differential of implied default risks.
• Canada lacks a dedicated CAD-denominated high yield market. Canadian issuers will issue in USD, and Canadian high yield investors will look at the USD market. If a large leveraged buyout occurs in Canada, it will have to be funded in the USD market, whereas they need CAD to pay for the shares. This creates a large expected flow in the cross-currency swap market, and the spreads on CAD basis swaps can move significantly. This has nothing to do with "Canada risk", it is just that the cross-currency funding market is relatively small and has a hard time absorbing big flows. You see similar events in the Australian dollar, and the Japanese yen (which has crazy amounts of exotic fixed income products sold to local investors that often require cross-currency hedges).

Some earlier analysis by economists essentially assumed that the basis would be zero; that is, cross-currency funding demand would move domestic interest rates such that the basis would disappear. This does not happen; the cross-currency funding markets and local currency bond markets are segmented enough to allow for a non-zero basis.

From the perspective of bond investors, the fact that the spreads in the basis swaps market can deviate from zero means that there are advantageous (and disadvantageous) directions to hedge bond portfolios. Hedging strategies may need to be adjusted to take this into account. But the fact that one can get a small spread pickup in some cross-currency trades is not really a free lunch. Even a 20 basis point spread pickup for the same credit risk may not be worth the extra risks associated with cross-currency hedge position.

### Does This Assume Efficient Markets?

Some dislike the concept of efficient markets, and look for ways in which arbitrage relationships break down. In this case, arbitrage generally rules.

For a single market-making bank, its pricers will treat either the cross-currency basis swap market or the currency forward market as being redundant information. One curve (in conjunction with the spot forex rate and domestic interest rate curves) is used to calculate the other. Therefore, a single dealer's quotes will be arbitrage-free. Arbitrage is only possible if two dealers' curves are incoherent. This tends to only happen when markets are highly stressed, and it would be impossible to lock in arbitrage profits (realised bid-offer spreads would be too wide).

### A Postscript On Post-Keynesian Economics

I recently reviewed the text Post-Keynesian Economics: New Foundations by Professor Marc Lavoie. I noted that I had some reservations with the book, which is not too surprising, given the scope of the text.

The sections on interest rate parity in Chapter 7 is where I would have written things differently. My views can be viewed as being consistent with Professor Lavoie's, but I would use a more "modern" framework to explain the concepts. His discussion of the topic is based on literature which was written before the development of the basis swap market, and so those authors had no choice but to have a somewhat looser understanding. To be clear, the analysis of covered interest rate parity is not "wrong", but it could be done in a more straightforward manner.

His comments on uncovered interest rate parity are where I have a greater reservations, which is once again the result of taking into account the analytical framework used in modern financial markets. I think this is one section where it might have been worthwhile to incorporate contributions from academic finance, while noting that earlier post-Keynesian economists are consistent with, and hence anticipated this "modern" framework.

Footnotes:

* Archaic textbooks will often refer to the "risk-free curve" which is used to price instruments like options. The implication being that the "risk free rate" is driven by the central government yield curve. This is incorrect; since only the government can borrow at that rate, you need to price instruments off of a private sector curve.

** What a "default risk free bank deposit" represents is an interesting philosophical issue, which I do not want to discuss here. My experience is that even market practitioners who trade these instruments all day do not agree on what swap rates really represent.

*** Conveniently, EUR bonds are annual coupons, and so there is no coupon to reinvest. I am using a simplified yield convention, which may or may not match exactly bond market quote conventions. The proceeds may differ slightly from 10.5 million EUR as a result of quote convention differences.

(c) Brian Romanchuk 2015

1. "...the hedged bond will have a yield that is a spread of x+y basis points versus the local currency LIBOR curve.."

Worth noting that that is only an approximation, based on x being small, the term short or a small interest rate differential between the currencies.

1. I threw in a "approximately"; I think I accidentally chopped it out when I rewrote the sentence. The precise translation from the spread in basis swaps to the swapped yield depends on pricing formulae, and yes, the approximation breaks down when the spreads are high (and/or the bond has a coupon that deviates markedly from the swap rate).

My feeling is that if someone is worried about getting that pricing exact will have access to the pricers that will do the job for them.

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