Introduction

• Covered interest parity (CIP) is the closest thing to a physical law in international finance. It holds that the interest rate differential between two currencies in the cash money markets should equal the differential between the forward and spot exchange rates. Otherwise, arbitrageurs could make a seemingly riskless profit.
  • For example, if the dollar is cheaper in terms of yen in the forward market than stipulated by CIP, then anyone able to borrow dollars at prevailing cash market rates could profit by entering an FX swap – selling dollars for yen at the spot rate today and repurchasing them cheaply at the forward rate at a future date.

Framework

• CIP is a textbook no-arbitrage condition according to which interest rates on two otherwise identical assets in two different currencies should be equal once the foreign currency risk is hedged:

\( \frac{F}{S} = \frac{1 + r}{1 + r^*} \)

where

𝑆 is the spot exchange rate in units of US dollar per foreign currency,

𝐹 is the corresponding forward exchange rate,

𝑟 is the US dollar interest rate, and

𝑟^∗ is the foreign currency interest rate.

Rearranging the 𝐶𝐼𝑃 equation yields the following relationship between (𝐹 – 𝑆), 𝑟 and 𝑟^∗:

\( \frac{F}{S} = \frac{1 + r}{1 + r^*} \) \( \Rightarrow \frac{F}{S} – 1 = \frac{1 + r}{1 + r^*} – 1 \) \( \Rightarrow \frac{F – S}{S} = \frac{1 + r}{1 + r^*} – 1 \) \( \Rightarrow F – S = S \left( \frac{1 + r}{1 + r^*} – 1 \right) \)

FX Swap

• The relationship underlying the CIP can be demonstrated in an FX swap, where one party borrows one currency from, and simultaneously lends another currency to, a second party. The borrowed amounts are exchanged at the spot rate, 𝑆, and then repaid at the pre-agreed forward rate, 𝐹, at maturity. The implicit rate of return in an 𝐹𝑋 swap is determined by the difference between 𝐹 and 𝑆, and the contract is typically quoted in forward points (𝐹 — 𝑆). Rearranging the CIP equation, the following equation was obtained earlier –

\(F – S = S \left( \frac{1 + r}{1 + r^*} – 1 \right) \)

• If the party lending a currency via 𝐹𝑋 swaps makes a higher or lower return than implied by the interest rate differential in the two currencies, then CIP fails to hold. Since the onset of the Global Financial Crisis (GFC), CIP has failed to hold. Typically, the US dollar has tended to command a premium in 𝐹𝑋 swaps. In that case, the above equality changes to an inequality, i.e.

\(F – S > S \left( \frac{1 + r}{1 + r^*} – 1 \right) \)

A positive (“wide”) value of 𝐹 𝑆, above, indicates that a party lending US dollars sells the foreign currency forward at a higher dollar price than warranted by the interest differential. Equivalently, a party borrowing US dollars via an 𝐹𝑋 swap is effectively paying a higher interest rate on the swapped dollars than is paid in the cash market.

Cross Currency Swap

• A cross-currency swap is similar to an FX Swap in which the two parties also simultaneously borrow and lend an equivalent amount of funds in two different currencies. There are some differences though –
  • These are longer-term instrument, typically above one year.
  • At maturity, the borrowed amounts are exchanged back at the initial spot rate, 𝑆.
  • During the life of the swap the counterparties also periodically exchange interest payments.

• In a cross-currency basis swap, the reference rates are the respective Libor rates plus the basis, b.

If the forward points (𝐹 – 𝑆) are greater than warranted by CIP, then, assuming a one period maturity, the basis, 𝑏, will effectively be the amount by which the interest rate on one of the legs has to be adjusted so that the parity with the pricing of FX swaps holds:

\( F – S = S \left( \frac{1 + r + b}{1 + r^*} – 1 \right) \) \(\Rightarrow F – S = S \left( \frac{1 + r + b}{1 + r^*}\right) – S \)

Continuing with the same example, the 𝐹𝑋 swap implied US dollar rate, F⁄_S (1 + 𝑟^∗), exceeds actual US dollar Libor, 1 + 𝑟, if the party borrowing US dollars in a cross-currency swap pays  the basis, 𝑏, on top of US dollar Libor.

• Thus, failure of CIP has implications for the relative cost of funding in the cash and swap markets. Whenever CIP fails, one party ends up paying the currency basis above the cash market rates to borrow the corresponding currency, while the other counterparty in effect receives an equivalent discount when borrowing the other currency.

Why CIP Can Fail

• A number of factors can cause 𝐶𝐼𝑃 to fail –
  • Market liquidity in the underlying instruments may evaporate, so that the difference between bid and ask prices for forward and spot transactions is non-trivial. 𝐶𝐼𝑃 deviations due to a drop in market liquidity can be approximated as

\( b \equiv \frac{F}{S} – \frac{F_b}{S_a} \)

where

𝑆_a is the spot ask rate, and

𝐹_b is the forward bid rate

• Credit risks in the underlying investments can also lead to failure of CIP.
  • A rise in counterparty credit risks in the interbank markets, typically captured using Libor-OIS spreads, could result in CIP deviations.
  • Deviations in CIP might result from differences in sovereign credit risks, typically measured using sovereign CDS spreads. CIP deviations measured using risk-free rates can be approximated as \(b\equiv rp\).

 where

𝑟𝑝 is the risk premium for the underlying investment over the duration of the swap.

• Deviations in CIP can arise if the demand to hedge one of the currencies is large. Then, even small risk premia can have big effects when scaled by the large size of the balance sheet exposures. CIP deviation can be proportional to the hedging demand multiplied by the per-dollar balance sheet costs of FX derivatives exposures

𝑏 ≡∝ 𝑟𝑝 × 𝐹𝑋 𝐻𝑒𝑑𝑔𝑖𝑛𝑔 𝐷𝑒𝑚𝑎𝑛𝑑

• Some specific constraints, and hence the instruments involved, also depend on arbitrageurs –
  • For highly rated supranational and quasi-government agencies, which can arbitrage the long- term basis thanks to their top credit rating by issuing bonds in US dollars at attractive rates and then swapping them out, 𝑟𝑝 is more closely related to the costs of placing bonds in different currencies.
  • For hedge funds, which rely on collateralized markets to fund CIP arbitrage, the price and availability of repo market funding will play a significant role.

Causes Of CIP Violations After Crisis

Demand for Currency Hedges: Why the Basis Opens Up

• Hedging of open FX positions is the main proximate driver of the demand for FX swaps. There are three sources of hedging demand that are rather insensitive to the size of the basis, and, hence, exert sustained pressure on it even when it is non-zero –
  • Banks
  • Institutional Investors
  • Non-financial firms

1. For a long time, banks have been the main players running currency mismatches on their balance sheets (managed mainly via swaps). Banking systems may be structurally short or long in specific currencies, given their core deposit base. A shortfall in foreign currency funding can then be managed by cash borrowing in money and bond markets. The remaining gaps between banks’ assets and liabilities in a given currency would be closed using currency derivatives such as FX swaps.
2. The second source of demand arises from the strategic hedging decisions of institutional  investors, such as insurance companies and pension funds. Institutional investors use swaps to strategically hedge foreign currency investments. In recent years, there has been term and credit spread compression by banks in response to unconventional monetary policies which has boosted these cross-currency investments and funding flows. Anything that induces these investors to increase or reduce their foreign currency investments tends to put pressure on the basis.
3. Another source of demand arises from non-financial firms’ debt issuance across currencies as they seek to borrow opportunistically in markets where credit spreads are narrower. This can become quite relevant when credit spreads differ systematically, for example when they are compressed by central bank large-scale asset purchases. Recently, for instance, many US firms needing dollars have been issuing in euros to take advantage of very attractive spreads in that currency and have then swapped the proceeds into dollars. This allows them to use the dollars for their business purposes while avoiding a currency mismatch in euros. Essentially, through the swap market, they borrow dollars and lend euros.

• Other factors could also put pressure on the basis, but those are generally excluded from  analysis because of data limitations. Examples can be –
  • Firms’ hedging of trade receivables or subsidiary cash flows
  • Speculative FX positions, which can rely on forwards and swaps (eg yen carry trades).

Limits to Arbitrage: Why the Basis Does Not Close

• After the crisis, there have been structural changes in pricing of market, credit, counterparty and liquidity risks by market participants, which have tightened limits to arbitrage.
  • As a result of tighter management of risks and related balance sheet constraints, arbitrage now incurs a cost per unit of balance sheet. This cost is passed on to the pricing of FX swaps, introducing a premium (or discount) in response to imbalances in the swap market.
• Arbitrage can be both costly and risky. Typically, it requires the arbitrageur to enlarge its balance sheet, incur credit risk in both borrowing and investing, and possibly face mark-to-market and liquidity risk (given the need to transfer collateral or take paper gains or losses) in the valuation of the positions.
• While these risks and costs exist all the time, they are being managed more actively post-crisis. Before the GFC, these risks were not fully priced in the relevant markets and, partly as a result, dealer banks had raised their leverage to dangerous levels. Since the crisis, pressure from shareholders, creditors and prudential authorities has reinforced and hard-wired participants’ awareness. As a result, leverage has declined and there has been less willingness to go for activities like arbitraging the basis, as these activities put heavy pressure on the balance sheet.
• Changes in regulation have reinforced market pressures for tight management of balance sheet risks. For example, changes related to CVAs have sought to incentivize dealers to price counterparty risk in their derivatives portfolios more accurately. Similarly, potential future exposure adjustment charges in both Basel III and US leverage ratios require market participants to hold capital in proportion to their derivatives and other exposures.
• These tighter limits on arbitrage make it harder to narrow the basis whenever it opens up.
• Even in the absence of bank funding strains like those seen during the GFC, a sufficiently high net demand for currency hedges could result in persistent deviations from CIP