Book 4. Liquidity and Treasury Risk

FRM Part 2

LTR 17. Covered Interest Parity Lost: Understanding the Cross-Currency Basis

Presented by: Sudhanshu

Module 1. Covered Interest Parity Violations

Module 1. Covered Interest Parity Violations

Topic 1. Covered Interest Parity (CIP)

Topic 2. Foreign Exchange (FX) Swaps

Topic 3. Cross-Currency Basis Swaps

Topic 4. Key Factors Affecting Cross-Currency Swap Basis

Topic 5. Why the Basis Opens Up: Demand for Currency Hedges

Topic 6. Why the Basis Does Not Close: Limits to Arbitrage

Topic 1. Covered Interest Parity (CIP)

• Definition: CIP is a no-arbitrage condition in which the interest rate differential between two currencies is equal to the differential between the forward and spot exchange rates. In theory, this should always hold true.

• Arbitrage: If CIP does not hold, a risk-free arbitrage opportunity exists. Traders would exploit this mispricing until it disappears.

• Formula:

  • ​

• Key Variables:

  • $S$ = Spot exchange rate

  • $F$ = Forward exchange rate

  • $r$ = Domestic currency interest rate (e.g., USD)

  •    = Foreign currency (FC) interest rate

• ​Forward premium form: Forward premium (F − S) in points equals spot rate times interest rate differential
• Two equivalent investment paths: (1) Direct USD investment at rate r, or (2) Indirect investment via spot conversion to FC at rate r*, with forward hedge at rate F
• No-arbitrage condition: Both paths must yield identical returns; otherwise risk-free arbitrage exists
• Note: In our future discussions, we will assume USD as domestic currency.

Topic 2. Foreign Exchange (FX) Swaps

• Definition: In an FX swap, the two parties agree to swap USD for an FC today at the spot rate (USD per FC) and simultaneously agree to swap back at the forward rate at maturity.

• Purpose: One party is lending USD and borrowing the FC, and the other party is lending the FC and borrowing USD.

• Quoting: FX swaps are typically quoted in forward points $(F-S)$, which represent the difference between the forward and spot rates.

• Post-2008 Trend: Since the 2008 financial crisis, the USD has often commanded a premium relative to the FC in FX swaps. This means that the party lending USD can sell the FC forward at a price F that is higher than indicated by the interest rate differential , leading to a violation of CIP where:

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Practice Questions: Q1

Q1. In an foreign exchange (FX) swap the:
A. price is quoted in forward points.
B. term is typically more than one year.
C. counterparties swap currencies back at the end of the contract at the original spot rate.
D. counterparties exchange net interest payments based on the reference rate during the term of
the swap.

Practice Questions: Q1 Answer

Explanation: A is correct.

An FX swap is quoted in forward points (F − S). The other choices are features of cross-currency swaps.

Practice Questions: Q2

Q2. Since the financial crisis of 2007–2009, the cross-currency basis for most major currencies relative
to the U.S. dollar (USD) has consistently been:
A. equal to zero.
B. greater than the interest rate differential.
C. greater than zero for the USD interest rate.
D. greater than the forward premium on the USD.

Practice Questions: Q2 Answer

Explanation: C is correct.

Since the 2007–2009 crisis, the USD has tended to command a premium relative to the foreign currency (FC) in FX swaps; the party lending USD can sell the FC forward at a price F that is higher than indicated by the interest rate differential. That means the cross-currency swap basis has been greater than zero.

Topic 3. Cross-Currency Basis Swaps

• Definition: Similar to FX swaps, currencies are exchanged at the spot rate at the beginning of the contract. However, there are key differences:

  • Maturity: They are typically longer-term contracts (often > 1 year).

  • Re-exchange: At maturity, currencies are swapped back at the original spot rate, not a forward rate.

  • Interest Payments: During the life of the contract, counterparties exchange interest payments based on the reference rates of the two currencies, adjusted by a "basis" $(b)$.

• The Cross-Currency Basis $(b)$: This is the amount by which one currency's interest rate must be adjusted for CIP to hold.​

  •  

• Impact of the Basis: When CIP doesn't hold, the party borrowing the premium-currency (e.g., USD) pays the basis in addition to the interest rate. The party borrowing the other currency pays less than its reference rate.
• Note: If CIP holds, the basis is zero and the cross-currency basis swap is simply

  a straightforward floating-for-flloating currency swap.

Practice Questions: Q3

Q3. The cross-currency swap basis is the:
A. interest rate differential in a cross-currency swap.
B. price to the long position in a cross-currency swap.
C. difference between the forward and spot exchange rates in a cross-currency swap.
D. amount by which the interest rate of one currency must be adjusted in a cross-currency swap so that covered interest parity (CIP) holds.

Practice Questions: Q3 Answer

Explanation: D is correct.

The cross-currency swap basis (b) is the amount by which the interest rate of one currency must be adjusted so that CIP holds. This is shown in the following formula:

Topic 4. Key Factors Affecting Cross-Currency Swap Basis

• Two Primary Drivers of CIP Deviations which stops the cross-currency basis from becoming zero: decline in market liquidity and increase in risk premia

• Decline in market liquidity
  • External financial crises reduce liquidity in underlying forward and spot FX contracts
  • Results in wider bid-ask spreads, increasing transaction costs and eliminating arbitrage opportunities
• Increase in risk premia
  • ​Counterparty credit risk: Higher risk in underlying FX markets
  • Sovereign credit risk: Increased risk in government bonds used for CIP arbitrage (measured via sovereign CDS spreads)
  • Even small risk premia increases significantly impact arbitrage execution when hedging demand for one currency is sufficiently large
• Result: Deviations from CIP cause cross-currency swap basis to diverge from zero during financial crises

Topic 5. Why the Basis Opens Up: Demand for Currency Hedges

• Persistent Violations: Since the 2007-2009 financial crisis, CIP violations have become more common, leading to a non-zero basis. This is primarily due to increased demand for currency hedging, even in non-crisis times.

• Sources of Hedging Demand:

  • Banks: Managing currency mismatches on their balance sheets using FX swaps

  • Institutional Investors (like insurance companies and banks): Hedging foreign currency risk in their investment portfolios using FX swaps

  • Non-financial Firms: Issuing foreign-currency denominated debt when credit spreads narrow in foreign debt markets and then swapping the FC proceeds back to USD using FX swaps.

Topic 6. Why the Basis Does Not Close: Limits to Arbitrage

• The Arbitrage Opportunity: In a perfect market, if the basis opens up, arbitrageurs should quickly close the gap. However, this doesn't happen in the real world.

• The Problem: CIP arbitrage is not risk-free. It requires expanding an arbitrageur's balance sheet, which exposes them to:

  • Counterparty Credit Risk: The risk that the other party in the swap will default.

  • Capital and Funding Risk: The risk of not having enough capital or funding to complete the trades.

  • Liquidity Risk: The risk of facing mark-to-market requirements.

• Post-Crisis Environment: After the 2008 crisis, regulators and investors put pressure on financial institutions to manage their balance sheets more carefully. This has limited the ability of arbitrageurs to take on these risks, which in turn has prevented them from fully closing the basis.