FRM Exam Part II · Covered Interest Parity Lost: Understanding the Cross-Currency Basis

FX Swaps and Cross-Currency Basis Swaps Explained

Updated 11 October 2026 · Fact-checked

An FX swap exchanges two currencies now and reverses the exchange at a forward date at a pre-agreed rate. A cross-currency basis swap exchanges floating rates in two currencies, plus a basis spread on the non-dollar leg. A negative basis means borrowing dollars synthetically costs more than borrowing them directly.

Understand FX Swaps and Cross-Currency Basis Swaps

Start with the problem. A European bank holds euros but needs dollars for a few months. It can borrow dollars in the market, or it can borrow euros and swap them into dollars. The second route is synthetic dollar funding.

An FX swap does this in two legs. You swap euros for dollars at the spot rate today. You agree to swap back at the forward rate on a future date. The forward rate is fixed on day one, so there is no exchange rate risk. The cost of the dollars is built into the gap between spot and forward. It is an exchange of principal, and the interest differential is embedded in the forward points. FX swaps usually cover short maturities, up to about one year.

A cross-currency basis swap works for longer terms. The two parties exchange principal at the start. During the life they pay floating interest in each currency, for example 3-month SOFR on the dollar leg and 3-month EURIBOR plus or minus a spread on the euro leg. At maturity they swap the principal back at the original spot rate. That spread is the cross-currency basis.

Under covered interest parity (CIP), the basis should be zero. Borrowing dollars directly and borrowing euros then swapping into dollars should cost the same. Since 2008 the basis has often been negative for the euro and yen against the dollar. A negative basis means the dollar borrower, who hands over euros as principal and receives dollars through the swap, receives EURIBOR plus a negative basis on the euros it handed over. It therefore earns less on its euro leg than it would with no basis. That shortfall is the extra cost of synthetic dollars. Synthetic dollars cost more than direct dollars. This reflects strong demand for dollar funding and limits on arbitrage such as balance sheet costs.

The quote is usually shown in basis points on the non-dollar leg. A quote of EUR/USD 3-year at -25 bp means the euro floating rate leg is EURIBOR - 25 bp against SOFR flat. The party that hands over euros and receives dollars at the start receives EURIBOR - 25 bp on the euros it handed over and pays SOFR on the dollars it received. It earns 25 bp less than in the no-basis case. For the exam, remember the sign, which leg carries the spread, and what it says about dollar scarcity.

Key formulas to remember

CIP condition (no basis): F ÷ S = (1 + r_domestic) ÷ (1 + r_foreign), with rates for the same horizon and exchange rate quoted as domestic per unit foreign; Forward-to-spot ratio equals the interest rate ratio. Basis is zero when this holds.
Cross-currency basis (simple, annualised, one period): x ≈ r_non-USD, implied − r_non-USD, direct; The implied rate is the non-dollar rate the FX swap market gives you when you hand over non-dollar currency and receive dollars, which is the synthetic dollar route. The direct rate is what you would earn lending the same currency in its own money market. A negative x means the swap market pays less on the non-dollar currency than the direct rate, so obtaining dollars through the swap costs more. Sign conventions vary by source, so check how the question defines it.
Forward points: Forward points = F − S; The forward points carry the interest differential plus any basis in an FX swap.
Basis swap quoting convention: Non-USD leg pays: floating rate + basis (bp). USD leg pays: floating rate flat; Negative basis means the non-USD leg pays below its reference rate. It signals a premium to obtain dollars.

How to solve FX Swaps and Cross-Currency Basis Swaps questions

Use this order for any question on FX swaps or cross-currency basis.

1Identify the instrument. Short-term with embedded forward points is an FX swap. Floating legs with a spread over several years is a cross-currency basis swap.
2Write down both legs. Note who pays or receives which currency at the start and at maturity.
3Check the principal exchange. Final exchange is at the initial spot rate in a basis swap, and at the forward rate in an FX swap.
4Locate the basis. Find which leg carries the spread, and read its sign.
5Interpret the sign. A negative basis against the dollar means dollars are expensive via the swap, so demand for dollars exceeds supply.
6Compare synthetic and direct costs. Add or subtract the basis from the non-dollar rate, then compare with direct dollar borrowing.
7Link to the risk. Name the exposure, such as rollover risk, funding liquidity risk or collateral calls.
8Check the answer has the right sign and units (bp or percent).

Quickest way: Sign and leg shortcut

When to use it: Use when the question gives a basis quote and asks which borrowing route is cheaper or what the sign means.

Assume the spread is on the non-dollar leg, as in the market convention.
Negative basis: synthetic dollars cost more than direct dollars.
As an approximation, the synthetic dollar cost is roughly the direct dollar rate plus the basis magnitude. The basis is defined on the non-dollar leg, so treat this as a rough guide, not an exact rule.
Positive or zero basis: synthetic funding is as cheap or cheaper, which is consistent with CIP holding.
Eliminate options that say the basis is a credit spread on the dollar leg or that the swap removes all funding risk.

Common mistakes in FX Swaps and Cross-Currency Basis Swaps

Treating an FX swap and a currency swap as the same product
Both exchange two currencies and both are used for funding.
Fix: FX swap: short-dated, principal exchange at spot and forward, interest embedded in forward points. Cross-currency basis swap: longer-dated, floating interest paid in each currency, with a spread.
Reading a negative basis as a gain for the dollar borrower
The word negative sounds like a discount.
Fix: A negative basis on the non-dollar leg means the dollar borrower pays a premium. Dollars obtained via the swap cost more than direct dollars.
Assuming CIP never fails because it is an arbitrage condition
Textbooks present parity as a no-arbitrage result.
Fix: Since the 2008 crisis the basis has been persistently non-zero. Balance sheet limits, regulatory costs and dollar demand restrict arbitrage.
Placing the spread on the dollar leg
The dollar is the reference currency, so students assume it carries the adjustment.
Fix: The market convention puts the basis on the non-dollar floating leg, with the dollar leg flat to its index.
Ignoring the final exchange rate in a basis swap
Students focus on the interest legs.
Fix: Principal comes back at the initial spot rate. That removes principal exchange rate risk but leaves mark-to-market and collateral exposure.
Thinking the swap eliminates rollover risk
The forward rate is fixed, so the position seems fully hedged.
Fix: Short FX swaps must be rolled. If the basis widens or dollars become scarce, rolling costs more or becomes unavailable.

Worked examples

Example 1

A bank that needs dollars enters a 1-year FX swap. It pays €10,00,000 and receives USD at spot of 1.10 USD per EUR. It agrees to reverse at a forward rate of 1.1110 USD per EUR. How many USD does it receive now, and how many does it pay back at maturity?

Show the solution

Dollars received at spot: 10,00,000 × 1.10 = USD 11,00,000.
Dollars paid back at forward: 10,00,000 × 1.1110 = USD 11,11,000.
The bank gets back its €10,00,000 in the second leg.
Extra dollars paid back: USD 11,11,000 − USD 11,00,000 = USD 11,000.
Express it as a rate: USD 11,000 ÷ USD 11,00,000 = 1%. This is the implied 1% cost of the dollars over the year.
Check with the ratio: F ÷ S = 1.1110 ÷ 1.10 = 1.01, so the forward is above spot. The euro trades at a forward premium and the dollar at a forward discount.
Interpret: the 1% cost is not all basis. Under CIP the forward premium would reflect the USD–EUR interest rate differential for the year. Only the part of the 1% above that interest differential is the basis.

Answer: It receives USD 11,00,000 now and pays back USD 11,11,000 at maturity to get its euros back. The extra USD 11,000 is an implied 1% cost of dollars for the year. It is built into the forward points, and only the part above the USD–EUR interest differential is the basis.

Example 2

A 5-year EUR/USD cross-currency basis swap is quoted at -30 bp. A euro-based bank with no direct access to dollars wants synthetic dollar funding. Explain what the quote means and who bears the cost.

Show the solution

Read the quote: the spread of -30 bp is attached to the euro floating leg, so the euro leg pays EURIBOR - 30 bp, and the dollar leg pays SOFR flat.
Identify the bank's position: it hands over euros as principal and receives dollars at the start. On the interest legs it receives EURIBOR - 30 bp on the euros it handed over and pays SOFR on the dollars it received.
Compare with CIP: if the basis were zero it would receive EURIBOR flat on the euro leg. It gets 30 bp less.
Conclude the cost: the bank earns 30 bp per year less on the euro leg, which is the premium for synthetic dollars.
Interpret: the negative basis shows dollar demand exceeds supply and arbitrage is limited.

Answer: The -30 bp means the euro leg is reduced by 30 bp. The euro-based bank receives EURIBOR - 30 bp on the euros it handed over and pays SOFR on the dollars. It bears a cost of 30 bp a year to obtain dollars synthetically, which is a departure from covered interest parity.

Exam tips

Always find which leg carries the spread and read its sign before choosing an answer.
Questions often link a negative basis to dollar shortage, so be ready to name the drivers: funding demand and limits to arbitrage.
Know the difference between FX swaps (short, embedded in forward points) and basis swaps (long, floating legs with a spread).
Expect an applied scenario about a bank's liquidity risk. Mention rollover risk and collateral calls.
Eliminate options that say the basis is a default premium, because it reflects funding supply and demand.

Practice questions from Covered Interest Parity Lost: Understanding the Cross-Currency Basis

FX Swaps and Cross-Currency Basis Swaps in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

FX Swaps and Cross-Currency Basis Swaps: frequently asked questions

What is a cross-currency basis swap?

It is a contract where two parties exchange principal in two currencies and pay floating interest in each. A spread, the basis, is added to the non-dollar leg. The final principal exchange happens at the initial spot rate.

What is the difference between an FX swap and a cross-currency swap?

An FX swap is usually short-dated and exchanges principal at spot and forward, with interest embedded in forward points. A cross-currency basis swap runs longer and exchanges floating interest payments in each currency during its life.

What does a negative cross-currency basis mean?

Against the dollar, it means borrowing dollars through the swap costs more than borrowing them directly. It points to strong demand for dollars and limits on arbitrage. It is a deviation from covered interest parity.

How do I read a cross-currency basis quote?

Read it in basis points on the non-dollar floating leg, against the dollar floating rate flat. For example, -25 bp on EUR/USD means the euro leg is EURIBOR minus 25 bp. Check the question for its sign convention.