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

Drivers of the Cross-Currency Basis: Funding Demand and Limits to Arbitrage

Updated 11 October 2026 · Fact-checked

The cross-currency basis is the gap between the dollar rate implied by FX swaps and the direct dollar rate. It opens when demand for dollar funding exceeds supply. It persists because arbitrage uses scarce bank balance sheet, which regulation, leverage limits and credit risk make costly. Arbitrage returns must beat that cost.

Understand Drivers of the Basis: Funding Demand and Limits to Arbitrage

Covered interest parity (CIP) says you should earn the same return borrowing dollars directly or borrowing euros and swapping them into dollars through an FX swap. Before 2008 this held closely. Since then it has often failed. The gap is the cross-currency basis, and by convention a negative basis means borrowing dollars through the swap costs more than borrowing dollars directly.

The first driver is imbalanced demand for dollar funding. Non-US banks, investors and corporates hold dollar assets or need dollars for trade. Many fund them in other currencies and hedge the currency risk with FX swaps. They pay a premium to receive dollars spot and return them later. The more one-sided this demand, the more negative the basis. Hedging demand from foreign investors in US assets can add to the pressure.

The second driver is limits to arbitrage. In theory, someone with dollars should lend them through the swap, collect the premium and close the gap. In practice, that trade is a balance sheet position. It expands assets and the leverage ratio exposure, and it uses capital, so it earns a return only if the basis exceeds the bank's cost of using that balance sheet. If the cost is higher than the basis, the gap stays open. It is not a free lunch.

Third, regulation and credit risk raise that cost. Leverage ratio rules, which are not risk-weighted, make low-margin, large-notional trades expensive. Banks that report at quarter-end or year-end tend to shrink balance sheets then, so the basis often widens at those dates. Counterparty credit risk, and the fact that a swap exchanges principal, add further cost. Central bank swap lines can cap the stress, but they do not remove the underlying imbalance.

So read the basis as a price of scarce dollar funding and scarce arbitrage capacity. It is not proof that arbitrage is impossible; it shows that arbitrage is costly and limited.

Key formulas to remember

CIP condition: F ÷ S = (1 + r_USD) ÷ (1 + r_foreign), with F and S in USD per unit of foreign currency; Holds with no frictions. F is the forward rate and S is the spot rate.
Cross-currency basis (sign convention): r_foreign implied via FX swap from USD = r_foreign direct + Basis; This is the market convention: the basis is a spread added to the foreign-currency rate (for example, EUR rate + basis = the EUR rate implied by borrowing USD and swapping). A negative basis means the implied foreign rate is lower, so USD borrowed through the swap costs more than USD borrowed directly. The supplier of dollars earns a premium of about −Basis. Use this convention throughout and check the sign convention in the question.
Arbitrage profitability rule: For a negative basis, arbitrage pays only if (−Basis) > cost of balance sheet use + credit and funding costs; −Basis is the premium earned for supplying dollars through the swap. If the cost exceeds that premium, the deviation persists without being exploited.

How to solve Drivers of the Basis: Funding Demand and Limits to Arbitrage questions

Use this method for any question on why the basis moved or why arbitrage did not close it.

1Identify the currency pair and the direction of the basis: is dollar funding more costly through the swap than direct?
2Find the demand side: who is short dollars, and who needs to hedge?
3Find the supply side: which banks provide dollars through swaps, and are they constrained?
4Check the date: quarter-end, year-end or a stress event often shrinks balance sheets.
5Name the constraint: leverage ratio, capital, risk limits or counterparty credit risk.
6Compare the basis to the arbitrageur's cost of balance sheet.
7Conclude with the interpretation: the gap persists because arbitrage is costly, not because CIP is irrelevant.

Quickest way: Demand, supply, cost: the three-check shortcut

When to use it: Use when you have about a minute and the options give several plausible causes.

Demand: is there a surge in dollar hedging or funding need? That widens the basis.
Supply: are dollar providers constrained by balance sheet, leverage ratio or dates like quarter-end? That also widens it.
Cost: does the basis exceed the cost of arbitrage? If not, it stays open.
Reject options that say arbitrage is impossible, or that CIP holds exactly after 2008.

Common mistakes in Drivers of the Basis: Funding Demand and Limits to Arbitrage

Saying the basis proves a free arbitrage exists.
Students compare rates and ignore the cost of using balance sheet.
Fix: Always net the balance sheet and credit costs against the basis. If costs are higher, there is no profitable arbitrage.
Blaming only demand for dollars.
The demand story is simple and familiar.
Fix: Give two sides: demand imbalance and constrained supply from banks.
Treating the leverage ratio as risk-weighted.
Mixing it up with risk-based capital ratios.
Fix: Remember the leverage ratio counts exposure without risk weights, so low-risk, low-margin trades are hit hard.
Getting the sign of the basis wrong.
Different sources quote the basis on different legs.
Fix: Read the stem and work out which leg is costlier. A negative basis normally means dollars cost more via the swap.
Assuming quarter-end moves mean the basis is random noise.
Students miss the link to window-dressing and reporting dates.
Fix: Link the widening to banks shrinking balance sheets on reporting dates when leverage rules are measured.

Worked examples

Example 1

The three-month EUR/USD cross-currency basis becomes more negative on the last day of the quarter and then narrows the next week. Which explanation fits best? A) US Treasuries become riskier at quarter-end; B) Banks reduce balance sheet usage at the reporting date, cutting supply of dollars through swaps; C) CIP starts to hold exactly at quarter-end; D) Euro interest rates fall permanently.

Show the solution

The move reverses within a week, so it is temporary rather than permanent. That rules out D.
CIP holding exactly would remove the basis, not widen it. That rules out C.
Nothing in the stem links the move to Treasury risk, and a Treasury risk change would not reverse neatly after the date. That rules out A.
Reporting-date balance sheet shrinkage reduces dollar supply through swaps, widening the basis, and it fades after the date. That is B.

Answer: B

Example 2

The cross-currency basis is −25 basis points a year (annualised), so a bank that supplies USD through an FX swap earns a dollar premium of 25 bps a year. Its internal cost of using balance sheet for this trade, including leverage ratio capital and funding charges, is 30 basis points a year. What should it do, and what does this show about the basis?

Show the solution

A negative basis of −25 bps means the premium earned for supplying dollars is −Basis = 25 bps a year.
Compare the premium with the cost: 25 bps against 30 bps. The premium must exceed the cost for the trade to pay.
Net return = 25 − 30 = −5 bps a year.
The trade loses 5 bps, so the bank should not do it.
If many banks face similar costs, no one closes the gap, and the basis stays open at −25 bps.

Answer: Do not do the trade. Net return is −5 bps a year. The basis persists because balance sheet costs exceed the dollar premium, which is a limit to arbitrage.

Exam tips

Expect case-style stems: you get a date or a regulatory change and must choose the cause of the basis move.
Always pair a demand cause with a supply or balance sheet cause when the options allow.
Watch for absolute words like always, never or impossible. They are usually wrong here.
Link quarter-end and year-end moves to reporting-date balance sheet constraints.
Check the sign convention before judging whether a basis widened or narrowed.

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

Drivers of the Basis: Funding Demand and Limits to Arbitrage: frequently asked questions

Why does the cross-currency basis widen at quarter-end?

Many banks cut balance sheet usage at reporting dates to meet leverage and other measures. That reduces dollar supply through FX swaps, so the swap price of dollars rises and the basis widens. It tends to narrow afterwards.

What is the difference between CIP arbitrage and funding cost?

CIP arbitrage compares the swap-implied dollar rate with the direct dollar rate. The funding cost is what the bank pays to hold the position on its balance sheet, including capital and credit costs. Arbitrage pays only if the basis exceeds that cost.

How does dollar funding demand drive the basis?

Non-US institutions that hold dollar assets, funded in other currencies, borrow dollars through FX swaps. When that demand is large and one-sided, the premium for dollars rises and the basis becomes more negative.

Does a negative basis mean CIP is wrong?

No. CIP is a no-arbitrage condition that assumes costless trading. A negative basis shows that frictions such as balance sheet costs and credit risk prevent arbitrage from closing the gap.