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

Implications of the Cross-Currency Basis for Liquidity Risk and Treasury Management

Updated 11 October 2026

The cross-currency basis is the deviation from covered interest parity in FX swap markets. A negative basis means a premium to obtain dollars through FX swaps, and signals dollar funding stress. Swap lines set a ceiling on the dollar price offered to central banks, limiting basis widening but not removing stress.

Understand Implications for Liquidity Risk and Treasury Management

Covered interest parity (CIP) says you should earn the same return whether you lend in your home currency or lend in a foreign currency and hedge the FX risk with a forward. If it held exactly, hedging would cost only the interest rate difference.

Since 2008 it has not held. The gap is the cross-currency basis. By market convention it is quoted as a spread added to the non-USD interest rate on the non-USD leg of the swap. A negative basis (for example EUR/USD at -30 bp) means that the party that lends euros and borrows dollars in the swap receives the euro rate minus 30 bp on the euro leg. Its effective dollar borrowing cost is therefore higher by 30 bp. Sign convention: swap-implied USD rate = USD market rate − basis, so a basis of -30 bp gives an implied USD rate 30 bp above the market rate. In plain words: dollars are in demand and cost more than the interest rates imply.

Why does this matter for liquidity risk? Many non-US banks, insurers and asset managers hold dollar assets but have limited dollar deposits. They fund the gap short term with FX swaps and basis swaps. This creates currency mismatch and rollover risk. If the basis widens, the cost of rolling the funding jumps. If dollar funding dries up, the institution may face a margin call or be forced to sell assets. Limits to arbitrage, such as balance sheet and leverage constraints on banks, stop others from closing the gap.

For investors, the basis changes currency-hedged returns. A USD investor who buys foreign bonds and hedges back to USD supplies dollars in the swap. When the basis is negative, that investor earns the size of the basis (its absolute value), which raises the hedged yield by that amount. An investor who must obtain dollars pays the premium. Examples are a European bank funding USD assets, or a euro investor who buys US bonds and hedges into euros. This is why hedged and unhedged choices change when the basis moves.

Central bank swap lines are the policy response. The Federal Reserve lends dollars to foreign central banks against their local currency. They on-lend to local banks. The rate charged to the foreign central bank sets a ceiling on the dollar funding cost offered through central banks, which limits how far the basis widens and usually narrows it. It does not cap the basis itself, and the basis can still exceed that level. It does not eliminate funding stress. Treasurers still need dollar buffers, diversified funding, and stress tests that include a wider basis and loss of FX swap access.

Key formulas to remember

Covered interest parity: F ÷ S = (1 + r_d) ÷ (1 + r_f); S and F are quoted as units of currency d per one unit of currency f. For a USD-per-EUR quote, d = USD and f = EUR, so r_d is the USD rate and r_f is the euro rate.
CIP with basis: r_USD(implied from swap) = r_USD(market) − basis; r_USD(market) is the USD money market rate. The basis is quoted as a spread added to the non-USD rate on the non-USD leg, so the party lending euros and borrowing dollars receives the euro rate plus the basis. When the basis is negative, that party receives less than the euro rate, and the implied USD rate is higher than the market rate by the size of the basis. Obtaining USD through the swap therefore costs more. Example: basis = −30 bp adds 30 bp.
Hedged yield to a USD investor: Hedged yield ≈ foreign yield + (USD short rate − foreign short rate) − basis; Approximation. A negative basis is subtracted, so the hedged yield rises by the size of the basis, because the USD investor supplies dollars in the swap. A positive basis would lower it.
Basis in basis points: Basis = −(swap-implied USD rate − USD money market rate) in bp; The basis is the spread on the non-USD leg. It is negative when the swap-implied USD rate is above the USD market rate, meaning a premium to obtain USD. Check the sign convention in the question.

How to solve Implications for Liquidity Risk and Treasury Management questions

Use this for any question on the basis, hedging costs, dollar funding or swap lines.

1Identify who needs which currency: who is lending dollars and who is borrowing them in the swap.
2Note the sign of the basis. Negative on the non-USD leg means dollars are costly.
3Work out the all-in cost: interest differential plus the basis, in the same units (bp or percent, annual).
4For hedged investing, start from the foreign yield and add the interest differential (USD rate minus foreign rate). Then subtract the basis, which adds a benefit if it is negative and you supply dollars. If you must obtain dollars, the negative basis is a cost to you.
5Decide whether the exposure is a funding gap, rollover or market liquidity problem, and name the risk precisely.
6Apply the mitigant: swap lines, dollar buffers, term funding, diversified counterparties, stress testing.
7Check the answer direction: a wider negative basis means a higher dollar cost for those who must obtain USD, and a higher hedged return for USD investors hedging foreign assets.

Quickest way: Sign and direction shortcut

When to use it: Use for conceptual or direction-of-effect multiple-choice questions with little time.

Ask: is the basis more negative? If yes, dollars are scarcer and costlier.
Whoever must obtain USD through swaps loses; whoever supplies USD gains.
Hedged foreign bond for a USD investor: yield up. US bond hedged by a euro investor: yield down.
Swap lines set a ceiling on the dollar price offered through central banks and limit basis widening, but they do not cap the basis or eliminate rollover risk.
Eliminate options that say the basis is risk-free arbitrage or that swap lines remove the risk.

Common mistakes in Implications for Liquidity Risk and Treasury Management

Treating CIP deviations as a free arbitrage.
Textbook CIP implies any gap is riskless profit.
Fix: Remember limits to arbitrage: bank balance sheet, leverage ratio and capital costs make the trade unattractive.
Getting the sign wrong.
Basis is quoted on the non-USD leg, so negative looks like a lower cost.
Fix: Read negative as a premium to borrow USD. Always ask who pays.
Adding the basis to hedge cost for the wrong party.
Students forget to check whether the investor supplies or obtains dollars.
Fix: Identify direction of the swap first: a USD investor hedging foreign bonds supplies dollars and earns the benefit. A euro investor hedging US bonds must obtain dollars and pays the premium.
Thinking swap lines fix solvency, cap the basis or remove risk.
Headlines say swap lines calm markets.
Fix: They provide dollar liquidity to central banks at a set rate, which limits basis widening. The basis can still exceed that level, and rollover and mismatch risk remain at the institution.
Mixing funding liquidity with market liquidity.
Both involve a dollar shortage.
Fix: Funding liquidity is the ability to roll or raise cash. Market liquidity is the ability to sell assets at low cost. Label which one the question tests.

Worked examples

Example 1

A US asset manager buys a 10-year euro bond yielding 3.00%. Euro short rate is 2.50%, USD short rate is 4.50%. The manager hedges with rolling FX swaps. The EUR/USD basis is -20 bp. Using the approximation, what is the hedged USD yield?

Show the solution

Interest differential: USD rate minus EUR rate = 4.50% − 2.50% = +2.00%.
Hedged yield ≈ foreign yield + (USD short rate − foreign short rate) − basis.
= 3.00% + 2.00% − (−0.20%).
= 3.00% + 2.00% + 0.20% = 5.20%.

Answer: About 5.20%. The negative basis adds 20 bp to the hedged yield compared with 5.00% under pure CIP, because the USD investor supplies dollars in the swap.

Example 2

A European bank funds USD assets with 3-month FX swaps. The EUR/USD basis moves from -10 bp to -60 bp. The bank has USD 5 billion of swaps to roll. What is the extra annual cost in USD, and what risk is shown?

Show the solution

Change in basis = 60 bp − 10 bp = 50 bp = 0.50%.
Extra annual cost = 0.50% × USD 5,000,000,000.
= 0.005 × 5,000,000,000 = USD 25,000,000 per year.
The risk is rollover of short-term dollar funding against a currency mismatch, which is funding liquidity risk.

Answer: USD 25 million extra annual cost. The exposure is funding liquidity (rollover) risk. The bank should hold dollar buffers, extend maturities and test a wider basis. Swap lines may help via its central bank.

Exam tips

Always fix the sign: negative basis means a USD premium. Check who pays before choosing an answer.
Expect questions linking the basis to hedged returns for investors and funding costs for banks.
Know that swap lines are central-bank to central-bank. They set a ceiling on the dollar price offered through central banks and limit basis widening, but do not cap the basis or remove stress.
Name the risk precisely: currency mismatch, rollover or funding liquidity.
Match the stress test to the risk: include wider basis and loss of FX swap access.

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

Implications for Liquidity Risk and Treasury Management: frequently asked questions

How does the cross-currency basis affect hedging costs?

The all-in hedge cost is the interest rate differential plus the basis. A negative basis raises the cost for anyone who must obtain USD through the swap, such as a euro investor hedging US bonds. A USD investor hedging foreign assets supplies dollars and earns more.

What do central bank swap lines do for dollar liquidity?

The Federal Reserve provides USD to foreign central banks against local currency. They on-lend to their banks. The rate charged sets a ceiling on the dollar funding cost offered through central banks, which limits basis widening and usually narrows it. It does not cap the basis or remove funding stress.

Why does the basis matter for FRM liquidity risk?

Institutions with dollar assets but few dollar deposits rely on FX swaps to fund. A wider basis raises rollover costs and can create funding strain. It is a key funding liquidity and currency mismatch issue.

How does the basis affect hedged foreign bond returns?

For a USD investor, hedged return is the foreign yield plus the interest differential, minus the basis. When the basis widens negative, the USD investor supplies dollars in the swap and the hedged yield rises. Investors who must obtain dollars, such as euro investors hedging US bonds, pay more.