FRM Exam Part I · Foreign Exchange Markets

Covered Interest Rate Parity Formula and Arbitrage

Updated 11 October 2026 · Fact-checked

Covered interest rate parity says the forward exchange rate must equal the spot rate adjusted for the interest rate difference between two currencies. If the forward differs, you can lock in a riskless profit by borrowing, converting, investing and selling forward. Solve by comparing two routes to the same future currency amount.

Understand Covered Interest Rate Parity

Start with a simple idea. You hold 1 unit of USD today and want USD in one year. You have two routes. Route one: invest the USD at the USD rate. Route two: convert to EUR at spot, invest at the EUR rate, and sell the EUR proceeds forward for USD at a rate fixed today. Both routes are riskless, so they must end with the same amount.

That equality gives covered interest rate parity (CIP). The word covered means the exchange rate risk is removed by a forward contract. The forward rate is therefore fixed by spot and the two interest rates. It does not depend on what anyone expects the spot rate to be.

The quote direction matters. Use the quote as domestic currency per one unit of foreign currency (for example USD per EUR). The currency with the higher interest rate trades at a forward discount. The currency with the lower interest rate trades at a forward premium. The forward points reflect the rate gap.

If the market forward is not equal to the CIP forward, covered interest arbitrage exists. You borrow the currency whose route is cheaper in forward-covered terms, lock the exchange rate with a forward, and keep the difference. Traders do this until prices close the gap.

Uncovered interest parity (UIP) is different. It links the expected future spot rate to the rate gap and leaves exchange rate risk open. CIP is a no-arbitrage identity. UIP is a statement about expectations and often fails in data.

Since the global financial crisis, CIP has shown persistent deviations, measured as the cross-currency basis. Bank balance sheet limits, regulatory capital costs, and funding demand for USD stop arbitrageurs from fully closing the gap. A negative basis on EUR/USD means borrowing USD through FX swaps costs more than the USD money market rate implies.

Key formulas to remember

CIP forward rate (discrete compounding): F = S × (1 + r_d × T) ÷ (1 + r_f × T); S and F are domestic per one foreign unit. r_d is the domestic rate, r_f the foreign rate, T in years using the money market day count.
CIP forward rate (continuous compounding): F = S × e^((r_d − r_f) × T); Use when the question gives continuously compounded rates.
Forward premium or discount: (F − S) ÷ S = (r_d − r_f) × T ÷ (1 + r_f × T) ≈ (r_d − r_f) × T; A positive value means the foreign currency is at a forward premium. The exact form is the first expression. The approximation drops the denominator (1 + r_f × T), so it is not exact. Use it to check direction and use the full formula for answers.
Uncovered interest parity: E(S_T) = S × (1 + r_d × T) ÷ (1 + r_f × T); Uses the expected future spot rate. It carries exchange rate risk, so it is not an arbitrage condition.
Cross-currency basis (idea): Basis = implied rate from FX swap − quoted money market rate; Zero under perfect CIP. A negative basis on a currency means its borrower pays extra to obtain the currency, usually USD, through FX swaps. Sign conventions vary, so read the question.

How to solve Covered Interest Rate Parity questions

Use the same routine for any CIP question. Write the quote direction first, because most errors come from flipping it.

1Write the quote as domestic per foreign (for example USD per EUR). Identify r_d and r_f accordingly.
2Convert the horizon T into years using the stated day count (for example days ÷ 360 for USD and EUR money markets).
3Compute the CIP forward: F = S × (1 + r_d × T) ÷ (1 + r_f × T).
4Compare it with the market forward. If they are equal, no arbitrage exists.
5If the market forward is higher than the CIP forward, the foreign currency is overpriced forward: sell it forward, invest in the foreign currency and borrow the domestic currency. If the market forward is lower, buy the foreign currency forward, borrow the foreign currency and invest in the domestic currency. In both cases you borrow the currency whose route is cheaper in forward-covered terms.
6Build the cash flows: borrow, convert, invest, and hedge with the forward. Compute the final amount in one currency.
7Subtract the repayment of the loan to get the profit, and state its currency.
8 Check the sign: the higher-rate currency should be at a forward discount.

Quickest way: Ratio shortcut for forward and arbitrage direction

When to use it: When you only need the CIP forward or the direction of arbitrage, not the full cash flow table.

Compute the growth factors: (1 + r_d × T) and (1 + r_f × T).
Multiply S by the ratio of those factors to get the fair forward.
Compare the fair forward with the quoted forward. Quoted above fair means sell the foreign currency forward; below means buy it forward.
For the profit, take the foreign currency amount at maturity × (quoted F − fair F). This equals the arbitrage profit only when the trade is sized by that foreign maturity amount. Example: EUR 1,030,000 × (1.1300 − 1.12136) ≈ USD 8,900. Discount only if the question asks for present value.
Use a financial calculator memory to store the two factors and avoid retyping.

Common mistakes in Covered Interest Rate Parity

Inverting the quote direction and using the wrong rate in the numerator.
Quotes such as EUR/USD and USD/EUR look alike, and the domestic currency changes with the quote.
Fix: Write 'domestic per foreign' before you start. The domestic rate goes in the numerator, the foreign rate in the denominator.
Using the interest rate difference with the approximation and treating it as exact.
The shortcut (r_d − r_f) is easy and appears in textbooks.
Fix: Use the full ratio formula for numeric answers. Use the approximation only to check direction.
Using 365 days when the question implies a 360-day money market basis, or mixing day counts.
Students default to the calendar year.
Fix: Use the day count stated in the question. If none is given, follow the convention in the problem, usually the T given in years.
Confusing CIP with UIP and using an expected spot rate to price the forward.
Both are called interest rate parity and both use the rate gap.
Fix: CIP uses a forward contract and is enforced by arbitrage. UIP uses an expectation and is not riskless.
Stating that the higher-interest currency trades at a forward premium.
Higher yield sounds like a better currency.
Fix: The higher-rate currency is at a forward discount, because its extra interest is offset by the forward rate.
Assuming CIP always holds exactly in real markets.
Textbook arbitrage is frictionless.
Fix: Know that persistent cross-currency basis deviations exist because of balance sheet and funding constraints, and that they are a risk topic in their own right.

Worked examples

Example 1

Spot is 1.1000 USD per EUR. One-year rates are 5% USD and 3% EUR (simple). The one-year forward is quoted at 1.1300. Show the arbitrage using 1,000,000 EUR equivalent borrowing and find the profit in USD at maturity.

Show the solution

CIP forward is 1.1000 × 1.05 ÷ 1.03 = 1.12136. The quoted forward 1.1300 is higher, so EUR is overpriced forward. Sell EUR forward, invest in EUR and borrow USD.
Borrow USD 1,100,000 (EUR 1,000,000 equivalent at spot) at 5%. Repayment at maturity is 1,100,000 × 1.05 = USD 1,155,000.
Convert at spot: USD 1,100,000 ÷ 1.1000 = EUR 1,000,000.
Invest EUR 1,000,000 at 3%. Value at maturity is EUR 1,030,000.
Sell EUR 1,030,000 forward at 1.1300 today. At maturity this gives 1,030,000 × 1.1300 = USD 1,163,900.
Profit = 1,163,900 − 1,155,000 = USD 8,900.
Check: EUR 1,030,000 × (1.1300 − 1.12136) ≈ USD 8,900.

Answer: Borrow USD, convert to EUR, invest in EUR and sell the EUR proceeds forward. Riskless profit is USD 8,900 at maturity.

Exam tips

Read the quote direction first and write it at the top of your working. Many wrong options in the answer list come from the inverted quote.
If the question asks for the direction of arbitrage, you only need to compare the quoted forward with the CIP forward. You do not need the full cash flows.
Check if rates are simple or continuously compounded. Use the matching formula.
For conceptual questions, remember: CIP is arbitrage-based and holds with forward cover; UIP depends on expectations; CIP deviations show up as the cross-currency basis.
Store the intermediate growth factors on the calculator and keep at least five decimals until the last step.

Practice questions from Foreign Exchange Markets

Covered Interest Rate Parity in other exams

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

Covered Interest Rate Parity: frequently asked questions

What is the covered interest rate parity formula?

F = S × (1 + r_d × T) ÷ (1 + r_f × T), with rates quoted per period and exchange rates as domestic per foreign. With continuous compounding, F = S × e^((r_d − r_f) × T).

What is the difference between covered and uncovered interest rate parity?

Covered parity uses a forward contract and is enforced by arbitrage. Uncovered parity uses the expected future spot rate and leaves currency risk open, so it can fail without an arbitrage opportunity.

How do I calculate covered interest arbitrage profit?

Compute the CIP forward and compare it to the market forward. Borrow in the currency that makes the loop profitable, convert, invest, lock the exchange rate with the forward, repay the loan, and keep the surplus.

Why does CIP not hold exactly since the financial crisis?

Banks face balance sheet and capital limits, and demand for USD funding is high. These frictions stop arbitrageurs from closing the gap fully, which shows up as a cross-currency basis.