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

Covered Interest Parity (CIP) Explained with Formula and Examples

Updated 11 October 2026 · Fact-checked

Covered interest parity says a hedged investment in two currencies must earn the same return. The forward rate equals the spot rate times (1 + domestic rate) ÷ (1 + foreign rate), for the same maturity. If it fails, you can earn a riskless profit. To solve questions, fix the quote convention first, then apply the formula.

Understand Covered Interest Rate Parity (CIP) Basics

Suppose you have 1 million USD for one year. You can lend it in the US at the USD rate. Or you can swap it into EUR at the spot rate, lend it in the euro area at the EUR rate, and lock in the rate to convert back with a forward contract. Both routes start and end in USD, and both are free of FX risk. So they must give the same USD amount.

That is covered interest parity (CIP). The word covered means the FX risk is hedged with a forward. The forward rate is not a forecast of the future spot rate. It is set by the spot rate and the interest rate gap between the two currencies.

The logic is no-arbitrage. If the hedged foreign route paid more, you would borrow at home, invest abroad, and hedge. That needs no capital and carries no risk. Traders doing this would push the spot, forward and rates back into line.

The currency with the higher interest rate trades at a forward discount. Its forward price is lower than spot, so the higher interest is offset by the forward loss. The currency with the lower rate trades at a forward premium.

This topic is the base for the cross-currency basis. The basis measures how far the market departs from CIP. Since 2008 CIP has often failed, especially for USD funding. You must know the clean CIP relation before you can read the deviation.

Key formulas to remember

CIP, direct quote (domestic per 1 foreign): F = S × (1 + r_d × T) ÷ (1 + r_f × T); S and F are units of domestic currency per 1 unit of foreign currency. Simple interest for money-market maturities. T in years.
CIP with compounding: F = S × (1 + r_d)^T ÷ (1 + r_f)^T; Use for longer maturities or when rates are annual compounded. Continuous form: F = S × e^((r_d − r_f)T).
Forward points: Forward points = F − S; Positive means the foreign currency is at a forward premium against the domestic one. Quoted in pips, so check the scaling.
Approximate forward premium: (F − S) ÷ S ≈ (r_d − r_f) × T; A quick check only. Do not use it when exact answers are options.
Arbitrage rule: If F_market > F_CIP, sell the forward, buy foreign currency spot, and lend abroad.; If F_market < F_CIP, do the reverse. Direction is set by which route returns more domestic currency.

How to solve Covered Interest Rate Parity (CIP) Basics questions

Use this order for any CIP question, whether it asks for a forward, an interest rate or an arbitrage profit.

1Read the quote. Identify which currency is the numerator, the domestic one, in S and F.
2List the rates for the same tenor. Check whether they are simple or compounded and the day count basis.
3Put the numerator currency's rate on top and the denominator currency's rate at the bottom: F = S × (1 + r_num × T) ÷ (1 + r_den × T).
4Compute and round only at the end.
5Check direction: higher rate in the numerator currency means F > S. Higher rate in the denominator currency means F < S.
6If given a market forward, compare it with the CIP forward. The gap shows the arbitrage direction.
7For arbitrage, build both routes from the same starting amount and compare the end values in one currency.
8For basis questions, treat the basis as the spread added to the rate that closes the gap between the market and CIP.

Quickest way: Rate ratio and direction check

When to use it: Use when time is short and you need a forward, or need to pick the right option from four numbers.

Find the ratio (1 + r_num × T) ÷ (1 + r_den × T).
Decide if it is above or below 1. That tells you if F is above or below S.
Eliminate options on the wrong side of S.
Compute the exact ratio only for the options left.
Use the approximation S × (1 + (r_num − r_den) × T) to sanity check.

Common mistakes in Covered Interest Rate Parity (CIP) Basics

Inverting the rate ratio
Quotes can be USD per EUR or EUR per USD, and students apply a memorised formula blindly.
Fix: Put the rate of the numerator currency on top. If the quote is USD per EUR, USD is on top.
Treating the forward as a forecast of future spot
The word forward suggests an expectation.
Fix: CIP forward comes from no-arbitrage and interest rates, not from views. Expected spot belongs to uncovered parity.
Using annual rates for a 3- or 6-month forward without scaling
Rates are quoted per annum and the tenor is easy to overlook.
Fix: Multiply each rate by T, for example 0.25 for three months, before adding 1.
Confusing covered and uncovered parity
Both link rates and exchange rates.
Fix: Covered uses a forward contract and is a no-arbitrage identity. Uncovered uses expected spot and carries FX risk.
Getting the arbitrage direction wrong
Students compare numbers without building the two routes.
Fix: Start with the same amount, compute the end amount in one currency for each route, and take the higher route.
Thinking the CIP relation always holds in practice
Textbook CIP is a clean identity.
Fix: Since 2008 persistent deviations, the cross-currency basis, have appeared. Frictions such as balance sheet costs limit arbitrage.

Worked examples

Example 1

EUR/USD spot is 1.1000 USD per EUR. The 1-year USD rate is 5.0% and the 1-year EUR rate is 3.0%, both simple. What is the 1-year CIP forward rate?

Show the solution

The quote is USD per EUR, so USD is the numerator currency.
Ratio = (1 + 0.05) ÷ (1 + 0.03) = 1.05 ÷ 1.03 = 1.019417.
F = 1.1000 × 1.019417 = 1.12136.
Direction check: USD rate is higher, so EUR trades at a forward premium, F > S. This agrees.

Answer: The forward is about 1.1214 USD per EUR.

Example 2

EUR/USD spot is 1.1000. The 1-year USD rate is 5.0% and the EUR rate is 3.0%, simple. The market 1-year forward is 1.1300. Is there an arbitrage? Describe it and the profit per USD 1,000,000 borrowed, ignoring costs.

Show the solution

The CIP forward is 1.12136 from the same inputs. The market forward 1.1300 is higher, so EUR is expensive forward.
Borrow USD 1,000,000 at 5%. You owe 1,050,000 in one year.
Convert at spot: 1,000,000 ÷ 1.1000 = EUR 909,090.91.
Lend EUR at 3%: 909,090.91 × 1.03 = EUR 936,363.64.
Sell EUR forward at 1.1300: 936,363.64 × 1.1300 = USD 1,058,090.91.
Profit = 1,058,090.91 − 1,050,000 = USD 8,090.91.

Answer: Yes. Borrow USD, buy EUR spot, lend EUR, and sell EUR forward. The riskless profit is about USD 8,091 per USD 1,000,000.

Exam tips

Write the quote convention beside the numbers before you calculate. Most lost marks come from inversion.
When four options are given, use the direction test first. It often removes two options.
Know that CIP is a no-arbitrage identity and uncovered parity is not. Expect conceptual options on this.
Link CIP to the basis. A negative basis means the market forward implies a higher cost of raising USD through FX swaps than CIP does.
Check whether the question uses simple or compounded rates. Use the one stated.

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

Covered Interest Rate Parity (CIP) Basics 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 (CIP) Basics: frequently asked questions

What is the covered interest parity formula?

With a domestic-per-foreign quote, F = S × (1 + r_d × T) ÷ (1 + r_f × T). Use compounding for longer maturities. The domestic currency is the numerator currency of the quote.

Why is it called covered?

Because the foreign investment is hedged with a forward contract, so the exchange rate risk is removed. The return is known at the start.

What is the difference between covered and uncovered interest parity?

Covered parity uses the forward rate and holds by arbitrage. Uncovered parity uses the expected future spot rate, so it involves FX risk and need not hold.

How does CIP relate to the cross-currency basis?

The basis measures the deviation from CIP. If CIP held exactly, the basis would be zero. Since 2008 it has often been non-zero, mainly in USD funding.