Updated for the 2026-2027 CFA® Level I curriculum.
Covered interest rate parity links spot exchange rates, forward exchange rates, and interest rates in two currencies. It sets the forward rate that removes any riskless profit from borrowing in one currency and investing in another. CFA Level I tests this relationship through direct forward-rate calculations and through arbitrage scenarios that ask you to identify the correct borrowing and investing direction.
Quick Answer
Covered interest rate parity states that the forward exchange rate must offset the interest rate differential between two currencies, so no riskless profit exists from covered arbitrage.
Using S_{d/f} as domestic currency per unit of foreign currency, the parity forward rate is
When the market forward rate departs from this parity value, traders can borrow, convert, invest, and hedge forward to lock a riskless profit.
Key Takeaways
Covered interest rate parity ties the forward exchange rate to the spot rate and the interest rate differential between two currencies.
Domestic currency and foreign currency must stay fixed to one quote convention throughout a calculation.
The parity forward rate formula is , with t matching the contract period.
Annual interest rates must convert to the exact time fraction before entering the formula.
A market forward rate above or below the parity forward rate signals a riskless covered interest arbitrage opportunity.
The arbitrage sequence borrows in one currency, converts spot, invests in the other currency, and locks reconversion with a forward contract.
Under a domestic/foreign price quote, the currency with the higher interest rate trades at a forward discount, and the lower interest rate currency trades at a forward premium.
What You Need to Know for CFA Level I
Define domestic currency and foreign currency, and identify which currency the spot and forward quotes are stated in.
Convert annual interest rates to the exact contract period before applying the parity formula.
Calculate the no-arbitrage parity forward rate from spot rates and interest rates.
Compare a given market forward rate against the parity forward rate to detect mispricing.
Choose the correct borrowing currency and investing currency based on which path produces the higher return.
Lock the arbitrage profit by reconverting terminal proceeds at the forward rate.
Explain why the higher interest rate currency trades at a forward discount under the defined quote.
The No-Arbitrage Link Between Spot, Forward, and Interest Rates
A domestic investor with cash to invest for a fixed period has two riskless ways to earn a return.
Path I invests the cash directly in the domestic currency at the domestic interest rate.
Path II converts the cash to the foreign currency at the spot rate, invests it at the foreign interest rate, and converts the proceeds back to the domestic currency at a forward rate agreed today.
Both paths start with the same cash and carry no default risk. The forward contract fixes the reconversion rate today, so Path II carries no exchange rate risk either. Because both paths are riskless and start with equal cash, they must produce equal terminal value. If they did not, an investor could borrow on the cheaper path and invest on the richer path for a riskless profit. Covered interest rate parity is this equality written as a formula.
Path | Action | Terminal Value (Domestic Currency) |
|---|---|---|
Path I | Invest domestic currency at for time t | Amount × |
Path II | Convert to foreign currency at , invest at for time t, convert back at | Amount × × × |
Setting Path I equal to Path II and solving for gives the parity forward rate formula covered next. This equality uses a contracted forward rate, not a forecast of the future spot rate, so uncovered parity and expected spot rates stay outside this page.
Covered Interest Parity Formula
Before using any formula, define the quote. means the price of one unit of foreign currency stated in domestic currency. If the domestic currency is USD and the foreign currency is EUR, = 1.1000 means one EUR costs 1.1000 USD.
Where:
= forward rate, domestic currency per unit of foreign currency
= spot rate, domestic currency per unit of foreign currency
= domestic annual interest rate
= foreign annual interest rate
= time to forward settlement, as a fraction of a year
This formula uses simple interest, and t must match the forward contract's exact period. A three-month contract uses t = 3/12 = 0.25. A six-month contract uses t = 6/12 = 0.50.
The numerator grows the domestic side by the domestic rate. The denominator grows the foreign side by the foreign rate. Multiplying the spot rate by this ratio produces the forward rate that keeps both investment paths equal.
How Covered Interest Arbitrage Works
When a market forward rate does not match the parity forward rate, a riskless profit exists. The arbitrage strategy always follows the same five steps.
Compare the market forward rate to the parity forward rate.
Borrow in the currency whose investment path currently produces the lower return.
Convert the borrowed amount to the other currency at the spot rate.
Invest the converted amount at that currency's interest rate for the contract period.
Sell the investment proceeds forward at the market forward rate, locking the reconversion rate today.
Time | Domestic-Side Cash Flow | Foreign-Side Cash Flow |
|---|---|---|
Time 0 | Borrow notional in the underyielding currency | Convert notional to the other currency at spot |
Time t | Repay loan plus accrued interest | Receive investment proceeds; convert at the contracted forward rate |
In practice, transaction costs and bid-ask spreads narrow or eliminate small mispricings. Real markets correct these gaps quickly, which keeps market forward rates close to parity most of the time. The Level I exam still expects you to work through the arbitrage mechanics on a frictionless basis.
Forward Premium and Discount Intuition
Covered interest rate parity also explains why one currency trades at a forward premium and the other at a forward discount.
Under the quote, if is greater than , then is greater than . The foreign currency costs more domestic currency forward than it does today, so the foreign currency trades at a forward premium. The domestic currency, which carries the higher interest rate, trades at a forward discount.
The general rule: the currency with the higher interest rate trades at a forward discount, and the currency with the lower interest rate trades at a forward premium, under a consistent price/base quote. Full point and percentage premium/discount calculations belong on the next note in this sequence.
Worked Example
Assume the domestic currency is USD and the foreign currency is EUR. Spot rate = 1.1000. The USD six-month rate is 5.00% annually. The EUR six-month rate is 3.00% annually. . The market quotes a six-month forward at 1.1150 USD/EUR.
Step 1: Calculate the parity forward
Step 2: Compare market and parity forwards.
The market forward (1.1150) exceeds the parity forward (1.1108). The market is paying more USD per EUR forward than the interest differential justifies, so the EUR forward rate is overpriced.
Step 3: Choose the arbitrage direction.
Since EUR is overpriced forward, the profitable path sells EUR forward. To sell EUR forward, the trader must hold EUR at maturity, which means investing in EUR. To invest in EUR, the trader must convert USD at spot, which means borrowing USD first.
Step 4: Run the numbers on a $10,000,000 notional.
Borrow $10,000,000 at 5% for six months. Repayment at t: $10,000,000 × 1.025 = $10,250,000.00
Convert to EUR at spot: $10,000,000 / 1.1000 = €9,090,909.09
Invest EUR at 3% for six months: €9,090,909.09 × 1.015 = €9,227,272.73
Sell EUR proceeds forward at 1.1150: €9,227,272.73 × 1.1150 = $10,288,409.09
Step 5: Calculate the profit.
The market forward overpriced EUR relative to the interest rate differential. Borrowing the underyielding path (USD) and investing in the hedged, overyielding path (EUR, sold forward) captures the mispricing as a locked, riskless profit. If the market forward had priced below 1.1108 instead, the correct direction reverses: borrow EUR, invest USD, and buy EUR forward to close the position.
Common Exam Traps
Swapping domestic and foreign rates. Placing r_f in the numerator and r_d in the denominator flips the parity relationship and produces a forward rate on the wrong side of spot.
Using annual rates without converting to the contract period. Level I contracts are often three-month or six-month. Skipping the t adjustment overstates the interest effect and distorts the parity forward.
Mixing quote direction between spot and forward. If the spot rate is domestic per foreign but the forward is treated as foreign per domestic, the ratio breaks. Confirm both rates use the same quote convention before calculating.
Calling an uncovered position "covered arbitrage." Covered arbitrage requires a forward contract that locks the reconversion rate. A position that waits for the future spot rate carries exchange rate risk and is not arbitrage.
Choosing the wrong borrowing side. Some candidates default to borrowing the currency with the lower interest rate. The correct choice depends on which path is underpriced relative to the market forward, not which rate looks smaller or larger.
Practice Question
An analyst gathers the following data for a three-month covered interest arbitrage exercise between the US dollar (domestic currency) and the British pound (foreign currency):
Spot rate: = 1.2500
USD three-month rate: 4.00% annually
GBP three-month rate: 6.00% annually
Market three-month forward rate: 1.2450
Based on covered interest rate parity, which of the following correctly identifies the mispricing and the arbitrage direction?
Borrow USD, convert to GBP at spot, invest in GBP, and buy GBP forward with USD, because the market forward overprices the pound relative to parity.
Borrow GBP, convert to USD at spot, invest in USD, and sell USD forward for GBP, because the market forward underprices the pound relative to parity.
Borrow USD, convert to GBP at spot, invest in GBP, and sell GBP forward for USD, because the market forward overprices the pound relative to parity.
Correct Answer: C
First calculate the parity forward with t = 0.25:
The market forward (1.2450) exceeds the parity forward (1.2438), so the market overprices the pound forward. The profitable path invests in GBP and sells the GBP proceeds forward at the rich market rate. Reaching that position requires borrowing USD, converting to GBP at spot, and investing in GBP. This matches option C.
Option A. The borrow and invest legs are correct, but buying GBP forward adds more pound exposure instead of removing it. A covered arbitrage must sell the currency it holds at maturity, not buy more of it. This answer fails the hedge step, not the direction step.
Option B. This answer reverses the entire strategy. It results from placing the foreign rate (6%) in the numerator and the domestic rate (4%) in the denominator, which pushes the calculated parity forward above the market rate and flips the diagnosis to "underprices." Swapping domestic and foreign rates is one of the most common errors on this topic.
Continue Your CFA Level I Prep With KeyPoint
Use structured lessons, practice questions, mock exams, and progress tracking to focus on the time you have left
FAQs About Spot-Forward Parity & Covered Interest
What is covered interest rate parity?
Covered interest rate parity is the no-arbitrage condition that sets the forward exchange rate so a hedged foreign investment earns the same return as a domestic investment, given the interest rate differential between the two currencies.
How does covered interest arbitrage remove a forward rate mispricing?
Traders borrow in the currency whose hedged return path is underyielding, convert at the spot rate, invest in the other currency, and lock the reconversion with a forward contract. The resulting trading pressure pushes the market forward rate back toward the parity value until the profit disappears.