Finance

Interest Rate Parity Calculator

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

Covered IRP (CIRP) assumes the exchange rate risk is locked in using a forward contract. The formula is exact and the condition generally holds for major currencies because arbitrageurs can execute the required trades. Uncovered IRP (UIRP) applies when no forward contract is used and the investor simply expects the spot rate to move as predicted. UIRP is an expectation, not a locked-in outcome, and empirical evidence shows it often fails - particularly at short horizons where the carry trade is profitable.

Q: Why does the forward rate differ from the spot rate?

The forward rate reflects the interest rate differential between the two currencies over the contract period. A currency with a higher interest rate is expected to depreciate over time, so its forward rate is lower than the spot rate. If the forward rate did not adjust this way, traders could borrow in the low-rate currency, invest in the high-rate currency, and hedge the exchange risk with a forward contract to earn a risk-free profit - competition eliminates that gap.

Q: What is the forward premium puzzle?

The forward premium puzzle (or Fama puzzle) is the empirical finding that currencies with higher interest rates tend to appreciate rather than depreciate as UIRP predicts. This means that on average, investors who borrow in low-rate currencies and invest in high-rate currencies (the carry trade) earn positive returns. The puzzle has persisted for decades and is one of the most discussed anomalies in international finance.

Q: How large a parity deviation signals an arbitrage opportunity?

For major currency pairs such as EUR/USD or USD/JPY, transaction costs are typically 2-10 basis points. Deviations below this threshold are unlikely to be profitable after costs. Deviations of 20 bps or more may represent genuine opportunities, but in practice, balance-sheet constraints, counterparty limits, and capital requirements prevent even large institutions from fully exploiting them. During financial crises, CIRP deviations for some pairs have exceeded 100 bps.

Q: What interest rates should I use in the calculator?

Use the risk-free rate for each country - typically the yield on short-term government securities (Treasury bills, Bunds, Gilts) or the central bank policy rate for the chosen horizon. For 3-month contracts, the 3-month government bill yield is most appropriate. For longer horizons, use the government bond yield matching the tenor. Avoid using lending or deposit rates from commercial banks, as these incorporate credit spreads that are not part of IRP.

Q: Can IRP be used to predict the future spot rate?

The CIRP forward rate is not a forecast - it is a no-arbitrage price that must exist to prevent risk-free profit with a forward contract. The UIRP expected spot rate is theoretically a forecast, but empirically it is a poor predictor of actual future spot rates. The forward rate consistently underperforms simple models such as the random walk for forecasting purposes. IRP is best understood as a pricing framework, not a forecasting tool.

Enter the spot exchange rate, domestic and foreign interest rates, and the investment horizon to get the Interest Rate Parity (IRP)-implied forward rate. The calculator covers both Covered IRP (CIRP) and Uncovered IRP (UIRP), shows the forward premium or discount as a percentage, measures parity deviation in basis points, and flags potential arbitrage when an observed market forward rate deviates from the theoretical rate.

By Sarah Klein, CFP · Updated June 7, 2026

Your details

Mode

Spot Exchange Rate (domestic per foreign)

Domestic Annual Interest Rate

Foreign Annual Interest Rate

Time Horizon

Observed Market Forward Rate (optional)

Currency

IRP-Implied Forward Rate

1.116019

The no-arbitrage forward exchange rate consistent with IRP

Forward Premium / Discount1.4563%

Interest Rate Differential1.5%

Parity Deviation-

Arbitrage SignalEnter an observed forward rate to check for arbitrage

Forward Premium/Discount (%)1.4563%

Interest Rate Differential (%)1.5%

Horizon (years)

IRP-Implied Forward Rate
Current Spot Rate

IRP forward rate: 1.1160 (domestic per foreign)

The Covered IRP (CIRP)-implied forward rate over 1 year is 1.116019.
The domestic currency trades at a premium - the annualised forward premium is 1.4563%.
The higher domestic rate (4.5% vs 3%) means IRP predicts the domestic currency will depreciate against the foreign currency over the period.

Next stepTo check for arbitrage, enter the observed market forward rate in the optional field above.

Compute the domestic growth factor(1 + 4.5000%)^1 = (1.045000)^1
1.04500000
Compute the foreign growth factor(1 + 3.0000%)^1 = (1.030000)^1
1.03000000
Apply CIRP formula: F = S x domestic factor / foreign factor1.1 x 1.045000 / 1.030000
1.116019
Calculate the annualised forward premium / discount((1.116019 - 1.1) / 1.1) x (1 / 1) x 100
1.4563%

Formula

F_{\text{CIRP}} = S \times \dfrac{(1+r_d)^T}{(1+r_f)^T}, \quad F_{\text{UIRP}} \approx S \times \bigl(1 + (r_d - r_f)\,T\bigr), \quad \text{Premium} = \dfrac{F-S}{S}\times\dfrac{1}{T}\times 100\%

Worked example

Spot EUR/USD = 1.10, US rate = 4.5%, EU rate = 3.0%, 1-year horizon. CIRP: F = 1.10 x (1.045 / 1.030) = 1.10 x 1.01456 = 1.11602. Forward premium = (1.11602 - 1.10) / 1.10 x 100 = 1.456%, which matches the interest rate differential of 1.5% (approximate). If the market quotes 1.1180, the deviation is (1.1180 - 1.11602) / 1.11602 x 10,000 = 17.7 bps, which may represent an arbitrage opportunity before transaction costs.

What is Interest Rate Parity?

Interest Rate Parity (IRP) is a fundamental no-arbitrage condition in international finance. It states that the difference in interest rates between two countries must equal the expected change in the exchange rate over the same period. If this relationship did not hold, traders could borrow in the low-rate currency, convert to the high-rate currency, invest at the higher rate, and lock in a risk-free profit. Competition among traders eliminates such opportunities, pushing exchange rates and forward prices to the levels described by IRP. The theory underpins how banks price currency forward contracts, cross-currency swaps, and foreign exchange hedging instruments.

Covered vs Uncovered Interest Rate Parity

Covered Interest Rate Parity (CIRP) applies when the exchange rate risk is fully hedged using a forward contract. The formula F = S x (1 + r_d)^T / (1 + r_f)^T gives the no-arbitrage forward price: any observed forward rate that deviates from this creates a covered interest arbitrage opportunity. CIRP is well supported empirically for major currency pairs, especially at short horizons, because large institutions can execute the trades required to close the gap. Uncovered Interest Rate Parity (UIRP) is the parallel condition without a forward contract: it predicts that the expected future spot rate will equal the current spot rate adjusted for the interest rate differential. UIRP is far less reliable empirically - the "forward premium puzzle" shows that high-interest-rate currencies often appreciate rather than depreciate, opposite to the UIRP prediction. This gap is what the carry trade exploits.

Forward Premium, Discount, and Parity Deviation

When the IRP-implied forward rate is above the spot rate, the domestic currency is at a forward discount (it buys fewer units of foreign currency in the future than today). Equivalently, the foreign currency is at a forward premium. The annualised forward premium or discount equals approximately the interest rate differential: a domestic rate of 4.5% versus a foreign rate of 3.0% implies a 1.5% annual forward discount for the domestic currency. The parity deviation is the gap between an observed market forward rate and the IRP-implied rate, expressed in basis points (hundredths of a percent). Deviations under 5-10 bps for major currency pairs are generally within transaction costs and do not represent exploitable arbitrage. Larger deviations, such as those seen during the 2008 financial crisis or COVID-19 stress episodes, can signal market dislocations or funding constraints.

How to Use This Calculator

Select Covered IRP for forward contract pricing or Uncovered IRP for expected spot rate estimation. Enter the spot exchange rate as domestic currency units per one unit of foreign currency (for example, 1.10 for EUR/USD where the US dollar is domestic and the euro is foreign). Input the annualised risk-free interest rates for each country - the government bond yield or central bank policy rate is typically used. Choose the investment horizon. The calculator returns the no-arbitrage forward rate, the annualised forward premium or discount, and the interest rate differential. Optionally, enter an observed market forward rate to compute the parity deviation in basis points and check whether an arbitrage opportunity exists.

Interest Rate Parity: Key Relationships

Condition	Interest Rates	Forward Rate vs Spot	Interpretation
Domestic premium	r_d > r_f	F > S (domestic depreciation)	Higher domestic rates - domestic currency expected to weaken
Foreign premium	r_d < r_f	F < S (domestic appreciation)	Lower domestic rates - domestic currency expected to strengthen
Rate parity	r_d = r_f	F = S (no change)	Equal rates - no forward movement predicted by IRP
CIRP holds	No arbitrage	Observed F = Implied F	No risk-free profit possible with a forward contract
CIRP violated	Arbitrage exists	Observed F != Implied F	Covered interest arbitrage may be profitable before transaction costs

Summary of how the interest rate differential drives the forward premium or discount under IRP.

Frequently asked questions

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

Covered IRP (CIRP) assumes the exchange rate risk is locked in using a forward contract. The formula is exact and the condition generally holds for major currencies because arbitrageurs can execute the required trades. Uncovered IRP (UIRP) applies when no forward contract is used and the investor simply expects the spot rate to move as predicted. UIRP is an expectation, not a locked-in outcome, and empirical evidence shows it often fails - particularly at short horizons where the carry trade is profitable.

Why does the forward rate differ from the spot rate?

The forward rate reflects the interest rate differential between the two currencies over the contract period. A currency with a higher interest rate is expected to depreciate over time, so its forward rate is lower than the spot rate. If the forward rate did not adjust this way, traders could borrow in the low-rate currency, invest in the high-rate currency, and hedge the exchange risk with a forward contract to earn a risk-free profit - competition eliminates that gap.

What is the forward premium puzzle?

The forward premium puzzle (or Fama puzzle) is the empirical finding that currencies with higher interest rates tend to appreciate rather than depreciate as UIRP predicts. This means that on average, investors who borrow in low-rate currencies and invest in high-rate currencies (the carry trade) earn positive returns. The puzzle has persisted for decades and is one of the most discussed anomalies in international finance.

How large a parity deviation signals an arbitrage opportunity?

For major currency pairs such as EUR/USD or USD/JPY, transaction costs are typically 2-10 basis points. Deviations below this threshold are unlikely to be profitable after costs. Deviations of 20 bps or more may represent genuine opportunities, but in practice, balance-sheet constraints, counterparty limits, and capital requirements prevent even large institutions from fully exploiting them. During financial crises, CIRP deviations for some pairs have exceeded 100 bps.

What interest rates should I use in the calculator?

Use the risk-free rate for each country - typically the yield on short-term government securities (Treasury bills, Bunds, Gilts) or the central bank policy rate for the chosen horizon. For 3-month contracts, the 3-month government bill yield is most appropriate. For longer horizons, use the government bond yield matching the tenor. Avoid using lending or deposit rates from commercial banks, as these incorporate credit spreads that are not part of IRP.

Can IRP be used to predict the future spot rate?

The CIRP forward rate is not a forecast - it is a no-arbitrage price that must exist to prevent risk-free profit with a forward contract. The UIRP expected spot rate is theoretically a forecast, but empirically it is a poor predictor of actual future spot rates. The forward rate consistently underperforms simple models such as the random walk for forecasting purposes. IRP is best understood as a pricing framework, not a forecasting tool.

Sources

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Written by Sarah Klein, CFP Certified Financial Planner · Chicago, USA

Fifteen years translating mortgage tables and amortization schedules into decisions that actually help real borrowers.

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