Covered interest rate parity (CIP) is the no-arbitrage relationship connecting a spot exchange rate, a forward exchange rate and the two currencies’ interest rates over matching dates. Under its frictionless funding assumptions, a deposit in one currency must give the same terminal amount as converting into another currency, investing there and fixing the conversion back with a forward contract. It is the starting point for pricing an FX forward and comparing direct funding with funding through currency markets.
“Covered” means that the future currency conversion is agreed today. The relationship does not require a forecast of the future spot rate.
Start with units, then follow the cash
Let and both mean USD per EUR: dollars paid or received for one euro, at spot and at the forward settlement date respectively. In market-pair notation this is EUR/USD, with EUR the base currency and USD the quote currency. Writing the units explicitly prevents an inverted formula.
Let and be the currencies’ deposit growth factors between the same start and end dates. Starting with dollars gives two covered routes:
Equating these dollar amounts gives
The equal-return comparison becomes an arbitrage argument when the same rates are available for borrowing as for lending and the trades can be executed together without costs or credit differences. Otherwise, comparing two deposits alone does not prove that a trader can finance the cheaper route.
For simple annual rates and , with year fractions and over those dates,
Different day-count conventions may assign different year fractions to the same dates. Use the accumulation factors that actually belong to the instruments; do not insert continuously compounded rates into this simple-interest formula.
One year, two routes, the same USD 103
Consider a synthetic market with USD per EUR, a USD simple annual rate of 3%, a EUR simple annual rate of 1%, and a one-year horizon with both year fractions equal to one. Assume matching borrowing and lending rates, negligible credit risk, assured settlement, no spreads, fees or collateral funding costs, and no currency-transfer restrictions.
| Route from USD 100 | At the start | At the end of one year |
|---|---|---|
| Deposit dollars | Invest USD 100 | Receive USD 103. |
| Convert, deposit euros, sell euros forward | Buy EUR ; invest it; agree today to sell the full maturity proceeds forward. | Receive EUR from the deposit, deliver it into the forward and receive exactly USD 103. |
The fractions are exact: and . The forward covers principal plus interest, not just the opening euro amount. Using the exact fraction for ,
Original synthetic funding ledger. Both simple-rate year fractions are one. All conversion rates are USD per EUR; the forward is agreed at the start and exchanged at maturity. Exact fractions avoid rounding a cash-flow identity.
Here the euro has a forward premium in USD-per-EUR units because the USD growth factor is higher. That premium offsets the euro deposit’s lower interest accrual in the covered comparison. It is not an extra return added on top of the higher dollar interest rate.
The FX primer lesson develops quotation direction and bid–ask conversions before introducing the continuously compounded form of CIP. The full lesson is available with a free signed-in account through its public preview entry.
Which side would an arbitrageur trade?
Keep the example’s assumptions and call an alternative executable forward quote , still in USD per EUR.
- If , borrow dollars, buy euros spot, deposit the euros and sell the full euro maturity amount forward. The converted proceeds exceed the dollar debt repayment.
- If , borrow euros, sell them spot, deposit the dollars and buy enough euros forward to repay the euro debt. The dollar deposit exceeds the forward purchase cost.
These directions follow the cash ledger, not a rule to borrow whichever currency happens to have the lower rate. With a bid–ask spread, the first route buys euros at the spot ask and sells euros at the forward bid; the reverse route sells at the spot bid and buys at the forward ask. Borrowing and deposit rates may also differ. The frictionless equality then becomes a set of executable trade thresholds rather than an instruction to trade every difference from a midpoint calculation.
Covered does not mean forecast
Uncovered interest rate parity concerns the expected return of an unhedged currency investment. Its comparison uses the uncertain future spot rate and an expectation under real-world probabilities. Equal expected returns require an additional assumption about currency risk compensation. CIP instead uses the forward rate already agreed today and a funding replication.
Consequently, CIP alone does not say that , that the euro will appreciate, or that a higher-yielding currency offers a superior realised return. The CFA Institute’s parity summary distinguishes the covered and uncovered conditions explicitly.
Why an observed basis needs a funding explanation
A cross-currency basis records a difference between funding through currency swaps and comparable direct cash-market funding. Its sign must be read with the currency leg and quotation convention specified; it is not universally “forward minus spot.”
The BIS analysis of CIP deviations explains how hedging demand and balance-sheet constraints can sustain a basis. Credit differences, executable spreads and access to funding also matter. A model discrepancy is therefore the beginning of an audit of matched dates, instruments, credit and financing capacity. A forward can cover the currency rate while leaving counterparty, settlement or funding liquidity risk.
Sources
- John C. Hull, Options, Futures, and Other Derivatives, 9th Global ed., Pearson, 2018, §5.10, pp. 140–141: currency-forward replication and both arbitrage directions. The example here uses original simple-interest assumptions rather than the book’s continuously compounded example.
- BIS, “Covered interest parity lost: understanding the cross-currency basis,” September 2016, especially Box A: the textbook comparison, funding differences and constraints on arbitrage. This is historical research, not a current market quote.
- CME Group, “Covered Interest Parity, Implied Forward FX Swaps, Cross-Currency Basis, and CME Group €STR futures”: forward pricing from comparable currency interest periods and the distinction between implied and observed prices.
- CFA Institute, “Currency Exchange Rates: Understanding Equilibrium Value,” 2026 curriculum summary: covered versus uncovered parity and the extra condition needed to connect forward rates to expected spot rates.