Interest Rate Parity Arbitrage

Two paths, and the results must match

Depositing dollars for a year, and "converting to euros, depositing for a year, then converting back with a forward," are both risk-free. The two paths must end at the same place, so the forward rate is set by the two countries' interest rate gap: the lower-rate currency is pricier forward. That's interest rate parity.

Out of line: borrow, convert, deposit, lock

When the forward strays from interest rate parity, borrow one currency, convert at spot, deposit to earn interest, and lock in the conversion back with a forward. All four steps happen at once and the profit is fixed on day one: that's covered interest arbitrage.

In reality, parity can stay out of line for a long time

After 2008, dollars obtained through FX swaps often cost more than borrowing dollars directly. This is the cross-currency basis. Banks are limited by capital and balance sheets and can't scale up the arbitrage indefinitely, so the gap can persist. The textbook "risk-free" assumes you can borrow at the quoted rate.

Key takeaways

• Forward rate = spot × (1 + quote currency rate × time) ÷ (1 + base currency rate × time).
• When the forward strays from this price: borrow one currency, convert it, deposit it to earn interest, and lock in the conversion back with a forward at the same time. The profit is locked in at the open.
• The forward rate used to lock in currency in the hedging course is pinned in place by exactly this kind of arbitrage.
• In reality, funding costs and balance sheet limits keep parity slightly off for long periods (the cross-currency basis); not everyone can borrow at the quoted rates.

Try it yourself

You can do these exercises in this lesson's interactive simulation:

1. Click "Example: 5% · 3% · 1.1300" and watch all four steps: what's the fair forward? How much do you net at expiry?
2. Click "Align to interest rate parity": can you still make money? Are the dollar-deposit path and the euro path now the same?
3. Drag the forward to 1.1100: which currency do you borrow now? How does the order of the four boxes change?
4. Set the euro rate to the same 5% as the dollar: what's the fair forward now? Why?

Quiz and explanations

1. EUR/USD spot is 1.10, the dollar rate is 5% and the euro rate is 3%. Roughly what's the fair one-year forward?

Answer: 1.1214.1.10 × 1.05 ÷ 1.03 ≈ 1.1214.

2. Does covered interest arbitrage carry exchange rate risk?

Answer: No, the rate for converting back is locked in with a forward at the open."Covered" means exactly that: the conversion rate back is locked in ahead of time with a forward.

3. Spot is 1.10, the dollar rate 5% and the euro rate 3%, and the one-year forward is quoted at 1.1300 (fair value about 1.1214). If you borrow $1,000,000 to run the arbitrage, roughly how much do you make after a year?

Answer: $8,091.$1,000,000 ÷ 1.10 = €909,091; deposited for a year it becomes €936,364; converted back at 1.13 that's $1,058,091. Repay $1,050,000 of principal and interest for a net gain of about $8,091.

Terms in this lesson

• covered interest arbitrage (Covered Interest Arbitrage): Borrow one currency, convert it and earn interest on deposit while locking in the rate back with a forward, profiting when the forward strays from interest rate parity.
• forward contract (Forward): An agreement to buy or sell on a future date at a price agreed today, often used to lock in an exchange rate.
• interest rate parity (Interest Rate Parity): The forward exchange rate is set by the interest rate gap between two currencies: the lower-rate currency trades at a higher forward price (a premium).
• cross-currency basis (Cross-Currency Basis): The gap between the implied rate for dollars obtained through FX swaps and the rate for borrowing dollars directly; since 2008 it has stayed non-zero (swapped dollars cost more), showing interest rate parity breaks down in practice due to funding and balance-sheet limits.