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Uncovered Interest Rate Parity Formula (UIP) Explained

What is the formula for uncovered interest rate parity?

Uncovered interest rate parity (UIP) is an international finance relationship that connects interest rate differences between two countries to the expected change in their exchange rate. In plain terms, UIP says that when one country’s interest rate is higher than another’s, the higher-yielding currency is expected to depreciate enough (on average) to offset the interest advantage—so there’s no “free lunch” from simply chasing yields without hedging.

UIP formula (most common notation)

The standard UIP condition is:

(1 + idomestic) = (1 + iforeign) × (E[St+1] / St)

Where:

idomestic = domestic interest rate for the period
iforeign = foreign interest rate for the same period
St = spot exchange rate today (domestic currency per 1 unit of foreign currency, by convention)
E[St+1] = expected spot exchange rate next period

Log/approximation form

For small rates, UIP is often written approximately as:

idomestic − iforeign ≈ (E[St+1] − St) / St

That right-hand side is the expected percentage change in the exchange rate (the expected depreciation of the domestic currency under this quote convention).

Why it matters for real-world money decisions

UIP comes up when comparing returns across currencies, planning international payments, or understanding why a higher advertised rate abroad may not translate into a higher outcome once exchange rates move. For practical steps on handling interest-related records and staying organized, see the guide at https://journalle.com/guide-declare-bank-interest-step-by-step-checklist/.

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FAQ

What is covered interest rate parity (CIP) and how is it different from UIP?

CIP uses the forward exchange rate (a hedged rate) instead of an expected future spot rate. UIP is “uncovered” because it relies on expectations about the future spot rate rather than locking in a forward contract.