Distinguish covered interest rate parity from uncovered interest rate parity.
The idea
Covered interest rate parity (CIP) links spot, forward and interest rates. With the spot rate S quoted as domestic currency per unit of foreign currency, the forward rate is F = S × (1 + i domestic) ÷ (1 + i foreign). It is enforced by riskless arbitrage, since a covered investment in either currency must earn the same return, and it holds without any view about future exchange rates. Uncovered interest rate parity (UIP) says that the expected future spot rate follows the same ratio. Expected S1 = S0 × (1 + i domestic) ÷ (1 + i foreign). The currency with the higher interest rate is expected to depreciate by the interest differential, so an unhedged investment earns the same expected return as a domestic one. UIP depends on expectations and risk-neutral investors, with no arbitrage to enforce it, and it often fails empirically. CIP holds closely in normal markets. UIP is a hypothesis.
Formulas
Expected future spot rate under uncovered interest rate parity
E(S1) = S0 × (1 + iD) ÷ (1 + iF)
- S0
- the spot rate today, domestic currency per unit of foreign currency
- iD
- the domestic interest rate for the period
- iF
- the foreign interest rate for the period
Same shape as covered parity, but it predicts an expectation, not a tradable forward, and needs risk-neutral investors. No arbitrage enforces it and it often fails, which is why carry trades earn a premium.
A practice question
Which statement describes covered interest rate parity?
- The expected future spot rate equals the spot rate adjusted for the interest rate differential, with no hedgingWhy not: That is uncovered interest rate parity, which depends on expectations.
- Interest rates are equal in all countries once inflation is taken into accountWhy not: That describes real interest rate equalization, not covered parity.
- The forward exchange rate equals the market's expectation of the future spot rateWhy not: That is the unbiased forward hypothesis; CIP holds regardless of expectations.
- The forward premium or discount equals the interest rate differential, enforced by riskless arbitrage - correct
CIP is a no-arbitrage relationship: borrowing in one currency, investing in another and covering with a forward earns no riskless profit, so the forward rate is set by spot and the interest rates.
A harder one
An investor borrows JPY at 0.5% and invests in AUD at 4.5% for one year with no hedge. Under uncovered interest rate parity, the expected change in the AUD against the JPY (JPY per AUD) is closest to:
- +3.98%Why not: Reversed sign; UIP predicts the high-rate AUD depreciates.
- -3.83% - correct
- 0.00%Why not: Assumes a random-walk exchange rate (no expected change), which is a different hypothesis from UIP.
- -4.50%Why not: Uses only the AUD interest rate and ignores the JPY borrowing rate and the compounding.
UIP: E[S1]/S0 = (1 + i JPY)/(1 + i AUD) = 1.005/1.045, so the AUD is expected to change by -3.83% against the JPY. That offsets the interest advantage and leaves no expected carry profit.
The hardest tier
Spot EUR/USD is 1.0850; one-year interest rates are 4% (USD) and 3% (EUR), and covered parity holds with a forward of 1.0955. An investor with USD 1,000,000 invests in EUR deposits and leaves the position unhedged. A year later spot is 1.0700. By how much do the unhedged USD proceeds fall short of the covered proceeds, closest to?
- USD 13,825Why not: Counts only the spot depreciation on the initial EUR amount, ignoring the interest earned and the forward premium.
- USD 53,825Why not: Omits the 3% EUR interest earned on the deposit when computing the unhedged proceeds.
- USD 15,760Why not: Reports the unhedged USD gain rather than the shortfall against the covered proceeds.
- USD 24,240 - correct
Covered proceeds = USD 1,040,000 (the parity-forward result). Unhedged: 921,659 x 1.03 = EUR 949,309 x 1.0700 = USD 1,015,761. Shortfall = USD 24,239. The unhedged position bore the exchange rate risk that the forward removed.
In the app: 6 practice questions on this outcome, spaced review that brings it back before you forget it.
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