Uncovered Interest Parity

Definition

Uncovered interest parity (UIP) states that the expected depreciation of the domestic currency equals the nominal interest rate differential: investing in either currency yields the same expected return. Under risk neutrality and rational expectations:

$E_t[\Delta s_{t+1}] = i_t - i_t^*$

where $s_t = \log(\text{domestic price of foreign currency})$ , $i_t$ is the domestic nominal interest rate, and $i_t^*$ is the foreign rate. High-interest-rate currencies are expected to depreciate by exactly their yield advantage.

Key Ideas

UIP is an equilibrium no-arbitrage condition in frictionless markets under risk neutrality. It does not require physical arbitrage — only that no excess expected return is available from currency speculation.
Covered interest parity (CIP) — $i_t - i_t^* = f_t - s_t$ (forward rate equals expected spot rate) is enforced by riskless arbitrage and holds closely in liquid markets (small deviations = bid-ask spreads). UIP adds the assumption that the forward rate equals the expected future spot rate.
The forward premium puzzle (Fama 1984) — The Fama regression $\Delta s_{t+1} = \alpha + \beta(i_t - i_t^*) + \eta_{t+1}$ consistently yields $\hat\beta < 0$ (often around $-0.9$ to $0$ ) rather than $\beta = 1$ . High-interest-rate currencies tend to appreciate, not depreciate — the opposite of UIP.
Engel-Hamilton (1990) failure: Even when exchange rates follow a Markov-switching segmented-trends process with statistically identifiable regime changes, interest rate differentials fail to predict which regime the exchange rate is in. During dollar appreciation episodes (state 2 of the model), U.S. interest rates were frequently lower than foreign rates — the wrong sign for UIP.
Peso problem — In a sample where agents rationally fear a large depreciation that never occurs, ex-post forward rate errors are biased without any failure of rationality. Named after the Mexican peso, which experienced persistent forward discounts before its 1976 devaluation.

How It Works

Fama (1984) Regression

The canonical test regresses realized depreciation on the lagged forward premium: $\Delta s_{t+1} = \alpha + \beta(i_t - i_t^*) + \eta_{t+1}$

Under UIP: $\alpha = 0$ , $\beta = 1$ . Empirically: $\hat\beta \approx -0.9$ across most currency pairs and sample periods (Fama 1984; Hodrick 1987). The forward premium predicts less depreciation than it should — and even the wrong direction.

Markov-Switching UIP Test (Engel-Hamilton 1990)

Under UIP in a two-state Markov-switching world, the interest differential should equal the probability-weighted expected depreciation:

$i_t - i_t^* = P(s_t = 1)\mu_1 + P(s_t = 2)\mu_2$

This is testable: the bivariate system $(\Delta y_t, i_t - i_t^*)$ should have the interest differential predicting regime probabilities. Engel-Hamilton find it does not — interest differentials contain no information about $s_t$ .

Carry Trade Profitability

UIP failure directly implies carry trade profits: borrow in low-interest-rate currency, invest in high-interest-rate currency, pocket the differential. If $\hat\beta < 1$ , expected returns to carry are positive because the interest advantage is not fully offset by expected depreciation. This is empirically robust but carries crash risk during risk-off episodes (sudden reversal of high-yield currency appreciation).

Why It Matters

UIP failure is one of the most robust empirical regularities in international finance and a major challenge to exchange rate theory.
If UIP fails, interest rate differentials contain no useful information about expected exchange rate changes — undermining monetary models, Taylor-rule exchange rate models, and any framework that assumes covered = uncovered parity.
The carry trade as a profitable strategy implies either a time-varying currency risk premium or persistent irrationality — both of which have significant implications for global capital flows and monetary policy transmission.

Open Questions

Are UIP deviations driven by time-varying currency risk premia (rational risk-return tradeoff), or by systematic expectation errors?
Does the peso problem fully account for the forward premium puzzle, or does a genuine risk premium persist even accounting for rare events?
UIP appears to hold better at very long horizons (5–10 years) and at very short horizons (intraday); the failure is concentrated at 1-month to 1-year horizons.