Openness in Goods & Financial Markets

Uncovered Interest Parity

coreExam · high

Uncovered interest parity (UIP) says the expected return on domestic and foreign bonds must be equal — otherwise arbitrage creates capital flows that adjust the exchange rate until equality holds. Exact: (1+i) = (1+i*)·(Eᵉ/E). Approximation: i ≈ i* + (Eᵉ − E)/E. Implications: CB rate cut depreciates currency; peg + free capital → no independent i.

Derivation

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The Parity Condition

An investor indifferent between domestic and foreign bonds requires equal expected returns:

(1 + i_t) = (1 + i^*_t) \cdot \frac{E^e_{t+1}}{E_t}

With small numbers, taking logs:

i_t \approx i^*_t + \frac{E^e_{t+1} - E_t}{E_t}

Mechanics

Invest 1 euro in a domestic bond → $(1+i_t)$ euros.
Or: convert to foreign ccy ( $E_t$ foreign ccy), invest at $i^*$ , convert back at $E^e_{t+1}$ → $E_t(1+i^*)/E^e_{t+1}$ euros.
UIP equates the two.

Solved for the Spot Rate

E_t = E^e_{t+1} \cdot \frac{1 + i^*_t}{1 + i_t}

A cut in $i$ (with $E^e$ anchored) makes the RHS bigger → ↓ $E_t$ (depreciation) if $E$ is foreign-per-domestic. Higher domestic rates → appreciation.

Fixed Exchange Rates

If $E = \bar{E}$ is fixed and expected to remain so, $E^e = \bar{E}$ and UIP collapses to:

i = i^*

Any independent monetary policy is impossible under fixed FX with perfect capital mobility — this is the impossible trinity.

Empirical Violations

UIP is systematically violated at short horizons: high- $i$ currencies tend to appreciate further rather than depreciate (the "carry trade" puzzle). Explanations include time-varying risk premia, peso problems, and expectation errors.

Worked Example

E_t = 1.10 USD/EUR. i_US = 3%, i_EU = 1%. Markets expect E^e_{t+1} = 1.12.

UIP check: 1 + i_US = 1.03. RHS = (1 + i_EU) × (E^e/E) = 1.01 × (1.12/1.10) = 1.01 × 1.0182 ≈ 1.0283.
LHS ≈ RHS (both about 1.028) → UIP roughly holds. Expected USD appreciation compensates for the lower US-EU gap.
If E^e rose to 1.14: RHS = 1.01 × 1.0364 ≈ 1.047 > 1.03. Capital flows from US to EU → E_t falls until equality is restored.

UIP roughly holds at E_t = 1.10 with these rates and expectation. A higher E^e would push E_t down (USD depreciation today) via arbitrage.

Common Mistakes

—Getting the quoting convention wrong. Under E = foreign/domestic, ↑E = domestic appreciation. Under E = domestic/foreign, ↑E = domestic depreciation.
—Confusing covered interest parity (CIP, uses forward rate, always holds) with UIP (uses expected future spot, often violated).
—Forgetting that UIP ties current E to expected future E — a forward-looking equation, not a contemporaneous one.
—Applying UIP with fixed FX without recognising it forces i = i* (impossible trinity).

Exam Cues

→Approximation: i ≈ i* + (E^e − E)/E. Interest differential equals expected depreciation of the domestic currency.
→CB cut (↓i, floating FX) → E falls → currency depreciates → amplifies monetary transmission via NX.
→Peg + free capital = no independent i. This is the structural constraint of fixed exchange regimes.
→EMS collapse 1992: Bundesbank ↑i → members forced to match or devalue. Soros bet against GBP peg — won.