Tim Olson
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75 lines
3.5 KiB
Markdown
75 lines
3.5 KiB
Markdown
---
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description: "FX carry trade that exploits the empirical failure of Uncovered Interest Rate Parity by buying high-interest-rate currencies and selling low-interest-rate currencies via forward contracts."
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tags: [fx, carry, interest-rate-differential, uirp]
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---
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# Carry Trade
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**Section**: 8.2 | **Asset Class**: FX | **Type**: Carry
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## Overview
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Uncovered Interest Rate Parity (UIRP) predicts that the excess return from investing in a high-interest-rate currency should be exactly offset by that currency's depreciation. Empirically the opposite tends to hold: high-interest-rate currencies appreciate on average. The carry trade exploits this "forward premium/discount anomaly" (Fama puzzle) by writing (selling) forwards on currencies at a forward premium and buying forwards on currencies at a forward discount.
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## Construction / Mechanics
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The UIRP condition (which does not reliably hold) is:
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```
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(1 + r_d) = [E_t(S(t+T)) / S(t)] × (1 + r_f) (440)
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```
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The no-arbitrage forward FX rate is given by Covered Interest Rate Parity (CIRP):
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```
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F(t,T) = S(t) × (1 + r_d) / (1 + r_f) (441)
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```
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- r_d: domestic risk-free interest rate
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- r_f: foreign risk-free interest rate
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- S(t): spot FX rate at time t (units of domestic currency per 1 unit of foreign)
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- F(t,T): forward FX rate for delivery at T
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- E_t(S(t+T)): expected future spot rate at time t
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**Trade logic:**
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- If F(t,T) > S(t) (forward premium, i.e., r_d > r_f): **sell** the forward (borrow foreign, invest domestic)
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- If F(t,T) < S(t) (forward discount, i.e., r_f > r_d): **buy** the forward (borrow domestic, invest foreign)
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## Return Profile
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Profits when the carry differential is not fully offset by spot rate moves — i.e., when UIRP fails (the typical empirical finding). Losses occur if the borrowed currency suddenly appreciates sharply against the invested currency ("carry unwind" or "crash risk").
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## Key Parameters / Signals
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| Signal | Description |
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|--------|-------------|
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| F(t,T) > S(t) | Sell the forward (currency at forward premium) |
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| F(t,T) < S(t) | Buy the forward (currency at forward discount) |
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| Typical horizon T | 1 month |
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## Variations
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### 8.2.1 High-Minus-Low (HML) Carry
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The carry trade can be applied cross-sectionally across a universe of N foreign currencies. Define the log forward discount for currency i:
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```
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D(t,T) = s(t) - f(t,T) (442)
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```
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where s(t) = ln(S(t)) and f(t,T) = ln(F(t,T)). By CIRP:
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```
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D(t,T) = ln((1 + r_f) / (1 + r_d)) ≈ r_f - r_d (443)
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```
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**Portfolio construction:**
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- Positive D(t,T): buy a forward on that currency (higher foreign rate)
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- Negative D(t,T): sell a forward on that currency (lower foreign rate)
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- Sort all N currencies by D(t,T); go long the top quantile, short the bottom quantile
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- Dollar-neutral (zero-cost) implementation by construction
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- Forwards are typically one-month tenors; portfolio rebalanced monthly
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The cross-sectional spread captures the "high-minus-low" carry factor, analogous to HML in equity factor models.
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## Notes
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- The single-pair carry trade is exposed to large drawdowns during "carry unwind" episodes (e.g., 2008), when risk-off flows reverse the trade sharply.
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- Cross-sectional (HML) implementation diversifies idiosyncratic currency risk but retains systematic crash risk.
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- Transaction costs (bid-ask spreads on forwards) are a meaningful drag, particularly for less-liquid currency pairs.
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- The trade is equivalent to borrowing the low-rate currency and lending the high-rate currency when transaction costs and FX hedging costs are ignored.
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