---
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."
tags: [fx, carry, interest-rate-differential, uirp]
---

# Carry Trade

**Section**: 8.2 | **Asset Class**: FX | **Type**: Carry

## Overview
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.

## Construction / Mechanics
The UIRP condition (which does not reliably hold) is:

```
(1 + r_d) = [E_t(S(t+T)) / S(t)] × (1 + r_f)              (440)
```

The no-arbitrage forward FX rate is given by Covered Interest Rate Parity (CIRP):

```
F(t,T) = S(t) × (1 + r_d) / (1 + r_f)                      (441)
```

- r_d: domestic risk-free interest rate
- r_f: foreign risk-free interest rate
- S(t): spot FX rate at time t (units of domestic currency per 1 unit of foreign)
- F(t,T): forward FX rate for delivery at T
- E_t(S(t+T)): expected future spot rate at time t

**Trade logic:**
- If F(t,T) > S(t) (forward premium, i.e., r_d > r_f): **sell** the forward (borrow foreign, invest domestic)
- If F(t,T) < S(t) (forward discount, i.e., r_f > r_d): **buy** the forward (borrow domestic, invest foreign)

## Return Profile
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").

## Key Parameters / Signals
| Signal | Description |
|--------|-------------|
| F(t,T) > S(t) | Sell the forward (currency at forward premium) |
| F(t,T) < S(t) | Buy the forward (currency at forward discount) |
| Typical horizon T | 1 month |

## Variations

### 8.2.1 High-Minus-Low (HML) Carry
The carry trade can be applied cross-sectionally across a universe of N foreign currencies. Define the log forward discount for currency i:

```
D(t,T) = s(t) - f(t,T)                                       (442)
```

where s(t) = ln(S(t)) and f(t,T) = ln(F(t,T)). By CIRP:

```
D(t,T) = ln((1 + r_f) / (1 + r_d)) ≈ r_f - r_d             (443)
```

**Portfolio construction:**
- Positive D(t,T): buy a forward on that currency (higher foreign rate)
- Negative D(t,T): sell a forward on that currency (lower foreign rate)
- Sort all N currencies by D(t,T); go long the top quantile, short the bottom quantile
- Dollar-neutral (zero-cost) implementation by construction
- Forwards are typically one-month tenors; portfolio rebalanced monthly

The cross-sectional spread captures the "high-minus-low" carry factor, analogous to HML in equity factor models.

## Notes
- 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.
- Cross-sectional (HML) implementation diversifies idiosyncratic currency risk but retains systematic crash risk.
- Transaction costs (bid-ask spreads on forwards) are a meaningful drag, particularly for less-liquid currency pairs.
- 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.