Free lesson · FX and commodities
Unhedged carry leaves exchange-rate risk
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Start with the idea
Earning a higher foreign interest rate can be overwhelmed by depreciation of the foreign currency.
Symbols, units & horizon
- N: domestic currency borrowed at entry
- r_f,r_d: foreign investment and domestic borrowing annual simple rates
- T: years
- S₀,S_T: domestic per foreign spot at entry/maturity
- Π: domestic-currency profit before other costs
- no currency hedge
When and why to use this
Quantify a currency carry position’s exposure to joint rate and FX scenarios.
Earning a higher foreign interest rate can be overwhelmed by depreciation of the foreign currency.
Borrow domestic currency, convert into foreign currency and invest for the same tenor. At maturity the domestic value of the foreign deposit depends on the realized exchange rate; subtract the domestic debt. This is risky carry, not the covered-parity identity.
A leveraged carry strategy also faces variation margin, financing rollovers and potentially correlated liquidation by other investors. Stress the funding currency strengthening and financing availability deteriorating together.
Unhedged carry leaves exchange-rate risk
- Convert N domestically borrowed units into N/S₀ foreign units.
- Accrue foreign interest and convert at realized S_T.
- Subtract domestic repayment N(1+r_dT).
Borrow $100 at 2%, foreign investment earns 6%, and foreign currency loses 5% in USD terms. Profit=100×(1.06×.95−1.02)=−$1.30.
Apply it in a strategy
- Freeze inputs at the stated decision time and record their units.
- Quantify a currency carry position’s exposure to joint rate and FX scenarios.
- Recompute the example, then change the material assumption and explain the difference.
Research deliverable
Unhedged carry leaves exchange-rate risk: produce the worked calculation, a timestamped input record and a written decision addressing this limitation: Interest advantage does not offset all depreciation, funding shocks or forced liquidation.
These are synthetic mechanics examples, not historical performance or paper replications. Module evidence and research boundaries record the 12 September 2026 review.
Python implementation
Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.
# Python 3.10+; standard library and NumPy only.
# Synthetic teaching inputs; conventions and units are defined in the notation above.
def unhedged_carry(notional,foreign_rate,domestic_rate,years,spot_before,spot_after):
if notional<=0 or years<0 or min(spot_before,spot_after)<=0: raise ValueError('Invalid notional, horizon or spot')
return notional*((1+foreign_rate*years)*spot_after/spot_before-(1+domestic_rate*years))
assert abs(unhedged_carry(100,.06,.02,1,1,.95)+1.3)<1e-12
print(unhedged_carry(100,.06,.02,1,1,.95))Continue learning
FX & Commodities: Quotes, Carry, Curves & Hedges — all lessons- Invert both units and bid/ask sides
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- Covered interest parity by matching currency cash flows
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- Futures profit and margin cash demands
- Rolling futures without inventing a cash profit
- Minimum-variance cross hedging and basis risk
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