Currency Carry with Futures

Exchange rates

• It is simplest to quote foreign currency prices in the domestic currency (dollars).
• Cost of a euro, cost of a peso, etc. is the same concept as the cost of a loaf of bread.
• A currency appreciates (relative to the dollar) when its cost rises and depreciates when its cost falls.

Currency carry trade

• The currency carry trade is to borrow in a low interest-rate currency (e.g., euro) and invest in a high interest-rate currency (e.g., peso).
• You earn the interest differential. Interest is called carry.
• The risk is that the high interest-rate currency may depreciate relative to the other.
• Empirically, this has been a profitable trade on average.

• Borrowing in euros, exchanging to pesos, and depositing pesos is shorting euros and going long pesos.
• Example: short (borrow) $100,000 of euros and go long $100,000 of pesos. Pay euro interest rate and receive peso interest rate. Earn the difference.
• But when we sell the pesos and cover the euro loan, prices may have moved.

Currency carry with futures

• Short euros and invest in $ = synthetic short euro future
• Borrow $ and buy pesos = synthetic long peso future
• Combining them equals currency carry trade ($ cancel)
• Combining actual long peso future and actual short euro future also equals currency carry trade

Backwardation and contango

• Futures price = spot price + cost of carry - convenience yield
• = spot price + domestic interest - foreign interest
• Low foreign interest \(\Rightarrow\) contango (euros)
• High foreign interest \(\Rightarrow\) backwardation (peso)
• So, currency carry trade = sell contango futures and buy backwardation futures

Expensive and cheap futures

• Sell contango futures = sell futures when futures price is high (relative to spot)
• Buy backwardation futures = buy futures when futures price is low (relative to spot)
• So, currency carry trade = sell expensive futures and buy cheap futures (relative to spot)

Appreciation and returns

• Consider selling 2-month euro (contango) futures and buying 2-month peso (backwardation) futures at date \(t\) and holding for 2 months, until futures price = spot
• On peso, make

Failure of expectations hypothesis

• On euro, make opposite. So, total is difference in slopes (which is positive) + difference in appreciations.
• Expectation hypothesis implies expected difference in appreciations cancels difference in slopes.
• Empirically, average difference in appreciations actually adds a bit to difference in slopes.
  • Peso (backwardation) actually appreciates a little.
  • Euro (contango) actually depreciates a little.