The mechanics of uncovered interest arbitrage
Uncovered interest arbitrage consists of taking a short position on (that is, borrowing)a currency and taking a corresponding long position on (that is, investing in)another currency without covering the long position.One of the two currencies may be the domestic currency and the other a foreign currency (although this is not necessarily the case).We will illustrate uncovered arbitrage by taking time 0 to be the time at which the operation is initiated and time 1 to be the time at which the investment matures and the short positions is covered.
Arbitrage from the domestic currency to a foreign currency
Arbitrage in this case consists of the following steps:
1.The arbitrage borrows domestic currency funds at the domestic interest rate, i.For simplicity, we assume that the amount borrowed is one domestic currency unit.
2.The borrowed funds are converted at the spot exchange rate, S0, obtaining 1/S0 foreign currency units.This amount is invested at the foreign interest rate, i*.
3.The foreign currency value of the invested amount at the end of the investment period is (1/S0)(1+i*).
4.This amount is reconverted into the domestic currency at the spot exchange rate prevailing at time 1, S1, to obtain (S1/S0)(1+i*)domestic currency units.
5.The value of the loan plus interest is (1+i)domestic currency units.
The uncovered margin, π, is the difference between the domestic currency value of the proceeds and the loan repayment, which gives
or approximately
whereS˙is the percentage change in the exchange rate between 0 and 1.Equation (5.32)tells us that the uncovered margin on arbitrage from the domestic to a foreign currency consists of the interest rate differential and the percentage change in the exchange rate.
Arbitrage from a foreign currency to the domestic currency
Arbitrage in this case consists of the following steps:
1.The arbitrage borrows foreign currency funds at the foreign interest rate, i*.For simplicity, we again assume that the amount borrowed is one foreign currency unit.
2.The borrowed funds are converted at the spot exchange rate, S0, obtaining S0 domestic currency units.This amount is invested at the domestic interest rate, i.
3.The domestic currency value of the invested amount at the end of the investment period is S0(1+i ).
4.This amount is reconverted into the foreign currency at the spot rate, S1, to obtain (S0/S1)(1+i)foreign currency units.
5.The value of the loan plus interest is (1+i*)foreign currency units.
The uncovered margin is the difference between the foreign currency value of the proceeds and the loan repayment, which gives
or approximately
Equation (5.34)tells us that the uncovered margin on arbitrage from the foreign to the domestic currency consists of the interest rate differential (measured the other way round)and the negative of the percentage change in the exchange rate.