475 SPreAD TrADINg IN CUrreNCY FUTUreS Of course, the market forces just described would come into play well before the forward/spot ratio increased to 0.82/0.80 = 1.025. The intervention of arbitrageurs will assure the six-month forward/spot ratio would not rise significantly above 1 + r 1/1 + r2 = 1.0099. A similar argument could be used to demonstrate that arbitrage intervention would keep the forward/spot ratio from declining significantly below 1.0099. In short, arbitrage activity will assure that the forward/spot ratio will be approximately defined by the above equation. This relationship is commonly referred to as the interest rate parity theorem. Since currency futures must converge with spot exchange rates at expiration, the price spread between a forward futures contract and a nearby expiring contract must reflect the prevailing interest rate ratio (between the eurodollar rate and the given eurocurrency rate). 4 Hence, a spread between two forward futures contracts can be interpreted as reflecting the market’s expectation for the inter- est rate ratio at the time of the nearby contract expiration. Specifically, if P 1 = price of the more nearby futures expiring at t1 and P2 = price of the forward futures contract expiring at time t 2, then P2/P1 will equal the expected interest rate ratio (expressed as 1+r1/1+r2) for term rates of duration t2 − t1 at time t1. It should be stressed that the forward interest rate ratio implied by spreads in futures will usually differ from the prevailing interest rate ratio. If the market expects the eurodollar rate to be greater than the foreign eurocurrency rate, forward futures for that currency will trade at a premium to more nearby futures—the wider the expected differential, the wider the spread. Conversely, if the foreign eurocurrency rate is expected to be greater than the eurodollar rate, forward futures will trade at a discount to nearby futures. The above relationships suggest that intracurrency spreads can be used to trade expectations regarding future interest rate differentials between different currencies. If a trader expected eurodol- lar rates to gain (move up more or down less) on a foreign eurocurrency rate (relative to the expected interest rate ratio implied by the intracurrency futures spread), this expectation could be expressed as a long forward/short nearby spread in that currency. Conversely, if the trader expected the foreign eurocurrency rate to gain on the eurodollar rate, the implied trade would be a long nearby/short forward intracurrency spread. As a technical point, a 1:1 spread ratio would fluctuate even if the implied forward interest rate ratio were unchanged. For example, if P 2 = $0.81/euro and P1 = $0.80/euro, a 10-percent increase in both rates would result in a 810-point price gain in the forward contract and only a 800-point gain in the nearby contract, even though the implied forward interest rate ratio would be unchanged (since an equal percentage change in each month would leave F/S unchanged). In order for the spread posi- tion to be unaffected by equal percentage price changes in both contracts, a development that would not affect the implied forward interest rate ratio, the spread would have to be implemented so that the dollar value of the long and short positions were equal. This parity will be achieved when the contract ratio is equal to the inverse of the price ratio. For example, given the above case of P 2 = $0.81 and 4 All references to interest rate ratios in this section should be understood to mean (1 + r1)/(l + r2) where r1 and r2 are the nonannualized rates of return for the time interim between S and F. Thus, in the above example, the interest rate ratio for the six-month period given annualized rates of 4.04 percent and 2.01 percent is equal to 1.02/1.01 = 1.0099. The reader should be careful not to misconstrue the intended definition of interest rate ratio with a literal interpretation, which in the above example would suggest a figure of 0.02/0.01 = 2.