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14 CHAPTER 1. SOME INSTITUTIONAL BACKGROUNDTable 1.1: Yen futures for June 1999 deliveryLong yen positionDate F T −k S T −k ∆F T −k ∆(F T −k V T ) Margin φ T −k6/16/98 0.7346 0.6942 0.0000 0.0 2835.0 1.05816/17/98 0.772 0.7263 0.0374 4675.0 7510.0 1.06287/17/98 0.7507 0.7163 -0.0213 -2662.5 4847.5 1.04798/17/98 0.7147 0.6859 -0.0360 -4500.0 347.5 1.04189/17/98 0.7860 0.7582 0.0713 8912.5 9260.0 1.036510/16/98 0.8948 0.8661 0.1088 13600.0 22860.0 1.033011/17/98 0.8498 0.8244 -0.0450 -5625.0 17235.0 1.030812/17/98 0.8815 0.8596 0.0317 3962.5 21197.5 1.025401/19/99 0.8976 0.8790 0.0161 2012.5 23210.0 1.021102/17/99 0.8524 0.8401 -0.0452 -5650.0 17560.0 1.014603/17/99 0.8575 0.8463 0.0051 637.5 18197.5 1.0131on the futures contract.The hedge comes about because there is a covered interest paritylikerelation that links the futures price to the spot exchange rate witheurocurrency rates as a reference point. Let i T −k be the Eurodollar rateat T − k which matures at T , i ∗ T −k be the analogous one-year Euroeurorate, assume a 360 day year, and letφ T −k = 1+ ki T −k360,1+ ki∗ T −k360be the ratio of the domestic to foreign gross returns on an eurocurrencydeposit that matures in k days. The parity relation for futures pricesisF T −k = φ T −k S T −k . (1.14)Here, the futures price varies in proportion to the spot price with φ T −kbeing the factor of proportionality. As contract approaches last tradingday, k → 0. It follows that φ T −k → 1, and F T = S T .Thismeansthatyou can obtain the foreign exchange in two equivalent ways. You canbuy a futures contract on the last trading day and take delivery, or you