Error-Correction: Forward and Spot

Error-Correction: Forward and Spot Prices: Certain commodities andfinancial instruments can be bought and sold on the spot market (for immediatedelivery) or for delivery at some specified future date. For example,6 CHAPTER 1 DIFFERENCE EQUATIONSsuppose that the price of a particular foreign currency on the spot market isst dollars and that the price of the currency for delivery one period into thefuture is ft dollars. Now, consider a speculator who purchased forward currencyat the price ft dollars per unit. At the beginning of period t + 1, thespeculator receives the currency and pays ft dollars per unit received. Sincespot foreign exchange can be sold at st+1, the speculator can earn a profit (orloss) of st+1 − ft per unit transacted.The Unbiased Forward Rate (UFR) hypothesis asserts that expected profitsfrom such speculative behavior should be zero. Formally, the hypothesisposits the following relationship between forward and spot exchange rates:st+1 = ft + t+1 (1.6)where t+1 has a mean value of zero from the perspective of time period t.In (1.6), the forward rate in t is an unbiased estimate of the spot rate int + 1. Thus, suppose you collected data on the two rates and estimated theregressionst+1 = 0 + 1ft + t+1If you were able to conclude that 0 = 0, 1 = 1, and that the regressionresiduals t+1 have a mean value of zero from the perspective of time period t,the UFR hypothesis could be maintained.The spot and forward markets are said to be in long-run equilibriumwhen t+1 = 0. Whenever st+1 turns out to differ from ft, some sort of adjustmentmust occur to restore the equilibrium in the subsequent period. Considerthe adjustment processst+2 = st