Spot and forward market efficiency
The efficiency of the spot foreign exchange market implies that spot exchange rates move in a random and unpredictable manner, reflecting the random arrival of new information.This means that it is not possible to make profit by speculating in the foreign exchange market by buying and selling currencies actively.It also means that the exchange rate follows a random walk, which means that period-to-period changes in the exchange rate are random and do not follow any pattern and hence are unpredictable.The random walk behavior may be represented by the equation

where εt is a random error term.This equation tells us that the level of the exchange rate today differs from the level yesterday (or last month or whatever)by a random term, εt, which can be positive or negative.Equation (5.23)may be rewritten as which says that the period-to-period change in the exchange rate is random and unpredictable.

The concept of forward market efficiency encompasses both the spot and forward markets.In this sense, the market is efficient if it reflects all available information, where the information is embodied in the forward rate.The forward rate performs this function because it represents the collective wisdom of many well-informed profit-seeking traders and also because it is revised quickly as new information becomes available.
Consider the following example of speculation on the relationship between the spot and forward rates.If a speculator believes that the one-period forward exchange rate is lower than the spot rate prevailing on the maturity date of the contract, it will be profitable to buy forward and sell spot on the maturity of the forward contract.Let S1 be the spot rate prevailing at time 1 where 0 is the present time and F be the forward rate agreed upon at time 0 for delivery at time 1.If the speculator is correct, he or she will make profit that is given by

If this speculator acts on the basis of public information, there is no reason why other speculators will not take part in this “feast”.The increase in the demand for forward contracts will raise the forward rate and reduce profit until the latter reaches the level of zero.At time 0, when the decision to speculate is taken, S1 is not known, which means that speculators have to act on the basis of their expectation with respect to the spot exchange rate.Hence, speculators will buy forward at 0 and sell spot at 1 if the expected value of the spot exchange rate (Se)is higher than the forward rate.This operation will come to an end if and when the expected value of the spot exchange rate is equal to the forward rate, that is if

The difference between the spot exchange rate at time 1 and the forward rate is also the forecasting error when the forward exchange rate is used as a forecaster of the spot rate.Market efficiency will hold in general if the forward exchange rate is an unbiased and efficient forecaster of the spot exchange rate.Unbiasedness means that, on average, the forward rate is equal to (and that it does not systematically underestimate)the spot exchange rate prevailing on the maturity date of the forward contract.Efficiency of forecasting means that it is not possible to improve the forecast by utilizing information other than what is embodied in the forward rate.This is why this kind of efficiency is alternatively known as unbiased efficiency.