Expectations Theory and Forward Exchange Rates

If foreign currency markets are efficient, the forward rate should reflect what market participants expect the future spot rate for a currency to be. For example, if market participants expected the one-year future spot rate (S₁) for DM to be $0.58, then what would the one-year forward rate (F₁) have to be^? It would also have to be $0.58. If the forward rate were lower than this amount, market participants would want to buy DM forward, thereby placing upward price pressure on the DM until an equilibrium is reached where the forward rate equals the expected future spot rate.

If the expected future spot rate is equivalent to the forward rate, we can say that the forward rate is an unbiased estimator of the future spot rate. It is important to recognize that this does not mean that the forward rate will always be equal to the actual future spot rate. Rather it means that the estimates of the future spot rate provided by the forward rate will not systematically overshoot or undershoot the actual future spot rate, but will equal it on average.

Evidence regarding the expectations theory of forward exchange rates indicates that, in general, the forward rate is an unbiased estimate of expected future spot rates, if risk in the currency markets is ignored. There is some evidence however, that when the forward rate implies a large change from the current spot rate, these forecasts tend to overshoot the actual future spot rate. Forward rates as unbiased estimates of expected future spot rates have important implications for managers. First, managers should not spend the firm's resources to buy forecasts of future exchange rates since unbiased forecasts are provided free in the marketplace. Second, managers will find that hedging their future foreign currency risk by making use of the forward market should be a cost-effective way of limiting this risk exposure. In the following sections some of these hedging techniques are considered.

The International Fisher Effect

The final piece in the international currency market puzzle is the relationship between interest rates and future spot currency rates. In his 1930 book, The theory of interest Irving Fisher established that in equilibrium lenders will receive a nominal rate of interest equal to a real interest rate plus an amount sufficient to offset the effects of expected inflation. Nominal interest rates are market rates stated in current, not real terms, such as the rates quoted in financial publications like the Wall Street Journal. Real rates of return are not directly observable. The real rate of return is the rate at which borrowing and lending in the financial markets are in equilibrium The real rate of return is equal to the real rate of growth in the economy, and it reflects the time preference of market participants between present and future consumption. The relationship between nominal (risk-free) rates of return, real rates of return, and expected inflation is

or:

(3.7)

where i is the nominal (and risk-free) rate of interest, i_r is the real rate of return, and π is the expected inflation rate. This relationship is often referred to as the Fisher effect. For example, if the annual real rate of return in France was 3 percent and the expected annual inflation rate was 8 percent, the nominal interest rate would be:

i = 0.03+0.08+(0.03)(0.08) = 0.1124 or 11.24%

Fisher argues that in the absence of government interference and holding risk constant, real rates of return across countries will be equalized through a process of arbitrage. If real rates of return are higher in the United States than in Japan, capital will flow to the United States from Japan until an equilibrium is reached. The assumption of equal real rates of return across countries ignores differences in risk and attitudes toward risk that may exist in different cultures. Also, to the extent that there are barriers to the movement of capital between countries, real rates of return may be different between countries. In spite of these limitations, the assumption of equal real returns is useful because (1) it is a reasonable representation of reality among the major industrialized countries, and (2) as capital markets become increasingly internationalized and barriers to capital flows fall, differences in real rates of return can be expected to decrease.

If real rates of return tend to be equalized across countries, it follows that differences in observed nominal rates between countries must be due primarily to different inflation expectations. Incorporating the equilibrium condition for real interest rates with relative PPP leads to what has been called the International Fisher Effect (IFE). The IFE states that differences in interest rates between two countries should be offset by equal, but opposite changes in the future spot exchange rate. For example, if one-year nominal interest rates are 10 percent in the United States and 7 percent in France, then IFE predicts that the French franc (FF) should increase in value relative to the U.S. dollar by approximately 3 percent.

The exact IFE relationship is:

(3.8)

where S₁, is the expected future (direct quote) spot rate at time period 1, S₀ is the current (direct quote) spot rate, i_h is the home country (U.S.) nominal interest late, and i_f, is the foreign country nominal interest rate. This relation­ship can be simplified to:

(3.9)

Using the example above, if one year U.S. nominal interest rates are 10 percent, one-year French nominal interest rates are 7 percent, and the current spot ex­change rate, S₀, is $0.16/FF, then the expected spot rate in one year, S_1; will be

S₁/$0.16 = (1+0.10)/(1 +0.07)

S₁ = $0.1645

The lower nominal French interest rate results in an expected increase in the value of the FF (decrease in the value of the $) of 2.80 percent.