T HE R ELATIONSHIP B ETWEEN THE F ORWARD R ATE AND THE F UTURE S POT R ATE

FINANCIAL MANAGEMENT

4.6 T HE R ELATIONSHIP B ETWEEN THE F ORWARD R ATE AND THE F UTURE S POT R ATE

Exhibit 4.17

Uncovered and Covered Interest Rate

Differentials (U.S. $versus Other Currencies)

Source: Bhar, Buk-Joogn, Kim, Ramprasad, and Toan M., Pham, ‘‘Exchange Rate Volatility and Its Impact on the Transaction Cost of Covered Interest Rate Parity.’’Japan and the World Economy, Vol. 16, 2004.

4.6 T

HE

R

ELATIONSHIP

B

ETWEEN THE

F

ORWARD

R

ATE

Exhibit 4.18

Relationship Between the Forward Rate and the Future Spot Rate

–2

–2 –1 1 2 3 4 5

–3 –4 –5

–3 –4 –5 –1 1 2 3 4 5

Parity line

I

J

Forward premium (+) or discount (–) on foreign currency (%) Expected change

in home currency value of foreign currency (%)

Ignoring risk for the moment, equilibrium is achieved only when the forward differential equals the expected change in the exchange rate. At this point, there is no longer any incentive to buy or sell the currency forward. This condition is illustrated in Exhibit 4.18. The vertical axis measures the expected change in the home currency value of the foreign currency, and the horizontal axis shows the forward discount or premium on the foreign currency. Parity prevails at point I, where the expected foreign currency depreciation of 2% is just matched by the 2%

forward discount on the foreign currency. Point J, however, is a position of disequilibrium because the expected 4% depreciation of the foreign currency exceeds the 3% forward discount on the foreign currency. We would, therefore, expect to see speculators selling the foreign currency forward for home currency, taking a 3% discount in the expectation of covering their commitment with 4% fewer units of HC.

A formal statement of theunbiased forward rate (UFR)condition is that the forward rate should reflect the expected future spot rate on the date of settlement of the forward contract:

f_t=e_t (4.19)

where e_t is the expected future exchange rate at time t (units of home currency per unit of foreign currency) andf_tis the forward rate for settlement at timet.

Application

Using UFR to Forecast the Future$/€Spot Rate

If the 90-day forward rate is€1=$0.8987, what is the expected value of the euro in 90 days?

Solution.Arbitrage should ensure that the market expects the spot value of the euro in 90 days to be about $0.8987.

Equation 4.19 can be transformed into the equation reflected in the parity line appearing in Exhibit 4.18, which is that the forward differential equals the expected change in the exchange rate, by subtracting 1 (e₀/e₀), from both sides, wheree₀is the current spot rate (HC per unit of foreign currency):¹⁷

f₁−e₀

e₀ = e₁−e₀

e₀ (4.20)

Market efficiency requires that people process information and form reasonable expecta- tions; it does not require thatf₁=e₁. Market efficiency allows for the possibility that risk-averse investors will demand a risk premium on forward contracts, much the same as they demand compensation for bearing the risk of investing in stocks. In this case, the forward rate will not reflect exclusively the expectation of the future spot rate.

The principal argument against the existence of a risk premium is that currency risk is largely diversifiable. If foreign exchange risk can be diversified away, no risk premium need be paid for holding a forward contract; the forward rate and expected future spot rate will be approximately equal. Ultimately, therefore, the unbiased nature of forward rates is an empirical, and not a theoretical, issue.

Empirical Evidence

A number of studies have examined the relation between forward rates and future spot rates.¹⁸ Of course, it would be unrealistic to expect a perfect correlation between forward and future spot rates because the future spot rate will be influenced by events, such as an oil crisis, that can be forecast only imperfectly, if at all.

Nonetheless, the general conclusion from early studies was that forward rates are unbiased predictors of future spot rates. But later studies, using more powerful econometric techniques, argue that the forward rate is a biased predictor, probably because of a risk premium.¹⁹ However, the premium appears to change signs—being positive at some times and negative at other times—and averages near zero. This result, which casts doubt on the risk premium story, should not be surprising given that testing the unbiased nature of the forward rate is equivalent to testing the international Fisher effect (assuming covered interest parity holds).

In effect, we wind up with the same conclusions: Over time, currencies bearing a forward discount (higher interest rate) depreciate relative to currencies with a forward premium (lower interest rate). That is, on average, the forward rate is unbiased. On the other hand, at any point in time, the forward rate appears to be a biased predictor of the future spot rate.

More specifically, the evidence indicates that one can profit on average by buying currencies selling at a forward discount (i.e., currencies whose interest rate is relatively high) and selling currencies trading at a forward premium (i.e., currencies whose interest rate is relatively low).

Nonetheless, research also suggests that this evidence of forward market inefficiency may be difficult to profit from on a risk-adjusted basis. One reason is the existence of what is known as the peso problem.

Thepeso problemrefers to the possibility that during the time period studied investors anticipated significant events that did not materialize, thereby invalidating statistical inferences

17Note that this condition can be derived through a combination of the international Fisher effect and interest parity theory.

Specifically, interest rate parity says that the interest differential equals the forward differential, whereas the IFE says that the interest differential equals the expected change in the spot rate. Things equal to the same thing are equal to each other, so the forward differential will equal the expected exchange rate change if both interest rate parity and the IFE hold.

18See, for example, Giddy and Dufey, ‘‘The Random Behavior of Flexible Exchange Rates’’; and Bradford Cornell, ‘‘Spot Rates, Forward Rates, and Market Efficiency,’’Journal of Financial Economics(January 1977): 55–65.

19See, for example, Lars P. Hansen and Robert J. Hodrick, ‘‘Forward Rates as Optimal Predictions of Future Spot Rates,’’

Journal of Political Economy(October 1980): 829–853.

based on data drawn from that period. The term derives from the experience of Mexico from 1955 to 1975. During this entire period, the peso was fixed at a rate of $0.125, yet continually sold at a forward discount because investors anticipated a large peso devaluation.

This devaluation eventually occurred in 1976, thereby validating the prediction embedded in the forward rate (and relative interest rates). However, those who limited their analysis on the relation between forward and future spot rates to data drawn only from 1955 to 1975 would have falsely concluded that the forward rate was a biased predictor of the future spot rate.

In their comprehensive survey of the research on bias in forward rates, Froot and Thaler conclude,

Whether or not there is really money to be made based on the apparent inefficiency of foreign exchange markets, it is worth emphasizing that the risk-return trade-off for a single currency is not very attractive. . . Although much of the risk in these [single currency] strategies may be diversifiable in principle, more complex diversified strategies may be much more costly, unreliable, or difficult to execute.²⁰

This evidence of bias suggests that the selective use of forward contracts—sell forward if the currency is at a forward premium and buy it forward if it is selling at a discount—may increase expected profits but at the expense of higher risk.