Term Paper: Forward Discount in Predicting Exchange

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[. . .] Hall's general to specific method was found to be more adequate than others. However, an opposite view, in favor of the Baysian Information Criterion was expressed by Stock (1994). Nontheless, the Hall method may also be used, as suggested by Stock, who left future researchers with the liberty of choice. Miah, Hassan and Alam used the Baysian Information Criterion.

The second test, known as the DF-GLS was proposed by Elliot (1996) as a solution to the size distorsion problems of the Augumented Dickey Fuller test. Actually, the DF-GLS is a modified version of the ADF test, which uses a detrended series instead of the original series (Detrending was perfomed using either a liniar trend or a constant. The use of a liniar trend was preffered in the above mentioned study.

A third test, the restricted cointegration test, was initially applied by Liu and Mdalla (1992) and Osterberg (2000), with further contributions by Granger (1981). This test represents a moe direct approach. If the actual rate of excahnge rate modifications is random, than its rational forecast should have a similar evoultion, which means that the two series are cointegrated with a factor of one and random residuals.


Literature reviews in this area have been previously conducted by various researchers, such as McDonald (2000), Maddala (1994) and Takagi (1991), who provide a comprehensive image of the concept of rationality of exchange rate expectations.

The review made by Takagi in 1991 concludes that there are three characteristics of the survey data regarding expectations of exchange rates. The first one is that the dispersion of expectations increases along with the forecast horizion. The second refers to the fact that the expected exchange rate changes are not very successful in actually resembling the real exchange-rate modifications, which leads to the conclusion that there is a great deal of uncertainty in this particular point. In the third place, it would seem that long-term expectations and short-term expectation have totally different trends, which is named a "twist" by the literature.

The unbiasedness hypothesis was tested by Dominguez (1986), Ito (1990), Chinn and Frankel (1994), based on various data sources, which resulted in very different results. Dominguez preferred to use data collected from Money Market Services; the results indicated that the unbiasedness hypothesis is not substantiated, at least within a horizon ranging from one week to three months. Approximately the same result were obtained by Cavaglia (1993), who used the EMS exchange rates published by Business International Corporation; the time horizon ranged from three months to a year.

Beng and Siong (1993) have conducted the most comprehensive study by observing the evolution of the Singapore currency against the U.S. Dollar for the 1984-1991 for all forecast horizons. The data used by Chinn and Frankel (1994) was provided by the Financial Times' Currency Forecaster (CDF) for February 1888 - February 1991 period; the result was that bias exists on a large scale in the available survey data. Another researcher, Ito (1990) benefited form the data collected by the Japanese Center for International Finance during the 1985-1987 period. Although for shorter horizions (one, three months) the unbiasedness was not evident, for longer periods of time it became unacceptable.

Conitegration tests were another method used by researchers to establish the degree of bias in expectation of foreign exchange moficiations. One of the most recent studies, conducted by Miah in 2003 arrived to approximately the same conclusions as the ones before it. Liu and Midala (1992) tested the Rational Expectation Hypothesis by using the same data as Dominguez, in 1986, which lead them to the conclusion that one-week forecast were unbiased, a fact which was not true for longer time intervals. Kim (1997) used survey data collected from Australia to establish whether the one-week and four-week forecast were rational. Osterberg (2000) made use of the Money Market Services data, which made him conclude that the one-week-ahead and four-week-ahead forecasts were rational.


The ADF test couldn't reject the null at 1% for the six-month-ahead horizion and at 5% for the other two time intervals. The DF-GLS test showed contradictory results for the six-months horizon, so the conclusion was that six-month-ahead forecast are nonstationary. As a general rule, it would seem that the German Mark / U.S. Dollar exchange rate date were nonstationary.

A similar conclusion was arrived at for the GB Pound / U.S. Dollar and Japanese Yen / Us Dollar exchange rates. In the case of the latter, there was not even a trend to be noticed.


The rational expectation hypothesis relating to the foreign exchange market modifications was analyzed and tested using various statistical methods using survey data which included three very important exchange rates: German Mark / U.S. Dollar, GB Pound / U.S. Dollar and Japanese Yen / U.S. Dollar. Econometric methods and their inappropriateness for evaluating time series was overcome by using the most modern discoveries in this field. Therefore, the examination of the relationship between the estimated exchange rates and the real exchange rates was possible with regard to a long-term horizon.

Overlapping forecasting causes the serial correlation problem, which was corrected by estimating the forecast errors as a moving average process.

One of the conclusions of the study is that the expectations of spot exchange rates at various horizons and the actual rates have unit roots. All exchange rates showed stationary forecast errors for the one-month and three-month ahead estimations, and the GB Pound / U.S. Dollar proved also stationary for the six-month ahead estimation, which was consistent with the results of the unit root tests.

Therefore, the rational expectation hypothesis is correct for one-month ahead estimations for all tested currencies, the three-month ahead forecasts are valid for the German Mark / U.S. Dollar and the GB Pound / U.S. Dollar. The only situation in which the six-month-ahead forecast proved right is that of the GB Pound / U.S. Dollar exchange rate.

However, twelve-month expectations were not rational even for the GB Pound / U.S. Dollar rate, which triggered the researchers to say that further insight might be provided by a much longer data ser. Another finding of the study was that there is a direct relation between the dispersion of expectations and the length of the time horizons.

The literature also speaks about other implications of the rational expectations hyphothesis, beside the unbiasedness of the survey data. such as the concept of orthogonality of forecast errors regarding the available information at the time of the forecast. The test of orthogonality, although not making the object of this study, was covered by Dominguez (1986), Frankel and Froot (1989), Ito (1990), Sobichewski (1994), MacDonald and Torrance (1989), Cavaglia, (1993), and Beng and Siong (1993), who arrived to the conclusion that exchange rate expectations are not supported by all the available information.

The conclusion of the study is that it is not the inability of the rational expectation hypothesis to present an adequate solution to the forward discount problem; the puzzle may be attributed to the existence of a risk premium. However, this conclusion is only applicable to those cases were the time-horizons satisfied the rational expectation hypothesis (three-months-ahead or six-moths ahead, at most; for the Japanese Yen / U.S. Dollar test, that is also an excessive conclusion). Failure of the rationality hypothesis could be a cause of the incapacity to correctly estimate the future modifications of exchange rates, along with the existence of the risk premium.


Beng, G.W. And W.K. Siong. (1993) Exchange Rate Expectations and Risk Premium in the Singapore/U.S. Dollar Exchange Rate: Evidence from Survey Data Applied Financial Economics, 3(4), pp. 365-73.

Bilson, John F.O., (1981) The Speculative Efficiency Hypothesis, Journal of Business, 54, pp. 435-452

Cavalgia, S.W., F.C. Verschoor and C.C.P. Wolff (1993a) Further Evidence on Exchange Rate Expectations Journal of International Money and Finance, 12 (1), pp. 78-98.

Cavalgia, S.W., F.C. Verschoor and C.C.P. Wolff (1993b) Asian Exchange Rate Expectations Journal of the Japanese and International Economics, 7(1), pp. 57-77.

Chinn, M. And Frankel J.A. (1994) Patterns in Exchange Rate Forecasts for Twenty-Five Currencies Journal of Money, Credit and Banking, 26 (4), pp. 759- 770.

Dickey, D.A. And Fuller, W.A. (1981) Likelihood Ration Statistics for Autoregressive Time Series with a Unit Root Econometrica, 49, pp. 1057-1072.

Dominguez, K.M. (1986) Are Foreign Exchange Forecasts Rational? New Evidence from Survey Data Economic Letters, 21(3), pp. 277-81.

Dominguez, K.M., and Frankel, J.A. (1993) Does Foreign Exchange Intervention Matter? The Portfolio Effect American Economic Review, 83(5), pp. 1356-69.

Elliot, F., Rothenberg, T.J. And Stock, J.H. (1996) Efficient Test for an Autoregressive Unit Root Econometrica, 64(4), pp. 813-36.

Engel, C. (1996) The Forward Discount Anomaly and the Risk Premium: A Survey of Recent Evidence, Journal of Empirical finance, 3, 123-192.

Fama, E. (1994), Forward and Spot Exchange Rates, Journal of Monetary Economics, 14, 319-338 Frankel, J.A., and Froot, K.A. (1989) Forward Discount Bias: Is It an Exchange Risk Premium? Quarterly Journal of Economics, pp139-61.

Frankel, J.A. And Froot, K.A. (1987)… [END OF PREVIEW]

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