Expectations Hypotheses Tests

We investigate the expectations hypotheses of the term structure of interest rates and of the foreign exchange market using vector autoregressive methods for U.S. dollar, Deutsche mark, and British pound interest rates and exchange rates. We examine Wald, Lagrange multiplier, and distance metric tests by iterating on approximate solutions that require only matrix inversions. Bias-corrected, constrained VARs provide Monte Carlo simulations. Wald tests grossly overreject the null, Lagrange multiplier tests slightly underreject, and distance metric tests overreject. A common interpretation emerges from the small sample statistics. The evidence against the expectations hypotheses is much less strong than under asymptotic inference. ACCORDING TO THE EXPECTATIONS HYPOTHESIS, information in current interest rates provides the conditional expectation of future asset prices. The expectations hypothesis of the term structure of interest rates ~EH-TS! states that the current term spread between a long-term interest rate and a short-term interest rate is the expected value of a weighted average of the expected future changes in the short-term interest rate. This theory, popularized in the writings of Fisher ~1930!, Keynes ~1930!, and Hicks ~1953!, continues to be a way that many economists think about the determination of long-term interest rates. Fisher ~1930! and Keynes ~1930! also discuss the expectations hypothesis in the foreign exchange market ~EH-FX!, which states that the interest-rate differential between two currencies is the conditional expected value of the rate of depreciation of the high interest-rate currency relative to the low interest-rate currency. Because of covered interest arbitrage, the interest differential equals the forward premium, which is the percentage difference between the forward exchange rate and the spot rate. Hence, the EH-FX is equivalent to the unbiasedness hypothesis, which is the proposition that the logarithm of the forward exchange rate is an unbiased predic* Bekaert and Hodrick are from Columbia University and are Research Associates of the National Bureau of Economic Research. Our research benefitted from the comments of Federico Bandi, Wayne Ferson, Matt Richardson, and the participants in seminars at the University of Copenhagen, BI-Oslo, INSEAD, the London School of Economics, the University of Washington, the Federal Reserve Board, the 2000 European Finance Association Meetings, the 2001 American Finance Association Meetings, and the Investment Forum 2000 Meetings. We thank David Ng and Paul Sengmueller of Columbia University and especially Joe Chen of Stanford University for research assistance. We also gratefully acknowledge financial support from the National Science Foundation. THE JOURNAL OF FINANCE • VOL. LVI, NO. 4 • AUGUST 2001