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Arbitrage, Cointegration, and Testing the Unbiasedness Hypothesis in Financial Markets

Published online by Cambridge University Press:  06 April 2009

Robin J. Brenner  and
Kenneth F. Kroner
Robin J. Brenner
Affiliation:
Trading Research Group, Merrill Lynch, World Financial Center, North Tower, 15th Floor, New York, NY 10281–1315
Kenneth F. Kroner
Affiliation:
Department of Economics, University of Arizona and Advanced Strategies and Research Group, Wells Fargo Nikko Investment Advisors, 45 Fremont Street, San Francisco, CA 94105.
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Abstract

We use a no-arbitrage, cost-of-carry asset pricing model to show that the existence of cointegration between spot and forward (futures) prices depends on the time-series properties of the cost-of-carry. We argue that the conditions for cointegration are more likely to hold in currency markets than in commodity markets, explaining many of the empirical results in the literature. We also use this model to demonstrate why the forward rate forecast error, the basis, and the forward premium are serially correlated, and to develop econometric tests of the “unbiasedness hypothesis” (sometimes called the “simple efficiency hypothesis”) in various financial markets. The unbiasedness hypothesis is so prevalent in the finance literature that many tests for it have been developed. We examine four of the common tests and and use our cointegration results to demonstrate why each of these tests should reject the null hypothesis of unbiasedness. We find strong support for our hypothesis in the existing empirical literature.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 30 , Issue 1 , March 1995 , pp. 23 - 42
Copyright
Copyright © School of Business Administration, University of Washington 1995

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References

Akella, S. R., and Patel, A.. “Are International Real Rates of Interest Cointegrated? Evidence from the Recent Floating Exchange Rate Period.” Unpubl. Manuscript, Univ. of Missouri (1991).Google Scholar
Amin, K. I., and Jarrow, R. A.. “Pricing Foreign Currency Options under Stochastic Interest Rates.” Journal of International Money and Finance, 10 (1991), 310–329.CrossRefGoogle Scholar
Backus, D. K., and Gregory, A. W.. “Risk Premiums in Asset Prices and Returns: A Comment on R. T. Baillie.” Econometric Reviews, 8 (1989), 187–195.CrossRefGoogle Scholar
Baillie, R. T. “Econometric Tests of Rationality and Market Efficiency.” Econometric Reviews, 8 (1989), 121–156.CrossRefGoogle Scholar
Baillie, R. T., and Bollerslev, T.. “Common Stochastic Trends in a System of Exchange Rates.” Journal of Finance, 44 (1989), 137–151.CrossRefGoogle Scholar
Baillie, R. T., and Bollerslev, T.. “A Multivariate Generalized ARCH Approach to Modelling Risk Premia in Forward Foreign Exchange Rate Markets.” Journal of International Money and Finance, 9 (1990), 309–324.CrossRefGoogle Scholar
Baillie, R. T.; Lippens, R. E.; and McMahon, P. C.. “Testing Rational Expectations and Efficiency in the Foreign Exchange Market.” Econometrica, 51 (1983), 553–563.CrossRefGoogle Scholar
Baillie, R. T., and McMahon, P.. The Foreign Exchange Market: Theory and Econometric Evidence. New York, NY: Cambridge Univ. Press (1989).Google Scholar
Baillie, R. T., and Myers, R. J.. “Bivariate GARCH Estimation of the Optimal Commodity Futures Hedge.” Journal of Applied Econometrics, 6 (1991), 109–124.CrossRefGoogle Scholar
Barnhart, S. W., and Szakmary, A. C.. “Testing the Unbiased Forward Rate Hypothesis: Evidence on Unit Roots, Cointegration, and Stochastic Coefficients.” Journal of Financial and Quantitative Analysis, 26 (1991), 245–267.CrossRefGoogle Scholar
Bessler, D. A., and Covey, T.. “Cointegration: Some Results on US Cattle Prices.” Journal of Futures Markets, 11 (1991), 461–474.CrossRefGoogle Scholar
Bilson, J. F. O. “The Speculative Efficiency Hypothesis.” Journal of Business, 54 (1981), 435–451.CrossRefGoogle Scholar
Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (1973), 637–659.CrossRefGoogle Scholar
Boothe, P., and Longworth, C.. “Foreign Exchange Market Efficiency Tests: Implications of Recent Empirical Findings.” Journal of International Money and Finance, 5 (1986), 135–152.CrossRefGoogle Scholar
Bossaerts, P. “Common Nonstationary Components of Asset Returns.” Journal of Economic Dynamics and Control, 12 (1988), 347–364.CrossRefGoogle Scholar
Bradley, M., and Lumpkin, S.. “The Treasury Yield Curve as a Cointegrated System.” Journal of Financial and Quantitative Analysis, 27 (1992), 449–463.CrossRefGoogle Scholar
Brenner, R. J., and Kroner, K. F.. “Arbitrage, Cointegration, and the Term Structure of Interest Rates.” Unpubl. Manuscript, Univ. of Arizona (1993).Google Scholar
Campbell, J. Y., and Shiller, R. J.. “Cointegration and Tests of Present Value Models.” Journal of Political Economy, 95 (1987), 1062–1088.CrossRefGoogle Scholar
Canarella, G., and Pollard, S.. “The Efficiency of the London Metals Exchange: A Test with Overlapping and Nonoverlapping Data.” Journal of Banking and Finance, 10 (1986), 575–593.CrossRefGoogle Scholar
Cerchi, M., and Havenner, A.. “Cointegration and Stock Prices: The Random Walk on Wall Street Revisited.” Journal of Economic Dynamics and Control, 12 (1988), 333–346.CrossRefGoogle Scholar
Chan, K. C.; Karolyi, G. A.; Longstaff, F. A.; and Sanders, A. B.. “An Empirical Comparison of Alternative Models of the Short-Term Interest Rate.” Journal of Finance, 47 (1992), 1209–1227.Google Scholar
Chowdhury, A. R. “Futures Market Efficiency: Evidence from Cointegration Tests.” Journal of Futures Markets, 11 (1991), 577–589.CrossRefGoogle Scholar
Copeland, L. S. “Cointegration Tests with Daily Exchange Rate Data.” Oxford Bulletin of Economics and Statistics, 53 (1991), 155–198.CrossRefGoogle Scholar
Corbae, D., and Ouliaris, S.. “Cointegration and Tests of Purchasing Power Parity.” Review of Economics and Statistics, 70 (1988), 508–511.CrossRefGoogle Scholar
Cornell, B., and Reinganum, M.. “Forward and Futures Prices: Evidence from the Foreign Exchange Markets.” Journal of Finance, 36 (1981), 1035–1045.CrossRefGoogle Scholar
Cumby, R. E., and Obstfeld, M.. “Exchange Rate Expectations and Nominal Interest Differentials: A Test of the Fisher Hypothesis.” Journal of Finance, 36 (1981), 697–704.Google Scholar
Duffie, D.Futures Markets. Englewood Cliffs, NJ: Prentice Hall (1989).Google Scholar
Dwyer, G. P., and Wallace, M. S.. “Cointegration and Market Efficiency.” Journal of International Money and Finance, 11 (1992), 318–327.CrossRefGoogle Scholar
Edwards, S. “Foreign Exchange Rates, Expectations and New Information.” Journal of Monetary Economics, 11 (1983), 321–336.CrossRefGoogle Scholar
Engle, R. F., and Granger, C. W. J.. “Co-Integration and Error Correction: Representation, Estimation and Testing.” Econometrica, 55 (1987), 251–276.CrossRefGoogle Scholar
Fama, E. F. “Efficient Capital Markets: A Review of Theory and Empirical Work.” Journal of Finance, 25 (1970), 383–414.CrossRefGoogle Scholar
Fama, E. F. “Forward and Spot Exchange Rates.” Journal of Monetary Economics, 14 (1984), 319–338.CrossRefGoogle Scholar
Frenkel, J. A. “Flexible Exchange Rates, Prices, and the Role of ‘News’: Lessons from the 1970's.” Journal of Political Economy, 89 (1981), 665–705.CrossRefGoogle Scholar
Geweke, J., and Feige, E.. “Some Joint Tests of the Efficiency of Markets for Forward Exchange.” The Review of Economics and Statistics, 61 (1979), 334–341.CrossRefGoogle Scholar
Gonzalo, J., and Granger, C. W. J.. “Estimation of Common Long-Memory Components in Cointegrated Systems.” Unpubl. Manuscript, Dept. of Economics, Univ. of California at San Diego (1991).Google Scholar
Granger, C. W. J. “Developments in the Study of Cointegrated Economic Variables.” Oxford Bulletin of Economics and Statistics, 48 (1986), 213–228.CrossRefGoogle Scholar
Gregory, A. W., and McCurdy, T. H.. “Testing the Unbiasedness Hypothesis in the Forward Foreign Exchange Market: A Specification Analysis.” Journal of International Money and Finance, 3 (1984), 357–368.CrossRefGoogle Scholar
Hakkio, C. S. “Expectations and the Forward Exchange Rate.” International Economic Review, 22 (1981), 663–678.CrossRefGoogle Scholar
Hakkio, C. S., and Rush, M.. “Market Efficiency and Cointegration: An Application to the Sterling and Deutschemark Exchange Markets.” Journal of International Money and Finance, 8 (1989), 75–88.CrossRefGoogle Scholar
Hall, A.; Anderson, H.; and Granger, C. W. J.. “Treasury Bill Yield Curves and Cointegration.” Review of Economics and Statistics, 74 (1992), 116–126.CrossRefGoogle Scholar
Hansen, L. P., and Hodrick, R. J.. “Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis.” Journal of Political Economy, 88 (1980), 829–853.CrossRefGoogle Scholar
Heath, D.; Jarrow, R. A.; and Morton, A.. “Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation.” Econometrica 60 (1992), 77–105.CrossRefGoogle Scholar
Hegde, S. P., and McDonald, B.. “On the Informational Role of Treasury Bill Futures.” Journal of Futures Markets, 6 (1986), 629–643.CrossRefGoogle Scholar
Hodrick, R. J.The Empirical Evidence on the Efficiency of Forward and Futures Foreign Exchange Markets. Chur, Switzerland: Harwood Academic Publishers (1987).Google Scholar
Hodrick, R. J., and Srivastava, S.. “An Investigation of Risk and Return in Forward Foreign Exchange.” Journal of International Money and Finance, 3 (1984), 5–29.CrossRefGoogle Scholar
Hodrick, R. J., and Srivastava, S.. “The Covariation of Risk Premium and Expected Future Spot Exchange Rates.” Journal of International Money and Finance, 5 (1986), S5–S22.CrossRefGoogle Scholar
Hsieh, D. A. “Tests of Rational Expectations and the Risk Premium in Forward Exchange Markets.” Journal of International Economics, 14 (1984), 143–154.Google Scholar
Hsieh, D. A., and Kulatilaka, N.. “Rational Expectations and Risk Premia in Forward Markets: Primary Metals at the London Exchange.” Journal of Finance, 37 (1982), 1199–1207.CrossRefGoogle Scholar
Kroner, K. F., and Sultan, J.. “Time Varying Distributions and Dynamic Hedging with Foreign Currency Futures.” Journal of Financial and Quantitativ e Analysis, 28 (1993), 535–551.CrossRefGoogle Scholar
Lai, K. S., and Lai, M.. “A Cointegration Test for Market Efficiency.” Journal of Futures Markets, 11 (1991), 567–576.CrossRefGoogle Scholar
Longworth, D. “Testing the Efficiency of the Canadian Dollar – U.S. Exchange Market under the Assumption of No Risk Premium.” Journal of Finance, 36 (1981), 43–49.Google Scholar
MacDonald, R., and Taylor, M.. “Metals Prices, Efficiency and Cointegration: Some Evidence from the London Metal Exchange.” Bulletin of Economic Research, 40 (1988), 235–239.CrossRefGoogle Scholar
Norrbin, S. C., and Reffett, K. L.. “Exogeneity and the Forward Rate Efficiency Hypothesis.” Unpubl. Manuscript, Dept. of Economics, Florida State Univ. (1993).Google Scholar
Nugent, J. “Further Evidence of Forward Exchange Market Efficiency: An Application of Cointegration using German and U.K. Data.” Economic and Social Reviews, 22 (1990), 35–42.Google Scholar
Park, J. Y., and Phillips, P. C. B.. “Statistical Inference in Regressions with Integrated Processes: Part 2.” Econometric Theory, 5 (1989), 95–131.CrossRefGoogle Scholar
Sanders, A., and Unal, H.. “On the Intertemporal Behavior of the Short-Term Rate of Interest.” Journal of Financial and Quantatitive Analysis, 23 (1988), 417–424.CrossRefGoogle Scholar
Schroeder, T. C., and Goodwin, B. K.. “Price Discovery and Cointegration for Live Hogs.” Journal of Futures Markets, 11 (1991), 685–696.CrossRefGoogle Scholar
Sephton, P. S., and Larsen, H. K.. “Tests of Exchange Market Efficiency: Fragile Evidence from Cointegration Tests.” Journal of International Money and Finance, 10 (1991), 561–570.CrossRefGoogle Scholar
Shea, G. “Benchmarking the Expectations Hypothesis of the Interest Rate Term Structure: An Analysis of Cointegration Vectors.” Journal of Business and Economic Statistics 10 (1992) 347–366.Google Scholar
Shen, C.-H., and Wang, L.-R.. “Examining the Validity of a Test of Futures Market Efficiency: A Comment.” Journal of Futures Markets, 10 (1990), 195–196.CrossRefGoogle Scholar
Taylor, M. P., and Tonks, I.. “The Internationalisation of Stock Markets and the Abolition of U.K. Exchange Control.” Review of Economics and Statistics, 71 (1989), 332–336.CrossRefGoogle Scholar