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Stochastic trends and cointegration in the market for equities

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  • Lucy F. Ackert
  • Marie D. Racine

Abstract

We use a no-arbitrage, cost-of-carry pricing model to examine whether equity spot and futures markets are cointegrated. A stock index and its futures price should be cointegrated if the cost of carry is stationary. Otherwise, the appropriate cointegrating relationship is trivariate and includes the index, futures price, and cost of carry. We study the relationships among the Standard and Poor's 500 index, associated index futures price series, and interest rate for January 4, 1988, through June 30, 1995, and find that all three series are nonstationary. We further find that the index and futures price are not cointegrated unless the cost of carry is included in the cointegrating relationship. Our findings are consistent with the no-arbitrage pricing model and do not appear to be sensitive to the presence of structural breaks in the series.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Atlanta in its series Working Paper with number 98-13.

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Date of creation: 1998
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Handle: RePEc:fip:fedawp:98-13

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Keywords: Cointegration ; Financial markets;

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  1. John Y. Campbell & Robert J. Shiller, 1988. "Cointegration and Tests of Present Value Models," NBER Working Papers 1885, National Bureau of Economic Research, Inc.
  2. Amin, Kaushik I. & Jarrow, Robert A., 1991. "Pricing foreign currency options under stochastic interest rates," Journal of International Money and Finance, Elsevier, vol. 10(3), pages 310-329, September.
  3. Baillie, Richard T & Bollerslev, Tim, 1989. " Common Stochastic Trends in a System of Exchange Rates," Journal of Finance, American Finance Association, vol. 44(1), pages 167-81, March.
  4. Engle, Robert F & Granger, Clive W J, 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing," Econometrica, Econometric Society, vol. 55(2), pages 251-76, March.
  5. Taylor, Mark P & Tonks, Ian, 1989. "The Internationalisation of Stock Markets and the Abolition of U.K. Exchange Control," The Review of Economics and Statistics, MIT Press, vol. 71(2), pages 332-36, May.
  6. Gregory, A.W. & Hansen, B.E., 1992. "Residual-Based Tests for Cointegration in Models with Regime Shifts," RCER Working Papers 335, University of Rochester - Center for Economic Research (RCER).
  7. Dickey, David A & Fuller, Wayne A, 1981. "Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root," Econometrica, Econometric Society, vol. 49(4), pages 1057-72, June.
  8. Harvey, Campbell R & Whaley, Robert E, 1991. " S&P 100 Index Option Volatility," Journal of Finance, American Finance Association, vol. 46(4), pages 1251-61, September.
  9. Cushing, Matthew J & Ackert, Lucy F, 1994. "Interest Rate Innovations and the Volatility of Long-Term Bond Yields," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 26(2), pages 203-17, May.
  10. Brenner, Robin J. & Kroner, Kenneth F., 1995. "Arbitrage, Cointegration, and Testing the Unbiasedness Hypothesis in Financial Markets," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(01), pages 23-42, March.
  11. Hakkio, Craig S. & Rush, Mark, 1989. "Market efficiency and cointegration: an application to the sterling and deutschemark exchange markets," Journal of International Money and Finance, Elsevier, vol. 8(1), pages 75-88, March.
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