Stochastic Trends and Cointegration in the Market for Equities

Lucy F. Ackert and Marie D. Racine
Federal Reserve Bank of Atlanta
Working Paper 98-13
August 1998

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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.

JEL classification: G10, G12

Key words: cointegration, cost-of-carry model

The authors gratefully acknowledge the financial assistance of the Social Science and Humanities Research Council of Canada. They also thank Jason Bilodeau, Paul Robinson, and Victoria Sampson for research assistance. The views expressed here are those of the authors and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.

Please address questions regarding content to Lucy F. Ackert, Research Department, Federal Reserve Bank of Atlanta, 104 Marietta Street, NW, Atlanta, Georgia 30303-2713, 404/498-8783,; or Marie D. Racine, School of Business and Economics, Wilfrid Laurier University, Waterloo, Ontario N2L 3C5, Canada, 519/884-1970 ext. 2776, 519/884-0201 (fax),