Mean-variance portfolio selection of cointegrated assets
This paper considers the continuous-time mean-variance portfolio selection problem in a financial market in which asset prices are cointegrated. The asset price dynamics are then postulated as the diffusion limit of the corresponding discrete-time error-correction model of cointegrated time series. The problem is completely solved in the sense that solutions of the continuous-time portfolio policy and the efficient frontier are obtained as explicit and closed-form formulas. The analytical results are applied to pairs trading using cointegration techniques. Numerical examples show that identifying a cointegrated pair with a high mean-reversion rate can generate significant statistical arbitrage profits once the current state of the economy sufficiently departs from the long-term equilibrium. We propose an index to simultaneously measure the departure level of a cointegrated pair from equilibrium and the mean-reversion speed based on the mean-variance paradigm. An empirical example is given to illustrate the use of the theory in practice.
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- 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.
- Michael Kohlmann & Tang Shanjian, 2000. "Optimal Control of Linear Stochastic Systems with Singular Costs, and the Mean-Variance Hedging Problem with Stochastic Market Conditions," CoFE Discussion Paper 00-13, Center of Finance and Econometrics, University of Konstanz.
- Lo, Andrew W & MacKinlay, A Craig, 1990.
"When Are Contrarian Profits Due to Stock Market Overreaction?,"
Review of Financial Studies,
Society for Financial Studies, vol. 3(2), pages 175-205.
- Andrew W. Lo & A. Craig MacKinlay, 1989. "When are Contrarian Profits Due to Stock Market Overreaction?," NBER Working Papers 2977, National Bureau of Economic Research, Inc.
- Lo, Andrew W. (Andrew Wen-Chuan) & MacKinlay, Archie Craig, 1955-., 1989. "When are contrarian profits due to stock market overreaction?," Working papers 3008-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Nguyen, Pascal & Portait, Roland, 2002. "Dynamic asset allocation with mean variance preferences and a solvency constraint," Journal of Economic Dynamics and Control, Elsevier, vol. 26(1), pages 11-32, January.
- Sweeney, Richard J., 2006. "Mean Reversion in G-10 Nominal Exchange Rates," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 41(03), pages 685-708, September.
- Maslyuk, Svetlana & Smyth, Russell, 2009. "Cointegration between oil spot and future prices of the same and different grades in the presence of structural change," Energy Policy, Elsevier, vol. 37(5), pages 1687-1693, May.
- Mylonidis, Nikolaos & Kollias, Christos, 2010. "Dynamic European stock market convergence: Evidence from rolling cointegration analysis in the first euro-decade," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2056-2064, September.
- Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
- Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
- Jorion, Philippe & Sweeney, Richard J., 1996. "Mean reversion in real exchange rates: evidence and implications for forecasting," Journal of International Money and Finance, Elsevier, vol. 15(4), pages 535-550, August.
- 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.
- Engle, Robert F & Granger, Clive W J, 1987.
"Co-integration and Error Correction: Representation, Estimation, and Testing,"
Econometric Society, vol. 55(2), pages 251-76, March.
- Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 39(3), pages 106-135.
- Kellard, Neil & Dunis, Christian & Sarantis, Nicholas, 2010. "Foreign exchange, fractional cointegration and the implied-realized volatility relation," Journal of Banking & Finance, Elsevier, vol. 34(4), pages 882-891, April.
- Wang, J. & Forsyth, P.A., 2010. "Numerical solution of the Hamilton-Jacobi-Bellman formulation for continuous time mean variance asset allocation," Journal of Economic Dynamics and Control, Elsevier, vol. 34(2), pages 207-230, February.
- Cerchi, Marlene & Havenner, Arthur, 1988. "Cointegration and stock prices : The random walk on wall street revisited," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 333-346.
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