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. Copyright © 2011 Elsevier B.V. All rights reserved.
CitationChiu, M. C., & Wong, H. Y. (2011). Mean–variance portfolio selection of cointegrated assets. Journal of Economic Dynamics and Control, 35(8), 1369-1385. doi: 10.1016/j.jedc.2011.04.003
- Mean–variance portfolio theory
- Pairs trade