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Optimal Portfolio Design for Statistical Arbitrage in Finance

Author

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  • Ziping Zhao
  • Rui Zhou
  • Zhongju Wang
  • Daniel P. Palomar

Abstract

In this paper, the optimal mean-reverting portfolio (MRP) design problem is considered, which plays an important role for the statistical arbitrage (a.k.a. pairs trading) strategy in financial markets. The target of the optimal MRP design is to construct a portfolio from the underlying assets that can exhibit a satisfactory mean reversion property and a desirable variance property. A general problem formulation is proposed by considering these two targets and an investment leverage constraint. To solve this problem, a successive convex approximation method is used. The performance of the proposed model and algorithms are verified by numerical simulations.

Suggested Citation

  • Ziping Zhao & Rui Zhou & Zhongju Wang & Daniel P. Palomar, 2018. "Optimal Portfolio Design for Statistical Arbitrage in Finance," Papers 1803.02974, arXiv.org.
    • Handle: RePEc:arx:papers:1803.02974
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    References listed on IDEAS

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    1. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    2. Ziping Zhao & Daniel P. Palomar, 2016. "Mean-Reverting Portfolio Design via Majorization-Minimization Method," Papers 1611.08393, arXiv.org.
    3. Barry R. Marks & Gordon P. Wright, 1978. "Technical Note—A General Inner Approximation Algorithm for Nonconvex Mathematical Programs," Operations Research, INFORMS, vol. 26(4), pages 681-683, August.
    4. Evan Gatev & William N. Goetzmann & K. Geert Rouwenhorst, 2006. "Pairs Trading: Performance of a Relative-Value Arbitrage Rule," The Review of Financial Studies, Society for Financial Studies, vol. 19(3), pages 797-827.
    5. João Frois Caldeira & Gulherme Valle Moura, 2013. "Selection of a Portfolio of Pairs Based on Cointegration: A Statistical Arbitrage Strategy," Brazilian Review of Finance, Brazilian Society of Finance, vol. 11(1), pages 49-80.
    6. Christopher Krauss, 2017. "Statistical Arbitrage Pairs Trading Strategies: Review And Outlook," Journal of Economic Surveys, Wiley Blackwell, vol. 31(2), pages 513-545, April.
    7. Marco Avellaneda & Jeong-Hyun Lee, 2010. "Statistical arbitrage in the US equities market," Quantitative Finance, Taylor & Francis Journals, vol. 10(7), pages 761-782.
    8. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    9. Ziping Zhao & Daniel P. Palomar, 2017. "Robust Maximum Likelihood Estimation of Sparse Vector Error Correction Model," Papers 1710.05513, arXiv.org.
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    Cited by:

    1. Derek Singh & Shuzhong Zhang, 2020. "Robust Arbitrage Conditions for Financial Markets," Papers 2004.09432, arXiv.org.
    2. Derek Singh & Shuzhong Zhang, 2021. "Robust Arbitrage Conditions for Financial Markets," SN Operations Research Forum, Springer, vol. 2(3), pages 1-52, September.

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