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A Mathematical Analysis of Technical Analysis

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  • Matthew Lorig
  • Zhou Zhou
  • Bin Zou

Abstract

In this paper, we investigate trading strategies based on exponential moving averages (ExpMAs) of an underlying risky asset. We study both logarithmic utility maximization and long-term growth rate maximization problems and find closed-form solutions when the drift of the underlying is modeled by either an Ornstein-Uhlenbeck process or a two-state continuous-time Markov chain. For the case of an Ornstein-Uhlenbeck drift, we carry out several Monte Carlo experiments in order to investigate how the performance of optimal ExpMA strategies is affected by variations in model parameters and by transaction costs.

Suggested Citation

  • Matthew Lorig & Zhou Zhou & Bin Zou, 2017. "A Mathematical Analysis of Technical Analysis," Papers 1710.09476, arXiv.org, revised Feb 2019.
    • Handle: RePEc:arx:papers:1710.09476
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    References listed on IDEAS

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    1. James, F. E., 1968. "Monthly Moving Averages—An Effective Investment Tool?*," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 3(3), pages 315-326, September.
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    5. Christopher J. Neely & David E. Rapach & Jun Tu & Guofu Zhou, 2014. "Forecasting the Equity Risk Premium: The Role of Technical Indicators," Management Science, INFORMS, vol. 60(7), pages 1772-1791, July.
    6. Han, Yufeng & Zhou, Guofu & Zhu, Yingzi, 2016. "A trend factor: Any economic gains from using information over investment horizons?," Journal of Financial Economics, Elsevier, vol. 122(2), pages 352-375.
    7. Merton, Robert C, 1969. "Lifetime Portfolio Selection under Uncertainty: The Continuous-Time Case," The Review of Economics and Statistics, MIT Press, vol. 51(3), pages 247-257, August.
    8. Kim, Tong Suk & Omberg, Edward, 1996. "Dynamic Nonmyopic Portfolio Behavior," The Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 141-161.
    9. Cox, John C. & Huang, Chi-fu, 1989. "Optimal consumption and portfolio policies when asset prices follow a diffusion process," Journal of Economic Theory, Elsevier, vol. 49(1), pages 33-83, October.
    10. Han, Yufeng & Yang, Ke & Zhou, Guofu, 2013. "A New Anomaly: The Cross-Sectional Profitability of Technical Analysis," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(5), pages 1433-1461, October.
    11. Taylor, Mark P. & Allen, Helen, 1992. "The use of technical analysis in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 11(3), pages 304-314, June.
    12. Brock, William & Lakonishok, Josef & LeBaron, Blake, 1992. "Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal of Finance, American Finance Association, vol. 47(5), pages 1731-1764, December.
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    Cited by:

    1. Marco Corazza & Claudio Pizzi & Andrea Marchioni, 2024. "A financial trading system with optimized indicator setting, trading rule definition, and signal aggregation through Particle Swarm Optimization," Computational Management Science, Springer, vol. 21(1), pages 1-29, June.
    2. Vicky Henderson & Saul Jacka & Ruiqi Liu, 2021. "The Support and Resistance Line Method: An Analysis via Optimal Stopping," Papers 2103.02331, arXiv.org.

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