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Following a trend with an exponential moving average: Analytical results for a Gaussian model

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  • Grebenkov, Denis S.
  • Serror, Jeremy

Abstract

We investigate how price variations of a stock are transformed into profits and losses (P&Ls) of a trend following strategy. In the frame of a Gaussian model, we derive the probability distribution of P&Ls and analyze its moments (mean, variance, skewness and kurtosis) and asymptotic behavior (quantiles). We show that the asymmetry of the distribution (with often small losses and less frequent but significant profits) is reminiscent to trend following strategies and less dependent on peculiarities of price variations. At short times, trend following strategies admit larger losses than one may anticipate from standard Gaussian estimates, while smaller losses are ensured at longer times. Simple explicit formulas characterizing the distribution of P&Ls illustrate the basic mechanisms of momentum trading, while general matrix representations can be applied to arbitrary Gaussian models. We also compute explicitly annualized risk adjusted P&L and strategy turnover to account for transaction costs. We deduce the trend following optimal timescale and its dependence on both auto-correlation level and transaction costs. Theoretical results are illustrated on the Dow Jones index.

Suggested Citation

  • Grebenkov, Denis S. & Serror, Jeremy, 2014. "Following a trend with an exponential moving average: Analytical results for a Gaussian model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 288-303.
    • Handle: RePEc:eee:phsmap:v:394:y:2014:i:c:p:288-303
    DOI: 10.1016/j.physa.2013.10.007
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    References listed on IDEAS

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    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
    2. Bouchaud,Jean-Philippe & Potters,Marc, 2003. "Theory of Financial Risk and Derivative Pricing," Cambridge Books, Cambridge University Press, number 9780521819169.
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    Cited by:

    1. Papailias, Fotis & Thomakos, Dimitrios D., 2015. "An improved moving average technical trading rule," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 458-469.

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