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高斯模型下的趋势跟踪损益分布与最优时间尺度

文章 arXiv papers · 作者: D. S. Grebenkov et al.
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总结

本文在高斯假设下分析趋势跟踪策略如何将股价变化转化为盈亏。研究推导了损益分布，并考察其均值、方差、偏度、峰度和尾部分位数。分析将策略结果的不对称性——频繁的小额亏损和较少发生的大额盈利——归因于趋势跟踪机制，而非仅仅归因于异常价格行为。

研究还给出了年化风险调整后损益和换手率的公式，并据此分析如何选择在收益与交易成本之间取得最佳平衡的时间尺度。报告称，短周期内的亏损可能大于标准高斯估计所暗示的水平，而较长时间尺度对亏损的约束更强。研究使用道琼斯指数展示理论结果。结论依赖高斯建模框架，本文并未证明这些公式能够反映所有真实市场行为。

核心观点

  • 本研究在高斯价格模型下推导趋势跟踪盈亏的概率分布。
  • 趋势跟踪损益可能呈正向不对称，即频繁出现较小亏损，较少出现较大盈利。
  • 短周期亏损可能超过标准高斯估计所暗示的水平。
  • 最佳趋势时间尺度取决于收益自相关和交易成本。
  • 研究通过换手率和年化风险调整损益来考虑交易成本。

标签

趋势跟踪动量统计学风险管理交易执行
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# Following a Trend with an Exponential Moving Average: Analytical Results for a Gaussian Model


# Following a Trend with an Exponential Moving Average: Analytical Results for a Gaussian Model









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.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。