英文标题：
《Following a Trend with an Exponential Moving Average: Analytical Results
  for a Gaussian Model》
---
作者：
D. S. Grebenkov and J. Serror
---
最新提交年份：
2013
---
英文摘要：
  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.
---
中文摘要：
我们研究股票价格变化如何转化为趋势跟踪策略的损益（P&L）。在高斯模型的框架下，我们推导了P&L的概率分布，并分析了其矩（均值、方差、偏度和峰度）和渐近行为（分位数）。我们发现，分布的不对称性（通常损失很小，不太频繁但利润很大）让人想起趋势跟踪策略，并且较少依赖于价格变化的特性。在短时间内，趋势跟踪策略承认损失比标准高斯估计可能预期的更大，而在较长时间内确保损失较小。描述损益分布的简单显式公式说明了动量交易的基本机制，而通用矩阵表示可以应用于任意高斯模型。我们还计算了明确的年化风险调整损益和战略周转率，以考虑交易成本。我们推导了趋势跟踪最优时间尺度及其对自相关水平和交易成本的依赖关系。理论结果如道琼斯指数所示。
---
分类信息：

一级分类：Quantitative Finance        数量金融学
二级分类：Statistical Finance        统计金融
分类描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
统计、计量经济学和经济物理学分析及其在金融市场和经济数据中的应用
--
一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--

---
PDF下载：
-->