英文標(biāo)題：
《Following a Trend with an Exponential Moving Average: Analytical Results
for a Gaussian Model》
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作者：
D. S. Grebenkov and J. Serror
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最新提交年份：
2013
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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.
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中文摘要：
我們研究股票價(jià)格變化如何轉(zhuǎn)化為趨勢(shì)跟蹤策略的損益（P&L）。在高斯模型的框架下，我們推導(dǎo)了P&L的概率分布，并分析了其矩（均值、方差、偏度和峰度）和漸近行為（分位數(shù)）。我們發(fā)現(xiàn)，分布的不對(duì)稱性（通常損失很小，不太頻繁但利潤很大）讓人想起趨勢(shì)跟蹤策略，并且較少依賴于價(jià)格變化的特性。在短時(shí)間內(nèi)，趨勢(shì)跟蹤策略承認(rèn)損失比標(biāo)準(zhǔn)高斯估計(jì)可能預(yù)期的更大，而在較長(zhǎng)時(shí)間內(nèi)確保損失較小。描述損益分布的簡(jiǎn)單顯式公式說明了動(dòng)量交易的基本機(jī)制，而通用矩陣表示可以應(yīng)用于任意高斯模型。我們還計(jì)算了明確的年化風(fēng)險(xiǎn)調(diào)整損益和戰(zhàn)略周轉(zhuǎn)率，以考慮交易成本。我們推導(dǎo)了趨勢(shì)跟蹤最優(yōu)時(shí)間尺度及其對(duì)自相關(guān)水平和交易成本的依賴關(guān)系。理論結(jié)果如道瓊斯指數(shù)所示。
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分類信息：
一級(jí)分類：Quantitative Finance 數(shù)量金融學(xué)
二級(jí)分類：Statistical Finance 統(tǒng)計(jì)金融
分類描述：Statistical, econometric and econophysics analyses with applications to financial markets and economic data
統(tǒng)計(jì)、計(jì)量經(jīng)濟(jì)學(xué)和經(jīng)濟(jì)物理學(xué)分析及其在金融市場(chǎng)和經(jīng)濟(jì)數(shù)據(jù)中的應(yīng)用
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一級(jí)分類：Physics 物理學(xué)
二級(jí)分類：Statistical Mechanics 統(tǒng)計(jì)力學(xué)
分類描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相變，熱力學(xué)，場(chǎng)論，非平衡現(xiàn)象，重整化群和標(biāo)度，可積模型，湍流
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