AI 中文总结
该研究提出统一方法设计趋势跟踪系统并分类，推导欧洲TF系统相关关系及预期回报等，经蒙特卡罗实验和实证评估，结果有助于从多方面对TF系统进行设计、模拟及绩效归因。
AI 中文摘要
我们提出一种统一的方法来设计趋势跟踪（TF）系统，并将其分为欧洲、美国和时间序列动量类别。对于欧洲TF系统，我们推导了损益、自相关和波动率归一化回报中的漂移之间的精确关系。分析了分数ARFIMA过程下的预期回报，表明当长期自相关为正时，TF系统是盈利的。在频域中，预期回报表示为波动率归一化回报的分析或经验谱的泊松核读数。推导了封闭形式的夏普比率等。蒙特卡罗实验证实了分析结果，实证评估了系统在流动性合约上的表现。我们的结果有助于从趋势持续性、均值回归、漂移和偏度等方面对TF系统进行设计、模拟和绩效归因。
英文摘要
We present a unified approach to designing trend-following (TF) systems and classify them into European, American, and Time Series Momentum categories. For European TF systems, we derive an exact relationship between profit-and-loss, autocorrelation, and drift in volatility-normalized returns. We analyze the expected return under fractional ARFIMA processes and show that TF systems are profitable when the long-term autocorrelation is positive, even under short-term mean reversion. In the frequency domain, the expected return is represented as a Poisson-kernel reading of the analytical or empirical spectrum of the volatility-normalized returns: the system profits at zero drift when the kernel-weighted spectral mass exceeds one, so trend-following alpha is excess spectral mass at low frequencies. Longer lookbacks benefit in addition from the squared drift of the return process. We derive the closed-form Sharpe ratio, with the excess kurtosis of the innovations entering through a single loading, and the net Sharpe ratio and cost-optimal span under trading costs. Under white noise, we derive the closed-form skewness of aggregated TF returns, which is positive at every horizon and peaks near half the filter span. Monte Carlo experiments confirm the analytical results. We show that the positive skewness of TF returns is structural under various model assumptions. Empirically, we evaluate the systems on liquid contracts, and show that all TF systems are strongly correlated and our analytical results can be applied for their performance attribution. Our results enable design, simulation, and performance attribution of TF systems from trend persistence, mean reversion, drift, and skewness.
