The Science and Practice of Trend-Following Systems

Battle Count: 76

This paper is directly and fundamentally relevant to quantitative trading. It provides the first unified analytical framework for trend-following systems (European, American, TSMOM), derives closed-form Sharpe ratios linking TF performance to autocorrelation and drift of volatility-normalized returns, establishes spectral interpretation of TF alpha, derives cost-optimal span selection, and validates all results on 84 liquid futures contracts. The results enable design, simulation, and performance attribution of TF systems. The paper bridges academic theory (fractional processes, spectral analysis) with industry practice (CTA systems, managed futures). The companion Python package enables immediate practical implementation.

The analytical formulas are closed-form and computationally straightforward once the autocorrelation function and drift are estimated. However, the theoretical framework requires understanding of EWMA filters, fractional ARFIMA processes, Poisson kernel spectral representations, Isserlis theorem extensions, and Wold decompositions. The empirical pipeline (volatility normalization, autocorrelation estimation, Sharpe ratio prediction) is moderate complexity. The Monte Carlo verification and grid backtests add computational requirements. The companion Python package significantly reduces implementation burden. The long-short filter with variance-preserving normalization and the net Sharpe ratio with turnover proxy require careful implementation.

The paper provides a Python package 'trendfollowing' on GitHub that reproduces all analytical results and exhibits. The futures dataset is included in the companion repository. All Monte Carlo simulations are fully specified with parameters (1000 paths, 50 years, 13000 observations per path). Analytical formulas are closed-form and verifiable. The paper explicitly states code and data availability.