Trend momentum
通过小波趋势分解发现，动量策略依赖的价格趋势具有比随机过程更长的持续期，并存在标度律，趋势动量指数可预测动量效应，证明市场非有效。
Momentum strategies have been repeatedly shown in the literature to outperform several markets. At the core of these strategies is an evaluation of the past performance of the underlying securities to set up a target portfolio. In this work, we show by experiment that the performance evaluation for individual securities used in these schemes is based on trends in price data. This is derived using a wavelet trend decomposition scheme for the security evaluation in comparison to the classical approach. We further verify that neither random walks nor fractional Brownian motions model that effect, which leads to the assumption that trends in real-world data have a different characteristic. By analysing the market index with respect to trend size, trend drift and trend volatility we show that these characteristics exhibit scaling laws. Specifically, the trend size seen in real-world data is significantly longer than that of random process models. We show by experiment that the associated ‘momentum exponent’ describing the scaling law for trend sizes is an indicator for the momentum effect. Additionally, we verify that momentum strategies exploit these long trends by analysing the longest held positions. We conclude by analysing this ‘momentum exponent’ for world indices and show that only a fraction of markets has exponents similar to previously used random processes. This means that trends are more prevalent in the real world than in theory. Consequently, markets cannot be efficient and trends as exploited by momentum strategies are an important contribution to investment success.