Since the discovery of momentum effect, people have started the journey of using the momentum effect to construct momentum strategies. As a result of coupling cross-sectional and time-series momentum strategy, dual momentum strategy (DM strategy) has been widely used in practice and closely followed by academics. To address the shortcoming of the classical DM strategy that has not considered the multi-fractal characteristics of the stock market, we construct the fractal dual momentum strategy (FDM strategy) from the two aspects of optimizing the ranking index of the cross-sectional momentum strategy by using fractal statistical measures and improving the timing selection of the time-series momentum strategy by using the trend entropy dimension. The empirical results show that the FDM strategy outperforms the DM strategy. Both in terms of the size and stability of the strategy returns, the FDM strategy shows an optimization effect compared with the DM strategy, which is beneficial to provide investors with better decision-making references.

自从发现动量效应以来，人们就开始了利用动量效应构建动量策略的旅程。双动量策略（DM策略）作为横截面动量策略与时间序列动量策略耦合的结果，在实践中得到了广泛的应用并受到学术界的密切关注。针对经典DM策略没有考虑股票市场多重分形特征的缺点，从优化截面动量策略排名指标两个方面构建分形双动量策略（FDM策略）通过使用分形统计措施并利用趋势熵维度改进时间序列动量策略的时机选择。实证结果表明FDM策略优于DM策略。无论是从策略收益规模还是稳定性来看，FDM策略均较DM策略表现出优化效果，有利于为投资者提供更好的决策参考。