Optimization study of momentum investment strategies under asymmetric power-law distribution of return rate

Abstract In the context that the tails of security returns obey an asymmetric power-law distribution, this paper constructs two fractal statistical measures based on fractal theory: fractal expectation and fractal variance. Subsequently, a new momentum strategy is constructed by introducing the fractal measures into the momentum strategy as measures of returns and risks to optimize the selection criterion. Finally, the empirical results show that the new momentum strategy outperforms the traditional momentum strategy and the risk-adjusted momentum strategy, confirming the effectiveness of fractal expectation and fractal variance.