Developing trading strategies based on fractal finance: An application of MF-DFA in the context of Islamic equities

We provide a new contribution to trading strategies by using multi-fractal de-trended fluctuation analysis (MF-DFA), imported from econophysics, to complement various momentum strategies. The method provides a single measure that can capture both persistency and anti-persistency in stock prices, accounting for multifractality. This study uses a sample of Islamic stocks listed in the U.S. Dow Jones Islamic market for a sample period covering 16 years starting in 1996. The findings show that the MF-DFA strategy produces monthly excess returns of 6.12%, outperforming other various momentum strategies. Even though the risk of the MF-DFA strategy may be relatively higher, it can still produce a Sharpe ratio of 0.164, which is substantially higher than that of the other strategies. When we control for the MF-DFA factor with the other factors, its pure factor return is still able to yield a monthly excess return of 1.35%. Finally, we combine the momentum and MF-DFA strategies, with the proportions of 90/10, 80/20, and 70/30 and by doing so we demonstrate that the MF-DFA measure can boost the total monthly excess returns as well as Sharpe ratio. The value added is non-linear which implies that the additional returns are associated with lower incremental risk.