Understanding the multifractality in portfolio excess returns

The multifractality in stock returns have been investigated extensively. However, whether the autocorrelations in portfolio returns are multifractal have not been considered in the literature. In this paper, we detect multifractal behavior of returns of portfolios constructed based on two popular trading rules, size and book-to-market (BM) ratio. Using the multifractal detrended fluctuation analysis, we find that the portfolio returns are significantly multifractal and the multifractality is mainly attributed to long-range dependence. We also investigate the multifractal cross-correlation between portfolio return and market average return using the detrended cross-correlation analysis. Our results show that the cross-correlations of small fluctuations are persistent, while those of large fluctuations are anti-persistent.