Long-range dependence and asset return anomaly

We investigate the significance of long-range dependence effect of asset prices in forecasting asset returns. By modeling asset price dynamics as a fractional Brownian motion process and using the corresponding Hurst parameter as a proxy to the long-range dependence of prices, a long-range dependence factor is constructed as the Hurst parameters estimated from daily logarithm returns of assets. Portfolio-level analysis and firm-level cross-sectional regressions reveal an abnormally negative returns associated with the long-range dependence factor, which is statistically significant. Specifically, a long-short strategy formed by sorting stocks with respect to the estimated Hurst parameters and then longing/shorting stocks in the lowest/highest deciles offers a \(13.13\%\) $13.13\%$ return per annum after accounting for transaction costs. The predictive regression method confirms that there is an anomalous return associated with the long-range dependence factor. Such anomalous returns is not explained by the identified risk factors in the existing literature and it is robust with respect to factor construction and portfolio formation parameters.