We consider long-only momentum returns to be composed of market returns plus<\/em> excess returns.<\/p>\n\n\n\n If excess returns over a specified period, n-days,<\/em> (say, 5- or 10-days) either trends or mean-reverts, then that can be used to trade the momentum portfolio.<\/p>\n\n\n\n One way to check if a time-series is trending is to calculate the Hurst exponent (H<\/strong>) over a rolling window (say, 5-years) of n-day <\/em>excess returns . If H<\/strong> < 0.5, then the time-series is mean-reverting; if H<\/strong> > 0.5, then it is trending, else it is random.<\/p>\n\n\n\n A simple strategy would be, for H<\/strong> < 0.5 (mean-reverting), if excess returns is greater than its median, then exit or<\/strong> if excess returns is less than its median, then enter.<\/p>\n\n\n\n The problem boils down to specifying the excess-return calculation periods (n-days<\/em>) and the Hurst exponent rolling windows so that it makes sense (avoid data-mining.)<\/p>\n\n\n\n We use the Barclays Euro-zone, UK, Japan and US momentum index data-sets to run our experiment. Since they provide both an excess-return index and a total-return index, we can use the former to time entries and exits in the latter.<\/p>\n\n\n\n We ran for two n-day<\/em> configurations: 5 and 10. We set the Hurst (and median) rolling window at 5-years. <\/p>\n\n\n\n We expected to find H<\/strong> to be either consistently above or below 0.5. My personal expectation was that H<\/strong> would be above 0.5 (trend.)<\/p>\n\n\n\n Using the Hurst exponent did not improve momentum returns. In both 5-day<\/em> and 10-day<\/em> configurations, a strategy that went long if n-day<\/em> returns were less than their median out-performed those that incorporated H<\/strong>.<\/p>\n\n\n\n The back-test using 5-day<\/em> returns mostly worked on Euro-zone and US momentum indices. So we are skeptical that this approach can be generalized and it will likely fall prey to data-mining.<\/p>\n\n\n\n The back-test using 10-day<\/em> returns saw buy-and-hold emerge a consistent winner.<\/p>\n\n\n\n The 5-day<\/em> H<\/strong> toggled between trending<\/em> and mean-reverting<\/em> but spent most of its time trending<\/em>. The 10-day<\/em> H<\/strong> was consistently trending<\/em>. For the specifications that we tested, momentum excess returns trends<\/strong>.<\/p>\n\n\n\n The R code is here: 5-day<\/a> and 10-day<\/a> config. You can login to pluto<\/a> and play around with the lookback<\/em> and statWindow<\/em> variables to see how H, median and back-test results change. <\/p>\n\n\n\nSetup<\/h3>\n\n\n\n
Results<\/h3>\n\n\n\n
Code and Charts<\/h3>\n\n\n\n