Treating cross‐sectional and time series momentum returns as forecasts

In this paper, we analyse theoretically the distributional properties and the forecastability of cross‐sectional momentum (CSM) and time series momentum (TSM) returns. By decomposing these returns into their fundamental building blocks, we expose their structural similarities and differences that shed valuable insights into the conditions under which one outperforms the other. Considering in detail the special case of two underlying assets, which captures much of the salient features of the general case, we provide explicit expressions for the probability density function and the first four moments of CSM and TSM returns. We then analyse and compare the performances of these momentum strategies using three different measures of predictability. Consistent with the findings in the empirical literature, all three measures draw the similar conclusion that TSM outperforms CSM when asset returns are positive and that this is primarily due to TSM being net long while CSM is net zero in the underlying assets in such situations.