Volume 41, Issue 3-4

Using the modelling and estimation framework of W. Cao, C. Hurvich and P. Soulier (2017), we perform a test of the mean ( T 2 {T_{2}} statistic) for a large collection of daily Fama–French factors and portfolio returns, and compare the results with those based on the standard t test. The T 2 {T_{2}} -based results provide clearly weaker evidence in favor of various premia and in some cases suggest their absence. On the US market, the discrepancy between the tests is particularly large for the momentum factor. Caution should be exercised when assessing the presence of a given premium with the t test.

We present a simple solution of the consumption-investment problem pair trading on a finite time horizon. The proof is based on the remark that the HJB equation can be reduced to a linear parabolic equation solvable explicitly. As a further development we obtain also a solution of the problem for the infinite time horizon.