Before revision:  Under these assumptions, we are able to prove that , if we consider a sufficiently large number of periods, the expected rate of return and the expected gross return are linear in the initial time value of the log earnings over price ratio , and their variance goes to zero with  rate of convergence equal to minus one .
After revision:  Under these assumptions, we are able to prove that , if we consider a sufficiently large number of periods, the expected rate of return and the expected gross return are linear in the initial time value of the log earnings over price ratio , and their variance goes to zero with rate of convergence consistent with the diffusive behaviour. Eventually this means that the momentum component may generate bubbles and crashes in the short and medium run, nevertheless the valuation ratio remains a good reference point of future long-run returns .