Drift and the Risk-Free Rate

It is proven, under a set of assumptions differing from the usual ones in theunboundedness of the time interval, that, in an economy in equilibrium consisting ofa risk-free cash account and an equity whose price process is a geometric Brownianmotion on [0,∞), the drift rate must be close to the risk-free rate; if the drift rate and the risk-free rate are constants, then = and the price process is thesame under both empirical and risk neutral measures. Contributing in some degreeperhaps to interest in this mathematical curiosity is the fact, based on empiricaldata taken at various times over an assortment of equities and relatively shortdurations, that no tests of the hypothesis of equality are rejected