One way of evaluating the simple efficient markets model of stock prices is to compare the volatility of the perfect-foresight price per share P* with that of the actual price per share Pt. The perfectforesight price Pt* is the present value at time t of actual future dividends Dt k, k 0, discounted at constant rate r. The simple efficient markets model asserts that Pt = EP*, which implies (if detrended series Pt and p* are stationary) that ca2(p*) ? u2(p). I found (Shiller 1981) evidence suggesting gross violation of this and other such variance inequalities. With annual U.S. data from 1871-1979, s(p)/s(p*) = 5.59. (Here, u and s denote population and sample standard deviations, respectively.) Allan Kleidon (1986) criticizes such methods of evaluating efficiency. By Monte Carlo methods he computes the probability that s(p)/s(p*) > 5 with 100 observations under the simple efficient markets hypothesis and assuming that log(Dt) = p. + log(Dt l) + Et, whereE, is independent normal N(O, u2) and p. is a constant. He finds that the probability may be substantial, as high as .397. In each of his 1,000 Monte Carlo iterations, Kleidon first generated 100 observations of a random normal variable with p. = .0095 and u .218. He cumulated and exponentiated these to produce a real dividend series Dt. He produced a price series from the dividend series by multiplying by (1 + g)/(r g), where r is the discount factor and g is the expected growth of dividends, equal to exp[V. + (U 2/2)]. Duplicating the procedure in my original paper, he estimated a trend by regressing ln(P,) on time t. With the slope coefficient b in this