The results in Table 1 are typical of those reported by others for tests based on serial covariances. (Cf. Kendall [21], Moore [31], Alexander [1], and the results of granger and Morgenstern [17] and Godfrey, Granger and Morgenstern [16] obtained by means of spectral analysis. )Specifically, there is no evidence of substantial linear dependence between lagged price changes or returns. In absolute terms the measured serial correlations are always close Looking hard, though, one can probably find evidence of statistically nificant "linear dependence in Table 1 (and again this is true of results re- ported by others). For the daily returns eleven of the serial correlations are more than twice their computed standard errors, and twenty-two out of thirty are positive. On the other hand twenty-one and twenty-four of the coefficients for the four and nine day differences are negative. But with samples of the size underlying Table 1(N= 1200-1700 observations per stock on a daily basis) statistically " significant" deviations from zero covariance are not necessarily a basis for rejecting the efficient markets model. For the results in Table the standard errors of the serial correlations were approximated as (1/ (N-1)), which for the daily data implies that a correlation as small as 06 is more than twice its standard error. But a coefficient this size implies that a linear relationship with the lagged price change can be used to explain about .36%o of the variation in the current price change, which is probably insig nificant from an economic viewpoint. In particular, it is unlikely that the small absolute levels of serial correlation that are always observed can be used as the basis of substantially profitable trading systems. 4 It is, of course, difficult to judge what degree of serial correlation would imply the existence of trading rules with substantial expected profits. (And indeed we shall soon have to be a little more precise about what is implied by substantial"profits. )Moreover, zero serial covariances are consistent with a fair game"model, but as noted earlier(in. 10), there are types of nonlinear dependence that imply the existence of profitable trading systems, and yet do not imply nonzero serial covariances. Thus, for many reasons it is desirable to directly test the profitability of various trading rules The first major evidence on trading rules was Alexander's [1, 2]. he tests a variety of systems, but the most thoroughly examined can be decribed follows: If the price of a security moves up at least y%o, buy and hold the security until its price moves down at least y% from a subsequent high, at Thich time simultaneously sell and go short. The short position is maintained until the price rises at least y %o above a subsequent low, at which time one covers the short position and buys. Moves less than y in either direction are price changes occur much more frequently than would be expected if the generating Gaussian, the expression(1/(N-1))3 understates the sampling dispersion of the seria coefficient, and thus leads to an overstatement of significance levels. In addition, the prooess wer 14. Given the evidence of Kendall [21], Mandelbrot [28], Fama [10] and others that large linear dependence. If, as the work of King [23] and Blume [7] indicates, there is a market factor whose behavior affects the returns on all securities, the sample behavior of this market factor may lead to a predominance of signs of one type in the serial correlations for individual securities even though the population serial correlations for both the market factor and the returns o individual securities are zero. For a more extensive analysis of these issues see [10]