Stock Market Prices Do Not Follow Random Walks: Evidence from a Simple Specification Test

Abstract

In this paper, we test the random walk hypothesis for weekly stock market returns by comparing variance estimators derived from data sampled at different frequencies. The random walk model is strongly rejected for the entire sample period (1962-1985) and for all sub-periods for a variety of aggregate returns indexes and size-sorted portfolios. Although the rejections are largely due to the behavior of small stocks, they cannot be ascribed to either the effects of infrequent trading or time-varying volatilities. Moreover, the rejection of the random walk cannot be interpreted as supporting a mean-reverting stationary model of asset prices, but is more consistent with a specific nonstationary alternative hypothesis.

An investigation into multivariate variance ratio statistics and their application to stock market predictability

“…We propose a simple analogue method for conducting inference that does not require the selection of a bandwidth parameter. We note that much of the evidence about predictability has been based on the Lo and MacKinlay (1988) standard errors, which we argue should be replaced by standard errors that rely on weaker more plausible assumptions. We show that in practice the standard errors can make a di¤erence, especially when the time series is short (such as when stationarity is of concern).…”

“…Variance ratio tests (Lo and MacKinlay (1988) and Poterba and Summers (1988)) are widely used in empirical …nance as a way of testing the weak form E¢ cient Markets Hypothesis (EMH) and to measure the degree and (cumulative) direction of departures from this hypothesis in …nancial time series. Indeed, this work has been extremely in ‡uential in understanding predictability in asset prices and in measuring market quality.…”

“…A lot of empirical work followed immediately after the seminal contributions. Lo and MacKinlay (1988) presented evidence regarding predictability of the US stock market. They concluded that the Random Walk Hypothesis was soundly rejected by weekly US stock market returns.…”

“…The value of the restriction is that it simpli…es the standard error calculation, although, as we show, the standard errors that allow for violations of this condition do not entail an inordinate increase in computation or complexity. Essentially, Lo and MacKinlay (1988) imposed an unnecessary assumption but fail to impose a necessary one. We propose modi…ed assumptions that still preserve the possibility of simple inference methods but allow for leverage e¤ects.…”

“…We propose modi…ed assumptions that still preserve the possibility of simple inference methods but allow for leverage e¤ects. Speci…cally, we establish the asymptotic distribution of our statistics under two sets of assumptions: (a) a stationary martingale di¤erence hypothesis with fourth unconditional moments; (b) uncorrelatedness as in Lo and MacKinlay (1988) and with an additional uncorrelatedness condition on the products of returns but without the additional noleverage condition. The asymptotic variance is di¤erent from that contained in Theorem 3 of Lo and MacKinlay (1988) (and used in much subsequent empirical work).…”