Is Violation of the Random Walk Assumption an Exception or a Rule in Capital Markets?

Abstract

Both the efficient market hypothesis and modern portfolio theory rest on the assumptions of the Gaussian probability distribution and independence of consecutive returns. This paper provides a brief excursion into the history of capital market research. A measure of long-range dependence (Hurst exponent) was applied to daily returns of selected stock indices and individual firms. The Hurst exponent was estimated using rescaled range analysis. The estimates are based on an unusually large sample of empirical-time series from capital markets. This method distinguishes whether the data-generating process follows random walk or exhibits antipersistent or persistent behavior. Both the efficient market hypothesis and modern portfolio theory assume that the data-generating process has no memory, i.e. follows Brownian motion. The random walk process is characterized by a Hurst exponent value of 0.5. Values greater than 0.5 and less than 1 indicate a persistence of local trends. Values between 0 and 0.5 indicate a process that reverts to the mean more often than a random process (mean-reverting process). The results indicated that the series of daily returns exhibit predominantly persistent or antipersistent behavior. Therefore, Brownian motion cannot be perceived as the norm for describing stock market behavior. These findings challenge the assumption of a random walk in stock prices, valuation models and assessment of risk.