Long range dependence in daily stock market returns

Fundamental assumptions of the efficient market hypothesis and modern portfolio theory are a Gaussian probability distribution and the independence of returns. This paper provides a brief historical review of efforts dealing with capital markets emphasizing efficiency and counter-tendencies to falsify the assumption of independence of returns and their normal distribution. This paper applies a measure of long-range dependence, rediscovered and promoted by Mandelbrot, to daily returns of selected stock indices and individual firms. The measure is called the Hurst exponent and was estimated using three different estimators – the original rescaled range analysis, detrended fluctuation analysis, and detrended moving averages. These methods allow the researcher to distinguish whether the data generating process is a process with memory. Both, the efficient market hypothesis and modern portfolio theory assume that the data generating process has no memory, i.e. follows the Brownian motion. A random process is characterized by a Hurst exponent value of 0.5. Values greater than 0.5 and less than 1 indicate a persistency of local trends, whereas values between 0 and 0.5 indicate a process that returns back to the mean occur more often than in a random process. The results of our empirical tests are in line with similar papers. The series of daily returns exhibit prevailingly persistent or antipersistent behavior and therefore the Brownian motion is not a suitable model that can describe standard behavior of stock markets. Our findings falsify the assumption of random walk in stock prices and are of significant impact on valuation models and an assessment of risk.