Is Violation of the Random Walk Assumption an Exception or a Rule in Capital Markets?
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Is Violation of the Random Walk Assumption an Exception or a Rule in Capital Markets? Ludwig O. Dittrich 1
& Pavel
Srbek 1
Accepted: 2 November 2020 # International Atlantic Economic Society 2020
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. Keywords Hurst exponent . Brownian motion . Rescaled range analysis . Random process . Stock markets . Long memory JEL G11 . G17
* Ludwig O. Dittrich [email protected]
1
Faculty of Economics and Management, Czech University of Life Sciences Prague, Kamýcká 129, 165 21, Prague 6 -, Suchdol, Czech Republic
Dittrich L.O., Srbek P.
Introduction The efficient market hypothesis (EMH), introduced by Fama (1965), is still a widely accepted conceptual framework for the description of capital market behavior, although the hypothesis has been rejected empirically many times. The assumptions of a normal probability distribution for asset returns and a random walk for asset prices are routinely applied for the sake of simplicity. If these assumptions hold, it is a very simple task to construct an optimal portfolio, which reflects the risk and return profile of an investor. In such a case, the expected return can be found with 95% probability within an interval of plus or minus two times the historical standard deviation of an asset’s returns. Regrettably, for investors and portfolio managers, empirical asset-return series exhibit much greater disorder. The series diverges widely from the theoretical expectations of well-behaved data-generating processes. They seem to be misbehaving. The concept of a well-behaved random walk as an appropriate representation of asset prices in capital markets is an old o
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