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.

中文翻译：

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违反随机游走假设是资本市场的例外还是规则？

有效市场假设和现代投资组合理论都基于高斯概率分布和连续收益独立性的假设。本文简要介绍了资本市场研究的历史。长期依赖（Hurst 指数）的度量被应用于选定股票指数和个别公司的每日回报。Hurst 指数是使用重新定标的极差分析来估计的。这些估计基于来自资本市场的异常大的经验时间序列样本。该方法区分数据生成过程是遵循随机游走还是表现出反持久性或持久性行为。有效市场假设和现代投资组合理论都假设数据生成过程没有记忆，即遵循布朗运动。随机游走过程的特点是 Hurst 指数值为 0.5。大于 0.5 且小于 1 的值表示局部趋势持续存在。0 到 0.5 之间的值表示一个过程比随机过程（回归均值过程）更频繁地恢复到均值。结果表明，这一系列每日回报主要表现出持久性或反持久性行为。因此，布朗运动不能被视为描述股票市场行为的规范。这些发现挑战了股票价格、估值模型和风险评估随机游走的假设。5 表示一个过程比随机过程更频繁地恢复到均值（均值恢复过程）。结果表明，这一系列每日回报主要表现出持久性或反持久性行为。因此，布朗运动不能被视为描述股票市场行为的规范。这些发现挑战了股票价格、估值模型和风险评估随机游走的假设。5 表示一个过程比随机过程更频繁地恢复到均值（均值恢复过程）。结果表明，这一系列每日回报主要表现出持久性或反持久性行为。因此，布朗运动不能被视为描述股票市场行为的规范。这些发现挑战了股票价格、估值模型和风险评估随机游动的假设。