Mean Reversion in International Stock Indexes and FTK Continuity Analysis

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Van den Hoek considers a number of existing studies which seek (but fail) to provide empirical evidence of mean reversion of stock prices. Many previous studies cite the random walk theory as evidence of mean reversion, while others consider irrational behavior of investors leading to eventual reversion to the mean. Van den Hoek expands on existing data pointing to mean reversion in stock indexes by widening the period examined and introducing a bootstrap method to identify the sample bias corrected speed of reversion and its confidence bounds. The methodology is explained in the appendix.

This paper divides existing literature into two categories: unspecified mean (random-walk theory) and specified mean (fundamental value process). While many studies of both categories exist, substantial evidence citing mean reversion is absent. This could be a result of the limited data used in previous studies, market abnormalities, or differing asset valuation models.

The first model compares the returns of individual countries and finds no statistically significant evidence of mean reversion when countries returns are considered individually. A larger sample size is needed in order to find significant evidence of mean reversion, so the author applies a panel data model to a previous study and finds that the speed of reversion depends on the time interval, and at a large interval, is insignificant. The half-lives are significant and range between 2.1 years and 23.6 years.

This paper also reviews the implications of adding a component of mean reversion and continuity analysis to Dutch pension funds and finds the analysis depends completely on the individual asset return distributions, listing out the effects of expected value, variance, skewness, kurtosis and autocorrelation on the analysis. Absolute mean reversion and relative mean reversion are considered for each portfolio. The variance of the portfolio can be analyzed to determine whether absolute or relative mean reversion is applied, as negative autocorrelation indicates relative mean reversion.

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