Mean reversion in stocks: A univariate linear time series analysis of book equity to market equity sorted U.S. portfolios

This master thesis treats the question whether prices of book equity to market equity sorted stock portfolios follow a random walk. In the theoretical part of the thesis, the random walk model is derived as a testable expression of market informational efficiency assuming constant expected returns and its statistical tests, namely the regression beta and the variance ratio, are discussed. As alternatives to the random walk, the structural models of fads and time varying expected returns are presented. A new model which incorporates the characteristics of the previous two models is also proposed. In the empirical part, the random walk test statistics are estimated. The random walk is rejected for portfolios with low BE/ME ratio by the variance ratio. The observationally equivalent ARMA forms of the alternative models are estimated and an ARMA(2,2) process is found to fit better the data. Moreover, to measure the ability of the statistical tests to reject the random walk when the alternative models considered are true, the power of the variance ratio and regression beta is calculated. The power of the variance ratio is higher than the regression beta and it deteriorates exponentially with the return interval.