The power and size of mean reversion tests

Abstract

The power of mean reversion tests has long been a tacit issue of the market efficiency literature. Early tests of market efficiency, as summarized in Fama Ž . 1970 , found no economically significant evidence of serial correlation in stock Ž . returns. However, Summers 1986 later suggested that this was because these tests lacked power: Summers suggested a model of AfadsB in which stock prices take long swings away from their fundamental values, and showed that even if a fads component such as this accounted for a large fraction of the variance of returns, the fads behavior might be difficult to detect by looking at short horizon autocorrelations of returns as these early tests had done. The intuition behind Summers’ reasoning was that if stock prices took large jumps away from their AfundamentalB or full-information values, and then only reverted back towards the fundamental price over a period of years, the autocorrelations of monthly or daily returns would capture only a small fraction of this mean reversion. Several attempts were made to develop tests that would have greater power Ž . against AfadsB hypotheses such as Summers’. Fama and French 1988a used a long horizon regression of multi-year returns on past multi-year returns, and Ž . Poterba and Summers 1988 used a variance ratio test to look for fads-type behavior in stock-index returns. In addition, variance ratio test are used by Ž . Ž . Cochrane 1988 and Lo and MacKinlay 1988 to investigate the time series properties of production and short horizon returns.