A new method based on range to detect mean reversion

Abstract

We propose a new measure of risk called the expected lifetime range (ELR) ratio, based on high and low prices. We point out that it becomes possible for us to uncover the evidence of mean reversion based on the new ELR ratio even when the classic Lo and MacKinlay (LM) (1988) statistic does not detect the same. We work with a moving average MA (1) model with MA parameter θ to make our point. Our empirical study on the Indian stock market shows that ELR ratio is able to detect mean reversion even when LM statistic does not.

Keywords

• Mean reversion
• Expected lifetime range ratio
• Moving average MA (1) model
• Lo and MacKinlay variance ratio statistic
• Indian stock market