A NEW METHOD BASED ON RANGE TO DETECT MEAN REVERSION

It is well established in financial time series literature, that if stock prices follow random walk behaviour, one cannot predict future stock returns based on the history of past returns. On the other hand, if the stock prices follow mean reverting behaviour, it is possible to partially predict future returns based on the past returns, as any shock to stock prices has a temporary component and there exists a tendency for the price series to return to its trend or path over time. Hence it becomes important to understand the behaviour of the stock price movements, i.e., whether the stock prices follow random walk or mean reversion. 

In this paper, we propose a new measure of risk called the expected lifetime range (ELR) ratio, based on high and low prices, and use it to explore the presence of mean reversion in the Indian stock market. We find the new ELR ratio to be more conclusive and superior in detecting the presence of mean reversion when compared to the variance ratio statistic proposed by Lo and MacKinlay (LM) (1988) which shows a strong tendency to find no evidence of mean reversion. Thus, it becomes possible for us to pinpoint the evidence of mean reversion based on the new ELR ratio even when the LM statistic does not detect the presence of mean reversion.   

We test our model empirically with Indian stock market data and our findings support the presence of mean reversion during the overall sample period (2001-2015) and also during the crisis and post-crisis period (2008-2015) based on our new ELR ratio, even though the traditional LM statistic fails to detect the same. This finding supports our theoretical model when we allow stochastic parameter in the moving average MA(1) process.  Also, we find that if the ELR ratio finds no evidence of mean reversion then the same will definitely be true for the LM statistic as in the case of the Indian stock market during the pre-crisis period (2001-2007).