Relationship between ETFs and underlying indices: a fractional cointegration approach

Abstract

ABSTRACT This article analyzes the long-run relationship between domestic equity Index ETFs and their respective underlying indices in various markets. In doing so, we study the inter-relationship between these ETFs and their underlying equity indices using the ‘traditional’ Cointegration (CVAR) and Fractional Cointegration (FCVAR) models. The FCVAR model is an extension of CVAR model that is geared towards capturing long memory in a multivariate framework. We examine if FCVAR is superior to the CVAR framework in terms of in-sample fit and out-sample forecasting performance. Our findings establish the presence of fractional cointegration between ETFs and their indices. However, our test outcomes are highly sensitive to model specifications and timelines considered for estimation. Due to the dynamic nature of such cointegration relationship, practitioners are nudged to exercise caution while engaging in hedging and pairs trading that involve ETFs. This is because such trades are bound to be premised on selective inferences drawn from certain multivariate model specifications, and hence, may not be generalizable across all model specifications.