Generalizing Price Discovery Measures with Leverage Corrections: Evidence from Leveraged Exchange-Traded Funds

Abstract

We extend price discovery analysis to interrelated securities characterized by non-unitary cointegrating relationships. Structural analysis reveals that existing price discovery measures exhibit leverage bias, which amplifies the responses of leveraged products to price shock and increases the likelihood of misidentifying them as price leaders. We propose to incorporate each market's long-run responses to the permanent shock to correct for this leverage bias, producing the leverage-corrected Price Information Leadership measure (CPIL), and its share (CPILS) and binary measure (CPILI), whose superioty are strongly supported by simulation evidence. We further examine price discoveries among six representative exchange-traded funds (ETFs) tracking the S&P 500 index, including the SPY ETF and five popular (inversely) leveraged ETFs (LETFs) issued by Proshares. Empirical results show that SPY dominates all LETFs for over 90% of the time, suggesting that the LETFs are mostly traded by herding investors and contain less incremental information.

Keywords: Price discovery, information share, leveraged products, Exchange-traded Funds (ETFs)