Financial interpretation of herd behavior index and its statistical estimation

Herd behavior received increasing attention as the key to understanding financial crises. Recently, Dhaene et al. (2012) proposed the herd behavior index (HIX) to measure the degree of the comonotonic movement of stock prices. Choi et al. (2013) introduced the revised version of HIX (RHIX) and illustrated why RHIX should be preferred to HIX in comparing herd behaviors based on simple toy models, but failed to offer any sufficient justification. The present paper investigates three aspects of RHIX. First, RHIX is explained as a useful tool to compare herd behaviors from different groups. For this, a new alternative representation of RHIX is provided. Second, we investigate the statistical estimation of RHIX. In particular, the realized version of RHIX is calculated using tick-by-tick stock prices and the asymptotics of bootstrap equivalence are provided to estimate the confidence interval of RHIX. Third, to extend application scope of RHIX, RHIX is employed in a clustering analysis.