Hellinger distance to normal distribution as market invariant

TL;DR

This paper explores using Hellinger distance from normal distribution as a market invariant for portfolio construction, revealing its potential for market segmentation despite sensitivity variations.

Contribution

It introduces Hellinger distance as a novel market invariant for portfolio imitation and market segmentation, with empirical analysis of its sensitivity.

Findings

Hellinger distance varies significantly across markets.

Mean sensitivity remains small, but some cases show extreme sensitivity.

Potential use in market segmentation.

Abstract

Main purpose of distance based portfolio constructions is in portfolio imitation. Here we construct portfolio based on Hellinger distance from normal distribution. We empirically found that minimum of this distance drastically varies from market to market. Thus we suppose that it may be regarded as a form of market invariant, in a sense of helpful tool for market segmentation. We analyze its sensitivity. Though mean sensitivity was small it showed extreme sensitivity in some cases.