Diversity and Arbitrage in a Regulatory Breakup Model

TL;DR

This paper proposes a regulatory model that maintains market diversity and eliminates arbitrage opportunities by breaking up large companies and merging others, compatible with existing market assumptions.

Contribution

It introduces a novel regulatory approach that enforces diversity in market models without disrupting the no-arbitrage condition, aligning with empirical market features.

Findings

Regulation removes arbitrage opportunities.

Market diversity is preserved through company breakups and mergers.

Model remains consistent with the equivalent martingale measure.

Abstract

In 1999 Robert Fernholz observed an inconsistency between the normative assumption of existence of an equivalent martingale measure (EMM) and the empirical reality of diversity in equity markets. We explore a method of imposing diversity on market models by a type of antitrust regulation that is compatible with EMMs. The regulatory procedure breaks up companies that become too large, while holding the total number of companies constant by imposing a simultaneous merge of other companies. The regulatory events are assumed to have no impact on portfolio values. As an example, regulation is imposed on a market model in which diversity is maintained via a log-pole in the drift of the largest company. The result is the removal of arbitrage opportunities from this market while maintaining the market's diversity.