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Diversity and relative arbitrage in equity markets

Fernholz, Robert, Karatzas, Ioannis and Kardaras, Constantinos ORCID: 0000-0001-6903-4506 (2005) Diversity and relative arbitrage in equity markets. Finance and Stochastics, 9 (1). pp. 1-27. ISSN 0949-2984

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Identification Number: 10.1007/s00780-004-0129-4


An equity market is called “diverse” if no single stock is ever allowed to dominate the entire market in terms of relative capitalization. In the context of the standard Itô-process model initiated by Samuelson (1965) we formulate this property (and the allied, successively weaker notions of “weak diversity” and “asymptotic weak diversity”) in precise terms. We show that diversity is possible to achieve, but delicate. Several examples are provided which illustrate these notions and show that weakly-diverse markets contain relative arbitrage opportunities: it is possible to outperform or underperform such markets over any given time-horizon. The existence of this type of relative arbitrage does not interfere with the development of contingent claim valuation, and has consequences for the pricing of long-term warrants and for put-call parity. Several open questions are suggested for further study.

Item Type: Article
Official URL:
Additional Information: © 2005 Springer-Verlag Berlin/Heidelberg
Divisions: Statistics
Subjects: H Social Sciences > HG Finance
Q Science > QA Mathematics
Date Deposited: 04 Dec 2017 09:56
Last Modified: 08 Jul 2024 07:24

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