KELLY TRADING AND MARKET EQUILIBRIUM

Hans-Peter Bermin and Magnus Holm ()
Additional contact information
Hans-Peter Bermin: Knut Wicksell Centre for Financial Studies, Lund University, Box 7080, S-220 07 Lund, Sweden
Magnus Holm: Hilbert Group, 171 Old Bakery Street, VLT 1455, Malta

International Journal of Theoretical and Applied Finance (IJTAF), 2023, vol. 26, issue 01, 1-33

Abstract: The Kelly framework is the natural multi-period extension of the one-period mean-variance model of Markowitz in the sense that the efficient frontier is characterized by trading strategies having maximal instantaneous Sharpe ratio. We show that Kelly traders naturally trade in such a way as to induce an equilibrium for the instantaneous covariance matrix. This equilibrium, arising from trading alone, has the property that the equilibrium correlation can be described as the saddle point of a stochastic differential game. However, because the game is not necessarily a zero-sum game the equilibrium volatility is shown to be lower than what is predicted from the game. The covariance equilibrium is fully specified by the rate of logarithmic return, the interest rate and the aggregate willingness to leverage seen in the market.

Keywords: Portfolio theory; Kelly criterion; fractional Kelly; market equilibrium (search for similar items in EconPapers)
JEL-codes: D53 G11 G12 (search for similar items in EconPapers)
Date: 2023
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0219024923500012
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijtafx:v:26:y:2023:i:01:n:s0219024923500012

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0219024923500012

Access Statistics for this article

International Journal of Theoretical and Applied Finance (IJTAF) is currently edited by L P Hughston

More articles in International Journal of Theoretical and Applied Finance (IJTAF) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().