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, Postal: Knut Wicksell Centre for Financial Studies, Lund University School of Economics and Management,
Magnus Holm: Hilbert Capital

No 2019/2, Knut Wicksell Working Paper Series from Lund University, Knut Wicksell Centre for Financial Studies

Abstract: We show that the Kelly framework is the natural multi-period extension of the one-period meanvariance model of Markowitz. Any allocation on the instantaneous Kelly efficient frontier can be reached by trading in the bank account and a particular mutual fund consisting of risky assets only. However, different to the mean-variance model there is an upper bound on the instantaneous Kelly efficient frontier. Any allocation surpassing this bound, called the optimal Kelly strategy, is known to be inefficient. We use the optimal Kelly strategy to deduce an expression for the instantaneous covariance matrix that results in market equilibrium. We show that this equilibrium is stable in the sense that any optimal Kelly trader, and most Kelly traders, will force the market covariance matrix towards equilibrium. We further investigate the role of a central bank setting the short-term interest rate. We show that an equilibrium rate exists but we argue that there is no market mechanism that will force the interest rate to this level. This motivates the short-term interest rate to be actively managed by the central bank.

Keywords: Portfolio theory; Kelly criterion; Market equilibrium; Central bank rate (search for similar items in EconPapers)
JEL-codes: G20 (search for similar items in EconPapers)
Pages: 28 pages
Date: 2019-12-17
References: Add references at CitEc
Citations:

Downloads: (external link)
https://lusem.lu.se/media/kwc/working-papers/2019/kwcwp2019_2.pdf Full text (text/html)
Our link check indicates that this URL is bad, the error code is: 404 Not Found (https://lusem.lu.se/media/kwc/working-papers/2019/kwcwp2019_2.pdf [301 Moved Permanently]--> https://www.lusem.lu.se/media/kwc/working-papers/2019/kwcwp2019_2.pdf)

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:hhs:luwick:2019_002

Access Statistics for this paper

More papers in Knut Wicksell Working Paper Series from Lund University, Knut Wicksell Centre for Financial Studies Knut Wicksell Centre for Financial Studies, Lund University School of Economics and Management, P.O. Box 7082, S-220 07 Lund, Sweden. Contact information at EDIRC.
Bibliographic data for series maintained by Jens Forssbaeck () and Frederik Lundtofte ( this e-mail address is bad, please contact ).