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KELLY TRADING AND MARKET EQUILIBRIUM

Bermin, Hans Peter LU and Holm, Magnus (2023) In International Journal of Theoretical and Applied Finance 26(1).
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... (More)

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.

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author
and
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
fractional Kelly, Kelly criterion, market equilibrium, Portfolio theory
in
International Journal of Theoretical and Applied Finance
volume
26
issue
1
publisher
World Scientific Publishing
external identifiers
  • scopus:85147526265
ISSN
0219-0249
DOI
10.1142/S0219024923500012
language
English
LU publication?
yes
id
6fb08ed1-c955-43fc-8847-cfe07dc84cc4
date added to LUP
2023-02-24 11:40:34
date last changed
2023-10-26 15:03:39
@article{6fb08ed1-c955-43fc-8847-cfe07dc84cc4,
  abstract     = {{<p>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.</p>}},
  author       = {{Bermin, Hans Peter and Holm, Magnus}},
  issn         = {{0219-0249}},
  keywords     = {{fractional Kelly; Kelly criterion; market equilibrium; Portfolio theory}},
  language     = {{eng}},
  number       = {{1}},
  publisher    = {{World Scientific Publishing}},
  series       = {{International Journal of Theoretical and Applied Finance}},
  title        = {{KELLY TRADING AND MARKET EQUILIBRIUM}},
  url          = {{http://dx.doi.org/10.1142/S0219024923500012}},
  doi          = {{10.1142/S0219024923500012}},
  volume       = {{26}},
  year         = {{2023}},
}