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Open AccessArticle

Nash Bargaining Over Margin Loans to Kelly Gamblers

Department of Economics, School of Public and Global Affairs, College of Liberal Arts and Sciences, Northern Illinois University, 514 Zulauf Hall, DeKalb, IL 60115, USA
Risks 2019, 7(3), 93; https://doi.org/10.3390/risks7030093
Received: 26 July 2019 / Revised: 15 August 2019 / Accepted: 20 August 2019 / Published: 27 August 2019
I derive practical formulas for optimal arrangements between sophisticated stock market investors (continuous-time Kelly gamblers or, more generally, CRRA investors) and the brokers who lend them cash for leveraged bets on a high Sharpe asset (i.e., the market portfolio). Rather than, say, the broker posting a monopoly price for margin loans, the gambler agrees to use a greater quantity of margin debt than he otherwise would in exchange for an interest rate that is lower than the broker would otherwise post. The gambler thereby attains a higher asymptotic capital growth rate and the broker enjoys a greater rate of intermediation profit than would be obtained under non-cooperation. If the threat point represents a complete breakdown of negotiations (resulting in zero margin loans), then we get an elegant rule of thumb: r L * = 3 / 4 r + 1 / 4 ν σ 2 / 2 , where r is the broker’s cost of funds, ν is the compound-annual growth rate of the market index, and σ is the annual volatility. We show that, regardless of the particular threat point, the gambler will negotiate to size his bets as if he himself could borrow at the broker’s call rate. View Full-Text
Keywords: Nash bargaining; margin loans; Kelly betting; log-optimal portfolios; continuously-rebalanced portfolios; net interest margin Nash bargaining; margin loans; Kelly betting; log-optimal portfolios; continuously-rebalanced portfolios; net interest margin
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Garivaltis, A. Nash Bargaining Over Margin Loans to Kelly Gamblers. Risks 2019, 7, 93.

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