Nash Bargaining Over Margin Loans to Kelly Gamblers

Authors

Alex Garivaltis

Document Type

Article

Abstract

I derive practical formulas for optimal arrangements between sophisticated stock market investors (namely, 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 obtain under non-cooperation. If the threat point represents a vicious breakdown of negotiations (resulting in zero margin loans), then we get an elegant rule of thumb: the negotiated interest rate is (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.

Publication Date

1-1-2019

Recommended Citation

Garivaltis, A., 2019. Nash Bargaining Over Margin Loans to Kelly Gamblers. Risks, 7(3), 93.

Original Citation

Garivaltis, A., 2019. Nash Bargaining Over Margin Loans to Kelly Gamblers. Risks, 7(3), 93.

Department

Department of Economics

Legacy Department

Department of Economics

Sponsorship

N.I.U. Open Access Publishing Fund

Language

eng

Publisher

Risks