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The Laws of Motion of the Broker Call Rate in the United States

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  • Alex Garivaltis

    (School of Public and Global Affairs, College of Liberal Arts and Sciences, Northern Illinois University, 514 Zulauf Hall, DeKalb, IL 60115, USA)

Abstract

In this paper, which is the third installment of the author’s trilogy on margin loan pricing, we analyze 1367 monthly observations of the U.S. broker call money rate, e.g., the interest rate at which stockbrokers can borrow to fund their margin loans to retail clients. We describe the basic features and mean-reverting behavior of this series and juxtapose the empirically-derived laws of motion with the author’s prior theories of margin loan pricing (Garivaltis 2019a, 2019b). This allows us to derive stochastic differential equations that govern the evolution of the margin loan interest rate and the leverage ratios of sophisticated brokerage clients (namely, continuous-time Kelly gamblers). Finally, we apply Merton’s (1974) arbitrage theory of corporate liability pricing to study theoretical constraints on the risk premia that could be generated in the market for call money. Apparently, if there is no arbitrage in the U.S. financial markets, the implication is that the total volume of call loans must constitute north of 70 % of the value of all leveraged portfolios.

Suggested Citation

  • Alex Garivaltis, 2019. "The Laws of Motion of the Broker Call Rate in the United States," IJFS, MDPI, vol. 7(4), pages 1-23, October.
    • Handle: RePEc:gam:jijfss:v:7:y:2019:i:4:p:56-:d:272663
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    References listed on IDEAS

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    1. Lepetit, Laetitia & Nys, Emmanuelle & Rous, Philippe & Tarazi, Amine, 2008. "The expansion of services in European banking: Implications for loan pricing and interest margins," Journal of Banking & Finance, Elsevier, vol. 32(11), pages 2325-2335, November.
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    6. Alex Garivaltis, 2019. "Nash Bargaining Over Margin Loans to Kelly Gamblers," Risks, MDPI, vol. 7(3), pages 1-14, August.
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    More about this item

    Keywords

    broker call rate; call money rate; margin loans; net interest margin; risk premium; mean-reverting processes; vasicek model; Kelly criterion; monopoly pricing; arbitrage pricing;
    All these keywords.

    JEL classification:

    • G1 - Financial Economics - - General Financial Markets
    • G2 - Financial Economics - - Financial Institutions and Services
    • G3 - Financial Economics - - Corporate Finance and Governance
    • F2 - International Economics - - International Factor Movements and International Business
    • F3 - International Economics - - International Finance
    • F41 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - Open Economy Macroeconomics
    • F42 - International Economics - - Macroeconomic Aspects of International Trade and Finance - - - International Policy Coordination and Transmission

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