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

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  • Alex Garivaltis

Abstract

In this paper, which is the third installment of the author's trilogy on margin loan pricing, we analyze $1,367$ monthly observations of the U.S. broker call money rate, which is the interest rate at which stock brokers 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-b). 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," Papers 1906.00946, arXiv.org, revised Oct 2022.
    • Handle: RePEc:arx:papers:1906.00946
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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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    4. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    5. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    6. Garivaltis, Alex, 2019. "Two resolutions of the margin loan pricing puzzle," Research in Economics, Elsevier, vol. 73(2), pages 199-207.
    7. Gikas A. Hardouvelis & Stavros Peristiani, 1992. "Margin Requirements, Speculative Trading, and Stock Price Fluctuations: The Case of Japan," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 107(4), pages 1333-1370.
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    10. Gikas A. Hardouvelis & Panayiotis Theodossiou, 2002. "The Asymmetric Relation Between Initial Margin Requirements and Stock Market Volatility Across Bull and Bear Markets," The Review of Financial Studies, Society for Financial Studies, vol. 15(5), pages 1525-1560.
    11. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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    More about this item

    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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