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

School of Public and Global Affairs, College of Liberal Arts and Sciences, Northern Illinois University, 514 Zulauf Hall, DeKalb, IL 60115, USA
Int. J. Financial Stud. 2019, 7(4), 56; https://doi.org/10.3390/ijfs7040056
Received: 2 August 2019 / Revised: 21 September 2019 / Accepted: 25 September 2019 / Published: 1 October 2019
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. View Full-Text
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 broker call rate; call money rate; margin loans; net interest margin; risk premium; mean-reverting processes; vasicek model; Kelly criterion; monopoly pricing; arbitrage pricing
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Garivaltis, A. The Laws of Motion of the Broker Call Rate in the United States. Int. J. Financial Stud. 2019, 7, 56.

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