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Two Resolutions of the Margin Loan Pricing Puzzle

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  • Alex Garivaltis

Abstract

This paper supplies two possible resolutions of Fortune's (2000) margin-loan pricing puzzle. Fortune (2000) noted that the margin loan interest rates charged by stock brokers are very high in relation to the actual (low) credit risk and the cost of funds. If we live in the Black-Scholes world, the brokers are presumably making arbitrage profits by shorting dynamically precise amounts of their clients' portfolios. First, we extend Fortune's (2000) application of Merton's (1974) no-arbitrage approach to allow for brokers that can only revise their hedges finitely many times during the term of the loan. We show that extremely small differences in the revision frequency can easily explain the observed variation in margin loan pricing. In fact, four additional revisions per three-day period serve to explain all of the currently observed heterogeneity. Second, we study monopolistic (or oligopolistic) margin loan pricing by brokers whose clients are continuous-time Kelly gamblers. The broker solves a general stochastic control problem that yields simple and pleasant formulas for the optimal interest rate and the net interest margin. If the author owned a brokerage, he would charge an interest rate of $(r+\nu)/2-\sigma^2/4$, where $r$ is the cost of funds, $\nu$ is the compound-annual growth rate of the S&P 500 index, and $\sigma$ is the volatility.

Suggested Citation

  • Alex Garivaltis, 2019. "Two Resolutions of the Margin Loan Pricing Puzzle," Papers 1906.01025, arXiv.org, revised Oct 2022.
    • Handle: RePEc:arx:papers:1906.01025
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    References listed on IDEAS

    as
    1. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    2. repec:bla:jfinan:v:43:y:1988:i:2:p:301-08 is not listed on IDEAS
    3. 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.
    4. Bernard Bensaid & Jean‐Philippe Lesne & Henri Pagès & José Scheinkman, 1992. "Derivative Asset Pricing With Transaction Costs1," Mathematical Finance, Wiley Blackwell, vol. 2(2), pages 63-86, April.
    5. 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.
    6. Peter Fortune, 2000. "Margin requirements, margin loans, and margin rates: practice and principles," New England Economic Review, Federal Reserve Bank of Boston, issue Sep, pages 19-44.
    7. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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    Cited by:

    1. 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.
    2. Alex Garivaltis, 2019. "Long Run Feedback in the Broker Call Money Market," Papers 1906.10084, arXiv.org, revised Oct 2022.

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    More about this item

    JEL classification:

    • C44 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Operations Research; Statistical Decision Theory
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • D53 - Microeconomics - - General Equilibrium and Disequilibrium - - - Financial Markets
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage

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