Two Resolutions of the Margin Loan Pricing Puzzle

TL;DR

This paper offers two explanations for the high margin loan interest rates: limited hedge revision frequency and monopolistic pricing strategies, resolving Fortune's margin-loan pricing puzzle.

Contribution

It extends the no-arbitrage model to include finite hedge revisions and analyzes monopolistic pricing with stochastic control, providing new insights into margin loan rate determination.

Findings

Small differences in hedge revision frequency explain rate heterogeneity.

Four additional hedge revisions per three days account for observed pricing variation.

Optimal interest rate formula derived for monopolistic brokers.

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.