  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.
