融资融券定价之谜的两种解决方案
Two Resolutions of the Margin Loan Pricing Puzzle
摘要：
本文提供了Fortune（2000）保证金-贷款定价难题的两种可能的解决方案。《财富》杂志（2000年）指出，股票经纪收取的保证金贷款利率相对于实际（低）信贷风险和资金成本而言非常高。如果我们生活在布莱克-斯科尔斯模型的世界里，那么经纪人大概是通过动态地做空客户投资组合的精确数量来赚取套利利润的。首先，我们扩展了Fortune（2000）对Merton（1974）的无套利方法的应用，允许经纪人在贷款期限内只能多次修改他们的套期保值。我们发现，修订频率的极小差异可以很容易地解释所观察到的保证金贷款定价的变化。事实上，每三天增加四次修订可以解释目前观察到的所有异质性。其次，我们研究了垄断（或寡头）的保证金贷款定价的经纪人，其客户是连续时间凯利赌徒。经纪人解决了一个一般的随机控制问题，产生简单和愉快的公式的最佳利率和净利息差。如果作者拥有一家经纪公司，他将收取$(r+ν)/2-σ^2/4$的利率，其中$r$是资金成本，$ν$是标准普尔500指数的复合年增长率，$σ$是波动率。
英文摘要：
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 $(r+ν)/2-σ^2/4$, where $r$ is the cost of funds, $ν$ is the compound-annual growth rate of the S&P 500 index, and $σ$ is the volatility.
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