The Doomsday Machine of Black Monday

How Automated Portfolio Insurance Turned a Dip into a Twenty-Two Percent Crash

An individual pension fund can protect its stock portfolio against a market crash without buying a single put option if it continuously adjusts its cash balance according to a mathematical formula. When sixty billion dollars of institutional capital execute that same formula at the same hour, however, the hedge creates the crash it was built to prevent. In 1976, after watching endowments flee the stock market during the 1973–1974 downturn, Berkeley finance professor Hayne Leland woke up with an insight derived from the 1973 Black-Scholes option-pricing equation. Together with colleague Mark Rubinstein and marketing executive John O'Brien, Leland founded Leland O'Brien Rubinstein Associates (LOR) in 1981 to sell a computerized product they called portfolio insurance.

Long-term protective put options did not trade in size for massive corporate pension funds in the early 1980s. Leland and Rubinstein showed that a computer could manufacture a synthetic protective put dynamically by holding a shifting blend of S&P 500 stocks and Treasury bills. Under Black-Scholes replication, two numbers govern the computer's trades: the synthetic put's hedge ratio ($\Delta_{\text{put}}$, the fraction of the portfolio that must be sold as prices decline) and its curvature sensitivity ($\Gamma$, the rate at which required selling accelerates for every point drop in the index $S$ at volatility $\sigma$ and horizon $T$). Both follow directly from the cumulative normal distribution $N(d_1)$:

Because gamma is strictly positive, replicating a protective floor requires a trend-following feedback rule. Whenever the stock market rises, the computer buys more equity exposure. Whenever the stock market falls, the computer must mechanically sell stocks and move into cash so the portfolio cannot breach its insured floor. To avoid paying commissions on five hundred individual equities, LOR and its competitors executed these dynamic sales by dumping S&P 500 index futures contracts on the Chicago Mercantile Exchange.

By October 1987, institutional funds had placed more than $60 billion under automated portfolio-insurance rules. None of the Black-Scholes models accounted for what happens when the hedger becomes the entire market. As Rubinstein later acknowledged, portfolio insurance worked smoothly only so long as a single investor used it, much like a theater fire exit that functions well only when a single patron runs for the door. During the week of October 14–16, 1987, rising interest rates, a falling dollar, and Congressional tax proposals pushed the Dow Jones Industrial Average down ten percent. That slide left portfolio-insurance computers with a huge backlog of unexecuted sell orders over the weekend.

When the bell rang on Monday, October 19, 1987, LOR and rival insurers flooded the Chicago S&P 500 futures pit with mechanical sell orders. Futures immediately dropped to a steep discount below the cash stock index in New York. Index arbitrageurs stepped in to profit from the spread. They bought cheap Chicago futures and simultaneously transmitted automated Designated Order Turnaround (DOT) orders to sell the underlying stocks on the New York Stock Exchange. That arbitrage transmitted the futures avalanche directly onto NYSE floor specialists, whose capital was exhausted before noon. As New York stock prices plunged, the lower index values fed back into the portfolio-insurance computers. Their positive-gamma equations calculated that $\Delta_{\text{put}}$ had grown even more negative and commanded another wave of futures sales regardless of price. By the 4:00 p.m. close, the Dow had fallen 508 points, losing 22.6 percent in a single session. Because dynamic delta-hedging requires selling shares whenever prices fall, the sixty billion dollars of insured pension portfolios acted as a synchronized mechanical seller that overwhelmed every human buyer on the floor in five hours.