By Dean Furbush
In the eighties program trading became a popular culprit whenever stock prices moved quickly, especially when they moved down. Some people, including the regulators at the Securities and Exchange Commission, thought that program trading caused, or at least exacerbated, the October 1987 market crash. But most financial economists argue that the importance of program trading has been overblown.
Although it carries connotations of computers trading without supervision or human control, program trading need not have anything to do with computers. And even when they are involved, computers simply speed up the process. The actual decisions to buy and sell are made by people, not computers. In many cases people use computers to calculate algorithms that facilitate decisions, and in almost all cases computers help route trades to each individual stock in the program, but people make the trading decisions and implement them.
Program trading has developed because of three interrelated conditions. First, individual investors are learning that trading a diversified portfolio of securities eliminates some of the risks of investing in individual stocks. Second, institutions hold and trade a higher fraction of equity than ever before. These professional investors execute their diversified trades directly in the stock market as program trades or in the futures and options markets, where investors or speculators can trade contracts that are tied to changes in market indexes such as the Standard and Poor’s 500. Third, technological advances have reduced trading costs.
Program trading has been associated with several trading strategies, including ones known as duration averaging, portfolio insurance, and index arbitrage. Understanding these strategies is important to understanding the role of program trading in our stock markets. People trade programs for just two reasons: either to accommodate an investment objective that includes several stocks, or for arbitrage purposes (i.e., to profit from price discrepancies between the stock market and so-called derivative markets such as the futures and options markets).
To understand the program trading that results from the pursuit of investment objectives, consider someone who invests, say, a thousand dollars in a mutual fund. When many investors make that decision, they collectively send a signal for the mutual fund to buy a portfolio of stocks—to make a program purchase. Similarly, a large number of mutual fund redemptions signals the fund to sell a portfolio of stocks. Both signals are, in effect, retail program trades that are efficiently channeled to the stock market through traditional program trades.
Several other, more complex investment strategies have been associated with program trading. Two notable investment strategies mentioned above are duration averaging and portfolio insurance. Both are used to decide how much of an investor’s funds to invest in stocks versus other instruments such as bonds.
Duration averaging is based on an old idea that is easier said than done—buy low and sell high. A fund manager will shift assets into the stock portfolio—buy—when prices are low, and shift assets out of the stock portfolio—sell—when prices are high. This strategy is an effective one if prices stay within a particular trading range. But it leads to losses if prices fall below the range, and misses opportunities for profit if prices rise above the range. If duration averaging has any effect on price volatility, it reduces it. The reason is that duration averagers buy when prices fall and sell when prices rise, which tends to reduce the size of the move in either direction.
The purpose of portfolio insurance is to “insure” a minimum value for a stock portfolio in a falling market, while also allowing participation in a rising market. For instance, a portfolio insurer might buy a “put” option on the S&P 500, giving him the right to sell the index at a predetermined level. If the index falls below that level, the insurer “exercises” or sells the put. The profit on the put offsets some or all of the decline in the value of the stocks the insurer holds. If stocks in the index rise, all the insurer loses is what he paid for the put.
Another technique, called dynamic hedging, can be mathematically equivalent to buying a put option. In a dynamic hedging strategy a fund manager sells stocks as prices fall and buys stocks as prices rise. By one view dynamic hedging or portfolio insurance can increase volatility because both create extra selling pressure when prices fall and extra buying pressure when prices rise.
But two factors mitigate the effect of program trading on price volatility, whether the trading is for duration averaging or portfolio insurance. First, neither strategy is based on fundamental information regarding stock prices. If prices fall purely because of portfolio insurance trading, they have fallen below their “fundamental” level, and buying by other investors then becomes profitable. The same is true for any price movement engendered by a non-information-based trade. Second, duration averaging and portfolio insurance strategies are generally cheaper to implement using the futures and options markets rather than through program trades of the stocks themselves.
That brings us to index arbitrage between the stock market and the futures and options markets, which is the most controversial form of program trading. Because the financial products sold in the futures and options markets are derived from an underlying cash product—in this case stocks—their prices are mathematically related. This mathematical relation is no more mysterious than the relation between the price of a six-pack of root beer and the price of a single can. When one price falls relative to its mathematical relation to the other, index arbitragers can buy the cheaper product, sell the other one, and lock in a gain. That’s what index arbitragers do whenever buying or selling by other traders causes futures or options prices to move too high or too low relative to underlying stock prices.
Thus, index arbitrage trading acts as a messenger, bringing the information impounded in prices from the futures market to the stock market. Suppose that prices are in a stable equilibrium, and the price of a futures contract is at its fair value in relation to stock prices. Now suppose there is good news about the economy. The news will be transmitted to the markets by buying in both the stock and futures markets, and prices will rise in both markets. For several reasons prices usually move faster in the futures market than in the stock market, so the futures price rises above its fair-value relation to the stock index. Enter index arbitrage, selling what has become relatively expensive—futures—and buying what has become relatively cheap—stocks. The effect is to bring prices back to their fair-value relation at the new, higher level caused by the good news. Thinking just about the stock side of the arbitrage, the program buy order was triggered by the price discrepancy, with index arbitragers not necessarily knowing or caring what caused prices to move. But the effect of the buy order was to transfer the news in futures prices to the stock market.
Any complexity in this arbitrage strategy is purely due to unfamiliarity with the products involved. In fact, arbitrage is no big deal; everyone does it every day. Suppose you are standing in a long line at McDonald’s and see a short line next to you. You quickly switch lines, “selling” the long line and “buying” the short one. When you do, the long line gets shorter and the short line gets longer. That’s arbitrage: you get a gain for no pain while equalizing prices—or the length of lines.
Now suppose one line is next to the door, so people step naturally to that line first. When a busload of hungry travelers arrives, the door line gets longer before people realize they can save time by switching to the less accessible line. The travelers get their orders filled faster (liquidity is higher) if McDonald’s allows line switching (arbitrage) from the door line (the futures market) to the short line (the stock market). In this analogy the futures market is the door line because prices move faster there; the door line lengthens first.
If McDonald’s banned line switching, there would be two effects: one cash register would be calm relative to the other, and customers would be fed more slowly. If the success of McDonald’s service was measured entirely by examining the level of calm or distress at the short-line cash register, McDonald’s policy decision would be clear: discourage arbitrage because it makes the short line longer. If effectively imposed, the rule would slow service throughout the restaurant. But tomorrow the bus might go to Kentucky Fried Chicken instead. Actions that discourage liquidity lower the use of the market, as investors respond to the high cost of trading (illiquidity) by taking their business elsewhere.
My research has shown that the volume of index arbitrage is indeed positively related to price volatility. But for the most part index arbitrage seems to respond to volatility, not the other way around. Robert Neal of the University of Washington found much the same thing by examining the association of stock index returns with index arbitrage trades, after accounting for information effects. He found that index arbitrage has a statistically significant, but not economically significant, effect on volatility. That is, index arbitrage matters, but not much. An average index arbitrage trade moves the stocks in the index by less than half a cent.
Program trading and its principal subset, index arbitrage, rank among the most widely misunderstood financial terms. The growth of program trading is due to fundamental changes over the past twenty-five years in the way individuals hold stocks. Rather than trade a few stocks directly through a retail broker, investors are now more likely to hold stocks indirectly through a mutual fund or a pension fund. When institutions use program trading for their customers’ accounts, the effect is to lower customer costs. When institutions use index arbitrage program trades, the effect is to link the markets and thus to enhance their overall liquidity.
Dean Furbush is executive vice president of Nasdaq Stock Market, Inc. He has served on the staff of the President’s Council of Economic Advisers and at the Office of Economic Analysis of the U.S. Securities and Exchange Commission. He was also economic adviser to the chairman of the Commodity Futures Trading Commission.
Brennan, Michael, and Eduardo Schwartz. “Arbitrage in Stock Index Futures.” Journal of Business 63 (1990): s7-s31.
Furbush, Dean. “Program Trading and Price Movement: Evidence from the October 1987 Market Crash.” Financial Management 18 (1989): 68-83.
Furbush, Dean. “Program Trading and Price Movements.” Ph.D. diss., University of Maryland, 1990.
Furbush, Dean., and Paul Laux. “The Price, Liquidity, and Volatility Response of Individual Stocks to Intermarket Trading: Is Index Arbitrage Special?” Working paper, University of Texas, Austin, 1993.
Fremault, Anne. “Stock Index Futures and Index Arbitrage in a Rational Expectations Model.” Journal of Business 64 (1991): 523-47.
Harris, Lawrence, George Sofianos, and Jim Shapiro. “Program Trading and Intraday Volatility.” NYSE working paper 90-03, 1992.
Miller, Jeffrey, Mara Miller, and Peter Brennan. Program Trading: The New Age of Investing. 1989.
Merton Miller, Jayaram Muthuswamy, and Robert Whaley. “Mean Reversion of S&P 500 Index Basis Changes: Arbitrage-Induced or Statistical Illusion?” Working paper no. 331, Graduate School of Business, University of Chicago, 1992.
Neal, Robert. “Direct Tests of Index Arbitrage Models.” Working paper, Department of Finance, University of Washington, 1993.
Program Trading Did Not Cause 1987 Crash
Program trading did not cause the 508-point drop in the Dow-Jones industrial average that occurred on October 19, 1987. That was the conclusion of my 1988 study conducted for the Securities and Exchange Commission and issued by its Office of Economic Analysis. The evidence for the conclusion is that the five-minute intervals during which program-trading volume was heavy were not the times when prices fell the most. In fact, between 1:00 and 4:00 p.m. on that day, the typical relation between index arbitrage and price movement was reversed: above-average price changes tended to occur when index-arbitrage volume was below average. The Dow-Jones industrial average declined twice as fast in the afternoon as it had in the morning. The precipitous price declines occurred when the normal index-arbitrage relation was most disrupted, not when index arbitrage was prevalent.