Whether the strategist uses the put or the call, if the underlying stock rises in value, he will want to sell the LEAPS option he owns and buy another one with a higher strike, in order to further protect the profits that build up as the stock rises.
In my opinion, the purchase of a LEAPS put is a more efficient way to protect long stock. However, the former strategy—selling the stock and replacing it with a long call—is usually preferred by broker- age firms.
THE EFFECT OF STOCK INDEX
Index Arbitrage
Index arbitrageis the easiest one to understand, for in this strategy the arbitrageur takes a position in a stock index futures contract and takes exactly the opposite position in the stocks themselves. For example, an arbitraguer might sell the S&P 500 futures and more or less simultaneously buy the correct amount of each of those 500 stocks, in order to set up a perfect hedge. With computerized trad- ing, 500 stocks can be bought almost simultaneously with the push of a button.
Arbitrage, by the way, is merely the simultaneous buying and selling of the same thing in two different forms. For arbitrage to be profitable, the arbitrageur must have at least a small positive dif- ferential in price between what he buys and what he sells. One com- mon example involves the strategy that we have spent a great deal of this chapter discussing—using options to establish a position that is equivalent to the underlying security. Thus, if you buy a call and sell a put, you have a position that is equivalent to long stock. If you then short the underlying stock, you have an arbitrage, because you bought the stock in one form (the option equivalent form) and sold the stock itself. Most of the time, arbitrage produces a profit that is only a fraction of a point; however, when done repeatedly, these profits add up. There are countless ways in which arbitrage can be done, but usually only member firms can trade arbitrage profitably, because commissions would wipe out the profits for a public trader or customer.
Arbitrage is an ancient and widely practiced trading method. It is both useful and necessary, especially in the derivatives markets, in order to provide liquidity and depth to markets. If arbitrage is not possible in a derivative contract, or if arbitrage is extremely difficult, the contract often fails within a short period of time.
Now let’s return to index arbitrage, specifically. If an index arbi- trage is established at favorable prices, the arbitrageur locks in a guaranteed profit on the trade. It may behoove us to spend a minute explaining why and when index arbitrage is profitable, for that knowledge is necessary for any day trader of index futures contracts, particularly, the S&P 500 Index futures. On any day, the trader can calculate the fair value of the S&P 500 futures contract. This fair
value is a function of only four things: (1) the price of the S&P 500 Cash Index, (2) interest rates, (3) the time until the contract expires, and (4) dividends on the S&P 500 stocks themselves. The actual for- mula is
Fair value of S&P futures = [SPX ×(1 + r)t] – dividends where SPX = S&P 500 Cash Index, r= the risk-free interest rate, and t= time remaining in years.
Example: Suppose the S&P 500 Cash Index is trading at 561.00. Also, there are 51 days remaining until the contract expires, short-term T-bill rates are 6 percent, and the total of all dividends to be paid by the S&P 500 stocks during the next 51 days is $3.23. Note that 51 days is 0.1397 year.
Fair value = [561.00 ×(1.06)0.1397] – 3.23
= [561.00 ×1.0082] – 3.23 = 562.36
Sometimes the fair value is stated strictly in terms of the premium of the futures contract, which in this case is 562.36 – 561.00 = 1.36, premium.
The premium of the futures versus the cash index fluctuates during the trading day as supply and demand forces the market around. If the futures acquire too much premium (we’ll define too muchshortly), they are said to be expensive; and arbitrageurs will sell the futures and buy stocks. This action alone will force the stock mar- ket higher for a short while, until the excess premium is removed from the futures. Since the arbitrageurs are selling futures at the same time that they are buying stocks, it usually only takes a short time before the arbitrage opportunity disappears—the arbitrageurs’
own actions force the premium of the futures versus the cash index to shrink.
In a similar manner, the futures may trade down below fair value;
that is, they are said to be trading at a “discount” [to fair value]. If futures get too cheap, then arbitrage can be done in the opposite manner: futures are bought and stocks are sold. If the arbitrageur has no position prior to establishing this position, then he must sell the stocksshort. Since selling stocks short requires that they be sold on
upticks, this form of arbitrage is more difficult to enact. However, many arbitrage firms will initially buy stocks and sell futures at fair value—meaning they have no profit in the position—in order to have
“ammunition” to be able to sell stocks (long) and buy futures when the futures go to extreme discounts.
Index arbitrage is available almost every trading day. All the arbi- trageur (arb) needs in order to make money is for the futures pre- mium to deviate from fair value by an amount large enough to cover the arb’s transaction costs (which are low).
Example: Suppose again that the fair value for the S&P 500 futures pre- mium is 1.36, as in the previous example. Arbitrageurs have quote machines that can display the S&P 500 Index in at least three ways: the last sale value (which is what is widely disseminated), the bid value, and the offer value. For example, the offer value would be the price that the arb would pay for the S&P 500 Cash Index if he were able to buy all 500 stocks on their current offering price.
An arb sees that the S&P 500 Cash Index is trading at 561.00 and the Index is offered at 561.50; that is, it would actually cost 561.50 for the arb to buy the Index in its correct composition (the proper amount of all 500 stocks). Furthermore, he notes that the futures are running to the upside, and they are currently selling at 563.75. So, if he could sell futures at 563.75 and buy the Cash Index on the offering at 561.50, he would have established the arbitrage at a 2.25-point differential. Since fair value is only 1.36, this means that he has 0.89 profit in his pocket (2.25 minus 1.36, less transaction costs, which will be quite small).
In reality, our mythical arbitrageur is not the only person in town who sees this opportunity. In fact, every index arbitrageur sees this opportunity on his quote machine. Therefore, they may all rush in at once to execute the arbitrage. This causes two things to happen: (1) the arbitrage opportunity usually disappears quickly, and (2) none of them actually get to buy the S&P 500 Cash Index at 561.50 because they are all forcing prices higher.
So, in reality, an index arbitrageur builds in a “fudge factor,” or slippage, to account for the fact that he may have to buy the Cash Index at a higher price than is shown on his screen. Most arbi- trageurs want to see the futures at least 0.70 to 0.90 overvalued or
undervalued before they will attempt to execute the arbitrage. For this reason, we do not constantly see the stock market being buffeted by buying and selling from index arbitrageurs. The futures don’t nor- mally get that far away from fair value; but, as stated earlier, they do get far enough out of line at least once or twice a day, almost every day, for arbitrage to be profitably established.
I have noticed a very easy way to tell if buy or sell arbitrage is actively being done in the market: watch an indicator called TICKI. It can be quoted on all the major quote machines. It is the net upticks or downticks of the 30 stocks in the Dow Jones Industrials. There- fore, its maximum value is +30 and its minimum value is –30. If TICKI rises to +22 or higher, you can be sure that computerized buy programs are being executed; if TICKI falls to –22 or lower, comput- erized sell programs are taking place. A trading system using this indicator is explained in Chapter 5.
So, the action of index arbitrage being established causes short- term movements in the stock market. However, it also causes the arbitrage opportunity to disappear (in theory), so index arbitrage does not have a lasting effect on the market. It may all be over within a matter of minutes, depending on what causes the futures to be mis- priced in the first place. In fact, you may wonder why the futures ever get overpriced or underpriced to begin with. Usually, it is because someone who is not interested in arbitrage decides to take a rela- tively large position in the futures. What follows is one of history’s classic examples.
In the winter of 1995, Barings Bank collapsed under the weight of a now- infamous trader who overextended the bank’s resources. Many people still don’t understand what happened there, but we can summarize the debacle:
the trader sold naked straddles on the Japanese stock market; and then, when the market suffered a rather severe and quick decline, he didn’t cover the naked short straddles. Instead, he bought index futures in an attempt to force the entire Japanese stock market higher in order to bring his position back to profitability. Perhaps the first part of this story belongs in Chapter 2, along with the discussion of selling naked straddles, but we prefer it here because it relates to index arbitrage as well.
Once the market fell initially, it was at levels below the break-even price of the straddles. The trader then decided to buy index futures on the
Japanese stock market. He was able to buy these on small amounts of mar- gin. As he bought enough of these futures, he created a large premium on the futures. This attracted index arbitrageurs, who actually bought Japanese stocks and sold the futures. Thus, the arbitrageurs were in fact forcing the Japanese stock market higher, but only briefly. After each bout of arbitrage buying, the index futures returned to approximately fair value, and the Bar- ings trader had to buy more futures and start the cycle all over again.
By the time that Barings ran out of money, the strategy had worked to a certain degree—open interest in the Japanese index futures was at its largest level in history, indicating that plenty of index arbitrageurs were loaded to the gills with positions. Unfortunately, the Japanese stock market dropped farther, due to natural market activity; and Barings was wiped out, for they not only were short straddles but now were also long massive amounts of index futures. Add to that the fact that they had bought those futures at inflated prices, which added more to the losses, and you have the story of how a long-standing institution went out of business in a very short time. The realproblem, of course, was that the trader—or his supervisors—
should have covered some or all of the short puts when the naked straddles first got into trouble. This would have meant taking a loss, but they would have still been in business.
Portfolio Insurance
Now let’s move on to the second of the three strategies that involve selling index futures against stocks that are owned, portfolio insur- ance. Many portfolio managers in the mid-1980s were attracted to the protective quality of owning puts against their stocks, but they didn’t like the cost of the (expensive) puts. If the market continued to rise, the puts that the manager bought would expire worthless, and his performance would suffer in comparison to both his competitors who didn’t buy puts and the overall stock market.
Despite this aversion to paying put premiums, the fast-rising markets of those years—which saw the Dow Jones Industrials nearly triple between 1982 and 1987—were making stockholders nervous;
and there was demand for a product that would offer downside pro- tection without having the onerous cost of owning puts. In addition, the protection should still afford room for upside appreciation if the market continued to rise.
In response to this demand, a strategy was created that was termed portfolio insurance. In essence, it worked like this: initially, the stockholder did nothing to hedge his stock position. However, if the market dropped by a certain fixed amount, then the portfolio manager would sell futures against a portion of his holdings, perhaps 10 percent to 20 percent on this first sale. Then, if the market dropped further, more futures would be sold to provide more protec- tion. Finally, if the market dropped far enough, enough futures would be sold so that the entire portfolio would be protected. This strategy had several attractive features. First, even though futures weren’t sold until the market started to fall, if the strategy was executed properly, the only loss to the portfolio would be approximately the same as the time value premium if puts had been bought in the first place. Sec- ond, if the market rallied initially, then there was no expense at all since no futures were sold. Finally, the portfolio manager was getting the benefit of selling futures, which trade at a premium to the cash index, so he eventually would be making a small profit from that pre- mium as well. On paper, the mathematics all worked out, and the strategy attracted several large institutions as practitioners.
Unfortunately, there was one flaw in the strategy, a flaw that is common to many theoretical attempts at trading in the market: it assumed a relatively stable and rational market environment in which to operate. This flaw led to disaster and was the main reason why the crash of 1987 became a crash, rather than just a very nasty down- turn in the market.
The stock market had peaked at just over 2,700 in late August of 1987 (the rally had begun from just below Dow 800 in August of 1982). It then fell back to about 2,500 but rallied again to 2,640 by the first week in October.
Some portfolio insurance was sold on that drop, and things seemed to be working fairly well, as intended.
The first sign that things might be getting dicey was a 92-point, one-day drop on October 6. However, the market seemed to weather that; and, although it slid some over the next week, there was actually a good rally on Tuesday, October 13, when the market was up over 70 points at midday and managed to close nearly 40 points higher, at just over 2,500. Again, the decline was orderly enough for most of the portfolio insurance to be sold, although rumors were circulating that some portfolio managers were
now becoming traders and hadn’t sold all the futures that they were sup- posed to. They were waiting for a further rally back toward 2,600. That rally never came (not for a couple of years, anyway).
Trouble began on Wednesday, Thursday, and Friday, October 14 through 16. The market was down 96, 57, and 109 points, respectively, on those three days. The swiftness of the decline left the portfolio insurance managers gasping for breath. They did not sell the required number of futures for two reasons: (1) the decline was so fast that it was almost impos- sible to sell that many futures in so short a time, and (2) the futures were trading at discounts to fair value, a fact not accounted for in the theory of the strategy. Thus, some of the portfolio managers did nothing (with the exception of praying, perhaps). To their dismay, their stocks were losing huge chunks of value; and they were not getting the protection that they had theorized from their short futures, since they were not short nearly as many futures as they were supposed to be.
Monday, October 19, only made the problem worse. The market gapped down 200 points right on the opening, and the portfolio insur- ance crowd hoped against hope for a reflex rally. When that rally did not materialize by about noon, they decided that they had to catch up on their futures selling and at least hold the losses to their current levels (the Dow was now just over the 2,000 level). So they waded in and sold futures . . . and sold futures . . . and sold even more futures. They were selling futures at 15.00 points discount to parity (forget fair value; forget theory; just sell the required number of futures!). Many professionals who were long stock realized that they could sell their long stocks and buy futures and lock in 15 points, so they did that. This added more selling pressure to the market, which continued to collapse until it finished off 508 points on that fateful day.
Obviously, there was plenty of natural selling in the stock mar- ket on the days leading up to, and including, October 19. But the portfolio insurance strategy exacerbated the decline to disastrous proportions. No one knows the exact extent to which portfolio insurance contributed to the debacle, but it was substantial. Not only that, the institutions practicing the strategy got hammered anyway, as they never did get their protection properly in place. In addition, they became the subject of derision from Wall Street; gov- ernment investigations were initiated; and, in general, things were very uncomfortable.
This fiasco pretty much ended the strategy of portfolio insurance as practiced with index futures. Two new measures that came out of the government investigation were that index futures trading limits be installed and that futures halt trading at various points if the Dow Jones Industrials should rise or fall too far, too fast. These rule changes effectively wiped out the portfolio insurance strategy using futures, for no money manager could ever trust that he would be able to sell his futures when he wanted to, even if he religiously followed the strategy to the letter. If the futures were locked limit down or if they weren’t available for trading, then he would never be able to sell the required number of futures.
Program Trading
Today, portfolio insurance is conducted with put options, which brings its own brand of problems. We discuss that strategy using puts shortly. First, however, let’s touch on the third use of futures as a hedge to a stock portfolio, program trading. This term is the catchall for all forms of computer-generated buy or sell programs that enter the marketplace. You often hear the financial media blame a market decline on “sell programs” or credit “buy programs” for a market advance. In reality, many of those “programs” are index arbitrage, but the media don’t make the distinction.
To professional traders who hedge stocks with futures, program tradinghas a distinctly different definition from index arbitrage. The name originally came from the functions provided by block desks to hedge themselves (or their customers) while large stock orders, or programs, were executed. A large customer might call one of the larger trading houses and give an order to buy millions of dollars worth of stock, say, by the close of trading. Usually, there is some sort of price level at which the trading house attempts to fill the order; otherwise, the client could pay up wildly for the stocks. If the trading house actually has to pay more for the stocks, it still gives the execution to the client at the client’s price and takes a loss for the difference in the house’s error account.
Since these trading houses are not in the business of losing money, they will often hedge themselves by buying some futures