8. ANEXOS
8.1. Anexo 1: ACTA DEL PROYECTO
A
t first glance, learning about the somewhat arcane practice of program trading and “arbitrage” (cap- italizing on price discrepancies in related mar- kets) may seem to be of little practical value for the typical individual stock index futures trader.True, knowledge of arbitrage activity, by itself, will not make you a great trader — or even a good trader. However, it can make you a better trader. At the very least, it gives you a better grasp of how the markets you trade function. Also, professional S&P 500 futures and Exchange Traded Fund (ETF) traders pay close attention to arbitrage activity because its potential short- term effects can mean the difference between profits and losses. One bit of practical trading information derived from pro- gram trading and arbitrage is the relationship (the “basis”) between S&P 500 futures and its underlying cash instrument, the S&P 500 index. Here, we will explore the concept of basis and explain its importance to both stock index traders and pro- fessional arbitrage traders, or arbitrageurs (“arbs” for short). Arbitrage
Arbitrage is the simultaneous purchase and sale of similar or identical instruments (often in different geographical loca- tions) to take advantage of short-term price discrepancies.
For example, gold trades in several major financial centers around the world — New York, London, Paris, Hong Kong and Tokyo. If gold were trading in New York for $330 per ounce and $332 per ounce in London, you could, in effect, buy gold in New York and immediately sell an equal amount in the London market and profit $2 per ounce.
Why would the metal be $2 higher in London? Short-term supply and demand fluctuations: Perhaps a European jeweler or metal fabricator placed a large order in the London market. This short-term demand may cause the price to rise in London relative to New York or other financial centers.
Throughout the world a cadre of gold traders watches their screens, waiting for such a moment. Armed with lightning-fast reflexes and state-of-the-art trade execution technology — not
to mention a few mil- lion or so in capital — they pounce. They will quickly buy as much gold in New York as possible and simulta- neously sell it in London, pocketing the $2 per ounce price differential.
Hundreds of arbs acting in concert around the world will have an almost immediate impact on the market: Gold will quickly rise in New York and fall just as quickly in London until the price differential disappears, or is so small an arb’s business costs would outweigh the possible profit.
Because arbitrage seeks to exploit short-lived price discrep- ancies, a successful arbitrage trade carries almost no risk — other than execution risk. Even though the trader would buy and sell immediately in both markets, there is a small chance that in the middle of the trade the market would move quick- ly against him or her and result in locking in a lower differen- tial, or worse, a loss. It’s part of the business. But over time, a skilled arbitrageur minimizes these events and can look for- ward to a lucrative business.
Stock index arbitrage (or index arbitrage) is a variation on this theme, played out with baskets of stocks traded largely on the New York Stock Exchange in the form of the S&P 500 index (most S&P 500 stocks trade on the NYSE, but some are listed on the AMEX and the Nasdaq), and a futures contract that trades in Chicago based on the index — the S&P 500 futures (SP).
Although arbitrage occurs with many stock indexes, activi- ty is particularly focused in the S&P 500 cash and futures mar- kets because they are exceptionally deep and liquid. (ETFs such as SPY and QQQ are also used in arbitrage.)
The next section will detail, step-by-step, how an index arbi- trage trade is executed and its effect on the market, taking into account fair value and basis (the futures premium or discount to the underlying cash), as well as buy and sell programs.
Fair value and basis
Fair value is the theoretical value of stock index futures at a particular time, given prevailing market conditions.
Theoretical fair value = cash index value [1 + (r – d)*(x/365)] where
R = Interest rate/financing costs D = Dividend yield on S&P cash X = Days to expiration of futures
For example, assume the following market conditions exist: March S&P 500 futures = 901.20
Cash S&P 500 index = 900.00 Days to futures expiration = 90
Interest rate/financing costs = 2.0 percent Dividend yield on S&P cash = 1.5 percent
Given these numbers, the theoretical fair value of the futures contract is:
Fair value = cash index value [1 + (r – d)*(x/365)] = 900.00 [1 + (.005)*(90/365)]
= 900.00 [1.0012328] = 901.10
Fair value itself isn’t of much use. It’s the premium or dis- count (how much the futures are trading above or below the cash index) that matters most. As previously mentioned, the “basis” is the difference between the futures price (either theo- retical or actual) and the cash index price. Using the informa- tion from the fair value example, the theoretical (“fair”) and actual basis are calculated as:
Theoretical premium/discount =
fair value of futures – actual cash index value (“fair basis”) = 901.10 – 900.00
= 1.10 pt. premium
Actual premium/discount =
actual level of futures – actual cash index value (“actual basis”) = 901.20 – 900.00
= 1.20 pt. premium
In this case, the S&P 500 futures should be trading at a pre- mium of about 1.1 points above the cash index. This doesn’t mean they always will. In fact, most of the time the futures will fluctuate slightly above and below the theoretical fair basis because of changes in order flow, supply and demand, and volatility, among other factors.
Only when supply and demand fluctuations cause a large shift away from the fair basis will arbitrage activity start to occur. In this example, the actual basis is 1.2 points, a mere .10
point away from theoretical basis. For arbitrageurs to make a profit, the actual basis has to increase (or decrease in some strate- gies) enough to cover an arbitrageur’s cost of doing business (the “hurdle rate”), which, in addition to interest rates, includes commissions, trader salaries, equipment and telecom lines.
In our arb program example, using the 1.10 point theoretical fair basis as reference, no arb activity would begin until the basis widened to around 2.10 points — a “hurdle rate” of 1.0 point. (Hurdle rates vary from firm to firm, but typically fall in the .75 to 1.25 point range.)
What would cause the basis to widen that much? Again, like the New York-London gold example, it would be the result of short-term supply and demand considerations. What if a large customer of a brokerage firm decided he wanted to gain expo- sure to the stock market via S&P 500 futures? If he put in a large enough buy order, say 500 to 1,000 contracts, the short- term demand would likely cause the S&P futures to begin to climb relative to the cash market. Once the discrepancy increased to the point arbs could profit from it, an intricately linked set of events would be set into motion.
After the large customer’s order hit the trading floor, here is how the market might look:
Actual value of S&P 500 futures = 902.20 (CME) Actual value of S&P 500 cash index = 900.00
(NYSE/AMEX/NASDAQ)
Actual Premium or basis = 2.20 (above “hurdle rate”) At this point some of the best and the brightest on Wall Street would employ index arbitrage. They would purchase the relatively cheap S&P 500 cash index, consisting mostly of NYSE issues, and simultaneously sell the relatively expensive S&P 500 futures contracts at CME.
Executing the trade
The precision required to pull off this kind of strategy is quite amazing. The futures side can be done rather quickly, because it involves only one instrument, the S&P 500 futures contract. But how do arbs accurately buy all the S&P 500 component stocks at the same time?
The answer is a system referred to as SuperDOT (Direct Order Turnaround System). The DOT system electronically routes orders directly to specialist posts on the floor of the NYSE. At the press of a button, a firm can send an order to the NYSE for immediate execution. The system can be pro- grammed with customized lists of stocks, thus allowing a trad- er to buy or sell all 500 issues in the S&P 500 at once. (The Nasdaq issues can be executed using ECNs or other order- routing mechanisms.)
In reality, most firms don’t buy all 500 stocks in the index. They have in-house research departments that put together lists of less than 500 names that track (hopefully) the S&P 500 with close precision. If you look at a list of all the components
in the S&P 500, you would notice the last 50 to 100 names have a very small weighing on the overall index; the top 40 stocks account for about 50 percent of the capitalization of the index.
How many shares of each component stock and how many futures are bought and sold depends largely on the size of the “program.” Remember, index arbitrage falls under the heading of program trading. Most programs are in the $10 million to $15 million range, but some are much larger.
A $10 million index arbitrage “buy program” would consist
of buying the cash basket of stocks and selling the futures. A “sell program” would involve selling the cash basket of stocks and buying the futures. However, you cannot simply divide $10 million in 500 equal installments; you must buy the stocks in the exact proportion to their weighting in the index.
For example, Microsoft (MSFT) is the largest stock in the S&P 500, accounting for around 3.62 percent of the total index. Therefore, an arb trader must spend 3.62 percent of his $10 mil- lion ($362,000) on MSFT. If MSFT’s current price is $57, that
FUTURES
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OPTIONSStrategiesStrategies
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he greatest benefit of understanding fair value, basis and index arbitrage lies in gauging the value of futures relative to the cash index. For the short-term S&P or E-mini S&P 500 futures trader, this is critical.A few months back a trader called the CME complaining about his fill in the S&P 500 futures contract. His call was routed to me at about 1:30 p.m.
DL: “By any chance did this bad fill happen about 30 min-
utes ago?”
Caller: “Yes, how did you know?”
DL: “By any chance did you put in a market order to buy
futures?”
Caller: “Yes. Again, nice guess.”
DL: “Did you know what the theoretical premium was
when you placed your order?”
Caller: “No! I simply put in a market order to buy one June S&P 500 futures contract. What’s the point of all this?” Here’s the point. At 1 p.m., the following prices were flash- ing on my screen:
June S&P 500 futures: 1410.10 June S&P 500 futures theoretical fair value: 1410.00
S&P 500 cash index: 1400.00
Cash/futures theoretical basis: (fair value – cash) 10.00 Cash/futures actual basis: (actual futures – cash) 10.10 A few minutes later, around 1:05 p.m., a large buy order entered the pit and drove futures prices higher relative to the cash market. The following prices were then in effect:
June S&P 500 futures: 1412.00 June S&P 500 theoretical fair value: 1410.00
S&P 500 cash index: 1400.00
Cash/futures theoretical basis (fair value – cash) 10.00 Cash/futures actual basis (actual futures – cash) 12.00
The caller’s market order to buy S&Ps hit right when the market was trading at 1412.00. He was filled at 1411.80—1.80 points above the theoretical premium level.
Within minutes, arbitrageurs and traders came into the market to take advantage of a basis level that had taken a stroll too far from equilibrium. Skilled arb traders sold expen- sive futures and bought cheap stock when the basis became too large, rapidly forcing prices back into line. The trader’s order hit the pit precisely when this activity began, producing an immediate loss of 1.80 points in the position ($450.00).
Was this really a poor fill, or was it more a result of bad timing that could have been prevented through familiarity with the pricing mechanisms in stock index futures contracts? Likely, it was the latter. By knowing futures were temporarily expensive relative to the cash index, the trader could have delayed his order by just a few moments and the futures would have returned to their normal fair value.
However, merely knowing the theoretical value of the futures isn’t enough. You must know what the premium (or basis) should be. In this example, the normal basis was 10. For a brief moment it was 12 points — two points too high.
Although cash and futures markets usually return to equi- librium quickly, extraordinary events may prevent this from happening. Fed Chairman Alan Greenspan’s 50-basis point rate cut in January 2001 is a great example.
Shortly after the announcement, both the regular and E-Mini S&P 500 futures contracts rocketed higher. Because futures are nearly always more responsive than the underly- ing cash market, equities took a lot longer to catch up. The trader who waited for the normal premium to reappear would have missed out on a fabulous rally.
If the market makes quick, violent moves up or down, wait- ing for fair value to reassert itself can result in costly lost opportunities. But over the long run, consistently buying or selling futures one to two points above or below theoretical basis is a prescription for poor trading results.