Single-Stock Futures Part 17

Pairs Trading

A popular strategy among many hedge funds and institutional traders is one called "pairs trading." The concept of pairs trading is very simple and is, in many ways, a variation of our fair value course during section 3. To implement pairs trading, you find two stocks that move together in predictable fashions. As we learned in the last course, this means finding stocks with high correlations.

You may be wondering how that's possible. After all, aren't stock price changes random? Yes, that's true. However, that does not mean that two stocks cannot move in similar fashions. This will be especially true if they are in the same industry, although that is not a prerequisite. For instance, if Dell Computer is expected to rise over the next year, then it's probably safe to say that IBM could be expected to rise as well. Likewise, if computer sales are soft, we could expect both Dell and IBM to decline. This expectation is captured by the fact that you will see the price of a stock rise when positive news is released about a competitor. If you see a headline that says Home Depot's sales are expected to double for the next quarter, you could expect to see the price of Lowe's stock to rise on that news as well.

Once a pair of stocks is identified as being highly correlated, the trader determines a range for that correlation. After all, the two stocks will never move perfectly together, no matter how close they may be. The trader attempts to determine when the spread between the two stocks is average, high, or low. When it is to the high side, the trader buys the one whose price is low and sells the one that's high. The idea is that the two prices can be expected to revert back to the average. If they do, the trader will make money from both sides, meaning he profits on the long and short positions. Because the trader is long and short, this strategy is also known as "long-short" and "market neutral."

The reason it is also called market neutral is because the trader is long and short stocks that are expected to move together. If the market rallies hard, both stocks may rise but the trader may be about neutral on profits or losses. This is because the profits on the long stock will be about equally matched on the losses from the short stock (this assumes the trader has equal dollars in both stocks). Likewise, if the markets plunge, the trader can again expect to be about at breakeven levels. Because the trader is indifferent to the market rising or falling, he is "market neutral." The only thing that matters to the pairs trader is the spread -- the difference in prices -- between the two chosen securities.

Law of One Price

Pairs trading is based on an economic principle called the "law of one price," which states that identical goods should cost the same across countries. Sometimes this law is loosely called the "Big Mac" law after a classic example asserting that a McDonald's Big Mac should cost the same in the U.S. as it does abroad. If it does not, then arbitrage is possible as people could buy it cheap in one country and sell it for more in another country. Of course, in the real world, risk, taxes, government regulations, import tariffs (not to mention transportation costs) will make it so that they are not exactly equal. However, you should get the idea that there is no reason for identical goods to cost different amounts across countries.

We can extend that reasoning to the stock market. If two stocks have the same payoffs in all states of the economy (i.e., they move together), then there is no reason for their prices to deviate. If they do, one can perform a "statistical arbitrage" between them by pairs trading. What do we mean by statistical arbitrage? That simply means that you are arbitraging probabilities and you will most likely make money. Notice how this is different from the standard use of the word arbitrage where the trader is guaranteed to make money.

In most cases, pairs trading is easier said than done. Most hedge funds use advanced statistical techniques to find pairs that truly are highly correlated over time and then will perform the pairs trading according to some rule such as when the spread increases by two standard deviations. However, this does not mean that it cannot be used on a simpler basis.

For example, you may notice two stocks in similar industries fluctuating around a fixed price. For example, you can see in Figure 1 that Pharmacia (PHA) and Medimune (MEDI), both in the healthcare/drug sector, fluctuated around $40 between 7/26/01 and 12/1/01. In this case, $40 is the "mean" and the highs and lows are fluctuations around that mean.

If this trend had persisted, you could have purchased MEDI and sold PHA around the time period shown by arrow A. This was a time when MEDI was cheap and PHA expensive with the expectation that they would revert to the mean of $40. You could then have sold the position at time period B, thus capturing a profit. It's also possible that you could have sold at time B and then repurchased at time C. In fact, active pairs traders will constantly flip back and forth with the market. They may buy at A, sell and simultaneously go short at B, buy and simultaneously go long at C. Remember too that futures traders can close a position and then change directions with one trade. If you were long five contracts of MEDI and short five PHA at time A, you could then sell 10 MEDI and buy 10 PHA at time B thus making you long five PHA and short five MEDI at time B. One execution, one commission, and you've instantaneously closed and changed directions. Because of the ease with which futures traders can go long and short, you can see where single-stock futures are a remarkable trading tool for pairs traders.

General Strategies

We've covered some specific strategies that are well suited for futures. At this point, we want to bring to your attention some general advantages of futures over stocks. While the following strategies are not specific, they are equally, if not more, important than the previous strategies since they get you to think of the various ways futures can be used to your benefit.

Diversification

Because of the low initial margin requirement, it should be obvious that futures can allow for safer investing through diversification. For instance, say you have $30,000 to invest in the stock market. If you buy quality companies, there's a good chance their share price will be high and you may not be able to afford many different stocks, which is key to diversification. Without going into the math, the bulk of company-specific risk (called unsystematic risk) is washed away once you hold a properly balanced portfolio of about 16 to 22 stocks in different industries in your portfolio. In other words, if you own a little bit of tech, financials, automotive, healthcare, food and beverage, etc, you will end up with minimum risk for a given level of return, or conversely, a maximum return for a given level of risk. With only $30,000, however, you may not be able to obtain this optimal amount. But with single-stock futures, you have access to a tool that may be a key to smarter investing.

If you wish to buy a stock and hold it for a long time, such as five or 10 years, there's probably no doubt that purchasing the stock is your best bet. But what if you generally hold a stock for one year or so? Would you rather have two or three stocks or a basket of 20 one-year contracts? After all, we've shown there's no difference between the two positions in terms of price movement. You're better off with a larger basket; and futures contracts give you this opportunity. Keep in mind if you do this that you may have to periodically send in money if a position goes against you. It may not be the best idea to invest all of your money so that you have some set aside to meet potential margincalls.

In addition, commodity futures are often highly uncorrelated with stocks. This simply means that there is no systematic association between commodities and stocks rising or falling together. The fact that many futures contracts are uncorrelated is a key to creating a properly diversified portfolio. We said earlier that unsystematic risk is nearly eliminated if you hold a properly balanced portfolio. Having low correlation between assets is what we mean by properly balanced -- and futures can be important for achieving this quality as demonstrated by the following facts:

• Stocks plunged 48% in 1973 and 1974 while the Goldman Sachs Agricultural Commodity Index rose 491%.

• Over the past 25 years, if you compare the major advances of the S&P 500 to futures, there were corresponding positive returns in futures as well. However, during all the largest S&P 500 stock declines, futures were positive. In all but one decline in the S&P 500, advances in futures completely offset losses in the S&P 500.

• Currently, the correlation between the S&P 500 and Barclay CTA Traders Index is .02[1] -- virtually non-existent.

Futures contracts can be your most effective source of portfolio balance. While nobody says you need to be 100% invested in futures, it is a mistake to completely ignore them.

Day-Trading

The diversification concept can be carried over to those who day-tradestocks. Day-traders are those who attempt to capture small price movements, up or down, during the day and close all positions by the end of the day. Most day-traders pick a stock they are comfortable with that they think will make a small move in a short time. Most of their expectations of these movements are based on technical analysis. Then they go for leverageby purchasing as many shares as they can with the money in their account. They hope to capture a sizeable profit on a small move many times through the day.

The problem with this approach is, once again, no diversification. The chances that a day-trader consistently picks a winning stock are slim to none. One or two losing trades quickly offset the winners. Futures contracts offer the leverageand diversification that day-traders seek. In fact, we can even carry it out one step further and buy the stocks we think will rise and short the ones we think will fall. Yes, this can be done with stocks too but it is far more expensive to meet the Reg Trequirements. The end result is that you cannot get the same diversification with stocks as you can with futures and will therefore not have the same performance.

In fact, on February 27, 2001, the Securities and Exchange Commission (SEC) approved amendments to NASD Rule 2520. These amendments make some significant changes to the margin requirements for those who day-trade stocks. First, if you buy and sell a stock on the same day in a margin account and you do so at least four times in a rolling five-day business period, you will be required to have a minimum equity balance of $25,000 before any more day-trades can be placed. On the good side, your "buying power" will be increased to a maximum of four times your excess margin. Regardless of this benefit, if you wish to actively day-trade stocks and do not keep a minimum balance of $25,000, then single-stock futures will be your only way to continue day trading.

Fine-Tuning and Rebalancing Your Portfolio

Futures are perfect for fine-tuning your existing positions. Say you have a long position that has fallen significantly but you are still bullish on it. You wish to purchase more shares to reduce you cost basis, which will allow you to reach breakeven sooner. Rather than spending a lot of money (and possibly being wrong), you can throw a relatively small amount toward a futures contract and gain the additional exposure without using all of your capital.

You can also use them to fine-tune your portfolio. Say you have a large blue-chip portfolio, but you think a couple of other sectors that you don't own are about to make a run. For just a little bit of money, you now have exposure to those sectors and can enhance your returns if you are correct without needing a lot of money to do so.

Hedging 401(k)Accounts

You may have a 401(k)or other tax advantaged account that does not allow sales except within certain time periods. If a stock in that account has made a nice run, you may not be able to do anything about if you're in a restricted time period. However, with futures contracts, you can short the contract covering the same stock in another account and that will offer you a hedgeand basically lock in a selling price. For example, say your company stock has run from $30 to $70 but you are not allowed to make a sale because it is a restricted time period. You can, instead, sell one futures contract in another account for every hundred shares of stock you own. If the stock continues to rise, the gain in the shares will offset the losses on the futures. If the stock falls, the gain in the futures contracts will offset the losses in the 401(k). Keep in mind this is one case where shorting stocks may not even work for you since many companies do not allow employees to short company stock. Futures may be your only tool.

Granted, if the stock falls, those gains on the futures contracts will be outside of your 401k but at least the money is not gone for good. It has merely been effectively transferred from your 401(k) to your personal account.

Please remember about marking-to-marketthough. If you short the futures contract and the stock continues to rise, you may get maintenance calls from your broker and will need to meet those. Even though you are effectively hedged with the long positions in the 401(k), you cannot access those funds until you sell those shares! So if you use futures in one account to hedgeanother account that you can't immediately access, make sure you have additional funds to meet potential maintenance calls.

Futures contracts can be used in nearly all the same ways as stock. There will be minor differences, for example, you won't receive dividends or voting rights with futures; but for the most part, all strategies for stocks can easily be replaced with futures. However, there are many strategies for futures that cannot be made with stocks. Because of this quality, futures contracts become an important trading tool for you to understand as the financial markets become increasingly complex.

[1]The Barclay CTA Traders Index is a portfolio of professionally managed futures.

Risks and Rewards

Single-stock futures are a new and exciting tool for hedgers and speculatorsalike. Despite their benefits, I often hear people criticize that adding one more investment class only adds to the confusion among the seemingly infinite number of choices already available. They insist there is no reason to learn about them, as they are perfectly happy with their stocks, bonds, and options.

Before you accept that way of thinking, we're going to show how market participants respond to any financial investment. It does not matter if it is new, such as single-stock futures, or an existing one, such as stocks and bonds. The method of pricing all assets depends on risk and return. To demonstrate how this is done, we're going to look at some gambling games just to make it fun. As we will find out, even games of chance are priced according to risk.

How Much Would You Pay?

Assume two games are offered, and in order to play you must bid on a ticket for that game. Only the top 100 bids will be accepted. If you win one of the top 100 spots, you are allowed to play that game. The following two games are offered:

Game 1: A coin is flipped. If the coin lands heads, each player wins $10. If it lands tails, they lose the price they paid for the ticket.

Game 2: A six-sided die is rolled and, if it lands on the number six, each player wins $10, otherwise they lose the price they paid for the ticket.

Also assume there are hundreds of thousands of people willing to play but that only 100 people can play at a time and that they are free to compete on price. Only the 100 highest bidders are allowed to play the game at any one time.

What can we expect to see happen with the prices of these two games?

Take a close look at the two games above and think about them for a moment. Which would you prefer to play? How will this preference affect its price?

First of all, we see that both have the same $10 payoff. However, each is subject to a different set of risks. Even if you do not have an understanding of probabilities, you should be able to conceive that you would win far more often playing the first game. On average, you would win every other time with the first game and every sixth time with the second. In other words, the second carries more uncertainty -- it is riskier. Because the frequency of wins is higher in the first, everybody prefers to play that game over the second one for any given cost.

While the fair price of this game can be found mathematically, we are going to assume that the gamblers have no such knowledge and must learn by trial and error.

Let's say that the first several rounds of the game are played with each gambler paying $1 for the ticket. On average, the gamblers will pay $1 every time but win $10 every other time. In other words, the gamblers will pay $2 to win $10, on average. This makes for a net gain of $8 every two games or $4 per game.

We can show this same result mathematically by looking at what are called expected values, which are nothing more than the sum of the gains and losses multiplied by their probabilities. Using expected values, we can show that half the time the gamblers will lose their dollar and half the time they will make $9 (pay $1 to play and receive $10):

-$1 (1/2) = -$.50

+$9 (1/2) = +$4.50

Net = +$4 per game

Regardless of how you look at it, the gamblers can expect an average gain of $4 per game. Because they expect net profits, they continue to play. The other gamblers not playing this game will see the profits mounting and become eager to play, but they cannot because all 100 seats are all filled. In order to play, they must bid higher than the going rate of $1. If the game is now bid to $2.00, the expected return to the gamblers becomes:

-$2 (1/2) = -$1

+$8 (1/2) = +$4

Net = +$3 per game

The additional dollar bid is countered by an additional dollar less of expected profit. The expected gain falls from $4 to $3. Still, the spectator gamblers see the profits continuing, although not as fast, so they continue to bid up the price to play. Eventually, the price will be bid to $5 to the point where gamblers can expect to break even, on average:

-$5 (1/2) = -$2.5

+$5 (1/2) = +$2.5

Net = $0 per game

At a bid of $5 per game, the gamblers are expected to neither win nor lose in the long run. If they bid $5 to play, they will lose $5 half the time and gain $5 half of the time. If the bids rise above this amount, even to just $5.01, the house will start to earn money per game (the gamblers would lose), on average, and the gamblers will learn to reduce their bets. So we find that, in the long run, the first game will be bid to a value of $5 and stay in equilibrium at that level. There is no incentive for gamblers to bid higher and no room to bid lower. If one gambler bids less than $5, another gambler will be willing to bid $5 to take his place.

What happens to the price of the second game? At some point through all of this bidding in the first game, some gamblers will try out the second game but will never bid more than the price of the first game. Remember, the first game is preferred for any given price because of the reduced risk. Therefore, the second game will never have a value greater than the first. However, this does not mean it will have no value; and gamblers will, at some point, give it a try.

Let's assume gamblers are able to participate by only paying one dollar. The gamblers who bid $1 will lose, on average, every five out of six games. Every sixth game, on average, they will pay their $1 fee but win $10 for a net gain of $9.

-$1 (5/6) = -$0.83

+ $9 (1/6) = +$1.50

Net = +$0.67 per game

This net expected gain is small but still positive, so gamblers will continue to bid up its price. From what we learned in the first game, we know that if there is a net expected gain, the gamblers will continue to bid higher. How much room is left for them to bid? Exactly the amount of the net expected gain. Because an expected gain of 0.67 remains after bidding $1, they will eventually bid this game to a price of $1.67. At that price, there will be no incentive to bid it higher and no room to bid it lower:

-$1.67 (5/6) = -$1.3916

+ $8.33 (1/6) = +$1.3883

Net = $0.0033 per game, which is approximately zero.[1]

When the price is in equilibrium, no gambler will bid it higher and, if someone bids lower, another gambler will quickly take his place by bidding higher. The end result is that the first game will be bid to a value of $5 and the second to a value of $1.67. We could also understand the rationale another way. The second game would take three times as long to win, on average, than the first. In the first game, gamblers could expect to win every two turns while those playing the second game could expect to win every six turns, which is exactly one-third as often. Because both games pay out $10, the value of the second game must be one-third that of the first or $5/3 = $1.67.

Efficient Market Theory

What we just demonstrated is a variation of a well-known financial theory called the Efficient Market Theory (EMT). While there are three different forms of EMT, the one we demonstrated is known as the semi-strong form and states that all publicly available information is priced into each and every asset just as was done with our gambling games. We can demonstrate EMT with a simpler version too by asking a simple question: Is it better to own a Porsche Boxster or a Ford Taurus? Although I'm sure you have an immediate answer, the correct answer may surprise you.

Many people are tempted to answer that the Porsche is clearly the better choice.

To find out if that's true, let's start by assuming that both the Ford Taurus and Porsche Boxster are both priced the same. With both cars priced the same, few would disagree that you are better off with the Porsche. If so, people will buy the Porsche over the Taurus. This will put buying pressure on the Porsche and raise its price relative to the Taurus. Say the Porsche is now bid up to a price $3,000 above the Taurus. Most would agree that it is still a better deal and continue to buy it. This action will continue until the markets are not so sure that an additional $1 is worth jumping from the Taurus to the Boxster. If it were worth it, they would do it.

While it may go against your intuition, as long as there is no net bidding up or down of prices between the two cars, you are equally well off with either one. While the Porsche may be faster and have higher quality and resale value (not to mention it just looks cooler), it also comes with higher repair bills, insurance rates and theft occurrences. The car market will reflect all pros and cons in the prices of the two cars. Similarly, the financial markets will price all assets to reflect their risks. Quality assets are bid up and riskier assets are sold off. This is why a government T-bill yielding 5% is equal to a more risky bond priced to yield 10%. The government bond is of higher quality but also has a lower yield. The markets realize that, all else constant, you are better off with the T-bill, so they continue to bid that price up until there is no net difference between the two bonds. If there were an advantage, the markets would continue taking action and reflect it in the price.

The important point to draw from this is that all markets, whether stocks, bonds, options, futures, real estate, coins, art -- even casinos -- will be priced according to risk. Granted, the financial markets are not as easy to price as the two gambling games we presented that offer a precise payout with exact probabilities. Nonetheless, the principle is the same and investors will bid the price up if they feel there is more reward (or less risk) and bid the price down if there is less reward (or more risk) as was done with these two gambling games.

Single-stock futures are just one of many investment markets, and they are priced according to risk. Do not be fooled by people who say they are too risky or that they are not worth learning. Just as with our gambling games, even though the second game was riskier did not mean that gamblers would not play it. They will for the right price. Whatever that price may be is up to the market to decide. The same holds true for single-stock futures. They have a unique set of risks and rewards that are unavailable with any other asset. Consequently, they will carry a price to reflect those risks and rewards.

Single-stock futures are simply another investment "game" from which to choose. If you choose to not allow single-stock futuresinto your investment portfolio, or to not even entertain the idea of learning about them, you are essentially blocking out the advantages they may offer for a particular situation. What's worse is that you will probably substitute them with a less efficient product to accomplish the same task. If you refuse to learn about them you will be limiting these new and innovative tools that were designed to efficiently help you control risk.

As the famous psychologist, Abraham Maslow, once said, "To the man who only has a hammer in the toolkit, every problem looks like a nail." Without single-stock futuresin your "toolkit," the investor who only uses stocks, bonds, or optionswill see those particular assets as the solution to every financial problem. If that were the case, then the other assets in the market would never have come into existence. Single-stock futures are the answer to a long-term problem of hedging risk. They allow us to quickly spread that risk off to speculators who are willing to accept it. They allow the investor or speculator to custom tailor risk and reward profiles in ways that cannot be done as efficiently without them. They are not a pointless product designed by brokers to sell, nor were they created under political pressures of the wealthy as a means to legally gamble for the fun of it.

The markets created them out of necessity. Single-stock futures can be used to hedge risk conservatively, speculate wildly, or any shade of gray in between. The choice of how to use them is up to you -- assuming you decide to use them. If you choose not to, you will leave behind an invaluable tool that allows you to be more proficient at maneuvering through the volatile conditions and uncertainties that exist in today's complex markets. I am convinced that using futures is essential for intelligent and successful investing.

I hope you are convinced, too.

[1] The reason it is not exactly zero is due to rounding. If we could assume that gamblers could split cents and pay amounts such as $1.6666667, we could then get the expected payout to exactly balance to zero.