THE WORLD OF ARBITRAGE
THE WORLD OF ARBITRAGE
Day traders work fast, looking to make lots of little profits during a single day. Arbitrage is a trading strategy that looks to make profits from small discrepancies in securities prices. The word arbitrage itself comes from the French word for judgment; a person who does arbitrage is an arbitrageur, or arb for short. The idea is that the arbitrageur arbitrates among the prices in the market to reach one final level.
In theory, arbitrage is riskless. It’s illogical for the same asset to trade at different prices, so eventually the two prices must converge. The person who buys at the lower price and sells at the higher one will make money with no risk. The challenge is that everyone is looking for these easy profits, so there may not be many of them out there. Good arbitrageurs have a paradoxical mix of patience, to wait for the right opportunity, and impatience, to place the trade the instant the opportunity appears. If you have the fortitude to watch the market, or if you are willing to have software do it for you, you’ll probably find enough good arbitrage opportunities to keep you busy.
True arbitrage involves buying and selling the same security, and many day traders use arbitrage as their primary investment strategy. They may use high levels of leverage to boost returns. Other traders follow trading strategies involving similar, but not identical, securities. These fall under the category of risk arbitrage. In this chapter, I cover the terms and strategies used by day traders who engage in arbitrage. I discuss the basics of arbitrage and how it can be put to good use by a patient trader. I outline the tools you can use to profit from price differences among similar securities. Finally, I list the many types of arbitrage you might want to include in your arsenal of trading strategies.
Obeying the Law of One Price
The key to success in any investment is buying low and selling high. But what’s low? And what’s high? Who knows?
In the financial markets, the general assumption is that, at least in the short run, the market price is the right price. Only investors, those patient, long-suffering accounting nerds willing to hold investments for years, will see deviations between the market price and the true worth of an investment. For everyone else, especially day traders, what you see is what you get.
Under the law of one price, the same asset has the same value everywhere. If markets allow for easy trading — and the financial markets certainly do — then any price discrepancies will be short-lived because traders will immediately step in to buy at the low price and sell at the high price.
Punishing violators of the law
But what happens if what you see in New York is not what you see in London? What happens if you notice that futures prices are not tracking movements in the underlying asset? How about if you see that the stock of every company in an industry has reacted to a news event except one?
Well, then, you have an opportunity to make money, but you’d better act fast — other people will probably see it, too. What you do is simple: You sell as much of the high-priced asset in the high-priced market as you can, borrowing shares if you need to, and then you immediately turn around and buy the low-priced asset in the low-priced market.
Think of the markets as a scale, and you, the arbitrageur, must bring fairness to them. When the markets are out of balance, you take from the high-priced market (the heavier side of the scale) and return it to the low-priced market (the lighter side) until both even out at a price in between.
If you start with a high price of $8 and a low price of $6, and then buy at $6 and sell at $8, your maximum profit is $2 — with no risk. Until the point where the two assets balance at $7, you can make a profit on the difference between them.
Of course, most price differences are on the order of pennies, not dollars, but if you can find enough of these little pricing errors and trade them in size, you can make good money.
Understanding arbitrage and market efficiency
The law of one price holds as long as markets are efficient. Market efficiency is a controversial topic in finance. In academic theory, markets are perfectly efficient, and arbitrage simply isn’t possible. That makes a lot of sense if you are testing different assumptions about how the markets would work in a perfect world. A long-term investor would say that markets are inefficient in the short run but perfectly efficient in the long run, so they believe that if they do their research now, the rest of the world will eventually come around, allowing them to make good money.
Traders are in between. The market price and volume are pretty much all the information they have to go on. It may be irrational, but that doesn’t matter today. The only thing a trader wants to know is if there is an opportunity to make money given what’s going on right now.
In the academic world, market efficiency comes in three flavors, with no form allowing for arbitrage:
- Strong form: Everything, even inside information known only to company executives, is reflected in the security’s price.
- Semi-strong form: Prices include all public information, so it may bepossible to profit from insider trading.
- Weak-form: Prices reflect all historical information, so research that uncovers new trends may be beneficial.
Those efficient-market true believers are convinced that arbitrage is imaginary because someone would’ve noticed a price difference between markets already and immediately acted to close it off. But who are those mysterious someones? They are day traders! Even the most devout efficient markets adherent would, if pressed, admit that day traders perform a valuable service in the name of market efficiency.
Those with a less-rigid view of market activity admit that arbitrage opportunities exist, but that they are few and far between. A trader who expects to make money from arbitrage had better pay close attention to the markets to act quickly when a moment happens. And, I’d say this is the case for most arbitrage strategies open to day traders.
Finally, those who don’t believe in market efficiency believe that market prices are usually out of sync with asset values. They do research in hopes of learning things that other people don’t know. This mindset favors investors more than traders, because it can take time for these price discrepancies to work themselves out.
Because arbitrage requires traders to work fast, it tends to work best for those traders who are willing and able to automate their trading. If you are comfortable with programming and relying on software to do your work, arbitrage might be a great strategy for you.
Scalping for Profits
The law of one price is all well and good, but prices change constantly during the day. They go up a little bit, they go down a little bit, they move every time an order is placed. There’s a way that traders can profit from those movements. It’s not exactly arbitrage, it’s scalping. Especially active in commodities markets, scalpers look to take advantage of changes in a security’s bid-ask spread. That’s the difference between the price that a broker will buy a security for from those who want to sell it (the bid) and the price that the broker will charge those who want to buy it (the ask — also called the offer in some markets).
In normal trading, the bid-ask spread tends to be more or less steady over time because the usual flow of supply and demand stays in balance. After all, under market efficiency, everyone has the same information, so their trading is consistent and allows the broker-dealers to generate a steady profit.
Sometimes, however, the spread is a little wider or narrower than normal, not because of a change in the information in the market, but because of short-term imbalances in supply and demand.
A basic scalping strategy looks like this:
- If the spread between the bid and the ask is wider than usual, then the ask is higher and the bid is lower than it should be. That’s because slightly more people want to buy than sell, so the brokers charge the buyers higher prices. The scalper uses this as a sign to sell.
- If the spread between the bid and the ask is narrower than usual, then the ask is lower and the bid is higher than it would normally be. That happens if there are slightly more sellers than buyers, and the broker wants to find buyers to pick up the slack. The scalper would be in there buying — and hoping that the selling pressure is short lived.
The scalper has to work quickly to make many small trades. He might buy at $20.25, sell at $20.50, and buy again at $20.30. He has to have a low trade cost structure in place or else he’ll pay out all his profits and more to the broker. He also has to be sure that the price changes aren’t driven by real information, because that will make market prices too volatile to make scalping profitable. Scalping is “picking up nickels in front of a steamroller,” some traders say, because of the risk of focusing on small price changes when bigger changes are underway.
Many day traders rely heavily on scalping, especially on slow market days. Because each trade carries a transaction cost, it can contribute to more costs than profits. Done right, though, it’s a nice way to make some steady profits.
Scalping, as defined here, is perfectly legal. However, the word is also used to describe some illegal activities, such as promoting a security in public and then selling it in private. If a big-name trader goes on his cable television show and talks about how great a stock is so that the price goes up and then sells it the next day when everyone else is buying, he has committed the crime of scalping.
Those Pesky Transaction Costs
Pure arbitrage works best in a world where trading is free. In reality, it costs good money to trade. Sometimes you might notice a price discrepancy that seems to last forever. You can’t work it because the profit wouldn’t cover your costs. And you know what? That may be true for everyone else out there.
In the real world, trading costs money. Consider all the costs of getting started: buying equipment, paying for Internet access, learning how to trade. Then there are the costs of doing business that vary with each transaction: commissions, fees, interest, the bid-ask spread, and taxes. You don’t make a profit on a trade unless it covers those costs.
Even if you work with a broker that charges little or no commission, and even if your broker charges no interest on day trading margin (loans against your securities account), you can bet that your broker is making money off you. That broker’s profit is showing up in the spread and the speed of execution, so there is a still a cost to arbitrage that must be covered, even on a seemingly free account. Trust me, brokerage firms are in business to make money, whether or not their customers do.
Add up those trading costs, and you can find yourself in a frustrating situation: You can see the opportunity right there staring you in the face, but you can’t take it. It either sits there, taunting you, or gets picked off by a trader who has lower costs than you do.
On the other hand, if you know what your costs are, you can avoid unprofitable opportunities. Don’t consider your fixed costs, like your office and your equipment. Those expenses don’t change with any given trade. (Yes, you have to cover them in the long run to stay in business, but you can ignore them in the short run.) Instead, figure out how much money you give to your broker on any given trade, on an order, per share, or per contract basis. Write that number down on a sticky note, and put it on your monitor so that you remember what you have to clear before you risk a trade. Just don’t get so fixated on covering your costs that you avoid exiting trades at the right time.
Risk Arbitrage and Its Tools
In its purest form, arbitrage is riskless because the purchase of an asset in one market and the sale of the asset in another happen simultaneously — you just let those profits flow right into your account. It is possible to do this, but not often. No day trader who pursues only riskless arbitrage stays in business long.
Return is a function of risk. The more risk you take, the greater the return you expect to make.
Because there are so few opportunities for true arbitrage, most day traders looking at arbitrage strategies actually practice risk arbitrage. Like true arbitrage, risk arbitrage attempts to generate profits from price discrepancies; but like the name says, risk arbitrage involves taking some risk. Yes, you buy one security and sell another in risk arbitrage, but it’s not always the same security and not always at the same time. For example, a day trader might buy the stock of an acquisition target and sell the stock of an acquirer in the hopes of making a profit as the deal nears the closing date.
Risk arbitrage usually involves strategies that unfold over time — possibly hours, but usually days or weeks. Pursuing these strategies puts you into the world of swing trading, which carries a little more risk than day trading.
In risk arbitrage, a trader is buying and selling similar securities. Much of the risk draws from the fact that the securities are not identical, so the law of one price isn’t absolute. Nevertheless, it forms the guiding principle, which is this: If you have two different ways to buy the same thing, then the prices of each purchase should be proportional. If they are not, then there’s an opportunity to make money. And what day trader doesn’t want to make money?
Arbitrageurs use a mix of different assets and techniques to create these different ways of buying the same thing. This section described some of their favorites.
Derivatives are options, futures, and related financial contracts that draw or derive their value from the value of something else, such as the price of a stock index or the current cost of corn. They offer a lower-cost, lower-obligation method of getting exposure to certain price changes. In the case of agricultural and energy commodities, derivatives are the only practical way for a day trader to own them. Because they are so closely tied to the value of the underlying security, derivatives form a useful “almost, but not quite” asset for traders looking for arbitrage situations. A trader may see a price discrepancy between the derivative and the underlying asset, thus noticing a profitable trading opportunity.
Using a derivative in tandem with its underlying security, traders can construct a range of risk arbitrage trades. For example, a trader looking to set up arbitrage on a merger could trade options on the stocks of the buying and selling companies rather than trading the stocks themselves. The more arbitrage opportunities there are, the greater the likelihood of making a low-risk profit.
Levering with leverage
It’s the process of borrowing money to trade in order to increase potential returns. The more money the trader borrows, the greater the return on capital that she can earn. Leverage is commonly used by day traders, because most trades with a one-day time horizon carry low returns unless they are magnified through borrowing.
That magic of magnification becomes especially important in arbitrage, because the price discrepancies between securities tend to be really small. The primary way to get a bigger return is to borrow money to do it.
However, leverage has a downside: Along with improving returns, it increases risk. Because even risk arbitrage strategies tend to have low risk, this may be acceptable. Just remember that you have to repay all borrowed money, no matter what happens to prices.
Short selling is another topic, and it creates another set of alternatives for setting up an arbitrage trade. Short selling allows a day trader to profit when a security’s price goes down. Instead of buying low and then selling, high, the trader sells high first and then buys back low. The short seller goes to her broker, borrows the security that she thinks will decline in price, sells it, and then buys it back in the market later so that she has the shares to repay the loan. (It all happens electronically, no office visits required!) Assuming she’s right and the price does indeed fall, she pockets the difference between the price where she sold the security and the price where she bought it back. Of course, that difference is her loss if the price goes up instead of down.
By adding short selling to the bag of tricks, an arbitrageur can find a lot more ways to profit from a price discrepancy in the market. New combinations of cheap and expensive assets — and more ways to trade them — give a day trader more opportunities to make trades during the day. The opposite of short is long. When a trader holds a security, he’s said to be long.
Feeling creative? Well, then, consider creating synthetic securities when looking for arbitrage opportunities. A synthetic security is a combination of assets that have the same profit-and loss-profile as another asset or group of assets. For example, a stock is a combination of a put option, which has value if the stock goes down in price, and a call option, which has value if the stock goes up in price. By thinking up ways to mimic the behavior of an asset through a synthetic security, a day trader can find more ways for an asset to be cheaper in one market than in another, leading to more potential arbitrage opportunities.
A typical arbitrage transaction involving a synthetic security involves shorting the real security and then buying a package of derivatives that match its risk and return.
Complex arbitrage trading strategies require more testing and simulation trading and may possibly involve losses while you fine-tune your methods. Be sure you feel comfortable with your trading method before you commit big time and big dollars to it.
An Array of Arbitrages
The tools of arbitrage — derivatives, leverage, short selling, synthetic securities — can be used in all sorts of ways to generate potentially profitable trades, and that’s what this section of the chapter covers. Most day traders who decide to do arbitrage will pick a few strategies to follow. After all, it’s hard enough to spot these opportunities; the trader who tries to do too much is the trader who will soon be looking for a new job. Armed with the information here, you can decide whether there’s an arbitrage strategy that matches your approach to the market so that you can make it your own.
The varieties of arbitrage transactions are listed here in alphabetical order. It’s not exhaustive; there are plenty of other ways to exploit price differences in the market, but some involve more time than a day trader is willing to commit. I’ve put them in alphabetical order. Some are more complex than others, some generate more opportunities than others, and some work best if you are willing to swing trade (hold for a few days) rather than day trade (close out all positions at the end of the day).
Many arbitrage strategies work best in combination with other strategies, such as news-driven trading. For example, it might take a news announcement to cause people to pay attention to a company’s stock so that there’s enough trading activity that day to close a price gap. If you know about the pricing problem ahead of time, you can swoop in and make the arbitrage that day.
There are certainly other types of arbitrage out there. Wherever people pay close attention to the markets and price changes, they find small price differences to turn into large, low-risk profits. If you think you’ve found an arbitrage strategy not listed here, by all means, go and test it and see if it will work for you.
Capital structure arbitrage
Companies issue securities in order to finance their business, and investment bankers are in the business of helping them do just that. Some companies are nice and simple. Microsoft, for example, uses only stock for financing and has only one class of stock. Others are far more complicated, using mixtures of different classes of stock and different issues of debt to finance the growth. General Electric, for example, has one class of common stock and seven different debt securities for its parent company and its finance subsidiary. Think that’s a lot? General Motors has ten different securities.
The way that a company is financed is its capital structure, and capital structure arbitrage looks for inappropriate price differences among all the different classes of stock and debt outstanding. Although all securities tied to the same business should trade in a similar fashion, they don’t always, and that creates opportunities.
Say, for example, that SuperTech Company has two classes of stock, one on its core business and one that tracks the performance of its nanotechnology subsidiary. (A tracking stock is a corporate finance gimmick that goes in and out of style; it’s stock on a subsidiary that is controlled by the parent company.) The parent company still has exposure to the nanotechnology subsidiary, but that is not reflected in its stock price. One day, the nanotechnology subsidiary announces great earnings, and the stock goes way up, but SuperTech stock doesn’t move even though it benefits. The capital structure arbitrageur immediately shorts the nanotech subsidiary tracking stock and buys the parent company stock (matching the size of the long and short positions so that they move up and down in tandem), waiting for people to realize that the discrepancy is there.
As part of designing their capital structure, some companies issue convertible bonds (sometimes called a convertible debenture) or convertible preferred stock. These securities are a cross between stocks and bonds. Like an ordinary bond, convertibles pay regular income to those who hold them (interest for convertible bonds and dividends for convertible preferred stock), but they also act a little like stock because the holders have the right to exchange the convertible security for ordinary common stock.
Here’s an example: a $1,000 convertible bond pays 7.5 percent interest and is convertible into 25 shares of stock. If the stock is less than $40 per share, the convertible holder will prefer to cash the interest or dividend checks. If the company’s stock trades above $40, the convertible holder would make more money giving up the income in order to get the stock cheap. Because of the benefit of conversion, the interest rate on a convertible security is usually below that on a regular corporate bond.
Because a convertible security carries a built-in option to buy the underlying stock, it generally trades in line with the stock. If the convertible’s price gets too high or too low, then an arbitrage opportunity presents itself.
Consider this case: A day trader notices that a convertible bond is selling at a lower price than it should be, given the current level of interest rates and the price of the company’s common stock. So, he buys the convertibles and sells the common stock short. When the stock’s price moves back into line, he collects a profit from both sides of the trade.
Fixed income and interest rate arbitrage
Fixed income securities are bonds, notes, and related securities that give their owners a regular interest payment. They are popular with conservative investors, especially retirees, who want to generate a regular income from the quarterly interest payments. They are considered to be safe, predictable, long-run investments, but they can fluctuate wildly in the short term, which makes them attractive to arbitrageurs.
Interest rates are the price of money, and so they affect the value of many kinds of securities. Fixed income securities have a great deal of interest-rate exposure, because they pay out interest. Some stocks have interest-rate exposure, too. Trading in foreign exchange is an attempt to profit from the changing price of one currency relative to another, and that’s usually a function of the difference in interest rates between the two countries. Derivatives have a regular expiration schedule, so they have some time value, and that’s
measured through interest rates.
With so many different assets affected by changes in interest rates, arbitrageurs pay attention. With fixed-income arbitrage, the trader breaks out the following:
- The time value of money
- The level of risk in the economy
- The likelihood of repayment
- The inflation-rate effects on different securities
If one of the numbers is out of whack, the trader constructs and executes an arbitrage trade to profit from it.
It’s rarely practical for a day trader to buy bonds outright. Instead, day traders looking at fixed income arbitrage and other interest-rate sensitive strategies usually rely on interest rate futures, offered by the Chicago Board of Trade.
How would this work? Think of a day trader monitoring interest rates on U.S. government securities. He notices that two-year treasury notes are trading at a higher yield than expected — especially relative to five-year treasury notes. He sells futures on the two-year treasury notes and then buys futures on the five-year treasury notes. When the difference between the two rates falls back where it should be, the futures trade will turn a profit.
Market observers talk a lot about the performance of the S&P 500 Index and the Dow Jones Industrial Average. These are market indexes, designed to represent the activity of the market, and are widely published for market observers to follow. The performance of the index is based on the performance of a group of securities, ranging from the 3,000 largest companies in the market (the Russell 3,000) to a mere 30 large companies (the Dow Jones Industrial Average).
Sure, an arbitrageur could buy all the stocks, and there are hedge funds that do just that. But very few people can do that. Instead, they get exposure to index performance through the many different securities based on the indexes. Buy-and-hold mutual fund investors can buy funds that hold all the same stocks in the same proportion as the index. Those with shorter-term profits in mind can buy exchange-traded funds, which are baskets of stocks listed on organized exchanges, or they can trade futures and options on the indexes.
Arbitrageurs love the idea of an asset — like an index — that has lots of different securities based on its value. That creates lots of opportunities for mispricing. Unless the index, the futures, the options, and the exchange-traded funds are all in line, some canny day trader can step in and make some money.
For example, suppose the S&P 500 futures contract is looking mighty cheap relative to the price of the S&P 500 Index. A trader can short an exchange traded fund on the index and then buy futures contracts to profit from the difference.
Every day, companies get bought and sold, and that creates arbitrage opportunities. In fact, one of the better-known arbitrage strategies out there is merger arbitrage, in which traders try to profit from the change in stock prices after a merger has been announced. It starts by looking at the following details in the merger announcement:
- The name of the acquiring company
- The name of the company being taken over (and no matter what PR people say, there are no mergers of equals)
- The price of the transaction
- The currency (cash, stock, debt)
- The date the merger is expected to close
Until the date that the merger actually closes, which may be different from the date in the merger announcement, any and every one of the announced details can change. The acquiring company may learn new information about the target company and change its mind. A third company might jump in and make an offer for more money. The shareholders may agree to support the deal only if they get cash instead of stock. All that drama creates opportunity, both for traders looking for one-day opportunities and for those willing to hold a position until the merger closing date.
Here’s an example. Let’s say that Major Bancorp offers to buy Downtown Bank for $50 per share in cash. Major Bancorp’s shares will probably fall in price, because its shareholders will be concerned that the merger will be a lot of trouble. Downtown Bank’s shares will go up in price, but not all the way to $50, because its shareholders know that there is some risk that the deal won’t go through. An arbitrageur would short Major Bancorp and buy Downtown Bank to profit from the concerns. If Overseas Banque decides to step in, then it might be a profitable idea to buy Major Bancorp and short Overseas Banque. (If another bidder steps in and places a higher offer for Downtown Bank, then the whole arbitrage unravels — hence, the risk.)
Options form the basis of many arbitrage strategies, especially for those day traders who work the stock market. First, many different types of options are available, even on the same security. The two main categories are puts, which bet on the underlying security price falling, and calls, which bet on the underlying security price rising. Puts and calls on the same security come in many different strike prices, depending on where you want to bet the price goes. Some options, known as American options, can be cashed in at any time between the date of issue and the expiration date, and you can exercise others, known as European options, only at the expiration date. With all those choices, there are bound to be a few price discrepancies for the alert arbitrageur.
Maybe a day trader notices that on a day when a company has a big announcement, the options exchanges seem to be assuming a slightly higher price for the stock than where the stock is actually trading. He decides to buy the underlying stock as well as a put; he also sells a call with the same strike price and expiration date as the put. This creates a synthetic security that has the same payoff as shorting the security, meaning that the trader has pulled off a riskless arbitrage transaction. He effectively bought the security cheap in the stock market and sold it at a higher price in the options market.
Pairs trading, which involves buying a cheap stock and shorting an expensive stock in the same industry group, is popular with many people who day trade stocks. (It’s also the core of traditional hedge-fund investing, although there are very few hedge funds that rely on it nowadays.)
A pairs trader watches an industry group and looks for situations where one company seems to be doing especially well or one is doing especially poorly. That would most likely indicate a problem in the way people are pricing the industry, because in general, what’s good for one company is good for all ofthem. A pairs trader would pay particular attention to news events that seem to affect all but one or two companies in the same industry. If one of them appears to be overvalued relative to the others, the pairs trader shorts the pricey stock and buys the cheapest one.
The pairs trader isn’t dealing with identical assets, of course, so the simultaneous purchase and sale is a lot riskier than it would be in true arbitrage. Sometimes, there’s a very good reason why one stock is more expensive and one is much cheaper than the rest of the industry. Good pairs traders are willing to do a little fundamental research so that they can avoid being short the winner and being long the loser in an industry undergoing big changes.
For Propeller-Heads Only: Statistical Arbitrage
Do you love crunching numbers? Are you comfortable with programming? Are you an actuary looking for a career change? If the answers to these questions are yes, then statistical arbitrage might be right for you. It involves the use of complex mathematical models to determine where a security should be priced. It’s based on the notion that securities prices move randomly along a normal curve. If all results are distributed normally, then reversion to the mean holds. That means that a security’s price will equal the average — the mean — price in the long run. If there are huge swings up, they have to be matched by huge swings down eventually, so that the mean does not change.
Here’s an example. A standard die has six sides. When you roll it, you are equally likely to get any one of those six results. The mean of the six sides is 3.5, or (1 + 2 + 3+ 4 + 5 + 6) / 6. If you roll the die 100 times, the average of all of those results should be close to the 3.5 mean. If your mean is actually 2.1, then chances are good that your next several rolls will have an average higher than 3.5 so that the total results will begin to close in on that 3.5 mean. If not, you haven’t figured out a fabulous new secret to rolling a die; it’s more likely that your die is loaded.
In statistical arbitrage, the trader works with huge databases of securities prices to determine where the average should be, especially relative to market conditions such as interest rate levels. If the current price is too high, it’s time to short it; if the price is too low, it’s time to buy.
Here’s an example of how it works: A day trader has data showing that for the past 20 years, food-processing companies have moved in a fixed percentage relative to unemployment rates. She notices that in the past month, the relationship has diverged, with the stock prices having decreased more than expected relative to the current economy. So, she buys the stocks expecting them to go up in price under the assumption that the normal relationship holds.
You might be a great statistician, but chances are good that big hedge funds and fancy brand-name brokerage firms have hired statisticians who are even better than you. (And even then, there is no guarantee of success — hedge fund Long-Term Capital Management failed in 1998 and nearly took the world’s financial markets down with it despite having two Nobel Prize winners on staff.) Just remember that statistical arbitrage brings you smack against the biggest of the Big Kahunas on Wall Street.