Arbitrage helps keep financial markets efficient, often with the aid of complex algorithms, pricing models, and lots of capital. Here’s a look at three types—index arbitrage, volatility arbitrage, and bond arbitrage.
Index arbitrage attempts to close up price inefficiencies across stocks, stock indices, ETFs, index futures, and other products
Volatility arbitrage uses theoretical pricing models to help determine the relationships between options strikes and expiration dates
Bond arbitrage (also called interest rate or fixed income) compares yields on similar bonds but must consider the different risks inherent in each bond issue
Arbitrage. It’s the rapid-fire buying and selling of the same (or similar) things across venues and markets in order to capture tiny price inefficiencies. Arbitrage can be a lucrative business for market makers, but it also helps keep markets in line and bid/ask spreads—especially for retail investors—tight and liquid.
Arbitrage is part of what 18th-century economist Adam Smith called the invisible hand—that is, the competitive forces of having many participants, each with different views of value and need. Their collective actions create an equilibrium in a free market.
With arbitrage, this hand isn’t really invisible; it’s hiding in plain sight—in the bid/ask spreads and transactional data you might see on the thinkorswim® platform from TD Ameritrade. Perhaps we should call it the camouflaged hand.
There are several types of arbitrage at work in modern markets. There’s pure arbitrage, where a price discrepancy in the exact same instrument is bought in one venue and sold in another until the discrepancy closes up. There’s relative value arbitrage, where the prices of two or more related securities fall out of line and are bought and sold until the relationship reforms. With relative value arbitrage, the price relationships are determined with the help of mathematical models and software.
Note: these explanations are meant to be high-level overviews. They’re simplified and nonexhaustive to help you understand the concepts. It takes experience, breadth, and lots of capital to be a true arbitrageur.
The S&P 500 Index (SPX), Nasdaq-100 (NDX), and other stock indices are made up of baskets of stocks, each weighted to a preset and published ratio. When the components and/or weightings in an index change—and they do change occasionally—these changes are made public as well.
Because the makeup of each index is no secret, anyone with enough resources could put together a basket of stocks that precisely mirrors the index. That’s the key to index arbitrage.
Each stock in an index—roughly 500 in the SPX, for example—is in constant motion as economic data, company announcements, and other news items change the equilibrium (there’s that camouflaged hand again) of each component. Meanwhile, other securities that derive their prices from an index—exchange-traded funds (ETFs), equity options, options on ETFs, index futures and options, and single-stock futures, to name a few—are also in constant motion, and most have tight bid/ask spreads throughout the trading day (and many securities are available in the off-hours as well).
Index arbitrage involves trading these products against each other which helps keep them all in line.
To explore volatility arbitrage, pull up an option chain like the one in figure 1. Notice how the bid/ask spreads fit a pattern—for example, the further out of the money a call is, the lower its value. And if you look to the deferred expiration date, the call with the same strike has more value. These relationships are kept in check by market makers and other participants, often with the aid of a theoretical options pricing calculator such as the Black-Scholes or Bjerksund-Stensland model.
One important input to these pricing models is implied volatility. When implied volatility levels of different strikes or expiration dates are out of line, arbitrageurs may trade them against one another in an attempt to capture price discrepancies. (Did those terms fly over your head? TD Ameritrade clients can access webcasts, videos, tutorials, and an immersive education curriculum—all for free.)
So suppose a big fund decides to buy 10,000 of the 225-strike calls. In and of itself, this trade would be hard to absorb without impacting the price of the option. But market makers running volatility arbitrage programs can spread their risk from this trade across other strikes, related products, and shares of the underlying stock to hedge the risks. These and other hedge trades can help cushion the blow of any one large order and keep prices in line.
And remember: any indices with the component stock will be affected by a large order. So any price inefficiencies caused by a big order will be closed up by index arbitrageurs.
Granted, this is a bit of an oversimplification of volatility arbitrage. Options pricing models assume a level of volatility, and the constant ebb and flow of market information can and does change the level of volatility implied by market prices. Plus, as options approach expiration, the theoretical assumptions implied by a model are replaced by certainty—at expiration an option is either out of the money and expires worthless or it’s in the money and exercised. So these relationships change over the life of an option.
But experienced traders running large volatility arbitrage programs don’t expect to win on every trade. They look for theoretical mathematical advantages. Over time and across markets, they trust that the theoretical advantages will turn into actual profits more often than not.
Suppose a company issued a $1,000 bond last year that matures in five years and pays an annual coupon of 4%. But then interest rates rise, and a few months later, the company issues another bond that pays 4.5%. What happens to that first bond’s price?
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Yep—it loses value. So if you were to buy it today, you could get it for less than $1,000—maybe $950. You’d get the 4% coupon each year (which is less than the 4.5% you could get with the new bond), but at maturity, you’ll get the face value of the bond—$1,000—which is $50 more than you paid for it. That extra $50 is meant to compensate the buyer for accepting a coupon that’s lower than the current prevailing price.
Millions of bonds and other fixed-income securities are bought and sold every day in the secondary market (meaning “after the initial issuance”). That includes Treasury securities and corporate bonds of varying maturities. And once again, it’s the arbitrageurs who help keep the yields in line.
But again there are complexities. Because each bond has its own risk profile based in part on the likelihood that the issuer will meet its obligations—coupon payment and repayment of principal—comparing two bonds is never truly apples-to-apples. But it can be close. Bonds are tracked by agencies such as Fitch Ratings, Moody’s, and S&P Global Ratings, which assign ratings based on default and other risks. (Here’s a refresher on bond pricing, ratings, and risk.)
Still, in general, when you buy a bond in the secondary market, its yield is being held in line (adjusted for risks) by bond arbitrage.
A few years ago, it was suggested that arbitrage—and specifically the high-frequency algorithms employed by today’s market-making operations—takes advantage of investors and engages in uncompetitive behavior, as evidenced by the fact that the big, well-funded market maker groups tend to make money day in and day out.
But is that a fair assessment? Or are they simply performing a service—like your dentist or your neighborhood grocery store—and their slim profit margins are a form of compensation for providing liquid and orderly markets?
For the retail crowd, it’s this ultra-fast (and ultra-competitive) arbitrage that has helped stock, bond, and options markets be deep, liquid, and competitive—arguably more so than ever.
It’s the same invisible (or camouflaged) hand at work. It’s just moving a lot faster these days.
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