Trading The Odds With Arbitrage (2024)

"I don't throw darts at a board. I bet on sure things. Read Sun Tzu, The Art of War. Every battle is won before it is ever fought." Many of you might recognize these words spoken by Gordon Gekko in the movie Wall Street. In the movie, Gekko makes a fortune as a pioneer of arbitrage. Unfortunately, such risk-free trading is not available to everyone.

However, there are several other forms of arbitrage that can be used to enhance the odds of executing a successful trade. Here we look at the concept of arbitrage, how market makers utilize "true arbitrage," and finally, how retail investors can take advantage of arbitrage opportunities.

Concepts of Arbitrage

Arbitrage, in its purest form, is defined as the purchase of securities on one market for immediate resale on another market in order to profit from a price discrepancy. This results in immediate risk-free profit.

For example, if a security's price on the New York Stock Exchange (NYSE) is trading out of sync with its corresponding futures contract on Chicago's exchange, a trader could simultaneously sell (short) the more expensive of the two and buy the other, thus profiting on the difference. This type of arbitrage requires the violation of at least one of these three conditions:

1. The same security must trade at the same price on all markets.
2. Two securities with identical cash flows must trade at the same price.
3. A security with a known price in the future (via a futures contract) must trade today at that price discounted by the risk-free rate.

Arbitrage, however, can take other forms. Risk arbitrage (or statistical arbitrage) is the second form of arbitrage that we will discuss. Unlike pure arbitrage, risk arbitrage entails—you guessed it—risk. Although considered "speculation," risk arbitrage has become one of the most popular (and retail-trader friendly) forms of arbitrage.

Example of Risk Arbitrage

Here's how it works: Let's say Company A is currently trading at $10/share. Company B, which wants to acquire Company A, decides to place a takeover bid on Company A for $15/share. This means that all of Company A's shares are now worth $15/share, but are trading at only $10/share.

Let's say the early trades (typically not retail trades) bid it up to $14/share. Now, there is still a $1/share difference—an opportunity for risk arbitrage. So where's the risk? The acquisition could fall through, in which case the shares would be worth only the original $10/share. Further below we will take a look at how you can gauge risk.

Market Makers and True Arbitrage

Market makers have several advantages over retail traders:

• Far more trading capital
• Generally more skill
• Access to up-to-the-second news
• Faster computers
• More complex software
• Access to the dealing desk

Combined, these factors make it nearly impossible for a retail trader to take advantage of pure arbitrage opportunities. Market makers use complex software that is run on top-of-the-line computers to locate such opportunities constantly. Once found, the differential is typically negligible, and requires a vast amount of capital in order to profit—retail traders would likely get burned by commission costs.

Needless to say, it is almost impossible for retail traders to compete in the risk-free genre of arbitrage.

Retail Traders and Risk Arbitrage

Despite the disadvantages of pure arbitrage, risk arbitrage is still accessible to most retail traders. Although this type of arbitrage requires taking on some risk, it is generally considered "playing the odds." Here we will examine some of the most common forms of arbitrage available to retail traders.

Takeover and Merger Arbitrage

The example of risk arbitrage we saw above demonstrates takeover and merger arbitrage, and it is probably the most common type of arbitrage. It typically involves locating an undervalued company that has been targeted by another company for a takeover bid. This bid would bring the company to its true, or intrinsic, value. If the merger goes through successfully, all those who took advantage of the opportunity will profit handsomely; however, if the merger falls through, the price may drop.

The key to success in this type of arbitrage is speed. Traders who utilize this method usually trade on Level II and have access to streaming market news. The second something is announced, they try to get in on the action before anyone else.

Risk Evaluation

Let's say you aren't among the first in, however. How do you know if it is still a good deal? Well, one way is to use Benjamin Graham's risk-arbitrage formula to determine optimal risk/reward. His equations state the following:

$\begin{aligned} &\text{Annual Return}=\frac{CG-L(100\%-C)}{YP}\\ &\textbf{where:}\\ &C=\text{The expected chance of success (\%)}\\ &P=\text{The current price of the security}\\ &L=\text{The expected loss in the event of a}\\ &\text{failure (usually original price)}\\ &Y=\text{The expected holding time in years}\\ &\text{(usually the time until the merger takes place)}\\ &G=\text{The expected gain in the event of a}\\ &\text{success (usually takeover price)} \end{aligned}$​AnnualReturn=YPCG−L(100%−C)​where:C=Theexpectedchanceofsuccess(%)P=ThecurrentpriceofthesecurityL=Theexpectedlossintheeventofafailure(usuallyoriginalprice)Y=Theexpectedholdingtimeinyears(usuallythetimeuntilthemergertakesplace)G=Theexpectedgainintheeventofasuccess(usuallytakeoverprice)​

Granted, this is highly empirical, but it will give you an idea of what to expect before you get into a merger arbitrage situation.

Liquidation Arbitrage

This is the type of arbitrage Gordon Gekko employed when he bought and sold off companies. Liquidation arbitrage involves estimating the value of the company's liquidation assets. For example, say Company A has a book (liquidation) value of $10/share and is currently trading at $7/share. If the company decides to liquidate, it presents an opportunity for arbitrage. In Gekko's case, he took over companies that he felt would provide a profit if he broke them apart and sold them—a practice employed in reality by larger institutions.

A version of Benjamin Graham's risk arbitrage formula used for takeover and merger arbitrage can be employed here. Simply replace the takeover price with the liquidation price, and holding time with the amount of time before liquidation.

Pairs Trading

Pairs trading (also known as relative-value arbitrage) is far less common than the two forms discussed above. This form of arbitrage relies on a strong correlation between two related or unrelated securities.

Here's how it works. First, you must find "pairs." Typically, high-probability pairs are big stocks in the same industry with similar long-term trading histories. Look for a high percent correlation. Then, you wait for a divergence in the pairs of between 5% to 7% that lasts for an extended period of time (two to three days). Finally, you can go long and/or short on the two securities based on the comparison of their pricing. Then, just wait until the prices come back together.

One example of securities that would be used in a pairs trade is GM and Ford. These two companies tend to have a high correlation. You can simply plot these two securities and wait for a significant divergence; then chances are these two prices will eventually return to a higher correlation, offering an opportunity in which profit can be attained.

How to Find Opportunity

Many of you may be wondering where you can find these accessible arbitrage opportunities. The fact is much of the information can be attained with tools that are available to everyone. Brokers typically provide newswire services that allow you to view news the second it comes out. Level II trading is also an option for individual traders and can give you an edge. Finally, screening software can help you locate undervalued securities (that have appropriate price/book ratio, PEG ratio, etc.).

There are also several paid services that locate these arbitrage opportunities for you. Such services are especially useful for pairs trading, which can involve more effort to find correlations between securities. Usually, these services will provide you with a daily or weekly spreadsheet outlining opportunities that you can utilize to profit.

The Bottom Line

Arbitrage is a very broad form of trading that encompasses many strategies; however, they all seek to take advantage of increased chances of success. Although the risk-free forms of pure arbitrage are typically unavailable to retail traders, there are several high-probability forms of risk arbitrage that offer retail traders opportunities to profit.