# Statistical Arbitrage: Definition, How It Works, and Example

## What Is Statistical Arbitrage?

In the world of finance, statistical arbitrage (or stat arb) refers to a group of trading strategies that utilize mean reversion analyses to invest in diverse portfolios of up to thousands of securities for a very short period of time, often only a few seconds but up to multiple days.

Known as a deeply quantitative, analytical approach to trading, stat arb aims to reduce exposure to beta as much as possible across two phases: "scoring" provides a ranking to each available stock according to investment desirability, and "risk reduction" combines desirable stocks into a specifically-designed portfolio aiming to lower risk. Investors typically identify arbitrage situations through mathematical modeling techniques.

### Key Takeaways

• Statistical arbitrage is a group of trading strategies employing large, diverse portfolios that are traded on a very short-term basis.
• This type of trading strategy assigns stocks a desirability ranking and then constructs a portfolio to reduce risk as much as possible.
• Statistical arbitrage is heavily reliant on computer models and analysis and is known as one of the most rigorous approaches to investing.

## Understanding Statistical Arbitrage

Statistical arbitrage strategies are market neutral because they involve opening both a long position and short position simultaneously to take advantage of inefficient pricing in correlated securities. For example, if a fund manager believes Coca-Cola is undervalued and Pepsi is overvalued, they would open a long position in Coca-Cola, and at the same time, open a short position in Pepsi. Investors often refer to statistical arbitrage as “pairs trading.”

Statistical arbitrage is not strictly limited to two securities. Investors can apply the concept to a group of correlated securities. Also, just because two stocks operate in different industries does not mean they cannot be correlated. For example, Citigroup, a banking stock, and Harley Davidson, a consumer cyclical stock, often have periods of high correlation.

## Risks of Statistical Arbitrage

Statistical arbitrage is not without risk. It depends heavily on the ability of market prices to return to a historical or predicted normal, commonly referred to as mean reversion. However, two stocks that operate in the same industry can remain uncorrelated for a significant amount of time due to both micro and macro factors.

For this reason, most statistical arbitrage strategies take advantage of high-frequency trading (HFT) algorithms to exploit tiny inefficiencies that often last for a matter of milliseconds. Large positions in both stocks are needed to generate sufficient profits from such minuscule price movements. This adds additional risk to statistical arbitrage strategies, although options can be used to help mitigate some of the risk.

## Simplifying Statistical Arbitrage Strategies

Trying to understand the math behind a statistical arbitrage strategy can be overwhelming. Fortunately, there is a more straightforward way to get started utilizing the basic concept. Investors can find two securities that are traditionally correlated, such as General Motors (GM) and Ford Motor Company (F), and then compare the two stocks by overlaying them on a price chart.

The chart below compares these two automakers. Investors can enter a trade when the two stocks get substantially out of sync with each other, such as in mid-February and in early May. For instance, traders would consider buying Ford in February and selling it in May in anticipation of its share price realigning with General Motor’s share price. However, there is no guarantee of when the two prices will re-converge; therefore, investors should always consider using stop-loss orders when employing this strategy.

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