# Arbitrage Strategies: Understanding Working of Statistical Arbitrage

Quantitative trading is used to identify opportunities for trading by using statistical techniques and quantitative analysis of the historical data. Quantitative trading is applicable to information which is quantifiable like macroeconomic events and price data of securities.Quantitative Trading models are used by Algo traders when trading of securities is based strictly on buy/sell decision of computer algorithms. An example of such a strategy which exploits quantitative techniques and is applied at Algorithmic trading desks is the statistical arbitrage strategy.

### Statistical Arbitrage

Statistical Arbitrage or Stat Arb has a history of being a hugely profitable algorithmic trading strategy for many big investment banks and hedge funds. Statistical arbitrage originated around 1980’s, led by Morgan Stanley and other banks, the strategy witnessed wide application in financial markets. The popularity of the strategy continued for more than two decades and different models were created around it to capture big profits.

To define it in simple terms, Statistical arbitrage comprises a set of quantitatively driven algorithmic trading strategies. These strategies look to exploit the relative price movements across thousands of financial instruments by analyzing the price patterns and the price differences between financial instruments. The end objective of such strategies is to generate alpha (higher than normal profits) for the trading firms. A point to note here is that Statistical arbitrage is not a high-frequency trading (HFT) strategy. It can be categorized as a medium-frequency strategy where the trading period occurs over the course of a few hours to a few days.

### Concepts used by Statistical Arbitrage Strategies

To analyze the price patterns and price differences, the strategies make use of statistical and mathematical models. Statistical arbitrage strategies can also be designed using factors such as lead/lag effects, corporate activity, short-term momentum etc. other than using the price data alone. This latter approach is referred to as a multi-factor Statistical Arbitrage model. The various concepts used by statistical arbitrage strategies include:

• Time Series Analysis
• AutoRegression and Co-integration
• Volatility modeling
• Principal Components Analysis
• Pattern finding techniques
• Machine learning techniques
• Efficient frontier analysis etc.

### Types of Statistical Arbitrage Strategies

The different Statistical arbitrage strategies include:

• Market Neutral Arbitrage
• Cross Asset Arbitrage
• Cross Market Arbitrage
• ETF Arbitrage

#### Market Neutral Arbitrage

It involves taking a long position in an undervalued asset and shorting an overvalued asset simultaneously. The asset is assumed to have similar volatilities and thus, an increase in the market will cause the long position to appreciate in value and the short position to depreciate by a roughly the same amount. The positions are squared off when the assets return to their normalized value.

#### Cross Market Arbitrage

It seeks to exploit the price discrepancy of the same asset across markets. The strategy buys the asset in the lower-valuing market and sells it in the more highly valuing market.

#### Cross Asset Arbitrage

This model bets on the price discrepancy between a financial asset and it’s underlying. For example, between a stock index future and the stocks that form the index.

#### ETF arbitrage

ETF arbitrage can be termed as a form of cross-asset arbitrage which identifies discrepancies between the value of an ETF and its underlying assets.

StatArb is an evolved version of pair trading strategies, in which stocks are put into pairs by fundamental or market-based similarities. When one stock in a pair outperforms the other, the poorer performing stock is bought along with the expectation that it climbs its outperforming partner. The position is hedged from market changes/movements by shorting the other outperforming stock.  Because of a large number of stocks involved in the statistical arbitrage strategy, the high portfolio turnover and the fairly small size of the spread one is trying to capture, the strategy is often implemented in an automated fashion and great attention is placed on reducing trading costs. Statistical arbitrage strategy has become a major force at both hedge funds and investment banks.

Figure 1: Implementation steps of a statistical arbitrage strategy

### How Statistical Arbitrage Strategy Works?

Securities such as stocks tend to trade in upward and downward cycles and a quantitative method seeks to capitalize on those trends. Trending behavior of quantitative trading uses software programs to track patterns or trends. Trends uncovered are based on the volume, frequency and the price of a security at which it is traded.

Figure 2: Statistical Arbitrage between two stocks under “Cement” Industry: ACC and Ambuja both listed at National Stock Exchange of India.

In the image above, the stock prices of ACC and Ambuja are represented over a period of six years. You can see both the stocks stay quite close to each other during the entire time span, with only a few certain instances of separation. It is in those separation periods that an arbitrage opportunity arises based on an assumption that the stock prices with move closer again.

The crux in identifying such opportunities lies in two main factors:

• Identifying the pairs which require advanced time series analysis and statistical tests
• Specifying the entry-exit points for the strategy to leverage the market position

There are plenty of in-built pair trading indicators on popular platforms to identify and trade in pairs. However, many a time, transaction cost which is a crucial factor in earning profits from a strategy, is usually not taken into account in calculating the projected returns. Therefore, it is recommended that traders make their own statistical arbitrage strategies keeping into account all the factors at the time of backtesting which will affect the final profitability of the trade.

### Risks in Statistical Arbitrage

Although Statistical arbitrage strategies have earned lots of profits for Quantitative trading firms, these strategies come with their own set of risks. Following are a couple of risks faced:

• The strategy heavily depends on the mean reversion of prices to their historical or predicted normal. This may not happen in certain cases and the prices can continue to drift away from the historical normal.
• Financial markets are in a constant flux and evolve based on events occurring across the globe. Hence, profit from statistical arbitrage models cannot be guaranteed all the time.

### Projects on Statistical Arbitrage by EPAT™ Alumni

Statistical Arbitrage strategies can be applied to different financial instruments and markets. The Executive Programme in Algorithmic Trading (EPAT™) includes a session on “Statistical Arbitrage and Pairs Trading” as part of the “Strategies” module. Many of our EPAT™ participants have successfully built pairs trading strategies during their course work. Listed below are some of the project blogs for your reference.

### Next Step

Access this project which is based on ‘Pair Trading – Statistical Arbitrage On Cash Stocks‘ and is coded in Python by Jonathan Narváez as part of the EPAT coursework at QuantInsti and also contains downloadable files.

Disclaimer: All investments and trading in the stock market involve risk. Any decisions to place trades in the financial markets, including trading in stock or options or other financial instruments is a personal decision that should only be made after thorough research, including a personal risk and financial assessment and the engagement of professional assistance to the extent you believe necessary. The trading strategies or related information mentioned in this article is for informational purposes only.