Statistical Arbitrage or StatArb is an arbitrage strategy in which an investor benefit when statistical mispricing occurs between a set of securities, futures or derivatives on two different exchanges at different prices.

The first step is to identify the two securities, derivatives or futures that are not following a constant pattern with the assumption that prices of instruments will always move in a definite pattern in the near future.

The next step is to long the undervalued security and short the overvalued one. Suppose there are two stocks A and B- say A underperforming B – arbitrageurs will buy or long A and sell or short B.

The arbitrage strategy expects that eventually the two stocks will return to the constant pattern. The understanding of advance software programming and stock market is important to capitalize on gains and to generates potential pairs stocks.

The arbitrageurs should compare price, size, price-earnings ratio (P/E ratio), price-book ratio (P/B ratio), total sales, debt levels, and dividends for a set of stocks.

The arbitrageurs should consider stocks in each pair from same sector and invest an equal amount of money in each stock. If you create a portfolio with 50-60 pairs, than 20% of the pairs should represent same sector. Suppose you have a portfolio with 50-60 pairs, at least 10-12 pairs should represent same sector and no more than 20% of money should be allocated to each sector. The diversification across pairs can help reduce the risk for your overall portfolio.

**Types of Statistical Arbitrage**

**1. Volatility Arbitrage: **Volatility Arbitrage (or vol arb) is a type of statistical arbitrage that is implemented through a delta neutral portfolio of an option and its underlier. The aim is take advantage of differences between the option’s implied volatility, and a forecast of the underlier’s future realized volatility.

According to Wikipedia: “The traders attempt to buy volatility when it is low and sell volatility when it is high. If a trader buys options as part of a delta-neutral portfolio, he is said to be *long volatility*. If he sells options, he is said to be *short volatility*. As the trading is done delta-neutral portfolio, buying an option suggest that the underlier’s future realized volatility will be high, while selling an option suggest that future realized volatility will be low.

Assume a call option is trading at $1.90 with the underlier’s price at $45.50 and is yielding an implied volatility of 17.5%. A short time later, the same option might trade at $2.50 with the underlier’s price at $46.36 and be yielding an implied volatility of 16.5%. Even though the option’s price is higher at the second measurement, the option is still considered cheaper because the implied volatility is lower. This is because the trader can sell stock needed to hedge the long call at a higher price.”

**2. Liquidation Arbitrage:** Liquidation arbitrage is a strategy to exploit the difference between a company’s current value and its estimated liquidation value.

**3. Risk Arbitrage or Merger Arbitrage: **An arbitrage strategy in which arbitrageur exploit the discrepancy between the market prices of the stocks of two firms being merged. It usually involves buying the stock of the acquiree firm and simultaneously selling the stock of the acquirer firm. When the merger occurs, the stock of the acquirer firm decreases slightly, and the stock of the acquiree firm increases significantly.

Suppose company A is trading at $40 a share. Then company X announces that they plan to buy it, in which case holders of stock get $80. Then the stock jumps to $70. It does not go to $80 since there is some chance the deal will not go through. Here the odds are 25% that it does not (assuming the stock is worth $40 in that case). The *convergence trade* is that the deal will go through and the stock really is worth $80. Here the person playing gains $10 if he is right, but loses $30 if he is wrong.

There are two types of merger, a cash merger and a stock merger.

**1. Cash merger: **In a cash merger, an acquirer proposes to purchase the shares of the target for a certain price in cash. Until the acquisition is completed, the stock of the target typically trades below the purchase price. An arbitrageur buys the stock of the target and makes a gain if the acquirer ultimately buys the stock.

**2. Stock Merger**: In a stock merger, the acquirer proposes to buy the target by exchanging its own stock for the stock of the target. An arbitrageur may then short sell the acquirer and buy the stock of the target. This process is called “setting a spread.” After the merger is completed, the target’s stock will be converted into stock of the acquirer based on the exchange ratio determined by the merger agreement. The arbitrageur delivers the converted stock into his short position to complete the arbitrage.