# How to Calculate the Volatility of Pair Trades

by Ben Taylor

Pair trading is a stock picking strategy that attempts to neutralize market risk. When picking stock pairs to trade, an investor chooses two stocks from the same market sector, such as smart phones or software development. The investor then takes a long position in one -- anticipating the price will rise -- and a short position in the other -- assuming it will fall -- thereby creating a hedge against systemic risk. By calculating the standard deviation of a ratio of the stocks' price per share (PPS) an investor can quantify and study the volatility related to a pair of stocks. Volatility, then, can help the investor determine when to open and close a position on a pair of stocks.

1. Pick a pair of stocks that tend to move in the same direction in the market. Calculate each stock's price per share (PPS) for a few consecutive days and record those values in a computer spreadsheet. Divide one stock's PPS by the other stock's PPS; according to Luminous Logic, if the two stocks' movement in the market is highly correlated, the quotient will be similar on most days.

2. Compute a pair ratio for the two stocks, then establish a statistical mean. For several trading days, divide the closing price of the first stock by the closing price of the second stock. Establish the statistical mean by adding the pair ratio for each day, then dividing that sum by the number of days in the data set.

3. Determine each pair ratio's difference from the statistical mean, then square each result. If one stock is valued at \$10 and the other at \$15, their pair ratio is 15/10 or 1.5. If the statistical mean is 4, calculate the square of 2.5; perform this calculation for each pair ratio.

4. Calculate standard deviation by averaging the squares of each pair ratio in the data set, then taking the square root of the average. Unless the data set you used comprises the entire population of data for each stock, consider calculating the sample standard deviation. To compute sample standard deviation, list the denominator (n - 1) for the population of pair ratios you have computed, where "n" is the total number of ratios in your data set.

5. Measure volatility by noting how far a stock's performance deviates from its mean on a given day. Stocks with higher volatility tend to have a higher standard deviation, according to the Money Chimp website. Use the pair's volatility to decide when to open a pair trading position; as the pair works back toward its statistics mean, close the position.

#### Tips

• Use a computer spreadsheet to organize your data and make calculations. You can use data entered into a computer spreadsheet to generate charts and graphs to visually represent the performance of your pair of stocks.
• You must use a margin trading account in order to take a short position on a stock.

#### Warning

• Short selling -- or taking a short position in -- a stock involves several unique risks. For example, since you must borrow stock in order to short sell it, you are exposed to the risk that your lender will recall the stock before you are ready to close your position.

### Items you will need

• Performance research