Pair Trading and Convergenge Arbitrage Essay Example

is a market neutral long/short strategy.This implies that we will try to find shares with similar betas, where we believe one stock will outperform the other one in the short term. By simultaneously taking both a long and short position the beta of the pair equals zero and the performance generated equals alpha.

Pair of stock prices that have historically moved together in a correlated manner, diverge when subjected to differential demand shocks. position on such a pair when its components diverge and unwinding the position when they next converge has existed since the early periods of stock trading.The starting point of this strategy is that stocks that have historically had the same trading patterns (i. e. constant price ratio) will have so in the future as well.

If there is a deviation from the historical mean, this creates a trading opportunity, which can be exploited. Gains are earned when the price relationship is restored Pair trading is a non-directional, relative value investment strategy that seeks to identify two companies with similar characteristics whose equity securities are currently trading at a price relationship that is out of their historical trading range.This investment strategy entails buying the undervalued security, while short selling the overvalued security, thereby maintaining market neutrality.

KEY CHARACTERISTICS

This definition lays out three main areas of focus that play out as subtexts to the overall idea of pairs trading and must be considered and understood before the unified strategy will make sense: Market neutrality, relative value or statistical arbitrage and technical analysis.Market neutrality is the first of the three major features of pairs trading selected for investigation.

The term “market-neutral” has come to be a quite

appealing label in the last several years and can refer to a wide variety of strategies. Many investors mistake the term to mean “risk free”. This misconception has been narrowly focused on in the marketing of these types of products, and, often, the label is applied to anything that could be considered, even loosely, something that reduces market exposure or systematic risk.A market-neutral strategy derives its returns from the relationship between the performance of its long positions and its short positions, regardless of whether this relationship is done on the security or portfolio level. The pairs system is essentially an arbitrage system that allows the trader to capture profits from the divergence of two correlated stocks.

Pairs trading contain elements of both relative value and statistical arbitrage in that it often uses a statistical model as the initial screen for creating a relative value trade.A careful pairs trader will perform several layers of analysis on top of the model output before any pairs are actually executed While it is certainly possible to create fundamentally driven pairs trades, the methodology suggested uses technical to perform the majority of the analysis required before trading; fundamentals are used simply as an overlay to ensure that there is no glaringly obvious reason to avoid a trade not captured in the technical indicators examined. When pair trading involves trading two correlated stocks; sell short one stock while simultaneously buying the other.The position has “hedged” itself to the market and therefore the market is free to do what it wants. If the market goes down, the short position should make money.

If it goes up, long position should make money. Of course, while

each side the trade is making money, there’s the other side that is losing money. Correlation is calculated by dividing the covariance of the percentage changes of each stock or index divided by the product of the standard deviations for the two stocks.Covariance is a measure of the tendency of the two stocks or indices to move together, and dividing the covariance by the standard deviations sets the correlation between +1 and -1.

The question when measuring the correlation coefficient between two stocks is about how much data to use. The correlation calculated using six months of daily data will almost certainly be different from the correlation and beta calculated using three years of monthly data. A good starting point is to use the correlation for approximately the same number of days the stock is expected be held for the pairs trade.A technique that doesn’t rely on more sophisticated statistical tests is to look at a range of dates for the calculations, say 30 days, 60 days, 90 days, and 120 days and see how similar the correlations are between them. The more similar they are, the more possibility that the two stocks or indices will continue to have that relationship.

Beta is another tool used in pairs trading that predicts the behavior of one stock based on information about another stock. It is a coefficient that measures the magnitude of the relationship between two stocks or indices and is calculated with a linear regression model.In the regression, the set of one stock’s percentage returns is set as the independent variable, and the other stock’s percentage returns is set as the dependent variable. The beta indicates the

magnitude of the relationship of the independent variable relative to the dependent variable.

In trading terms, beta indicates how much a stock will move when another stock or index moves 1%. Beta is usually displayed as the percentage that a stock moves against a particular index. Beta is used to determine how many share of each stock to execute for the pairs trade.Because beta measures the magnitude of the relationship between two stocks or indices, you can apply beta to the delta of the positions to determine the quantity for each stock in the pair. Remember that delta is an estimate of how much an option will change in value for a 1.

00 change in the stock price. For example, if stock A has a beta of 2. 00 relative to stock B, then if stock B moves up 1%, then stock A is expected to move up 2%. That means 200 shares of stock B are needed to have the same potential risk/reward profile as 100 shares of stock A.That way, one is not significantly riskier than the other, and the deltas can be roughly equivalent in the pairs positions. Once it is determined that how many deltas are for each stock or index of the pairs for trade, trades that will give you the correct relative exposure can be found.

INSTRUMENTS FOR PAIR TRADING

Pair Trading strategy can be used a. Between the STOCKS b. Between the OPTIONS c. Between the STOCKS and OPTIONS Stocks are relatively easy to execute in actively traded stocks, but have virtually unlimited risk if you’re wrong.That is, if you expect that a spread between two stocks will revert to a

mean, but if it does not, you can lose a lot of money on both the long and short stock positions of the pairs trade. I use stocks only when I am highly confident in the trade.

Options are a good vehicle for pairs trading, and can simply be used as stock substitutes: long calls for long stock, long puts for short stock. Options have limited risk, but can be tougher to execute quickly. Options also usually have higher “slippage” in execution than stocks do.Also, buying options has its own risks, such as time decay and exposure to drops in implied volatility (vega). Option spreads have many advantages, such as limited risk and reduced exposure to gamma, theta, and vega.

They can also used to create situations where you can still profit if the spread between the pairs trade does not move the way you expect it will. When looking for strategies comprising the pair, one should try to have roughly the same dollar amount of risk between the positions. That is, probable gain or loss of roughly the same amount between the two verticals.The reason for doing this is to have the ability for one half of the pairs trade to make or lose as much as the other in the event that the pair does not move in the way expected.

Adjust the trade quantities to make the risk/reward of the long and short verticals equal. That is, buy two 2. 50-point verticals and sell one 5. 00-point vertical. Such a position could be considered to have equal risk and reward between the two verticals. The limited risk characteristics of vertical spreads provides a natural “stop”

for the pairs trade.

When the sides of the pairs trade are of equal risk and reward, for example selling a 5. 00-point vertical and buying a 5. 00-point vertical, a credit is preferable. The initial credit allows for extreme moves in the spread and still provide the potential for profit. When paying for a pair trade, that is, incurring a debit upon execution, it is better to have one side to be able to make more money than the other.

For example, selling a 2. 00-point wide vertical and buying a 2. 50-point wide vertical.In a very large move in both underlying stocks or indices, the profits on the long vertical are potentially greater than the loss on the short.

So, a small debit is acceptable, as long as the long vertical’s profits exceed both the loss on the short vertical and that initial debit. If both the long 2. 50-point and short 2. 00-point verticals reach their maximum value, the profit of the long should offset the loss on the short 2. 00-point vertical and the initial debit.

If both the long and short verticals reach their minimum values, the loss on the pairs trade is restricted to that minimum debit.Thus, in both cases where the pairs of stocks or indices make extreme price moves, there is a potential profit to balance the potential loss.

STRATEGY

The starting point of this strategy is that stocks that have historically had the same trading patterns (i. e. constant price ratio) will have so in the future as well. If there is a deviation from the historical mean, this creates a trading opportunity, which can be exploited. Gains are earned

when the price relationship is restored. Summary: find two stocks prices of which have historically moved together, ean reversion in the ratio of the prices, correlation is not key . Gains earned when the historical price relationship is restored . Free resources invested in risk-free interest rate. Testing for the mean reversion The challenge in this strategy is identifying stocks that tend to move together and therefore make potential pairs.

Our aim is to identify pairs of stocks with mean-reverting relative prices. To find out if two stocks are mean-reverting the test conducted is the Dickey-Fuller test of the log ratio of the pair.If the null hypothesis can be rejected on the 99% confidence level the price ratio is following a weak stationary process and is thereby mean-reverting. Research has shown that if the confidence level is relaxed, the pairs do not mean-revert good enough to generate satisfactory returns.

This implies that a very large number of regressions will be run to identify the pairs. If you have 200 stocks, you will have to run 19 900 regressions, which makes this quite computer-power and time consuming.

PAIRS TRADING MODEL

Screening Pairs By conducting this procedure, a large number of pairs will be generated. The problem is that all of them do not have the same or similar betas, which makes it difficult for us to stay market neutral. Therefore a trading rule is introduced regarding the spread of betas within a pair.The beta spread must be no larger than 0.2, in order for a trade to be executed. The betas are measured on a two-year rolling window on daily data. This gives mean-reverting pairs with a limited beta

spread, but to further eliminate the risk we also want to stay sector neutral. This implies that we only want to open a position in a pair that is within the same sector.

Due to the different volatility within different sectors, we expect sectors showing high volatility to produce very few pairs, while sectors with low volatility to generate more pairs.Another factor influencing the number of pairs generated is the homogeneity of the sector. A sector like Commercial services is expected to generate very few pairs, but Financials on the other hand should give many trading opportunities. The reason why, is that companies within the Financial sector have more homogenous operations and earnings.

Trading rules The screening process described gives a large set of pairs that are both market and sector neutral, which can be used to take positions. This should not be done randomly, since timing is an important issue.Basic rule will be to open a position when the ratio of two share prices hits the 2 rolling standard deviation and close it when the ratio returns to the mean. However, we do not want to open a position in a pair with a spread that is wide and getting wider.

This can partly be avoided by the following procedure: We actually want to open a position when the price ratio deviates with more than two standard deviations from the 250 days rolling mean. The position is not opened when the ratio breaks the two-standard-deviations limit for the first time, but rather when it crosses it to revert to the mean again. e have an open position when the pair is on its way back again summary:

--Open position when the ratio hits the 2 standard deviation band for two consecutive times. -- Close position when the ratio hits the mean Risk control Furthermore, there will be some additional rules to prevent us from loosing too much money on one single trade.

If the ratio develops in an unfavourable way, we will use a stop-loss and close the position as we have lost 20% of the initial size of the position. Finally, we will never keep a position for more that 50 days.On average, the mean reversion will occur in approximately 35 days , and there is no reason to wait for a pair to revert fully, if there is very little return to be earned. The potential return to be earned must always be higher than the return earned on the benchmark or in the fixed income market. The maximum holding period of a position is therefore set to 50 days. This should be enough time for the pairs to revert, but also a short enough time not to loose time value.

The rules described are totally based on statistics and predetermined numbers.In addition, there is a possibility for us to make our own decisions. If we for example are aware of fundamentals that are not taken into account in the calculations and that indicates that there will be no mean reversion for a specific pairs, we can of course avoid investing in such pairs. From the rules it can be concluded that we will open our last position no later than 50 days before the trading game ends.

The last 50 days we will spend trying to close the trades at the most

optimal points of time. Summary: . Stop loss at 20% of position value . Beta spread < 0.. Sector neutrality . Maximum holding period < 50 trading days . 10 equally weighted positions

Risks

Through this strategy we do almost totally avoid the systematic market risk. The reason there is still some market risk exposure, is that a minor beta spread is allowed for. In order to find a sufficient number of pairs, we have to accept this beta spread, but the spread is so small that in practise the market risk we are exposed to is ignorable.

Also the industry risk is eliminated, since we are only investing in pairs belonging to the same industry. The main risk we are being exposed to is then the risk of stock specific events, that is the risk of fundamental changes implying that the prices may never mean revert again, or at least not within 50 days. In order to control for this risk we use the rules of stop-loss and maximum holding period. This risk is further reduced through diversification, which is obtained by simultaneously investing in several pairs.

Initially we plan to open approximately 10 different positions. Finally, we do face the risk that the trading game does not last long enough.It might be the case that our strategy is successful in the long run, but that a few short run failures will ruin our overall excess return possibilities. Steps in pair trading:

• Selecting pairs of highly correlated stocks from the same industry. Suggested correlation is greater than 85%.
• Find the price ratio of the pairs for the desired period (1 year) ,mean and the 3 standard deviations on
  

the either side.

Keep track if trade is not going according to your desired direction….. a. book loss if spread is going against desired direction by more than 5% or 20 % of the margin money is at risk b.

If pair is not reverting back and is dull without movement for 35 days. 8. close the position if there is any potential announcement in coming days.