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# W4290 Project Pair Trading

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Tweet## Albert Xiong

on 10 December 2012#### Transcript of W4290 Project Pair Trading

title Selection Strategy

—find the best pairs What is pair trading? Market Factor Method

Minimum Distance Method

ADF Test

Two Granger Causality Test When a pair of financial instruments has historically moved together and kept a specific pattern for their spread, we could take advantage of any disturbance over this historic trend When can we use pair trading? Market-neutral equity trading strategies exploit mispricing in a pair of similar stocks. In the theory, more possibilities emerge in a fluctuated market condition. Therefore, it is not surprising that market-neutral trading performs well in extreme market conditions How do we accomplish a pair trading? (1) Select a pair using a reliable pair selection criterion

(2) Mimic the motion of the given pair by stochastic model and estimate the parameters

(3) A low-risk high-return trading strategy with the given pair(s)

(4) A comprehensive back-testing methodology using in sample and out of sample data Market Factor Method Healthcare

Technology

Basic Materials

Energy Minimum Distance Method

(MDM) The main idea to this selection criterion is to select pairs that have had similar historical price moves. To select pairs from the pool of stocks, the sum of squared deviations is used: Then we can find the pairs with minimum D(x,y) ADF Test we use ADF test to test the pairs for mean

reversion and stationary 1.We choose pairs of assets of ideally identical β, and at most with ∆β ≤ 0.1. The β’s are based on one year daily data.

2 We explored 20 stocks from each of the four different sectors respectively for selecting pairs. Two-way Granger Causality Test —shows the interaction between two financial assets

The optimal pair of stocks will pass the Granger Causality Test in both ways, which shows their

high positive correlation According to the table above, we select pair #3 (HAL-DNR) and #4 (ABX-ACET) as an optimal group. Pair Trading Strategy Jin Feng Liqi Xiong Nian Ji

Qinxuan Miao Ran Wei Rong Gao The Coca-Cola Company (KO) PepsiCo Inc. (PEP) Look Similar?

Can we use that similarity

to make profit?

Estimate Parameters

Trading Rules

Back

Test (cc) image by nuonsolarteam on Flickr

Theory and

Model

Conclusion The Spreading Model Use Rolling Window to choose the data we will use in estimation Estimation of Parameters Use Least Square Estimation to estimate parameters Mu and Sigma every day based on the data of the latest 30 days Trading Process

— achieve good return Trading positions are opened when the spread reaches the upper threshold (2 Sigma)

after having crossed it previously.

Trading positions are closed when the spread drops below the lower threshold (0.5 Sigma)

and profits are made. The risk free rate is set as 3%

The transaction fee is 0.5% for each transaction Update our investment portfolio according to the status of our pairs (open or close):

Move money into risk free account from newly closed pairs

Take money from risk free account and reinvest in the newly opened pairs and risk free account with the same weight The Actual Return for Each Pair in Each Trade Based on Jan.1 2001 – Dec.31 2005 in sample data to select pairs Open Position & Close Position Trading Rules Assumptions Trading Rules and Back Test Here, We use rolling window again to choose the best upper threshold (2 Sigma) Also, we set some rules to control the risk:

In order to use stop-loss strategy, if the realized loss is greater than 10%, we would close that pair

Considering transaction fee, we only trade the pair when the expected return is greater than 2 times risk free rate Back Test Result From Jan.1 2006 to Mar.31 2012, according to our defined trading rules,

we can find 27 and 37 opportunities to trade pair #3 and pair #4 (our optimal pairs), respectively. The cumulative returns are shown below: Finally, we obtain a Compounded Annual Return of 8.9% over a period of 6 years.

When compared with the returns from S&P 500 index, namely 1.76% each year over the same period, we find the returns of our strategy to be excellent. Conclusions Future Work

— next step The End

Thank You In this trading strategy we considered assets from the same asset class for trading pairs. In future, we would like to work on pairs that might exist across asset classes.

In the back-testing and in the algorithmic implementation we considered the time period as 1 day. We plan to analyze our trading strategy for different time periods and find the best conceivable time period.

We would also like to analyze the sensitivity of our trading strategy to different kinds/levels of transaction fees; as in reality the transaction fees can be a at fee or a percentage fee. And the percentage fee also varies according to the type of investors. So, analysis on transaction fees would help us identify how well our strategy suits with different investors.

Q&A time Ornstein-Uhlenbeck (OU) process to depict the spread of the pair

The above equation can be written as

Full transcript—find the best pairs What is pair trading? Market Factor Method

Minimum Distance Method

ADF Test

Two Granger Causality Test When a pair of financial instruments has historically moved together and kept a specific pattern for their spread, we could take advantage of any disturbance over this historic trend When can we use pair trading? Market-neutral equity trading strategies exploit mispricing in a pair of similar stocks. In the theory, more possibilities emerge in a fluctuated market condition. Therefore, it is not surprising that market-neutral trading performs well in extreme market conditions How do we accomplish a pair trading? (1) Select a pair using a reliable pair selection criterion

(2) Mimic the motion of the given pair by stochastic model and estimate the parameters

(3) A low-risk high-return trading strategy with the given pair(s)

(4) A comprehensive back-testing methodology using in sample and out of sample data Market Factor Method Healthcare

Technology

Basic Materials

Energy Minimum Distance Method

(MDM) The main idea to this selection criterion is to select pairs that have had similar historical price moves. To select pairs from the pool of stocks, the sum of squared deviations is used: Then we can find the pairs with minimum D(x,y) ADF Test we use ADF test to test the pairs for mean

reversion and stationary 1.We choose pairs of assets of ideally identical β, and at most with ∆β ≤ 0.1. The β’s are based on one year daily data.

2 We explored 20 stocks from each of the four different sectors respectively for selecting pairs. Two-way Granger Causality Test —shows the interaction between two financial assets

The optimal pair of stocks will pass the Granger Causality Test in both ways, which shows their

high positive correlation According to the table above, we select pair #3 (HAL-DNR) and #4 (ABX-ACET) as an optimal group. Pair Trading Strategy Jin Feng Liqi Xiong Nian Ji

Qinxuan Miao Ran Wei Rong Gao The Coca-Cola Company (KO) PepsiCo Inc. (PEP) Look Similar?

Can we use that similarity

to make profit?

Estimate Parameters

Trading Rules

Back

Test (cc) image by nuonsolarteam on Flickr

Theory and

Model

Conclusion The Spreading Model Use Rolling Window to choose the data we will use in estimation Estimation of Parameters Use Least Square Estimation to estimate parameters Mu and Sigma every day based on the data of the latest 30 days Trading Process

— achieve good return Trading positions are opened when the spread reaches the upper threshold (2 Sigma)

after having crossed it previously.

Trading positions are closed when the spread drops below the lower threshold (0.5 Sigma)

and profits are made. The risk free rate is set as 3%

The transaction fee is 0.5% for each transaction Update our investment portfolio according to the status of our pairs (open or close):

Move money into risk free account from newly closed pairs

Take money from risk free account and reinvest in the newly opened pairs and risk free account with the same weight The Actual Return for Each Pair in Each Trade Based on Jan.1 2001 – Dec.31 2005 in sample data to select pairs Open Position & Close Position Trading Rules Assumptions Trading Rules and Back Test Here, We use rolling window again to choose the best upper threshold (2 Sigma) Also, we set some rules to control the risk:

In order to use stop-loss strategy, if the realized loss is greater than 10%, we would close that pair

Considering transaction fee, we only trade the pair when the expected return is greater than 2 times risk free rate Back Test Result From Jan.1 2006 to Mar.31 2012, according to our defined trading rules,

we can find 27 and 37 opportunities to trade pair #3 and pair #4 (our optimal pairs), respectively. The cumulative returns are shown below: Finally, we obtain a Compounded Annual Return of 8.9% over a period of 6 years.

When compared with the returns from S&P 500 index, namely 1.76% each year over the same period, we find the returns of our strategy to be excellent. Conclusions Future Work

— next step The End

Thank You In this trading strategy we considered assets from the same asset class for trading pairs. In future, we would like to work on pairs that might exist across asset classes.

In the back-testing and in the algorithmic implementation we considered the time period as 1 day. We plan to analyze our trading strategy for different time periods and find the best conceivable time period.

We would also like to analyze the sensitivity of our trading strategy to different kinds/levels of transaction fees; as in reality the transaction fees can be a at fee or a percentage fee. And the percentage fee also varies according to the type of investors. So, analysis on transaction fees would help us identify how well our strategy suits with different investors.

Q&A time Ornstein-Uhlenbeck (OU) process to depict the spread of the pair

The above equation can be written as