Implementation of Pairs Trading Strategies Aldwin Shen Weishun

Implementation of Pairs Trading Strategies Aldwin Shen Weishun

Implementation of Pairs Trading Strategies Aldwin Shen Weishun Han Xue Maurice Tjie Zeng Fanchao Nanyang MFE FE8827: Quantitative Trading Strategies April 2011 CONTENT 1. Introduction 2. Search Process & Criteria

3. Trading Strategies 4. Results & Analysis 5. Conclusion 6. Reference 1. INTRODUCTION Executive Summary Search for profitable pairs for the implementation of pair-trading strategies using the method of cointegration Establish a search process and search criteria Explore various pair-trading strategies Analyze results on various trading instruments, i.e. Stocks, ETF, Stock Indices

1. INTRODUCTION Pair-Trading Long one asset against short another (buy the cheap one and sell the expensive one) Mean-Reversion Strategy: Spread between two highly correlated assets tends to mean revert Stock-Picking Strategy: Eliminates systematic market risk and capitalize on mispricing in stocks This report focus on the mean-reversion strategy 1. INTRODUCTION Stationarity & Cointegration Construct a mean-reverting spread through linear

combination Cointegrating factor (the hedge ratio) is determined by the Johansen method Spread is checked to be stationary using the Augmented-Dicky-Fuller test 1. INTRODUCTION Trading Instruments Equity: 50 US stocks from different sectors: Technology, Industrials, Energy, Consumer Staples, Finances, Material, Healthcare ETF: 13 ETFs replicating index in various countries: Dow Jones, Midcap Value, Midcap Growth, Brazil, Germany, UK, Australia.

Indices: 10 Major Indexes: DJIA, Nasdaq, S&P, DAX, CAC, STI, HSI, Nikkei, etc 2. SEARCH PROCESS & CRITERIA Search Process Search process is run between individual asset in each instrument class via a MATLAB script Search process is initiated with 40 days of historical data recursively from 31st Dec 2009 If statistical test for mean reversion is significant (taking 95% confidence level), the spread is extended with 20 days The iteration is repeated until there is no significant evidence for mean reversion

2. SEARCH PROCESS & CRITERIA Pair-Trade Criteria Factors suggesting suitable trading pairs include: Length: Longest period showing significant evidence of mean reversion t-statistic: More negative t-statistic signifying a more statistically significant evidence of mean reversion 3. TRADING STRATEGIES Back-testing Procedure Trading pairs are determined from the search procedure using historical data recursively from

31st Dec 2009 Identified trading pairs are back-tested using historical data from 1st Jan 2010 to 31st Dec 2010 to determine the cumulative profit 3 different trading strategies are employed on the 3 different classes of trading instruments 3. TRADING STRATEGIES Trading Strategy I Using calibrated hedge ratio & mean to trade without recalibration or rebalancing Strategy - Buy when z < mean + 0.5 * sigma - Sell when z > mean + 0.5 * sigma

Intuition: Assumes mean reversion about the historical long-term mean exist 3. TRADING STRATEGIES Trading Strategy II Adopts a dynamic calibration of hedge ratio & mean for a window of every 10 trading days and used to trade for the next 10 trading days with rebalancing Strategy - Buy when z < mean + 0.5 * sigma - Sell when z > mean + 0.5 * sigma

Intuition: Assumes mean reversion about a mean with stochastic drift exist 3. TRADING STRATEGIES Trading Strategy III Using calibrated hedge ratio to trade without recalibration or rebalancing Strategy - Buy when zt < zt-1 + 0.5 * sigma - Sell when zt > zt-1 + 0.5 * sigma Intuition: Assumes that mean reversion follows immediately after a price shock

4. RESULTS Search for Cointegrated Pairs Results on the search of cointegrated pairs for Equity Top 10 Equity Pairs based on Length No 1 2 3 4 5 6 7 8 9

10 Stock I GR AMZN CVX CVX CVX CVX CVX CVX CVX CVX

Stock II F NYX LM MS AA HD WFC VLO JNJ MCD Length 159

79 59 59 59 59 59 59 59 59 Beta T-statistics 7.38 -3.987 4.18

-3.941 2.42 -4.749 2.42 -4.749 5.53 -4.665 2.81 -4.613 2.76 -4.584 4.35 -4.534 1.24

-4.514 1.26 -4.489 Mean Std. Deviation 0.823 5.163 1.416 26.152 0.214 4.422 0.214 4.422 0.495

6.520 0.122 3.272 0.231 4.804 0.546 7.149 0.056 2.439 0.059 1.925 4. RESULTS Search for Cointegrated Pairs Results on the search of cointegrated pairs for

ETF and Indices Top 5 ETF Pairs based on T-Statistics No ETF I 1 MSCI Pacific Ex. Japan 2 iShares Australia 3 iShares Dow Jones Transportation 4 MSCI Brazil 5 MSCI Germany

ETF II MSCI UK MSCI UK S&P Global Energy Russell Midcap Growth Index Fund S&P Global Energy Length 39 39 39 39 39

Beta T-statistics 2.545 -3.345 1.415 -3.260 2.013 -3.230 1.703 -3.201 0.623 -3.199 Mean Std. Deviation 0.002

0.492 -0.001 0.350 0.033 2.886 0.055 2.909 0.002 0.325 Top 5 Indices Pairs based on T-Statistics No 1 2

3 4 5 Indices I Dow Jones Dow Jones CAC S&P 500 CAC Indices II Nikkei 225 Hang Seng

Nikkei 225 FSSTI KOSPI Length 39 39 39 39 39 Beta T-statistics 1.045 -3.880

0.472 -3.749 0.386 -3.668 0.397 -3.564 2.353 -3.235 Mean Std. Deviation 15.278 392.753 7.371 303.495

3.363 102.133 0.195 12.719 1.046 68.074 4. RESULTS & ANALYSIS - EQUITY Trading Strategy I GR Vs F P&L: -2.44 4. RESULTS & ANALYSIS - EQUITY Trading Strategy I AMZN Vs NYX P&L: 12.63

4. RESULTS & ANALYSIS - EQUITY Trading Strategy I CVX Vs LM P&L: 9.63 4. RESULTS & ANALYSIS - EQUITY Trading Strategy I: Analysis Spread is not mean reverting around the historical long-term mean. A trading position is entered into and the position is held for prolonged period as there is no exit signal. Not a feasible trading strategy.

4. RESULTS & ANALYSIS - EQUITY Trading Strategy II GR Vs F P&L: 20.57 4. RESULTS & ANALYSIS - EQUITY Trading Strategy II AMZN Vs NYX P&L: 56.80 4. RESULTS & ANALYSIS - EQUITY Trading Strategy II CVX Vs LM P&L: 5.31 4. RESULTS & ANALYSIS - EQUITY Trading Strategy II: Analysis

Shows a higher trading activity compared to Strategy I and is consistently profitable for the pairs analyzed. Apparently the most appropriate pair-trading strategy for Equity. 4. RESULTS & ANALYSIS - EQUITY Trading Strategy III GR Vs F P&L: 44.10 4. RESULTS & ANALYSIS - EQUITY Trading Strategy III AMZN Vs NYX P&L: -40.89

4. RESULTS & ANALYSIS - EQUITY Trading Strategy III CVX Vs LM P&L: 0.58 4. RESULTS & ANALYSIS - EQUITY Trading Strategy III: Analysis Displays inconsistent performance across the pairs analyzed. There is a possibility of huge profits as well as huge losses. This implies that there is no specific reaction to price shocks for equity pair-trading. 4. RESULTS & ANALYSIS - ETF Trading Strategy I

MSCI Pac Ex-Jap Vs MSCI UK P&L: -1.06 4. RESULTS & ANALYSIS - ETF Trading Strategy I iShares Aust Index Vs MSCI UK P&L: 6.55 4. RESULTS & ANALYSIS - ETF Trading Strategy I: Analysis Spread is not mean reverting around the historical long-term mean. A trading position is entered into and the position is held for prolonged period with few exit signals. Trading activity is more as compared to Equity. Not a feasible trading strategy.

4. RESULTS & ANALYSIS - ETF Trading Strategy II MSCI Pac Ex-Jap Vs MSCI UK P&L: 15.82 4. RESULTS & ANALYSIS - ETF Trading Strategy II iShares Aust Index Vs MSCI UK P&L: 9.70 4. RESULTS & ANALYSIS - ETF Trading Strategy II: Analysis Shows a higher trading activity compared to Strategy I and is consistently profitable for the pairs analyzed.

It is an appropriate strategy for ETF. 4. RESULTS & ANALYSIS - ETF Trading Strategy III MSCI Pac Ex-Jap Vs MSCI UK P&L: 20.76 4. RESULTS & ANALYSIS - ETF Trading Strategy III iShares Aust Index Vs MSCI UK P&L: 10.61 4. RESULTS & ANALYSIS - ETF Trading Strategy III: Analysis Shows a higher trading activity compared to Strategy I and is consistently profitable for the

pairs analyzed. It is an appropriate strategy for ETF. This implies that ETF pair trades mean-revert closely after price shocks. 4. RESULTS & ANALYSIS - INDICES Trading Strategy I DJIA Vs NIKKEI 225 P&L: 2948.51 4. RESULTS & ANALYSIS - INDICES Trading Strategy I FTSE 100 Vs NIKKEI 225 P&L: 425.30 4. RESULTS & ANALYSIS - INDICES

Trading Strategy I CAC 40 Vs NIKKEI 225 P&L: 425.30 4. RESULTS & ANALYSIS - INDICES Trading Strategy I: Analysis Spread is not mean reverting around the historical long-term mean. A trading position is entered into and the position is held for prolonged period with few exit signals. Not a feasible trading strategy. 4. RESULTS & ANALYSIS - INDICES Trading Strategy II DJIA Vs NIKKEI 225 P&L: 2002.62

4. RESULTS & ANALYSIS - INDICES Trading Strategy II FTSE 100 Vs NIKKEI 225 P&L: 1153.89 4. RESULTS & ANALYSIS - INDICES Trading Strategy II CAC 40 Vs NIKKEI 225 P&L: 813.38 4. RESULTS & ANALYSIS - INDICES Trading Strategy II: Analysis Shows a higher trading activity compared to Strategy I and is consistently profitable for the pairs analyzed.

Profits analyzed may not be accurate as the pairs are analyzed based on the spot indices and not index futures and tick value is not accounted for. However, it gives a clear indication of relative performance amongst the trading strategies. It is an appropriate strategy for Indices. 4. RESULTS & ANALYSIS - INDICES Trading Strategy III DJIA Vs NIKKEI 225 P&L: 6471.68 4. RESULTS & ANALYSIS - INDICES Trading Strategy III FTSE 100 Vs NIKKEI 225 P&L: 2044.30

4. RESULTS & ANALYSIS - INDICES Trading Strategy III CAC 40 Vs NIKKEI 225 P&L: 2108.45 4. RESULTS & ANALYSIS - INDICES Trading Strategy III: Analysis Shows a higher trading activity compared to Strategy I and is consistently profitable for the pairs analyzed. Apparently this is the most profitable strategy for indices. This implies that Indices pair trades mean-revert closely after price shocks.

5. CONCLUSION The pair trading search process is most easily applicable to Equity as there are more individual assets to compare and easier to arrive at profitable pairs. Using the length and t-statistic of mean reversion from the search procedure is a useful indication of profitable pairs for trading. Pair trading performance for ETF and Indices are more consistent as compared to that of Equity. 5. CONCLUSION Trading Strategy I is not an appropriate trading

strategy for the classes of trading instruments analyzed as there exists a stochastic drift away from the historical long-term mean. Trading Strategy II is the most appropriate trading strategy for Equity. Trading Strategy II & III are equally appropriate for ETF pair trading. Trading Strategy III is the most profitable trading strategy for Indices however Trading Strategy is appropriate as well. 6. REFERENCE yvind Foshaug. Implementation of Pairs Trading Strategies. Faculty of Science. Koortwegde Vries Institute for Mathematics. Master of

Science Thesis. 2010. Ernest Chan. Quantitative Trading: How to Build Your Own Algorithmic Trading Business. Haksun Li. Lecture Materials Quantitative Trading Strategies course in M.Sc Financial Engineering, NTU. 2011 7. APPENDICES README FILE Guide to run the Pair Trading Program is available in README.txt in the Pairs Trading directory. Alternatively, 1. Open Directory : "Pairs Trading" with MATLAB 2. Run GUI.m 3. Type the ticker for Asset 1 and Asset 2

- Both Asset 1 and Asset 2 must be from the same Asset classes - The ticker code can be found in the next slide 4. Choose the corresponding Asset Class for the two tickers from the drop down menu 5. Choose Strategy that we want to backtest 6. Wait for several minutes for the backtesting to complete 7. Three graphs will pop-up and Final P&L is shown in lower left corner of the window 1. Position 2. Price 3. Profit 8. Close the Window before running another backtesting 9. To run a new backtesting with different strategy/ticker, repeat step 2 7. APPENDICES README FILE TICKER

AAPL AMZN CSCO DELL EBAY GOOG INTC MSFT NFLX YHOO CAT GE HON TYC

UPS MMM BA FDX CSX GR XOM FTI NE SLB CVX Equity TICKER

Apple Inc. VLO Amazon.com Inc KO Cisco Systems K Dell Inc. KFT eBay Inc. EL Google Inc. F Intel Corp. GT

MicrosoftCorp. HD NetFlix Inc. MCD Yahoo Inc. AA Caterpillar Inc. FMC General Electric AGN Honeywell Int'l Inc. JNJ Tyco International PFE United Parcel Service MRK

3M Co AXP Boeing Company BLK FedEx Corporation BAC CSX Corp. GS Goodrich Corporation JPM Exxon Mobil Corp. LM FMC Technologies Inc. MS Noble Corp NYX

Schlumberger Ltd. WFC Chevron Corp. COF Equity Valero Energy Coca Cola Co. Kellogg Co. KraftFoods Inc-A Estee Lauder Cos. Ford Motor Goodyear Tire & Rubber Home Depot

McDonald's Corp. Alcoa Inc FMC Corporation Allergan Inc Johnson & Johnson Pfizer Inc. Merck & Co. American Express Co Blackrock Bank of America Corp Goldman Sachs Group JPMorgan Chase & Co. Legg Mason Morgan Stanley

NYSE Euronext Wells Fargo Capital One Financial TICKER 016382 016383 016386 016387 016389 016391 016399 016415 016425

016428 016434 016435 016442 ETF iShares Gold Trust iShares Australia Index Fund iShares MSCI Brazil Free Index Fund iShares MSCI Canada Index Fund iShares MSCI Pacific ex-Japan Index Fund iShares MSCI U.K. Index Fund iShares MSCI Germany Index Fund iShares Dow Jones Transportation Average Index

iShares S&P Global energy iShares S&P Lat Am 40 iShares Russell Midcap Value Index Fund iShares Russell Midcap Growth Index Fund iShares Nasdaq Biotech TICKER INDU SPX CCMP UKX CAC DAX NYK HSI

KOSPI FSSTI INDEX DOW JONES INDUSTRIAL AVERAGE S&P 500 INDEX NASDAQ COMPOSITE INDEX FTSE 100 INDEC CAC 40 INDEC DAX INDEX NIKKEI 225 HANG SENG INDEX KOSPI INDEX FTSE STRAITS TIMES INDEX

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