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- 1. Statistical arbitrage and pairs trading Nikos S. Thomaidis, PhD1 Dept. of Economics, Aristotle University of Thessaloniki, GREECE Dept. of Financial Engineering & Management University of the Aegean, GREECE email: nthomaid@fme.aegean.gr Dept URL: http://labs.fme.aegean.gr/decision/ Personal web site: http://users.otenet.gr/~ ntho18 1 in collaboration with Nicholas Kondakis, Kepler Asset Management LLC, NY(http://www.keplerfunds.com) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 2. Outline Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 3. Outline What is pairs trading? Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 4. Outline What is pairs trading? Developing a pairs trading system from scratch Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 5. Outline What is pairs trading? Developing a pairs trading system from scratch Empirical study: statistical arbitrage between Dow Jones Industrial Average (DJIA) stocks Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 6. Outline What is pairs trading? Developing a pairs trading system from scratch Empirical study: statistical arbitrage between Dow Jones Industrial Average (DJIA) stocks Conclusions Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 7. Outline What is pairs trading? Developing a pairs trading system from scratch Empirical study: statistical arbitrage between Dow Jones Industrial Average (DJIA) stocks Conclusions Trading risks Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 8. Outline What is pairs trading? Developing a pairs trading system from scratch Empirical study: statistical arbitrage between Dow Jones Industrial Average (DJIA) stocks Conclusions Trading risks Opportunities Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 9. Outline What is pairs trading? Developing a pairs trading system from scratch Empirical study: statistical arbitrage between Dow Jones Industrial Average (DJIA) stocks Conclusions Trading risks Opportunities Future challenges Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 10. Pairs trading: the history 2 See [Pole, 2007, Vidyamurthy, 2004] and http://www.pairtradefinder.com/forum/viewtopic.php?f=3&t=14 for interesting facts and information on the history of the topic. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 11. Pairs trading: the history Pairs trading has at least twenty-ﬁve years of history on Wall Street. 2 See [Pole, 2007, Vidyamurthy, 2004] and http://www.pairtradefinder.com/forum/viewtopic.php?f=3&t=14 for interesting facts and information on the history of the topic. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 12. Pairs trading: the history Pairs trading has at least twenty-ﬁve years of history on Wall Street. Already in the mid 80’s, Morgan Stanley - and perhaps other investment companies - have started developing programs that could buy/sell stocks in pair combinations2 . 2 See [Pole, 2007, Vidyamurthy, 2004] and http://www.pairtradefinder.com/forum/viewtopic.php?f=3&t=14 for interesting facts and information on the history of the topic. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 13. Pairs trading: the history Pairs trading has at least twenty-ﬁve years of history on Wall Street. Already in the mid 80’s, Morgan Stanley - and perhaps other investment companies - have started developing programs that could buy/sell stocks in pair combinations2 . These strategies were strongly quantitative (generating trading rules using statistical/mathematical techniques, executing trades through an automated computer-based system). 2 See [Pole, 2007, Vidyamurthy, 2004] and http://www.pairtradefinder.com/forum/viewtopic.php?f=3&t=14 for interesting facts and information on the history of the topic. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 14. Pairs trading: the history Pairs trading has at least twenty-ﬁve years of history on Wall Street. Already in the mid 80’s, Morgan Stanley - and perhaps other investment companies - have started developing programs that could buy/sell stocks in pair combinations2 . These strategies were strongly quantitative (generating trading rules using statistical/mathematical techniques, executing trades through an automated computer-based system). Cross-disciplinary work (mathematicians, statisticians, physicists, computer scientists, ﬁnance experts). 2 See [Pole, 2007, Vidyamurthy, 2004] and http://www.pairtradefinder.com/forum/viewtopic.php?f=3&t=14 for interesting facts and information on the history of the topic. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 15. Pairs trading: main idea Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 16. Pairs trading: main idea Capitalise on market imbalances between two or more securities, in anticipation of making money when the inequality is corrected in the future [Whistler, 2004] Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 17. Pairs trading: main idea Capitalise on market imbalances between two or more securities, in anticipation of making money when the inequality is corrected in the future [Whistler, 2004] Find two securities that have moved together over the near past Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 18. Pairs trading: main idea Capitalise on market imbalances between two or more securities, in anticipation of making money when the inequality is corrected in the future [Whistler, 2004] Find two securities that have moved together over the near past When the distance (spread) between their prices goes above a threshold, short the overvalued and buy the undervalued one Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 19. Pairs trading: main idea Capitalise on market imbalances between two or more securities, in anticipation of making money when the inequality is corrected in the future [Whistler, 2004] Find two securities that have moved together over the near past When the distance (spread) between their prices goes above a threshold, short the overvalued and buy the undervalued one If securities return to the historical norm, prices will converge in the near future and you will end up with a proﬁt Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 20. So what is pairs trading? Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 21. So what is pairs trading? a market-neutral trading strategy: generates proﬁt under all market conditions (uptrend, downtrend, or sideways movements) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 22. So what is pairs trading? a market-neutral trading strategy: generates proﬁt under all market conditions (uptrend, downtrend, or sideways movements) a statistical arbitrage trading strategy: proﬁt from temporal mispricings of an asset relative to its fundamental value. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 23. So what is pairs trading? a market-neutral trading strategy: generates proﬁt under all market conditions (uptrend, downtrend, or sideways movements) a statistical arbitrage trading strategy: proﬁt from temporal mispricings of an asset relative to its fundamental value. a long/short equity strategy: long positions are hedged with short positions in the same or related sectors, so that the investor should be little aﬀected by sector-wide events Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 24. So what is pairs trading? a market-neutral trading strategy: generates proﬁt under all market conditions (uptrend, downtrend, or sideways movements) a statistical arbitrage trading strategy: proﬁt from temporal mispricings of an asset relative to its fundamental value. a long/short equity strategy: long positions are hedged with short positions in the same or related sectors, so that the investor should be little aﬀected by sector-wide events relative-value trading, Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 25. So what is pairs trading? a market-neutral trading strategy: generates proﬁt under all market conditions (uptrend, downtrend, or sideways movements) a statistical arbitrage trading strategy: proﬁt from temporal mispricings of an asset relative to its fundamental value. a long/short equity strategy: long positions are hedged with short positions in the same or related sectors, so that the investor should be little aﬀected by sector-wide events relative-value trading, convergence trading, Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 26. So what is pairs trading? a market-neutral trading strategy: generates proﬁt under all market conditions (uptrend, downtrend, or sideways movements) a statistical arbitrage trading strategy: proﬁt from temporal mispricings of an asset relative to its fundamental value. a long/short equity strategy: long positions are hedged with short positions in the same or related sectors, so that the investor should be little aﬀected by sector-wide events relative-value trading, convergence trading, and so on... Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 27. So what is pairs trading? a market-neutral trading strategy: generates proﬁt under all market conditions (uptrend, downtrend, or sideways movements) a statistical arbitrage trading strategy: proﬁt from temporal mispricings of an asset relative to its fundamental value. a long/short equity strategy: long positions are hedged with short positions in the same or related sectors, so that the investor should be little aﬀected by sector-wide events relative-value trading, convergence trading, and so on... Pairs trading → group trading Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 28. Why pairs work: the drunk and his dog A humorous metaphor adapted from [Murray, 1994] to the context of pairs trading. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 29. Why pairs work: the drunk and his dog A humorous metaphor adapted from [Murray, 1994] to the context of pairs trading. A drunk customer sets out from the pub (“Gin Palace”) and starts wandering in the streets (random walk, unit-root, integrated stochastic process) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 30. Why pairs work: the drunk and his dog A humorous metaphor adapted from [Murray, 1994] to the context of pairs trading. A drunk customer sets out from the pub (“Gin Palace”) and starts wandering in the streets (random walk, unit-root, integrated stochastic process) The accompanying dog thinks: “I can’t let him get too far oﬀ; after all, my role is to protect him!” Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 31. Why pairs work: the drunk and his dog A humorous metaphor adapted from [Murray, 1994] to the context of pairs trading. A drunk customer sets out from the pub (“Gin Palace”) and starts wandering in the streets (random walk, unit-root, integrated stochastic process) The accompanying dog thinks: “I can’t let him get too far oﬀ; after all, my role is to protect him!” So, the dog assesses how far the drunk is and moves accordingly to close the gap Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 32. The drunk and his dog: the story continues Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 33. The drunk and his dog: the story continues Rory and Gary, two regular customers, look outside the pub’s window and bet on the drunk’s and the dog’ s position Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 34. The drunk and his dog: the story continues Rory and Gary, two regular customers, look outside the pub’s window and bet on the drunk’s and the dog’ s position They observe the drunk and the dog individually but their course looks no diﬀerent than a random walk (growing variance in location, lack of predictability) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 35. The drunk and his dog: the story continues Rory and Gary, two regular customers, look outside the pub’s window and bet on the drunk’s and the dog’ s position They observe the drunk and the dog individually but their course looks no diﬀerent than a random walk (growing variance in location, lack of predictability) Suddenly, Gary throws the idea: “Well, it’s all a matter of ﬁnding the drunk, the dog must not be far away” Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 36. The drunk and his dog: the story continues Rory and Gary, two regular customers, look outside the pub’s window and bet on the drunk’s and the dog’ s position They observe the drunk and the dog individually but their course looks no diﬀerent than a random walk (growing variance in location, lack of predictability) Suddenly, Gary throws the idea: “Well, it’s all a matter of ﬁnding the drunk, the dog must not be far away” He is right because the gap between the two fellows should occasionally open and close but never being out of control (co-integration) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 37. The drunk and his dog: the story continues Rory and Gary, two regular customers, look outside the pub’s window and bet on the drunk’s and the dog’ s position They observe the drunk and the dog individually but their course looks no diﬀerent than a random walk (growing variance in location, lack of predictability) Suddenly, Gary throws the idea: “Well, it’s all a matter of ﬁnding the drunk, the dog must not be far away” He is right because the gap between the two fellows should occasionally open and close but never being out of control (co-integration) Rory and Gary eventually agree to play the following game: Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 38. The drunk and his dog: the story continues Rory and Gary, two regular customers, look outside the pub’s window and bet on the drunk’s and the dog’ s position They observe the drunk and the dog individually but their course looks no diﬀerent than a random walk (growing variance in location, lack of predictability) Suddenly, Gary throws the idea: “Well, it’s all a matter of ﬁnding the drunk, the dog must not be far away” He is right because the gap between the two fellows should occasionally open and close but never being out of control (co-integration) Rory and Gary eventually agree to play the following game: “Why not betting on their relative distance rather than their absolute positions?” Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 39. An actual traded pair 1.05 GT 1 HPQ 0.95 0.9 0.85 0.8 0.75 0.7 0.65 Mar93 Dec95 Sep98 May01 Feb04 Nov06 Aug09 May12 Figure 1: Normalised price paths of Goodyear (GT) and Hewlett Packard (HPQ). Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 40. Why pairs trading is successful? A behavioural-ﬁnance explanation: New information is rapidly impounded in stock prices through investment activity (market eﬃciency) Stock price movements reﬂect all publicly available information (future earnings prospects, corporate news, political events) Two securities that are close substitutes for each other respond similarly to incoming news Overreaction and herding behaviour of uninformed and “noisy” investors often drives prices apart But, any deviation is temporary and rational traders are expected to close the “gaps” in the long run Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 41. Basic steps in developing a pairs trading system Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 42. Basic steps in developing a pairs trading system Group formation Pick closely-related stocks and detect stable relative price relationships Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 43. Basic steps in developing a pairs trading system Group formation Pick closely-related stocks and detect stable relative price relationships Group trading Determine the direction of the relationship (divergence, re-convergence) Find suitable trade-open and trade-close points Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 44. Basic steps in developing a pairs trading system Group formation Pick closely-related stocks and detect stable relative price relationships Group trading Determine the direction of the relationship (divergence, re-convergence) Find suitable trade-open and trade-close points Risk management Minimise divergence risk (the gap between stocks further widens) Fine-tune parameters with respect to a trading performance criterion (maximise expected return, maximise a reward-risk ratio, etc) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 45. Group formation strategy Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 46. Maximum price correlation (MPC) 1 Choose a charting time-frame 2 Compute the correlation of historical price series, e.g. Correlation coeﬃcient Pair 1 Stock 1 Stock 3 0.91 Pair 2 Stock 1 Stock 5 0.87 Pair 3 Stock 2 Stock 4 0.81 Pair 4 Stock 8 Stock 10 0.76 ... ... ... Pair 19 Stock 13 Stock 26 0.26 Pair 20 Stock 26 Stock 27 0.17 3 Pick the top 20% of pairs (i.e 4 pairs) with the highest historical correlation 4 Formed groups: {1, 3, 5}, {2, 4}, {8, 10} Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 47. Minimum normalised price distance (MNPD) Popular in literature [Gatev et al., 2006, Andrade et al., 2005] Construct a cumulative total return index for each stock over the formation period t crt,i ≡ (1 + rτ,i ), t = 1, 2, ..., T τ =1 where cr0,i = 1 and rt,i is the t-period’s return on stock i . Introduce a “distance” measure: e.g. Euclidean distance T d(i , j) ≡ |cr ,i − cr ,j | ≡ (crt,i − crt,j )2 t=1 Rank stock pairs based on increasing values of d - pick the top a% of the list for group formation Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 48. Identify stationary relationships (1/5) Applying techniques from co-integration analysis [Engle and Granger, 1987, Burgess, 2000, Vidyamurthy, 2004] Assume that a group of stocks with price vector Pt = (Pt1 , Pt2 , . . . , PtN ) satisfy the relationship Pt1 = c + β2 Pt2 + · · · + βn PtN + Zt where Zt is the mispricing index (captures temporal deviations from equilibrium) The coeﬃcients of the relationship can be estimated using Ordinary Least Squares (OLS) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 49. Identify stationary relationships (2/5) Construct a portfolio as follows: Stocks 1 2 3 ··· N Positions +1 ˆ -β2 ˆ - β3 ··· ˆ - βN ˆ where βi is the OLS estimate of βi and “+” (“-”) indicates a long (short) position ˆ ˆ The portfolio value Zt ≡ β · Pt , where ˆ ˆ ˆ ˆ β ≡ (1, −β2 , −β3 , . . . , −βN ) is by construction mean-reverting (ﬂuctuates around c , ˆ the OLS estimate of c) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 50. Identify relationships with OLS (3/5) 15 Stock 1 Stock 2 Prices 10 5 0 50 100 150 200 250 Group formation sample Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 51. Identify relationships with OLS (4/5) 14.5 actual price pairs Equilibrium relationship: equilibrium relationship 14 −−−−−−−−−−−−−−−−−− P2 = 14.843 − 0.257 P1 13.5 positive mispricing 13 Stock 2 12.5 negative mispricing 12 11.5 11 5.5 6 6.5 7 7.5 8 8.5 Stock 1 Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 52. Identify relationships with OLS (5/5) 16.5 Stock 2 overpriced relative to Stock 1 16 15.5 Relative mispricing 15 14.5 14 Zt=P2 + 0.257 P1 13.5 Stock 2 underpriced relative to Stock 1 13 0 50 100 150 200 250 Group formation sample Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 53. Conditions for meaningful capital allocations The average capital invested on each stock (average price × number of shares) must be below 80% and above 5% The ratio between the maximum and the minimum number of shares held from each asset should not exceed 10. etc These place restrictions on the beta coeﬃcients (stock holdings) → restricted OLS estimation Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 54. Group trading Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 55. Trading strategyaa See also [Thomaidis et al., 2006, Thomaidis and Kondakis, 2012] Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 56. Trading strategyaa See also [Thomaidis et al., 2006, Thomaidis and Kondakis, 2012] Open a position in a group, over the trading period, when the mispricing index diverges by a certain threshold ˆ Buy the portfolio, if Zt < ZtL,α ˆtH,α Sell the portfolio, if Zt > Z where ZtL,α , ZtH,α is a 100 × (1 − 2α)% conﬁdence ˆ ˆ “envelope” on the value of the mispricing. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 57. Trading strategyaa See also [Thomaidis et al., 2006, Thomaidis and Kondakis, 2012] Open a position in a group, over the trading period, when the mispricing index diverges by a certain threshold ˆ Buy the portfolio, if Zt < ZtL,α ˆtH,α Sell the portfolio, if Zt > Z where ZtL,α , ZtH,α is a 100 × (1 − 2α)% conﬁdence ˆ ˆ “envelope” on the value of the mispricing. Unwind the position after h periods of time Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 58. Trading strategyaa See also [Thomaidis et al., 2006, Thomaidis and Kondakis, 2012] Open a position in a group, over the trading period, when the mispricing index diverges by a certain threshold ˆ Buy the portfolio, if Zt < ZtL,α ˆtH,α Sell the portfolio, if Zt > Z where ZtL,α , ZtH,α is a 100 × (1 − 2α)% conﬁdence ˆ ˆ “envelope” on the value of the mispricing. Unwind the position after h periods of time unless Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 59. Trading strategyaa See also [Thomaidis et al., 2006, Thomaidis and Kondakis, 2012] Open a position in a group, over the trading period, when the mispricing index diverges by a certain threshold ˆ Buy the portfolio, if Zt < ZtL,α ˆtH,α Sell the portfolio, if Zt > Z where ZtL,α , ZtH,α is a 100 × (1 − 2α)% conﬁdence ˆ ˆ “envelope” on the value of the mispricing. Unwind the position after h periods of time unless the mispricing index continues to diverge (does not cross up the lower bound or cross down the upper bound) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 60. Trading strategyaa See also [Thomaidis et al., 2006, Thomaidis and Kondakis, 2012] Open a position in a group, over the trading period, when the mispricing index diverges by a certain threshold ˆ Buy the portfolio, if Zt < ZtL,α ˆtH,α Sell the portfolio, if Zt > Z where ZtL,α , ZtH,α is a 100 × (1 − 2α)% conﬁdence ˆ ˆ “envelope” on the value of the mispricing. Unwind the position after h periods of time unless the mispricing index continues to diverge (does not cross up the lower bound or cross down the upper bound) Close the position earlier and open a new position if the synthetic re-converges and crosses the opposite bound Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 61. Trading strategyaa See also [Thomaidis et al., 2006, Thomaidis and Kondakis, 2012] Open a position in a group, over the trading period, when the mispricing index diverges by a certain threshold ˆ Buy the portfolio, if Zt < ZtL,α ˆtH,α Sell the portfolio, if Zt > Z where ZtL,α , ZtH,α is a 100 × (1 − 2α)% conﬁdence ˆ ˆ “envelope” on the value of the mispricing. Unwind the position after h periods of time unless the mispricing index continues to diverge (does not cross up the lower bound or cross down the upper bound) Close the position earlier and open a new position if the synthetic re-converges and crosses the opposite bound ZtL,α , ZtH,α is of the form c ± zα σZ , where c , σZ are the ˆ ˆ ˆ ˆ ˆ ˆ sample mean and standard deviation of the synthetic value over the formation period and zα is the critical value from a N(0, 1) distribution. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 62. Example: trading a group of 2 stocks (1/2) GOODYEAR (GT) vs HEWLETT PACKARD (HPQ) 42 20 GT 40 HPQ 18Price ($) Price ($) 38 16 36 14 34 12 0 20 40 60 80 100 120 Trading period 24 23 22Mispricing 21 20 19 Zt=PGT −1.06 PHPQ Mispricing index Confidence bounds Long positions Short positions 18 0 20 40 60 80 100 120 Trading period Figure 3:Mispricing index: Zt = PGT − 1.06PHPQ , Trading parameters: HOP = 1day , αL = 10%, αH = 5% . Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 63. Example: trading a group of 2 stocks (2/2) 24 23 22Mispricing 21 20 19 Mispricing index Confidence bounds Long positions Short positions 18 0 20 40 60 80 100 120 Trading period 8Cumulative return (%) 6 4 2 0 −2 0 20 40 60 80 100 120 Trading period Figure 4: HOP=1 day, αL = 10%, αH = 5% . Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 64. Example: trading a group of 4 stocks (1/2) 1.6 AA AXP CAT IBM Long positions Short positionsNormalised prices 1.4 1.2 1 0.8 0 50 100 150 200 250 Trading period 0 −1 Mispricing −2 −3 Mispricing index Confidence bounds Long positions Short positions −4 0 50 100 150 200 250 Trading period Figure 5: HOP=1 day, αL = 20%, αH = 20% . Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 65. Example: trading a group of 4 stocks(2/2) 0 −1Mispricing −2 −3 Mispricing index Confidence bounds Long positions Short positions −4 0 50 100 150 200 250 Trading period 30Cumulative return (%) 20 10 0 −10 0 50 100 150 200 250 Trading period Figure 6: HOP=1 day, αL = 20%, αH = 20% . Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 66. System performance measurement Are there truly successful rules that deliver consistent return or risk-adjusted return? Performance indicators (mean, std, downside std, information ratio (IR), downside IR) How does performance vary with diﬀerent market conditions? Can high returns be explained by speciﬁc exposure to industry and other systematic risk factors? Are we capturing other patterns of stock movements (price reversals)? How skillful is our system in terms of picking the right pairs/ﬁnding price equilibriums? How able is our system to early detect price divergence and predict re-convergence points? Do our strategies require too much trading? Do our strategies maintain their performance ranking over time? Do the best remain the best and the worst remain the worst? Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 67. Experimental set-up Daily prices of 30 stock members of Dow Jones Industrial Average (DJIA) index (with dividends reinvested) Sample period: 3 Jan 1994 to 24 Feb 2010 Group formation: Window length (WL) {125, 250} days Screen out DJIA stocks with one or more days without a trade (identify relatively liquid stocks and facilitate pairs formation) Choose matching stocks based on MNPD and MPC criteria (form groups from the 5%, 20% or 50% highest-ranking pairs of the list) Trading strategy Trading period: subsequent {50, 125, 150} days Hold-out period (HOP): {1, 5, 10, 25} days αL , αH ∈ {1, 5, 10, 20, 40}% A total of 3, 600 parametrisations Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 68. Best trading strategies Design parameters3 Best strategy (Mean return) Best strategy (IR) Sample: 1994-2010 WL 125 125 TP 150 150 GFC MPC - 5% MPC - 20% HOP 25 25 αL (%) 40 10 αH (%) 1 1 3 WL: Length of moving window, TP: Trading period, GFC: Group formation criterion, HOP: Position holdout period. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 69. Performance of best trading strategies Trading measures Best strategy Best strategy (IR) Buy & hold portfolio (Mean return) Sample: 1994-2010 (784 observations) Mean(%) 11.65 7.78 5.92 Stdev(%) 26.44 9.94 22.00 DStdev(%) 23.75 6.48 16.54 IR 0.44 0.78 0.27 DIR 0.49 1.20 0.36 Table 1: Average weekly performance (annualised measures). Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 70. Portfolios of good strategies Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 71. Portfolios of good strategies No investor would risk putting all his money in a single strategy Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 72. Portfolios of good strategies No investor would risk putting all his money in a single strategy Mixing-up diﬀerent parameter combinations Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 73. Portfolios of good strategies No investor would risk putting all his money in a single strategy Mixing-up diﬀerent parameter combinations “Bundles” of trading strategies: “Distribute your capital evenly between the top-a % of the parameterisations” Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 74. Performance of mixtures - Mean return Percentage of trading strategies Best Buy & Strategies 100 90 65 35 10 strategy hold Mean(%) 1.98 2.46 3.42 4.64 6.48 11.65 5.92 Stdev(%) 3.65 3.63 3.69 4.00 6.19 26.44 22.00 DStdev(%) 2.26 2.19 2.10 2.16 2.71 23.75 16.54 IR 0.54 0.68 0.93 1.16 1.05 0.44 0.27 DIR 0.88 1.12 1.63 2.15 2.39 0.49 0.36 Table 2: Average weekly performance on the full sample period (annualised measures). Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 75. Performance of mixtures - Information ratio (1/2) Percentage of trading strategies Best Buy & Strategies 100 90 65 35 10 strategy hold Mean(%) 1.98 2.46 3.42 4.43 5.93 7.78 5.92 Stdev(%) 3.65 3.63 3.66 3.65 4.31 9.94 22.00 DStdev(%) 2.26 2.19 2.09 2.18 2.55 6.48 16.54 IR 0.54 0.68 0.93 1.22 1.37 0.78 0.27 DIR 0.88 1.12 1.64 2.03 2.32 1.20 0.36 Table 3: Average weekly performance on the full sample period (annualised measures). Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 76. Performance of mixtures - Information ratio (2/2) IR−maximising strategies 350 top−100 300 top−90 top−65 top−35 250 top−10 best strategy Cumulative return (%) 200 buy & hold 150 100 50 0 −50 Dec95 Sep98 May01 Feb04 Nov06 Aug09 Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 77. Systematic risk exposure 200 Market SMB HML Top−10%(IR) 150 cumulative return (%) 100 50 0 −50 Mar93 Dec95 Sep98 May01 Feb04 Nov06 Aug09 May12 Figure 7: Historical performance of the top-10% portfolio (IR) and systematic factors of risk. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 78. Systematic risk exposure Percentage of trading strategies Strategies Best strategy 100 90 65 35 10 Alpha 0.00 0.00 0.00 0.00 0.00 0.00 (0.12) (0.04) (0.00) (0.00) (0.00) (0.00) MKT -0.15 -0.15 -0.13 -0.11 -0.15 -0.46 (0.01) (0.01) (0.01) (0.04) (0.03) (0.00) SMB 0.00 -0.00 -0.01 -0.00 0.00 0.02 (0.83) (0.89) (0.53) (0.82) (0.89) (0.40) HML -0.00 -0.00 -0.01 -0.01 -0.03 -0.11 (0.98) (0.82) (0.50) (0.49) (0.10) (0.01) MOM -0.04 -0.04 -0.03 -0.03 -0.03 -0.04 (0.00) (0.00) (0.00) (0.00) (0.00) (0.09) LTR -0.02 -0.01 -0.00 0.00 -0.00 -0.07 (0.36) (0.52) (0.87) (0.81) (0.89) (0.06) STR 0.04 0.03 0.03 0.03 0.01 -0.02 (0.00) (0.00) (0.00) (0.00) (0.09) (0.30) Consumer Durables 0.04 0.04 0.04 0.03 0.04 0.15 (0.00) (0.00) (0.00) (0.01) (0.00) (0.00) Manufacturing 0.00 0.00 0.00 -0.01 -0.01 0.03 (0.95) (0.96) (0.88) (0.69) (0.61) (0.56) HiTec 0.03 0.03 0.03 0.03 0.03 0.09 (0.03) (0.03) (0.05) (0.08) (0.14) (0.04) Health 0.02 0.02 0.02 0.02 0.02 0.03 (0.04) (0.04) (0.06) (0.10) (0.14) (0.20) Other 0.01 0.01 0.01 0.01 0.04 0.14 (0.39) (0.36) (0.44) (0.55) (0.10) (0.00) Table 4: OLS estimates of the regression equation. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 79. Trading costs Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 80. Trading costs Pairs trading is a cost-sensitive strategy Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 81. Trading costs Pairs trading is a cost-sensitive strategy It involves Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 82. Trading costs Pairs trading is a cost-sensitive strategy It involves Frequent re-balancing of trading positions Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 83. Trading costs Pairs trading is a cost-sensitive strategy It involves Frequent re-balancing of trading positions Multiple openings and closings of trades Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 84. Trading costs Pairs trading is a cost-sensitive strategy It involves Frequent re-balancing of trading positions Multiple openings and closings of trades Short-selling Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 85. Trading costs Pairs trading is a cost-sensitive strategy It involves Frequent re-balancing of trading positions Multiple openings and closings of trades Short-selling Transaction costs, margin requirements, etc Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 86. Trading costs Pairs trading is a cost-sensitive strategy It involves Frequent re-balancing of trading positions Multiple openings and closings of trades Short-selling Transaction costs, margin requirements, etc How the strategies are expected to perform in a more realistic market environment? Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 87. Trading costs Pairs trading is a cost-sensitive strategy It involves Frequent re-balancing of trading positions Multiple openings and closings of trades Short-selling Transaction costs, margin requirements, etc How the strategies are expected to perform in a more realistic market environment? Can generated proﬁts oﬀset trading costs? Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 88. Descriptive statistics (1/2) Top-10% (IR) portfolio of strategies Sample period Total days in sample: 4065 Total trading days in sample: 3865.7 Total number of traded stocks: 35 Group formation Total number of formed groups: 71.43 Average size of groups: 4.51 (1.59) Group trading Total number of group openings during study: 195.76 Number of groups that never open: 4.19 Average number of active groups per trading day: 1.17 (0.45) Fraction of trading time groups are open: 0.88 Average number of times a group is opened over the trading period: 3.32 (2.24) Average duration of positions (days): 27.59 (28.94) Average duration of long positions (days): 24.50 (30.66) Average duration of short positions (days): 30.15 (27.05) Notes: (1) Averages over all parametrisations, (2) Standard deviation in parentheses. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 89. Descriptive statistics (2/2) Top-10% (IR) portfolio of strategies Divergence risk Percentage of groups that never open: 3.21 Percentage of groups opened once but never converging in the trading period: 26.31 Percentage of groups that have mul- tiple round-trip trades and a ﬁnal di- vergent trade: 57.13 Percentage of groups with no ﬁnal di- vergent trade: 13.34 Note: Averages over all 360 parametrisations. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 90. The impact of transaction costs (1/2) Transaction cost4 0 bps 10 bps Strategies Best at Zero Cost Best Best at Zero Cost Best Mean(%) 5.93 5.93 5.38 5.78 Stdev(%) 4.31 4.31 4.34 4.30 DStdev(%) 2.55 2.55 2.54 2.54 IR 1.37 1.37 1.24 1.35 DIR 2.32 2.32 2.12 2.27 Transaction cost 50 bps Buy & hold Strategies Best at Zero Cost Best Mean(%) 4.93 5.34 5.92 Stdev(%) 4.33 4.28 22.00 DStdev(%) 2.55 2.55 16.54 IR 1.14 1.25 0.27 DIR 1.93 2.10 0.36 Table 5: Top-10% (IR) portfolio. 4 Fixed cost per unit of trading volume. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 91. The impact of transaction costs (2/2) 160 0 bps 140 10 bps 50 bps 120 cumulative return (%) 100 80 60 40 20 0 −20 Mar93 Dec95 Sep98 May01 Feb04 Nov06 Aug09 May12 Figure 8: Historical performance of the top-10% (IR) portfolio assuming diﬀerent levels of transaction costs. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 92. Data snooping (1/2) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 93. Data snooping (1/2) Statistical arbitrage strategies are highly parametrised Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 94. Data snooping (1/2) Statistical arbitrage strategies are highly parametrised If we experiment with enough parameter settings, some of them are likely to beat the benchmark under any performance measures, by chance alone Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 95. Data snooping (1/2) Statistical arbitrage strategies are highly parametrised If we experiment with enough parameter settings, some of them are likely to beat the benchmark under any performance measures, by chance alone For example, strategies that went short in DJIA stocks during the period Apr 2008 - Oct 2008, would possibly outperform the market portfolio in a longer sample Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 96. Data snooping (1/2) Statistical arbitrage strategies are highly parametrised If we experiment with enough parameter settings, some of them are likely to beat the benchmark under any performance measures, by chance alone For example, strategies that went short in DJIA stocks during the period Apr 2008 - Oct 2008, would possibly outperform the market portfolio in a longer sample Simply because of the special characteristics of this single period Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 97. Data snooping (1/2) Statistical arbitrage strategies are highly parametrised If we experiment with enough parameter settings, some of them are likely to beat the benchmark under any performance measures, by chance alone For example, strategies that went short in DJIA stocks during the period Apr 2008 - Oct 2008, would possibly outperform the market portfolio in a longer sample Simply because of the special characteristics of this single period Data snooping(“dredging” or “ﬁshing”): The practice of hand-tailoring the trading strategy to the data under consideration [Sullivan et al., 1999, White, 2000] Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 98. Data snooping (2/2) Is the seemingly outstanding performance Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 99. Data snooping (2/2) Is the seemingly outstanding performance → due to genuine superiority? Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 100. Data snooping (2/2) Is the seemingly outstanding performance → due to genuine superiority? or... Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 101. Data snooping (2/2) Is the seemingly outstanding performance → due to genuine superiority? or... → due to luck? Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 102. Data snooping quotations “Given enough computer time, we are sure that we can ﬁnd a mechanical trading rule which ‘works’ on a table of random numbers, provided of course that we are allowed to test the rule on the same table of numbers which we used to discover the rule.” [Jensen and Bennington, 1970] “Even when no exploitable [trading] model exists, looking long enough and hard enough at a given set of data will often reveal one or more [trading strategies] that look good, but are in fact useless.” [White, 2000] “If you have 20,000 traders in the market, sure enough you’ll have someone who’s been up every day for the past few years and will show you a beautiful P&L. If you put enough monkeys on typewriters, one of the monkeys will write the Iliad in ancient Greek. But would you bet any money that he’s going to write the Odyssey next?” [Taleb, 1997]5 5 Random Walk: Taleb on Mistakes that Market Traders can make, http://equity.blogspot.com/2008/11/taleb-on-mistakes-that-market-traders.html Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 103. How to eliminate data snooping biases? Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 104. How to eliminate data snooping biases? Using an estimation and validation (test) data set Helps observing model performance beyond the training sample Sensitive with respect to the particular choice of sample periods (training and testing) Sensitive to market conditions Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 105. How to eliminate data snooping biases? Using an estimation and validation (test) data set Helps observing model performance beyond the training sample Sensitive with respect to the particular choice of sample periods (training and testing) Sensitive to market conditions Using multiple estimation/validation periods Reported performance is less prone to data-snooping biases Problems arise if these periods are consecutive The choice of periods can introduce further bias Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 106. How to eliminate data snooping biases? Using an estimation and validation (test) data set Helps observing model performance beyond the training sample Sensitive with respect to the particular choice of sample periods (training and testing) Sensitive to market conditions Using multiple estimation/validation periods Reported performance is less prone to data-snooping biases Problems arise if these periods are consecutive The choice of periods can introduce further bias Statistical techniques Little sensitivity to market conditions Helps exploring new market scenarios (beyond those present in the dataset) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 107. How would you choose your sample periods? Buy & hold strategy 350 300 2007 2001 2000 250 2004 Cumulative return (%) 1999 2006 2002 2005 200 2003 1998 150 2008 100 1997 2010 50 1996 2009 1995 0 1994 −50 Mar93 Dec95 Sep98 May01 Feb04 Nov06 Aug09 May12 Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 108. Trading performance comparisons (1/2) Splitting the data set into estimation and validation periods Sample 1 Sample 2 Sample 3 Sample 4 Estimation 1994- 96 1997-99 2000-02 2003-06 period Validation pe- 1997- 99 2000-02 2003-05 2006-10 riod Number of observations 756 days 756 days 756 days 1041 days (validation set) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 109. Trading performance comparisons (2/2) Validation period 1 Validation set 2 10 150 25 30 Top−10% (IR) IR=1.21 IR=0.27 Buy & hold 20 20 cumulative return (%) cumulative return (%) cumulative return (%) cumulative return (%) 100 15 10 5 10 0 50 5 −10 0 Top−10% (IR) IR=−0.17 IR=1.28 Buy & hold 0 −20 0 −5 −30 Jun96 Jan97 Jul97 Feb98 Sep98 Mar99 Oct99 Apr00 Oct99 Apr00 Nov00 May01 Dec01 Jul02 Jan03 Validation set 3 Validation set 4 5 50 20 50 IR=0.52 Top−10% (IR) IR= −0.55 Top−10% (IR) Buy & hold Buy & hold IR= 0.78 cumulative return (%) cumulative return (%) cumulative return (%) cumulative return (%) 10 0 0 0 0 −50 IR=0.05 −5 −50 −10 −100 Jul02 Jan03 Aug03 Feb04 Sep04 Mar05 Oct05 May06 Oct05 May06 Nov06 Jun07 Dec07 Jul08 Jan09 Aug09 Mar10 Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 110. Statistical techniques Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 111. Statistical techniques Random portfolios [Burns, 2006] How skillful is our strategy in terms of picking the right stocks Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 112. Statistical techniques Random portfolios [Burns, 2006] How skillful is our strategy in terms of picking the right stocks at the right combination? Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 113. Statistical techniques Random portfolios [Burns, 2006] How skillful is our strategy in terms of picking the right stocks at the right combination? “Monkey” trading Is our trading system superior to a “monkey”, which opens and closes trading positions at random points? Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 114. Statistical techniques Random portfolios [Burns, 2006] How skillful is our strategy in terms of picking the right stocks at the right combination? “Monkey” trading Is our trading system superior to a “monkey”, which opens and closes trading positions at random points? Other more sophisticated approaches: Reality Check [White, 2000] Test of Superior Predictive Performance [Hansen, 2005] False discovery rate [Bajgrowiczy and Scailletz, 2009] Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 115. Skillful vs lucky stock picking 1 months of consecutive out performarnce 0.8 group formation skillsProbability of superior 0.6 0.4 0.2 months of consecutive under performarnce 0 Dec95 Sep98 May01 Feb04 Nov06 Aug09 0.3 90th percentile Top−10% (IR) strategy 0.2 0.1 Monthly return 0 −0.1 Median −0.2 10th percentile Dec95 Sep98 May01 Feb04 Nov06 Aug09 Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 116. Group-selection skills: interesting statistics Based on the probability of “superiority” Percentage of skilled months: 63.10% Percentage of unskilled months: 36.90% Average number of consecutive skillful-picking months: 2.51 Average number of consecutive unskilled-picking months: 1.47 Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 117. Do stock-picking beneﬁts accumulate over time? 300 Top−10% (IR) strategy 250 Probability of outperformance: 98.20% 200 Cumulative return (%) 150 100 50 0 −50 −100 Mar93 Dec95 Sep98 May01 Feb04 Nov06 Aug09 May12 Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 118. Is my trading system as smart as a monkey? 6 6 This particular monkey-trader was recruited from http://www.free-extras.com/images/monkey_thinking-236.htm . Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 119. Skillful vs lucky trading 1 months of consecutive out performarnce 0.8 group formation skillsProbability of superior 0.6 0.4 0.2 months of consecutive under performarnce 0 Dec95 Sep98 May01 Feb04 Nov06 Aug09 0.2 Top−10% (IR) strategy 90th percentile 0.1 Monthly return 0 −0.1 Median 10th percentile −0.2 Dec95 Sep98 May01 Feb04 Nov06 Aug09 Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 120. Group-trading skills: interesting statistics Percentage of skilled months: 66.31% Percentage of unskilled months: 32.62% Average number of consecutive skilled months: 2.88 Average number of consecutive unskilled months: 1.49 Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 121. Beating the monkey in terms of cumulative return 300 Top−10% (IR) strategy 250 Probability of outperformance: 98.20% 200 Cumulative return (%) 150 100 50 0 −50 −100 Mar93 Dec95 Sep98 May01 Feb04 Nov06 Aug09 May12 Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 122. How to improve your pairs trading system Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 123. How to improve your pairs trading system Use ﬁrm fundamentals to select stocks with similar factor risk exposure Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 124. How to improve your pairs trading system Use ﬁrm fundamentals to select stocks with similar factor risk exposure Trade at higher frequencies (microstructure information) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 125. How to improve your pairs trading system Use ﬁrm fundamentals to select stocks with similar factor risk exposure Trade at higher frequencies (microstructure information) Select stocks with similar response patterns to market disturbances Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 126. How to improve your pairs trading system Use ﬁrm fundamentals to select stocks with similar factor risk exposure Trade at higher frequencies (microstructure information) Select stocks with similar response patterns to market disturbances → Event-response analysis [Pole, 2007] Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 127. How to improve your pairs trading system Use ﬁrm fundamentals to select stocks with similar factor risk exposure Trade at higher frequencies (microstructure information) Select stocks with similar response patterns to market disturbances → Event-response analysis [Pole, 2007] Incorporate any type of prior expert knowledge Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 128. How to improve your pairs trading system Use ﬁrm fundamentals to select stocks with similar factor risk exposure Trade at higher frequencies (microstructure information) Select stocks with similar response patterns to market disturbances → Event-response analysis [Pole, 2007] Incorporate any type of prior expert knowledge Achieve the right balance between automation and human intervention Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 129. How to improve your pairs trading system Use ﬁrm fundamentals to select stocks with similar factor risk exposure Trade at higher frequencies (microstructure information) Select stocks with similar response patterns to market disturbances → Event-response analysis [Pole, 2007] Incorporate any type of prior expert knowledge Achieve the right balance between automation and human intervention Is it possible to select the best-performing rules ex ante? Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 130. How to improve your pairs trading system Use ﬁrm fundamentals to select stocks with similar factor risk exposure Trade at higher frequencies (microstructure information) Select stocks with similar response patterns to market disturbances → Event-response analysis [Pole, 2007] Incorporate any type of prior expert knowledge Achieve the right balance between automation and human intervention Is it possible to select the best-performing rules ex ante? Historical (in-sample) performance Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 131. How to improve your pairs trading system Use ﬁrm fundamentals to select stocks with similar factor risk exposure Trade at higher frequencies (microstructure information) Select stocks with similar response patterns to market disturbances → Event-response analysis [Pole, 2007] Incorporate any type of prior expert knowledge Achieve the right balance between automation and human intervention Is it possible to select the best-performing rules ex ante? Historical (in-sample) performance Economic conditions (picking those rules that perform better with a particular state of the business and market cycle) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 132. Event-response analysis 1.35 1.3 1.25 local maxima 1.2 Normalised price 1.15 local minima 1.1 1.05 1 0.95 0 20 40 60 80 100 120 140 Group formation period (days) . Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 133. Epilogue Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 134. Epilogue Pairs trading is a statistical arbitrate trading strategy Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 135. Epilogue Pairs trading is a statistical arbitrate trading strategy Performs better under limiting conditions Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 136. Epilogue Pairs trading is a statistical arbitrate trading strategy Performs better under limiting conditions inﬁnitely-dimensional asset universe Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 137. Epilogue Pairs trading is a statistical arbitrate trading strategy Performs better under limiting conditions inﬁnitely-dimensional asset universe inﬁnite amount of trading time, etc Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 138. Epilogue Pairs trading is a statistical arbitrate trading strategy Performs better under limiting conditions inﬁnitely-dimensional asset universe inﬁnite amount of trading time, etc Computational challenges (processing huge amounts of information, asset selection, ﬁne-tuning, model estimation) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 139. Epilogue Pairs trading is a statistical arbitrate trading strategy Performs better under limiting conditions inﬁnitely-dimensional asset universe inﬁnite amount of trading time, etc Computational challenges (processing huge amounts of information, asset selection, ﬁne-tuning, model estimation) Implementation challenges (high portfolio turnover, trading costs, execution risk) Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 140. Epilogue Pairs trading is a statistical arbitrate trading strategy Performs better under limiting conditions inﬁnitely-dimensional asset universe inﬁnite amount of trading time, etc Computational challenges (processing huge amounts of information, asset selection, ﬁne-tuning, model estimation) Implementation challenges (high portfolio turnover, trading costs, execution risk) If beneﬁts exceed costs your system is a hit! Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 141. References I Andrade, S., Vadim, P., and Seasholes, M. (2005). Understanding the proﬁtability of pairs trading. working paper. Bajgrowiczy, P. and Scailletz, O. (2009). Technical trading revisited: False discoveries, persistence tests, and transaction costs. working paper. Burgess, N. (2000). Statistical arbitrage models of the FTSE 100. In Abu-Mostafa, Y., LeBaron, B., Lo, A. W., and Weigend, A. S., editors, Computational Finance 1999, pages 297–312. The MIT Press. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 142. References II Burns, P. (2006). Random portfolios for evaluating trading strategies. working paper. Engle, R. F. and Granger, C. W. J. (1987). Co-integration and error correction: Representation, estimation, and testing. Econometrica, 55:251–276. Gatev, E., Goetzmann, W., and Rouwenhorst, K. (2006). Pairs trading: performance of a relative-value arbitrage rule. The Review of Financial Studies, 19(3):797–827. Hansen, P. (2005). A test for superior predictive ability. Journal of Business & Economic Statistics, 23(5):365–380. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 143. References III Jensen, M. and Bennington, G. (1970). Random walks and technical theories: some additional evidence. The Journal of Finance, 25:469 – 482. Murray, M. (1994). A drunk and her dog: An illustration of cointegration and error correction. The American Statistician, 48(1):37–39. Pole, A. (2007). Statistical arbitrage: algorithmic trading insights and techniques. John Wiley and Sons, Inc. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 144. References IV Sullivan, R., Timmermann, A., and White, H. (1999). Data-snooping, technical trading model performance and the bootstrap. The Journal of Finance, 54:1647–1691. Thomaidis, N. S. and Kondakis, N. (2012). Detecting statistical arbitrage opportunities using a combined neural network - GARCH model. Working paper available from SSRN. Thomaidis, N. S., Kondakis, N., and Dounias, G. (2006). An intelligent statistical arbitrage trading system. Lecture Notes in Artiﬁcial Intelligence, 3955:596–599. Vidyamurthy, G. (2004). Pairs trading: quantitative methods and analysis. John Wiley and Sons, Inc. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading
- 145. References V Whistler, M. (2004). Trading pairs: capturing proﬁts and hedging risk with statistical arbitrage strategies. John Wiley and Sons, Inc. White, H. (2000). A reality check for data snooping. Econometrica, 68(5):1097–1126. Nikos S. Thomaidis, PhD Statistical arbitrage and pairs trading

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