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Research Papers by College of Management, Mahidol University “Statistical Arbitrage in SET and TFEX : Pair Trading Strategy

from Threshold Co-integration Model”

The 2014 Capital Market Research Scholarship for Graduate Students

By

Surasak Choedpasuporn, Master Degree

Piyapas Tharavanij, Ph.D. & Assoc.Prof. Tatre Jantarakolico, Ph.D., Research Advisors

20 February 2015

Research Objectives & Benefit for Thai Capital Market • How does a future price relate to its underlying asset and another series from the

same underlying asset.

• Is Pair-Trading Strategy profitable in Thailand Stock & Futures Market

• How can we improve the pair trading strategy

• How attractive to use the pair trading strategy in Thailand Stock & Futures Market

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Executive Summary • Study 5-minutes intraday price relationship between pairs of assets in SET and

TFEX.

• 3 pairs of series of the same underlying asset (SET50, KTB, TRUE) which trade between 2/Jul/14 – 29/Aug/14 are studied.

• Found long-run relationship and short-run dynamic of the prices of pairs.

• With the existence of the transaction cost, the price relationship is estimated following the Threshold Vector Error Correction Model (TVECM)

• TVECM pair trading strategy is formulated. The performance of the TVECM pair trading strategy is superior to the traditional pair trading strategy.

• Present amount of trading volume in TFEX is too low to be attractive applying the pair trading strategy.

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Pair Trading Strategy – Market Neutral (Profitable in any market condition)

– Choose a pair of highly correlated price securities

• When the pair diverges, open ‘Short’ position in outperforming one and ‘Long’ position in underperforming one.

• When the pair converges, close all positions Open ‘Short’ position

Open ‘Long’ position

Close both positions

4 Traditional Pair Trading uses Moving Average 2 S.D. as positioning signal

Threshold Co-integration Pair Trading Strategy • Threshold Vector Error Correction Model (TVECM )

– With existence of Transaction Cost (ex.Commission), the Adjustment Process could be Asymmetric.

– In different regime, speed of adjustment might be different.

“No-arbitrage band”

If the mispricing is too small to cover the transaction cost.

Then, adjustment speed might be small.

Regime 3

Regime 1

Regime 2

Speed of adjustment : High

Speed of adjustment : Low

Speed of adjustment : Zero

Upper Threshold

Lower Threshold

Mispricing

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Threshold Co-integration Pair Trading Strategy

-0.001

-0.0008

-0.0006

-0.0004

-0.0002

0

0.0002

0.0004

ECT

LowThr

UpThr

Regime 3

Regime 1

Regime 2

Data : S50U14 & S50Z14 (freq : 5mins)

Example of Threshold Co-integration Behavior

TVECM Pair Trading 1

Regime 3

Regime 1

Regime 2

Open Positions Type 1

Positions Type 1 – Short Asset 1 & Long Asset 2 Positions Type 2 – Long Asset 1 & Short Asset 2

Close Positions

Open Positions Type 2

Trading Rule 1

Close Positions

Trading Rule

Regime 3

Regime 1

Regime 2

Open Positions Type 1

Positions Type 1 – Short Asset 1 & Long Asset 2 Positions Type 2 – Long Asset 1 & Short Asset 2

Close Positions Type 1 & open Positions Type 2

Trading Rule 2

Performance Measurement • Time-rolling (Out-sample Test)

1) Set Training Period = 600 periods (10 trading days) to estimate threshold values 2) Execute trading rule for next 300 periods (5 trading days) 3) Move forward 300 periods, redo steps 1) & 2) and repeat until end of data

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Time-rolling#1

Training Period Execute Period

Apply Time Rolling#1’s

Parameters

Time-rolling#2 Move forward

300 periods

Training Period Execute Period

Apply Time Rolling#2’s

Parameters

Data • Data selection criteria

– Asset from SET and TFEX markets

– Pair Formulate

• Spot and its future

• 2 different contract month futures from same underlying asset

– Data Frequency : 5 mins

– Missing data (no trade) < 10%

• Selected Data & Pairs (Trading period : 2/Jul/14 – 29/Aug/14 (2,439 Obs))

– Pair 1 - Assets : S50U14 & S50Z14

– Pair 2 - Assets : KTB & KTBU14

– Pair 3 - Assets : TRUE & TRUEU14

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Empirical Results (Compare training & execute period)

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Trading Rule

Pair 1 (S50U14 & S50Z14) 200 stocks / contract

Pair 2 (KTB & KTBU14)

1,000 stocks / contract

Pair 3 (TRUE & TRUEU14) 1,000 stocks / contract

Training : 600

Execute : 300 Training : 300

Execute : 60

Training : 600

Execute : 300 Training : 300

Execute : 60

Training : 600

Execute : 300 Training : 300

Execute : 60

Trading Rule 1

*No. of Transactions

132 152 192 226 160 196

Gross Profit 3,820 5,100 7,660 9,890 6,076 6,852

**Transaction Cost

1,848 2,128 7,182 8,453 5,774 7,073

Net Profit 1,972 2,972 478 1,437 302 (-221)

Trading Rule

2

*No. of Transactions

82 86 124 178 128 136

Gross Profit 2,940 3,100 5,280 8,750 5,585 5,820

**Transaction Cost

1,148 1,204 4,641 6,658 4,620 4,908

Net Profit 1,792 1,896 639 2,092 965 912

Traditional Pair Trading

(2SD)

*No. of Transactions

36 60 40 46 46 34

Gross Profit 1,280 1,820 1,790 1,770 1,535 1,257

**Transaction Cost

504 840 1,496 1,720 1,659 1,226

Net Profit 776 980 294 50 (-124) 31

Conclusion

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• Found long-run, short-run relationships – S50U14 & S50Z14

– KTB & KTBU14

– TRUE & TRUEU14

• At 5-min frequency, found arbitrage opportunities for – S50U14 & S50Z14

– KTB & KTBU14

– TRUE & TRUEU14

• Both TVECM Pair Trading Strategy (Trading Rule 2) are superior to Traditional Pair Trading Strategy

Conclusion (cont’d) • Attractiveness : Potential maximum profit in real-life for Prop. Trade in 2 months

• Pair 1 : S50U14 & S50Z14

– Average trading volume = 73 contracts per period (5 mins)

– Estimated potential maximum profit = THB 143,956

• Pair 2 : KTB & KTBU14

– Average trading volume = 66 contracts per period (5 mins)

– Estimated potential maximum profit = THB 42,174

• Pair 3 : TRUE & TRUEU14

– Average trading volume = 211 contracts per period (5 mins)

– Estimated potential maximum profit = THB 201,716

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References • Balke, N. S., & Fomby, T. B. (1997). Threshold cointegration. International economic review, 627-645.

• Dickey, D. A., & Fuller, W. A. (1981). Likelihood ratio statistics for autoregressive time series with a unit root. Econometrica: Journal of the Econometric Society, 1057-1072.

• Engle, R. F., & Granger, C. W. (1987). Co-integration and error correction: representation, estimation, and testing. Econometrica: journal of the Econometric Society, 251-276.

• Fama, E. F. (1965). The behavior of stock-market prices. Journal of business, 34-105.

• Fama, E. F. (1970). Efficient capital markets: A review of theory and empirical work*. The journal of Finance, 25(2), 383-417.

• Gatev, E., Goetzmann, W. N., & Rouwenhorst, K. G. (2006). Pairs trading: Performance of a relative-value arbitrage rule. Review of Financial Studies, 19(3), 797-827.

• Granger, C. W. (1981). Some properties of time series data and their use in econometric model specification. Journal of econometrics, 16(1), 121-130.

• Hansen, B. E., & Seo, B. (2002). Testing for two-regime threshold cointegration in vector error-correction models. Journal of econometrics, 110(2), 293-318.

• Johansen, S. (1991). Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models. Econometrica: Journal of the Econometric Society, 1551-1580.

• Kaewmongkolsri, C. (2011). Lead-lag Relationship and Price Discovery in KTB Spot and KTB Futures Markets. Faculty of Commerce and Accountancy, Thammasat University.

• Nestorovski, M., Naumoski, A. (2013). Economic Crisis and the Equity Risk Premium. 9th International ASECU Conference on "Systemic Economic Crisis: Current Issues and Perspectives".

• Songyoo, K. (2013). Optimal Positioning in Thailand's Spot and Futures Markets: Arbitrage Signaling from Threshold Cointegration Model (Dissertation, Thammasat University).

• Thongthip, S. (2010). Lead-lag Relationship and Mispricing in SET50 Index Cash and Futures Markets (Doctoral dissertation, Faculty of Economics, Thammasat University).

• Vidyamurthy, G. (2004). Pairs Trading: quantitative methods and analysis (Vol. 217). John Wiley & Sons.

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