DISCOVERING ARBITRAGE OPPORTUNITIES IN THE FUTURES AND THAILAND MARKET: PAIRS TRADING STRATEGY FROM THE PREG CO-INTEGRATION MODEL. The performance of the TVECM pairs trading strategy is superior to the traditional pairs trading strategy. One approach to profiting from derivatives in both risk management and profit speculation is the Pairs Trading Strategy.
In some countries, the Pairs Trading Strategy is widely used, especially in fund equity risk (Hedge Fund) (Caldeira & Moura, 2012). Pairs Trading Strategy (also known as Market Neutral Strategy) is a possible way that investors can expect high returns with low risk. The principles of the Pairs Trading strategy is to invest in two assets whose prices can be expected to be closely related at the same time.
Pair Trading Strategy can be applied to many types of assets, including equities, derivatives and commodity products. The TVECM can also be applied to generate trading signals for position timing in Pair Trading Strategy (Songyoo, 2013). This article aims to further study the TVECM pair trading strategy in a broader dimension.
The performance of the TVECM pair trading strategy is measured and compared with the performance of traditional pair trading strategy.
LITERATURE REVIEW
Theories
- Efficient Market Hypothesis & Cost of Carry Model
- Mispricing, Arbitrage Opportunity & Pair Trading
If so, the difference between future price and spot price should be constant and there is no arbitrage opportunity. However, if the market is not fully efficient, the gap will not be constant and there is an arbitrage opportunity (Songyoo, 2013). If the market is not fully efficient and the difference between the future price and the spot price is not constant, there will be a chance that the future price will not equal the spot price plus its carrying cost, or they will price incorrectly.
For example, the future price ft, is higher than the spot price plus the cost of carrying. In this scenario, there will be an arbitrage opportunity to sell expensive (ft, T) and buy cheap (St). The Pairs Trading Strategy comes into play when investors find the existence of an arbitrage opportunity.
As we know the future price and spot price will move together but they may differ in some cases. Opening a 'Short Selling' position in the expensive and simultaneously opening a 'Long Buying' position.
Empirical Research
METHODOLOGY
- Unit Roots
- Co-integration & Error Correction Model
- Threshold Vector Error Correction Model
- Trading rule for pair trading strategy
- Performance measurement of trading strategy
To maintain the long-term relationship, there must be a mechanism to adjust the deviation of the two variables to return to their long-term equilibrium. If you use the Trace test or the Maximum Eigenvalues โโtest, there is no cointegration if the null hypothesis is not rejected. If the null hypothesis is rejected, cointegration occurs. If the cointegration exists, test the next step by testing for a threshold or nonlinear property of the time series.
For this reason, Hansen & Seo (2002) proposed an MLE method using the Grid Search method, illustrated in Figure 2.1. This method generates all possible pairs of the ฮฒ (co-integrating vector) and ฮณ (threshold value) within a range and constraints, and then tests each pair to find the optimal ฮฒ (co-integrating vector) and ฮณ (threshold value) using of the AIC and SBIC selection criteria. By applying this concept in the Pair Trading Strategy, we can use the threshold values โโand regimes as a signaling instrument.
From the study of Songyoo (2013), we found that using the 3-regime TVECM, most of the observation was found to fall into Regime 2. If the observation falls into Regime 1 or Regime 3, the mispricing gap will be strong enough to earn a profit. Since the transaction cost is considered to greatly affect the performance of the trading rule, we adjust the trading rule to reduce trading over the small misprice gap by skipping closing the position when the observation returns to Mode 2, and instead, we close the position only when the observation passes through regime 1 to regime 3 or vice versa.
To be realistic, we perform an out-of-sample test using a time shift in our measurement. Third, after the end of the execution period of the rule from the second step, move the training period forward by the same length as the execution period, and repeat the first and second steps until the end of the data. SET50 Future THB 7 per contract 200 units per contract Stock Future THB 35 per contract 1,000 units per contract.
Apply these transaction costs, we can calculate the net profit as the execution of the trading strategy. Apart from the absolute return from the net profit, we compare the performance with the traditional pair trading strategy. The position opening will happen when the observation deviates from the moving average more than 2 times standard deviations.
DATA
Data and pair selection criteria
Data and pair selection result
EMPIRICAL RESULT
- Unit root test and long-run relationship estimation
- Short-run dynamic estimation
- Threshold Vector Error Correction Model Estimation
- Time rolling test
- Hansen-Seo Test
- Trading Rule Performance Measurement
The cointegration equation of the long-run relationship for the log price series S50U14 and the log price series S50Z14 is the following equation. For the pair of log S50U14 and log S50Z14, the optimal offsets are selected by the SBIC criteria as shown in Table 5.2, and the evaluation result is shown as the following equation. For a pair of log S50U14 and log S50Z14, the optimal lags are selected by the SBIC criteria as shown in Table 5.4, and the result of TVECM evaluation in regime three is shown in Table 5.5.
Out-of-sample performance or time-rolling procedure is used to make the portfolio simulation more realistic. The first time running will be a training period from July 2, 2014 to July 16, 2014 consisting of 10 trading days or 600 observations. Time roll no.3) of Pair 1 no threshold parameter can be estimated, in this case we skip this time roll.
However, we can still use the estimated threshold parameters to use as signal points in the pairs trading strategy. For 1 pair of S50U14 - S50Z14, the original TVECM pairs trading strategy generates the best result of 1,972 THB net profit for trading 1 contract at a time. For KTB - KTBU14 pair 2, the adjusted TVECM pairs trading strategy generates the best result of 639 THB of net profit for trading 1 contract at a time.
For pair 3 TRUE - TRUEU14 customized TVECM pair trading strategy produces the best result of 965 THB net profit for trading 1 contract at a time. For further studies, we have shortened the length of the training period and the execution period, which will make the pairs trading rule more responsive to price data. In this part, for the first time, a training period will be set from July 9, 2014 to July 16, 2014, which will consist of 5 trading days or 300 observations.
For 1 S50U14 - S50Z14 pair, the original TVECM pair trading strategy also produces the best result of 2972 โโTHB net profit for trading 1 contract at a time. For pair 2 KTB โ KTBU14 customized TVECM pair trading strategy also produces the best result of 2,092 THB net profit for trading 1 contract at a time. For pair 3 TRUE - TRUEU14 customized TVECM pair trading strategy also produces the best result of 912 THB net profit for trading 1 contract at a time.
CONCLUSION
When trading more than one contract, the liquidity of the asset will be the main problem. Either way, we estimate the maximum possible return for each pair by calculating the average trading volume per period and then multiplying it by the return for one contract.
APPENDICES
APPENDIX A
EMPIRICAL RESULT OF PAIR 2 : KTB & KTBU14
Unit root test and long-run relationship estimation
Both log of KTB price series and log of KTBU14 price series are I(1) as illustrated in figure A.1 and figure A.2. The cointegration residuals for both series are I(0) or log of KTB price series and log of KTBU14 price series are cointegrated of order (1,1) as illustrated in Figure A.3. The cointegrating equation for the long-term relationship of log of KTB price series and log of KTBU14 price series is as the following equation.
Short-run dynamic estimation
Threshold Vector Error Correction Model Estimation
For pairs of log KTB and log KTBU14, the optimal delays are selected by SBIC criteria as shown in Table A.4, and the result of TVECM estimation under Three regime is shown in Table A.5.
APPENDIX B
EMPIRICAL RESULT OF PAIR 3 : TRUE & TRUEU14
Unit root test and long-run relationship estimation
Both the TRUE price series log and the TRUEU14 price series log are I(1) as illustrated in Figure B.1 and Figure B.2. The residual of the cointegration of both series is I(0) or the log of the TRUE price series and the log of the TRUEU14 price series is cointegrated of order (1,1) as illustrated in Figure B.3. The cointegrating long-run relationship equation for the log of the TRUE price series and the log of the TRUEU14 price series is as the following equation.
Short-run dynamic estimation
Threshold Vector Error Correction Model Estimation
