## PAIR TRADING STRATEGY IN INDIAN CAPITAL MARKET: Natural Pair(2)

Mean of Natural pair strategy returns is = ^strategy = 386%

Mean of 1000 random return from NSE Nifty 50 index = ^Naive = 16.89%

 ANOVA natural_pair simulation Sum of Squares df Mean Square F Sig. Between Groups 635.342 1 635.342 481.458 0.000 Within Groups 1397.477 1059 1.320 Total 2032.819 1060

Table.6: ANOVA result for natural pairs

Two series of variables are grouped and tested. Test result signifies that F value is very high compared to Critical F value. Hence the Null hypothesis is rejected at 99% confidence level. So, the means of Pair strategy return and Naive return are statistically different. Pair strategy return is much higher than the Naive return, and hence its recommended to invest in natural pair to cash the arbitrage opportunity.

Artificial Pair with 2 stocks formed using Equal Method

For this segment of bivariate pairs, trade signal wise generated no of trades are plotted to get the trend.

 Trade signal Avg. No. of Trades 0.7/0.5 6.6 0.7/0.4 5.1 0.6/0.4 6.9 0.6/0.3 5.5 0.5/0.3 7.5 0.5/0.2 5.8 0.4/0.2 8.0 0.4/0.1 6.1 0.3/0.1 7.9

Table 7: Avg no. of trade for equal weight method

All the 101 bivariate pairs with equal weigh are not found feasible for trading. Empirical result shows, pairs with low correlation with the trading asset are having higher volatility and hence give uncertain return. So, a cut off correlation is derived for this segment, which is shown graphically below. The cut off correlation value is 0.75. For further analysis the pairs with correlation above 0.75 are only considered as they follow conventional risk-return relationship. 54 such pairs are found in this segment.

For these 54 pairs individual sample 2-tail t-test is done for each trading signal to check the statistical significance of the obtained returns. The test result includes mean return for each signal, standard deviation of each signal set, and t statistics. The test result is shown below:

 One-Sample Statistics N Mean Std. Deviation Std. Error Mean 0.7/0.5 54 2.558 1.865 0.254 0.7/0.4 54 3.569 4.632 0.630 0.6/0.4 54 2.631 2.753 0.375 0.6/0.3 54 2.613 2.169 0.295 0.5/0.3 54 7.373 33.520 4.561 0.5/0.2 54 2.219 1.312 0.179 0.4/0.2 54 2.121 2.218 0.302 0.4/0.1 54 3.095 7.591 1.033 0.3/0.1 54 2.102 2.923 0.398

Table 8: Mean stat for bivariate pair: equal

 One-Sample Test Test Value = 0 TradeSignal t Df Sig. (2-tailed) MeanDifference 95% Confidence Interval of the Difference Lower Upper 0.7/0.5 10.078 53 6.41E-14 2.56E+00 2.05E+00 3.07E+00 0.7/0.4 5.662 53 6.20E-07 3.57E+00 2.30E+00 4.83E+00 0.6/0.4 7.024 53 4.12E-09 2.63E+00 1.88E+00 3.38E+00 0.6/0.3 8.855 53 4.95E-12 2.61E+00 2.02E+00 3.20E+00 0.5/0.3 1.616 53 1.12E-01 7.37E+00 -1.78E+00 1.65E+01 0.5/0.2 12.429 53 2.47E-17 2.22E+00 1.86E+00 2.58E+00 0.4/0.2 7.028 53 4.07E-09 2.12E+00 1.52E+00 2.73E+00 0.4/0.1 2.996 53 4.15E-03 3.10E+00 1.02E+00 5.17E+00 0.3/0.1 5.285 53 2.41E-06 2.10E+00 1.30E+00 2.90E+00

Table 9.