All the 85 trivariate pairs with correlation weigh are not found feasible for trading. Cut off correlation is derived for this segment, which is shown graphically below. The cut off correlation value is 0.68. For further analysis the pairs with correlation above 0.68 are only considered as they follow conventional risk-return relationship. 60 such pairs are found in this segment.

For these 60 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 60 2.623 2.207 0.285
0.7/0.4 60 4.302 6.597 0.852
0.6/0.4 60 3.195 3.522 0.455
0.6/0.3 60 2.718 1.886 0.244
0.5/0.3 60 3.950 5.982 0.772
0.5/0.2 60 2.166 1.440 0.186
0.4/0.2 60 1.895 1.949 0.252
0.4/0.1 60 2.339 5.806 0.750
0.3/0.1 60 1.314 1.221 0.158

Table 18: mean stat for trivariate pairs (correlation)

One-Sample Test
Test Value = 0
t df Sig. (2-tailed) MeanDifference 95% Confidence Interval of the Difference
Lower Upper
0.7/0.5 9.208 59 5.16E-13 2.62E+00 2.05E+00 3.19E+00
0.7/0.4 5.051 59 4.52E-06 4.30E+00 2.60E+00 6.01E+00
0.6/0.4 7.025 59 2.45E-09 3.19E+00 2.28E+00 4.10E+00
0.6/0.3 11.162 59 3.56E-16 2.72E+00 2.23E+00 3.21E+00
0.5/0.3 5.115 59 3.59E-06 3.95E+00 2.40E+00 5.50E+00
0.5/0.2 11.649 59 6.22E-17 2.17E+00 1.79E+00 2.54E+00
0.4/0.2 7.530 59 3.42E-10 1.90E+00 1.39E+00 2.40E+00
0.4/0.1 3.120 59 2.80E-03 2.34E+00 8.39E-01 3.84E+00
0.3/0.1 8.336 59 1.48E-11 1.31E+00 9.98E-01 1.63E+00

Table 19: t stat for trivariate pair (correlation)

For 59 degree of freedom t critical value (2 tailed) at 95% confidence level is 2.000. In the test result all the obtained t values are greater than the critical value, which suggests that the return series of every trade signal are statistically significant at 95% confidence level. In other words, it suggests that the average returns are feasible and reproducible in the future following the same trade signal.

This trivariate correlation weigh pair trading strategy return is statistically compared with the naive approach return. For the purpose the average of all signal return of every eligible pair is compared with the 1000 random simulation return from the NSE Index in the same time frame of the study. One way ANOVA testing has been done for mean comparison.

Mean of Bivariate equal weight pair strategy returns is = ^strategy = 272%

Mean of 1000 random return from NSE Nifty 50 index = ^Naive = 14.03%

artificial_pair correl tri simulation
Sum of Squares df MeanSquare F Sig.
Between Groups 377.38 1 377.38 947.19 4.6236E-149
Within Groups 421.53 1058 0.40
Total 798.91 1059

Table 20.

Representative APR 391%

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