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.**