Advanced Statistics: Pairs Trading QID QLD 2.0
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
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| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.093 | ||||
| SD | 0.127 | ||||
| Sharpe ratio (Glass type estimate) | -0.735 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.727 | ||||
| df | 67.000 | ||||
| t | -1.750 | ||||
| p | 0.958 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.565 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.100 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.559 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.106 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.777 | ||||
| Upside Potential Ratio | 0.313 | ||||
| Upside part of mean | 0.038 | ||||
| Downside part of mean | -0.131 | ||||
| Upside SD | 0.047 | ||||
| Downside SD | 0.120 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 63.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.310 | ||||
| Mean of criterion | -0.093 | ||||
| SD of predictor | 0.191 | ||||
| SD of criterion | 0.127 | ||||
| Covariance | 0.004 | ||||
| r | 0.160 | ||||
| b (slope, estimate of beta) | 0.107 | ||||
| a (intercept, estimate of alpha) | -0.126 | ||||
| Mean Square Error | 0.016 | ||||
| DF error | 66.000 | ||||
| t(b) | 1.320 | ||||
| p(b) | 0.096 | ||||
| t(a) | -2.155 | ||||
| p(a) | 0.983 | ||||
| Lowerbound of 95% confidence interval for beta | -0.055 | ||||
| Upperbound of 95% confidence interval for beta | 0.268 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.244 | ||||
| Upperbound of 95% confidence interval for alpha | -0.009 | ||||
| Treynor index (mean / b) | -0.875 | ||||
| Jensen alpha (a) | -0.126 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.102 | ||||
| SD | 0.139 | ||||
| Sharpe ratio (Glass type estimate) | -0.734 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.725 | ||||
| df | 67.000 | ||||
| t | -1.746 | ||||
| p | 0.957 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.564 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.102 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.558 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.107 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.763 | ||||
| Upside Potential Ratio | 0.271 | ||||
| Upside part of mean | 0.036 | ||||
| Downside part of mean | -0.139 | ||||
| Upside SD | 0.045 | ||||
| Downside SD | 0.134 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 63.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.288 | ||||
| Mean of criterion | -0.102 | ||||
| SD of predictor | 0.185 | ||||
| SD of criterion | 0.139 | ||||
| Covariance | 0.004 | ||||
| r | 0.162 | ||||
| b (slope, estimate of beta) | 0.122 | ||||
| a (intercept, estimate of alpha) | -0.138 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 66.000 | ||||
| t(b) | 1.334 | ||||
| p(b) | 0.093 | ||||
| t(a) | -2.151 | ||||
| p(a) | 0.982 | ||||
| Lowerbound of 95% confidence interval for beta | -0.061 | ||||
| Upperbound of 95% confidence interval for beta | 0.306 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.265 | ||||
| Upperbound of 95% confidence interval for alpha | -0.010 | ||||
| Treynor index (mean / b) | -0.836 | ||||
| Jensen alpha (a) | -0.138 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.072 | ||||
| Expected Shortfall on VaR | 0.087 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.076 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 68.000 | ||||
| Minimum | 0.757 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.087 | ||||
| Mean of quarter 1 | 0.970 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.014 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.147 | ||||
| Mean of outliers low | 0.949 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.074 | ||||
| Mean of outliers high | 1.046 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.682 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.601 | ||||
| VaR(95%) (regression method) | 0.039 | ||||
| Expected Shortfall (regression method) | 0.186 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.402 | ||||
| Quartile 1 | 0.402 | ||||
| Median | 0.402 | ||||
| Quartile 3 | 0.402 | ||||
| Maximum | 0.402 | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.050 | ||||
| Compounded annual return (geometric extrapolation) | -0.057 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.141 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.648 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.090 | ||||
| SD | 0.152 | ||||
| Sharpe ratio (Glass type estimate) | -0.592 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.592 | ||||
| df | 1498.000 | ||||
| t | -1.417 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.412 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.227 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.412 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.228 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.798 | ||||
| Upside Potential Ratio | 1.527 | ||||
| Upside part of mean | 0.172 | ||||
| Downside part of mean | -0.263 | ||||
| Upside SD | 0.102 | ||||
| Downside SD | 0.113 | ||||
| N nonnegative terms | 58.000 | ||||
| N negative terms | 1441.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1499.000 | ||||
| Mean of predictor | 0.341 | ||||
| Mean of criterion | -0.090 | ||||
| SD of predictor | 0.291 | ||||
| SD of criterion | 0.152 | ||||
| Covariance | 0.004 | ||||
| r | 0.079 | ||||
| b (slope, estimate of beta) | 0.041 | ||||
| a (intercept, estimate of alpha) | -0.104 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 1497.000 | ||||
| t(b) | 3.070 | ||||
| p(b) | 0.450 | ||||
| t(a) | -1.639 | ||||
| p(a) | 0.527 | ||||
| Lowerbound of 95% confidence interval for beta | 0.015 | ||||
| Upperbound of 95% confidence interval for beta | 0.068 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.229 | ||||
| Upperbound of 95% confidence interval for alpha | 0.021 | ||||
| Treynor index (mean / b) | -2.182 | ||||
| Jensen alpha (a) | -0.104 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.102 | ||||
| SD | 0.153 | ||||
| Sharpe ratio (Glass type estimate) | -0.666 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.666 | ||||
| df | 1498.000 | ||||
| t | -1.593 | ||||
| p | 0.521 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.486 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.154 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.485 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.154 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.859 | ||||
| Upside Potential Ratio | 1.414 | ||||
| Upside part of mean | 0.167 | ||||
| Downside part of mean | -0.269 | ||||
| Upside SD | 0.097 | ||||
| Downside SD | 0.118 | ||||
| N nonnegative terms | 58.000 | ||||
| N negative terms | 1441.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1499.000 | ||||
| Mean of predictor | 0.299 | ||||
| Mean of criterion | -0.102 | ||||
| SD of predictor | 0.291 | ||||
| SD of criterion | 0.153 | ||||
| Covariance | 0.004 | ||||
| r | 0.082 | ||||
| b (slope, estimate of beta) | 0.043 | ||||
| a (intercept, estimate of alpha) | -0.115 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 1497.000 | ||||
| t(b) | 3.188 | ||||
| p(b) | 0.448 | ||||
| t(a) | -1.796 | ||||
| p(a) | 0.530 | ||||
| Lowerbound of 95% confidence interval for beta | 0.017 | ||||
| Upperbound of 95% confidence interval for beta | 0.070 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.240 | ||||
| Upperbound of 95% confidence interval for alpha | 0.011 | ||||
| Treynor index (mean / b) | -2.360 | ||||
| Jensen alpha (a) | -0.115 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1499.000 | ||||
| Minimum | 0.849 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.178 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 75.000 | ||||
| Percentage of outliers low | 0.050 | ||||
| Mean of outliers low | 0.983 | ||||
| Number of outliers high | 62.000 | ||||
| Percentage of outliers high | 0.041 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.068 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.489 | ||||
| VaR(95%) (regression method) | -0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.066 | ||||
| Quartile 1 | 0.150 | ||||
| Median | 0.234 | ||||
| Quartile 3 | 0.318 | ||||
| Maximum | 0.402 | ||||
| Mean of quarter 1 | 0.066 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.402 | ||||
| Inter Quartile Range | 0.168 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.049 | ||||
| Compounded annual return (geometric extrapolation) | -0.056 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.140 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.140 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.854 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.045 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.374 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.973 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.375 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.000 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8688123051968524.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | 54488443861920236075211026333696.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||