Advanced Statistics: Zig Zag North
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 | 0.858 | ||||
| SD | 0.742 | ||||
| Sharpe ratio (Glass type estimate) | 1.157 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.144 | ||||
| df | 67.000 | ||||
| t | 2.753 | ||||
| p | 0.004 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.306 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.999 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.298 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.989 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.748 | ||||
| Upside Potential Ratio | 4.244 | ||||
| Upside part of mean | 1.326 | ||||
| Downside part of mean | -0.467 | ||||
| Upside SD | 0.712 | ||||
| Downside SD | 0.312 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 22.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.315 | ||||
| Mean of criterion | 0.858 | ||||
| SD of predictor | 0.363 | ||||
| SD of criterion | 0.742 | ||||
| Covariance | 0.133 | ||||
| r | 0.494 | ||||
| b (slope, estimate of beta) | 1.010 | ||||
| a (intercept, estimate of alpha) | 0.540 | ||||
| Mean Square Error | 0.423 | ||||
| DF error | 66.000 | ||||
| t(b) | 4.615 | ||||
| p(b) | 0.000 | ||||
| t(a) | 1.918 | ||||
| p(a) | 0.030 | ||||
| Lowerbound of 95% confidence interval for beta | 0.573 | ||||
| Upperbound of 95% confidence interval for beta | 1.447 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.022 | ||||
| Upperbound of 95% confidence interval for alpha | 1.103 | ||||
| Treynor index (mean / b) | 0.850 | ||||
| Jensen alpha (a) | 0.540 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.609 | ||||
| SD | 0.657 | ||||
| Sharpe ratio (Glass type estimate) | 0.927 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.916 | ||||
| df | 67.000 | ||||
| t | 2.206 | ||||
| p | 0.015 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.085 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.761 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.078 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.754 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.646 | ||||
| Upside Potential Ratio | 3.068 | ||||
| Upside part of mean | 1.136 | ||||
| Downside part of mean | -0.526 | ||||
| Upside SD | 0.566 | ||||
| Downside SD | 0.370 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 22.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.249 | ||||
| Mean of criterion | 0.609 | ||||
| SD of predictor | 0.350 | ||||
| SD of criterion | 0.657 | ||||
| Covariance | 0.111 | ||||
| r | 0.481 | ||||
| b (slope, estimate of beta) | 0.903 | ||||
| a (intercept, estimate of alpha) | 0.384 | ||||
| Mean Square Error | 0.337 | ||||
| DF error | 66.000 | ||||
| t(b) | 4.453 | ||||
| p(b) | 0.000 | ||||
| t(a) | 1.541 | ||||
| p(a) | 0.064 | ||||
| Lowerbound of 95% confidence interval for beta | 0.498 | ||||
| Upperbound of 95% confidence interval for beta | 1.308 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.114 | ||||
| Upperbound of 95% confidence interval for alpha | 0.882 | ||||
| Treynor index (mean / b) | 0.675 | ||||
| Jensen alpha (a) | 0.384 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.230 | ||||
| Expected Shortfall on VaR | 0.287 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.065 | ||||
| Expected Shortfall on VaR | 0.145 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 68.000 | ||||
| Minimum | 0.573 | ||||
| Quartile 1 | 0.964 | ||||
| Median | 1.057 | ||||
| Quartile 3 | 1.131 | ||||
| Maximum | 1.869 | ||||
| Mean of quarter 1 | 0.854 | ||||
| Mean of quarter 2 | 1.023 | ||||
| Mean of quarter 3 | 1.089 | ||||
| Mean of quarter 4 | 1.335 | ||||
| Inter Quartile Range | 0.167 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.641 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.074 | ||||
| Mean of outliers high | 1.651 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.056 | ||||
| VaR(95%) (moments method) | 0.122 | ||||
| Expected Shortfall (moments method) | 0.176 | ||||
| Extreme Value Index (regression method) | 0.492 | ||||
| VaR(95%) (regression method) | 0.137 | ||||
| Expected Shortfall (regression method) | 0.298 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.013 | ||||
| Quartile 1 | 0.080 | ||||
| Median | 0.113 | ||||
| Quartile 3 | 0.296 | ||||
| Maximum | 0.514 | ||||
| Mean of quarter 1 | 0.040 | ||||
| Mean of quarter 2 | 0.108 | ||||
| Mean of quarter 3 | 0.233 | ||||
| Mean of quarter 4 | 0.414 | ||||
| Inter Quartile Range | 0.216 | ||||
| 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) | -10.619 | ||||
| VaR(95%) (moments method) | 0.447 | ||||
| Expected Shortfall (moments method) | 0.447 | ||||
| Extreme Value Index (regression method) | -1.548 | ||||
| VaR(95%) (regression method) | 0.582 | ||||
| Expected Shortfall (regression method) | 0.597 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 6.974 | ||||
| Compounded annual return (geometric extrapolation) | 0.922 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.794 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.227 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.212 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.065 | ||||
| SD | 0.886 | ||||
| Sharpe ratio (Glass type estimate) | 1.202 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.201 | ||||
| df | 1497.000 | ||||
| t | 2.874 | ||||
| p | 0.453 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.381 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.022 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.380 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.022 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.866 | ||||
| Upside Potential Ratio | 8.071 | ||||
| Upside part of mean | 4.605 | ||||
| Downside part of mean | -3.540 | ||||
| Upside SD | 0.681 | ||||
| Downside SD | 0.571 | ||||
| N nonnegative terms | 849.000 | ||||
| N negative terms | 649.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1498.000 | ||||
| Mean of predictor | 0.483 | ||||
| Mean of criterion | 1.065 | ||||
| SD of predictor | 0.648 | ||||
| SD of criterion | 0.886 | ||||
| Covariance | 0.098 | ||||
| r | 0.171 | ||||
| b (slope, estimate of beta) | 0.234 | ||||
| a (intercept, estimate of alpha) | 0.952 | ||||
| Mean Square Error | 0.762 | ||||
| DF error | 1496.000 | ||||
| t(b) | 6.712 | ||||
| p(b) | 0.415 | ||||
| t(a) | 2.604 | ||||
| p(a) | 0.466 | ||||
| Lowerbound of 95% confidence interval for beta | 0.165 | ||||
| Upperbound of 95% confidence interval for beta | 0.302 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.235 | ||||
| Upperbound of 95% confidence interval for alpha | 1.669 | ||||
| Treynor index (mean / b) | 4.553 | ||||
| Jensen alpha (a) | 0.952 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.676 | ||||
| SD | 0.881 | ||||
| Sharpe ratio (Glass type estimate) | 0.768 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.768 | ||||
| df | 1497.000 | ||||
| t | 1.836 | ||||
| p | 0.470 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.052 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.588 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.052 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.588 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.081 | ||||
| Upside Potential Ratio | 7.035 | ||||
| Upside part of mean | 4.400 | ||||
| Downside part of mean | -3.723 | ||||
| Upside SD | 0.621 | ||||
| Downside SD | 0.625 | ||||
| N nonnegative terms | 849.000 | ||||
| N negative terms | 649.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1498.000 | ||||
| Mean of predictor | 0.280 | ||||
| Mean of criterion | 0.676 | ||||
| SD of predictor | 0.635 | ||||
| SD of criterion | 0.881 | ||||
| Covariance | 0.088 | ||||
| r | 0.157 | ||||
| b (slope, estimate of beta) | 0.218 | ||||
| a (intercept, estimate of alpha) | 0.615 | ||||
| Mean Square Error | 0.757 | ||||
| DF error | 1496.000 | ||||
| t(b) | 6.159 | ||||
| p(b) | 0.421 | ||||
| t(a) | 1.691 | ||||
| p(a) | 0.478 | ||||
| Lowerbound of 95% confidence interval for beta | 0.148 | ||||
| Upperbound of 95% confidence interval for beta | 0.287 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | 1.329 | ||||
| Treynor index (mean / b) | 3.104 | ||||
| Jensen alpha (a) | 0.615 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.083 | ||||
| Expected Shortfall on VaR | 0.104 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.061 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1498.000 | ||||
| Minimum | 0.670 | ||||
| Quartile 1 | 0.988 | ||||
| Median | 1.003 | ||||
| Quartile 3 | 1.019 | ||||
| Maximum | 1.493 | ||||
| Mean of quarter 1 | 0.950 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.010 | ||||
| Mean of quarter 4 | 1.060 | ||||
| Inter Quartile Range | 0.031 | ||||
| Number outliers low | 87.000 | ||||
| Percentage of outliers low | 0.058 | ||||
| Mean of outliers low | 0.881 | ||||
| Number of outliers high | 101.000 | ||||
| Percentage of outliers high | 0.067 | ||||
| Mean of outliers high | 1.126 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.480 | ||||
| VaR(95%) (moments method) | 0.045 | ||||
| Expected Shortfall (moments method) | 0.102 | ||||
| Extreme Value Index (regression method) | 0.211 | ||||
| VaR(95%) (regression method) | 0.044 | ||||
| Expected Shortfall (regression method) | 0.073 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 67.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.016 | ||||
| Median | 0.044 | ||||
| Quartile 3 | 0.133 | ||||
| Maximum | 0.608 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | 0.027 | ||||
| Mean of quarter 3 | 0.078 | ||||
| Mean of quarter 4 | 0.265 | ||||
| Inter Quartile Range | 0.118 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.060 | ||||
| Mean of outliers high | 0.480 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.141 | ||||
| VaR(95%) (moments method) | 0.277 | ||||
| Expected Shortfall (moments method) | 0.394 | ||||
| Extreme Value Index (regression method) | -0.479 | ||||
| VaR(95%) (regression method) | 0.246 | ||||
| Expected Shortfall (regression method) | 0.277 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 10.573 | ||||
| Compounded annual return (geometric extrapolation) | 1.055 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.737 | ||||
| Compounded annual return / average of 25% largest draw downs | 3.981 | ||||
| Compounded annual return / Expected Shortfall lognormal | 10.179 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 4.011 | ||||
| SD | 1.400 | ||||
| Sharpe ratio (Glass type estimate) | 2.866 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.849 | ||||
| df | 130.000 | ||||
| t | 2.027 | ||||
| p | 0.413 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.067 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 5.654 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.056 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 5.643 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4.748 | ||||
| Upside Potential Ratio | 12.776 | ||||
| Upside part of mean | 10.793 | ||||
| Downside part of mean | -6.781 | ||||
| Upside SD | 1.137 | ||||
| Downside SD | 0.845 | ||||
| N nonnegative terms | 75.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.705 | ||||
| Mean of criterion | 4.011 | ||||
| SD of predictor | 0.505 | ||||
| SD of criterion | 1.400 | ||||
| Covariance | 0.621 | ||||
| r | 0.878 | ||||
| b (slope, estimate of beta) | 2.434 | ||||
| a (intercept, estimate of alpha) | -0.137 | ||||
| Mean Square Error | 0.451 | ||||
| DF error | 129.000 | ||||
| t(b) | 20.866 | ||||
| p(b) | 0.025 | ||||
| t(a) | -0.141 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | 2.203 | ||||
| Upperbound of 95% confidence interval for beta | 2.664 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.058 | ||||
| Upperbound of 95% confidence interval for alpha | 1.783 | ||||
| Treynor index (mean / b) | 1.648 | ||||
| Jensen alpha (a) | -0.137 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 3.034 | ||||
| SD | 1.384 | ||||
| Sharpe ratio (Glass type estimate) | 2.193 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.180 | ||||
| df | 130.000 | ||||
| t | 1.551 | ||||
| p | 0.433 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.596 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.974 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.604 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.965 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.344 | ||||
| Upside Potential Ratio | 11.247 | ||||
| Upside part of mean | 10.207 | ||||
| Downside part of mean | -7.173 | ||||
| Upside SD | 1.054 | ||||
| Downside SD | 0.908 | ||||
| N nonnegative terms | 75.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.574 | ||||
| Mean of criterion | 3.034 | ||||
| SD of predictor | 0.501 | ||||
| SD of criterion | 1.384 | ||||
| Covariance | 0.609 | ||||
| r | 0.878 | ||||
| b (slope, estimate of beta) | 2.424 | ||||
| a (intercept, estimate of alpha) | -0.782 | ||||
| Mean Square Error | 0.441 | ||||
| DF error | 129.000 | ||||
| t(b) | 20.876 | ||||
| p(b) | 0.025 | ||||
| t(a) | -0.817 | ||||
| p(a) | 0.546 | ||||
| Lowerbound of 95% confidence interval for beta | 2.194 | ||||
| Upperbound of 95% confidence interval for beta | 2.654 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.674 | ||||
| Upperbound of 95% confidence interval for alpha | 1.111 | ||||
| Treynor index (mean / b) | 1.252 | ||||
| Jensen alpha (a) | -0.782 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.121 | ||||
| Expected Shortfall on VaR | 0.151 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.054 | ||||
| Expected Shortfall on VaR | 0.107 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.812 | ||||
| Quartile 1 | 0.965 | ||||
| Median | 1.014 | ||||
| Quartile 3 | 1.067 | ||||
| Maximum | 1.298 | ||||
| Mean of quarter 1 | 0.908 | ||||
| Mean of quarter 2 | 0.992 | ||||
| Mean of quarter 3 | 1.042 | ||||
| Mean of quarter 4 | 1.121 | ||||
| Inter Quartile Range | 0.101 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.812 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.282 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.438 | ||||
| VaR(95%) (moments method) | 0.086 | ||||
| Expected Shortfall (moments method) | 0.101 | ||||
| Extreme Value Index (regression method) | -0.789 | ||||
| VaR(95%) (regression method) | 0.100 | ||||
| Expected Shortfall (regression method) | 0.111 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.012 | ||||
| Quartile 1 | 0.029 | ||||
| Median | 0.105 | ||||
| Quartile 3 | 0.174 | ||||
| Maximum | 0.605 | ||||
| Mean of quarter 1 | 0.020 | ||||
| Mean of quarter 2 | 0.065 | ||||
| Mean of quarter 3 | 0.151 | ||||
| Mean of quarter 4 | 0.337 | ||||
| Inter Quartile Range | 0.145 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.091 | ||||
| Mean of outliers high | 0.605 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.261 | ||||
| VaR(95%) (moments method) | 0.378 | ||||
| Expected Shortfall (moments method) | 0.617 | ||||
| Extreme Value Index (regression method) | 2.391 | ||||
| VaR(95%) (regression method) | 0.718 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 7.322 | ||||
| Compounded annual return (geometric extrapolation) | 20.724 | ||||
| Calmar ratio (compounded annual return / max draw down) | 34.257 | ||||
| Compounded annual return / average of 25% largest draw downs | 61.573 | ||||
| Compounded annual return / Expected Shortfall lognormal | 136.822 | ||||