Advanced Statistics: Zetatech Trading System
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 | -0.321 | ||||
| SD | 0.854 | ||||
| Sharpe ratio (Glass type estimate) | -0.376 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.370 | ||||
| df | 41.000 | ||||
| t | -0.704 | ||||
| p | 0.757 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.425 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.677 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.420 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.681 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.455 | ||||
| Upside Potential Ratio | 0.629 | ||||
| Upside part of mean | 0.444 | ||||
| Downside part of mean | -0.766 | ||||
| Upside SD | 0.470 | ||||
| Downside SD | 0.707 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 42.000 | ||||
| Mean of predictor | 0.487 | ||||
| Mean of criterion | -0.321 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.854 | ||||
| Covariance | -0.040 | ||||
| r | -0.192 | ||||
| b (slope, estimate of beta) | -0.671 | ||||
| a (intercept, estimate of alpha) | 0.005 | ||||
| Mean Square Error | 0.720 | ||||
| DF error | 40.000 | ||||
| t(b) | -1.241 | ||||
| p(b) | 0.889 | ||||
| t(a) | 0.010 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -1.765 | ||||
| Upperbound of 95% confidence interval for beta | 0.422 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.055 | ||||
| Upperbound of 95% confidence interval for alpha | 1.065 | ||||
| Treynor index (mean / b) | 0.479 | ||||
| Jensen alpha (a) | 0.005 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.676 | ||||
| SD | 4.515 | ||||
| Sharpe ratio (Glass type estimate) | -0.593 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.582 | ||||
| df | 41.000 | ||||
| t | -1.109 | ||||
| p | 0.863 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.644 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.466 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.637 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.474 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.593 | ||||
| Upside Potential Ratio | 0.081 | ||||
| Upside part of mean | 0.366 | ||||
| Downside part of mean | -3.042 | ||||
| Upside SD | 0.359 | ||||
| Downside SD | 4.513 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 42.000 | ||||
| Mean of predictor | 0.449 | ||||
| Mean of criterion | -2.676 | ||||
| SD of predictor | 0.229 | ||||
| SD of criterion | 4.515 | ||||
| Covariance | -0.233 | ||||
| r | -0.226 | ||||
| b (slope, estimate of beta) | -4.465 | ||||
| a (intercept, estimate of alpha) | -0.669 | ||||
| Mean Square Error | 19.830 | ||||
| DF error | 40.000 | ||||
| t(b) | -1.467 | ||||
| p(b) | 0.925 | ||||
| t(a) | -0.244 | ||||
| p(a) | 0.596 | ||||
| Lowerbound of 95% confidence interval for beta | -10.615 | ||||
| Upperbound of 95% confidence interval for beta | 1.685 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.217 | ||||
| Upperbound of 95% confidence interval for alpha | 4.879 | ||||
| Treynor index (mean / b) | 0.599 | ||||
| Jensen alpha (a) | -0.669 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.906 | ||||
| Expected Shortfall on VaR | 0.940 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.195 | ||||
| Expected Shortfall on VaR | 0.416 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 42.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.802 | ||||
| Mean of quarter 1 | 0.768 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.144 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.167 | ||||
| Mean of outliers low | 0.635 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.190 | ||||
| Mean of outliers high | 1.198 | ||||
| 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) | 0.473 | ||||
| VaR(95%) (regression method) | 0.369 | ||||
| Expected Shortfall (regression method) | 1.086 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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) | -0.286 | ||||
| Compounded annual return (geometric extrapolation) | -0.928 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.928 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.987 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1090.167 | ||||
| SD | 1347.360 | ||||
| Sharpe ratio (Glass type estimate) | 0.809 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.808 | ||||
| df | 929.000 | ||||
| t | 1.524 | ||||
| p | 0.064 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.232 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.850 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.232 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.849 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 742.160 | ||||
| Upside Potential Ratio | 744.971 | ||||
| Upside part of mean | 1094.295 | ||||
| Downside part of mean | -4.128 | ||||
| Upside SD | 1348.317 | ||||
| Downside SD | 1.469 | ||||
| N nonnegative terms | 166.000 | ||||
| N negative terms | 764.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 930.000 | ||||
| Mean of predictor | 0.527 | ||||
| Mean of criterion | 1090.167 | ||||
| SD of predictor | 0.304 | ||||
| SD of criterion | 1347.360 | ||||
| Covariance | -0.034 | ||||
| r | -0.000 | ||||
| b (slope, estimate of beta) | -0.372 | ||||
| a (intercept, estimate of alpha) | 1090.363 | ||||
| Mean Square Error | 1817334.038 | ||||
| DF error | 928.000 | ||||
| t(b) | -0.003 | ||||
| p(b) | 0.501 | ||||
| t(a) | 1.515 | ||||
| p(a) | 0.065 | ||||
| Lowerbound of 95% confidence interval for beta | -286.165 | ||||
| Upperbound of 95% confidence interval for beta | 285.422 | ||||
| Lowerbound of 95% confidence interval for alpha | -321.935 | ||||
| Upperbound of 95% confidence interval for alpha | 2502.662 | ||||
| Treynor index (mean / b) | -2932.990 | ||||
| Jensen alpha (a) | 1090.363 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.639 | ||||
| SD | 10.228 | ||||
| Sharpe ratio (Glass type estimate) | -0.258 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.258 | ||||
| df | 929.000 | ||||
| t | -0.486 | ||||
| p | 0.686 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.298 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.782 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.298 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.783 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.339 | ||||
| Upside Potential Ratio | 1.211 | ||||
| Upside part of mean | 9.435 | ||||
| Downside part of mean | -12.074 | ||||
| Upside SD | 6.621 | ||||
| Downside SD | 7.790 | ||||
| N nonnegative terms | 166.000 | ||||
| N negative terms | 764.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 930.000 | ||||
| Mean of predictor | 0.480 | ||||
| Mean of criterion | -2.639 | ||||
| SD of predictor | 0.306 | ||||
| SD of criterion | 10.228 | ||||
| Covariance | -0.116 | ||||
| r | -0.037 | ||||
| b (slope, estimate of beta) | -1.240 | ||||
| a (intercept, estimate of alpha) | -2.043 | ||||
| Mean Square Error | 104.572 | ||||
| DF error | 928.000 | ||||
| t(b) | -1.130 | ||||
| p(b) | 0.871 | ||||
| t(a) | -0.375 | ||||
| p(a) | 0.646 | ||||
| Lowerbound of 95% confidence interval for beta | -3.393 | ||||
| Upperbound of 95% confidence interval for beta | 0.913 | ||||
| Lowerbound of 95% confidence interval for alpha | -12.745 | ||||
| Upperbound of 95% confidence interval for alpha | 8.659 | ||||
| Treynor index (mean / b) | 2.128 | ||||
| Jensen alpha (a) | -2.043 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.650 | ||||
| Expected Shortfall on VaR | 0.724 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.048 | ||||
| Expected Shortfall on VaR | 0.109 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 930.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2152.667 | ||||
| Mean of quarter 1 | 0.938 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 17.671 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 121.000 | ||||
| Percentage of outliers low | 0.130 | ||||
| Mean of outliers low | 0.880 | ||||
| Number of outliers high | 167.000 | ||||
| Percentage of outliers high | 0.180 | ||||
| Mean of outliers high | 24.260 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.188 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| Extreme Value Index (regression method) | 0.178 | ||||
| VaR(95%) (regression method) | 0.041 | ||||
| Expected Shortfall (regression method) | 0.097 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.044 | ||||
| Quartile 3 | 0.111 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.031 | ||||
| Mean of quarter 3 | 0.074 | ||||
| Mean of quarter 4 | 0.492 | ||||
| Inter Quartile Range | 0.090 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.182 | ||||
| Mean of outliers high | 0.667 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.353 | ||||
| VaR(95%) (moments method) | 0.428 | ||||
| Expected Shortfall (moments method) | 0.463 | ||||
| Extreme Value Index (regression method) | 0.802 | ||||
| VaR(95%) (regression method) | 1.050 | ||||
| Expected Shortfall (regression method) | 6.129 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.282 | ||||
| Compounded annual return (geometric extrapolation) | -0.925 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.925 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.882 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.277 | ||||
| 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 | 1.002 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.468 | ||||
| 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 | 0.891 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.472 | ||||
| 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) | -8739992327746323.000 | ||||
| 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) | 567378933076448817268156400664576.000 | ||||
| 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 | ||||