Advanced Statistics: Aristoteles Premium
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 | 0.359 | ||||
| SD | 1.007 | ||||
| Sharpe ratio (Glass type estimate) | 0.356 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.351 | ||||
| df | 55.000 | ||||
| t | 0.770 | ||||
| p | 0.222 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.555 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.264 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.558 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.261 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.903 | ||||
| Upside Potential Ratio | 1.771 | ||||
| Upside part of mean | 0.703 | ||||
| Downside part of mean | -0.345 | ||||
| Upside SD | 0.921 | ||||
| Downside SD | 0.397 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 56.000 | ||||
| Mean of predictor | 0.348 | ||||
| Mean of criterion | 0.359 | ||||
| SD of predictor | 0.277 | ||||
| SD of criterion | 1.007 | ||||
| Covariance | -0.096 | ||||
| r | -0.345 | ||||
| b (slope, estimate of beta) | -1.256 | ||||
| a (intercept, estimate of alpha) | 0.796 | ||||
| Mean Square Error | 0.909 | ||||
| DF error | 54.000 | ||||
| t(b) | -2.702 | ||||
| p(b) | 0.995 | ||||
| t(a) | 1.693 | ||||
| p(a) | 0.048 | ||||
| Lowerbound of 95% confidence interval for beta | -2.188 | ||||
| Upperbound of 95% confidence interval for beta | -0.324 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.147 | ||||
| Upperbound of 95% confidence interval for alpha | 1.738 | ||||
| Treynor index (mean / b) | -0.286 | ||||
| Jensen alpha (a) | 0.796 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 0.925 | ||||
| Sharpe ratio (Glass type estimate) | -0.041 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.040 | ||||
| df | 55.000 | ||||
| t | -0.089 | ||||
| p | 0.535 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.948 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.866 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.948 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.867 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.053 | ||||
| Upside Potential Ratio | 0.667 | ||||
| Upside part of mean | 0.474 | ||||
| Downside part of mean | -0.512 | ||||
| Upside SD | 0.579 | ||||
| Downside SD | 0.711 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 56.000 | ||||
| Mean of predictor | 0.308 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.925 | ||||
| Covariance | -0.068 | ||||
| r | -0.279 | ||||
| b (slope, estimate of beta) | -0.982 | ||||
| a (intercept, estimate of alpha) | 0.264 | ||||
| Mean Square Error | 0.803 | ||||
| DF error | 54.000 | ||||
| t(b) | -2.138 | ||||
| p(b) | 0.981 | ||||
| t(a) | 0.602 | ||||
| p(a) | 0.275 | ||||
| Lowerbound of 95% confidence interval for beta | -1.902 | ||||
| Upperbound of 95% confidence interval for beta | -0.061 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.615 | ||||
| Upperbound of 95% confidence interval for alpha | 1.143 | ||||
| Treynor index (mean / b) | 0.039 | ||||
| Jensen alpha (a) | 0.264 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.357 | ||||
| Expected Shortfall on VaR | 0.423 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.079 | ||||
| Expected Shortfall on VaR | 0.178 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 56.000 | ||||
| Minimum | 0.229 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 2.646 | ||||
| Mean of quarter 1 | 0.895 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.238 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.143 | ||||
| Mean of outliers low | 0.817 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 1.469 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.463 | ||||
| VaR(95%) (moments method) | 0.043 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 2.189 | ||||
| VaR(95%) (regression method) | 0.059 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.069 | ||||
| Quartile 1 | 0.260 | ||||
| Median | 0.451 | ||||
| Quartile 3 | 0.643 | ||||
| Maximum | 0.834 | ||||
| Mean of quarter 1 | 0.069 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.834 | ||||
| Inter Quartile Range | 0.382 | ||||
| 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) | 0.006 | ||||
| Compounded annual return (geometric extrapolation) | 0.006 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.007 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.007 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.014 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.783 | ||||
| SD | 1.493 | ||||
| Sharpe ratio (Glass type estimate) | 0.525 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.524 | ||||
| df | 1239.000 | ||||
| t | 1.141 | ||||
| p | 0.479 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.377 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.426 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.377 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.425 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.194 | ||||
| Upside Potential Ratio | 4.046 | ||||
| Upside part of mean | 2.654 | ||||
| Downside part of mean | -1.870 | ||||
| Upside SD | 1.342 | ||||
| Downside SD | 0.656 | ||||
| N nonnegative terms | 334.000 | ||||
| N negative terms | 906.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1240.000 | ||||
| Mean of predictor | 0.377 | ||||
| Mean of criterion | 0.783 | ||||
| SD of predictor | 0.342 | ||||
| SD of criterion | 1.493 | ||||
| Covariance | -0.113 | ||||
| r | -0.222 | ||||
| b (slope, estimate of beta) | -0.967 | ||||
| a (intercept, estimate of alpha) | 1.147 | ||||
| Mean Square Error | 2.123 | ||||
| DF error | 1238.000 | ||||
| t(b) | -7.997 | ||||
| p(b) | 0.611 | ||||
| t(a) | 1.709 | ||||
| p(a) | 0.476 | ||||
| Lowerbound of 95% confidence interval for beta | -1.204 | ||||
| Upperbound of 95% confidence interval for beta | -0.730 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.169 | ||||
| Upperbound of 95% confidence interval for alpha | 2.464 | ||||
| Treynor index (mean / b) | -0.810 | ||||
| Jensen alpha (a) | 1.147 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 1.238 | ||||
| Sharpe ratio (Glass type estimate) | -0.031 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.031 | ||||
| df | 1239.000 | ||||
| t | -0.067 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.932 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.870 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.932 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.870 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.045 | ||||
| Upside Potential Ratio | 2.510 | ||||
| Upside part of mean | 2.133 | ||||
| Downside part of mean | -2.171 | ||||
| Upside SD | 0.899 | ||||
| Downside SD | 0.850 | ||||
| N nonnegative terms | 334.000 | ||||
| N negative terms | 906.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1240.000 | ||||
| Mean of predictor | 0.318 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.340 | ||||
| SD of criterion | 1.238 | ||||
| Covariance | -0.090 | ||||
| r | -0.215 | ||||
| b (slope, estimate of beta) | -0.783 | ||||
| a (intercept, estimate of alpha) | 0.211 | ||||
| Mean Square Error | 1.463 | ||||
| DF error | 1238.000 | ||||
| t(b) | -7.737 | ||||
| p(b) | 0.607 | ||||
| t(a) | 0.379 | ||||
| p(a) | 0.495 | ||||
| Lowerbound of 95% confidence interval for beta | -0.981 | ||||
| Upperbound of 95% confidence interval for beta | -0.584 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.881 | ||||
| Upperbound of 95% confidence interval for alpha | 1.304 | ||||
| Treynor index (mean / b) | 0.049 | ||||
| Jensen alpha (a) | 0.211 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.118 | ||||
| Expected Shortfall on VaR | 0.146 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.046 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1240.000 | ||||
| Minimum | 0.406 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 3.028 | ||||
| Mean of quarter 1 | 0.972 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.041 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 199.000 | ||||
| Percentage of outliers low | 0.160 | ||||
| Mean of outliers low | 0.957 | ||||
| Number of outliers high | 208.000 | ||||
| Percentage of outliers high | 0.168 | ||||
| Mean of outliers high | 1.060 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.976 | ||||
| VaR(95%) (moments method) | 0.009 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.405 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 14.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.022 | ||||
| Median | 0.054 | ||||
| Quartile 3 | 0.199 | ||||
| Maximum | 0.945 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.031 | ||||
| Mean of quarter 3 | 0.092 | ||||
| Mean of quarter 4 | 0.522 | ||||
| Inter Quartile Range | 0.177 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.816 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.386 | ||||
| VaR(95%) (moments method) | 0.603 | ||||
| Expected Shortfall (moments method) | 1.152 | ||||
| Extreme Value Index (regression method) | 5.463 | ||||
| VaR(95%) (regression method) | 1.115 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.006 | ||||
| Compounded annual return (geometric extrapolation) | 0.006 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.006 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.012 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.041 | ||||
| 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 | 1.028 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.370 | ||||
| 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 | 0.958 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.373 | ||||
| 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) | -8690083091169246.000 | ||||
| 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) | 134408205235052134363505461559296.000 | ||||
| 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 | ||||