Advanced Statistics: GSystem
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 | -0.016 | ||||
| SD | 0.246 | ||||
| Sharpe ratio (Glass type estimate) | -0.066 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.065 | ||||
| df | 52.000 | ||||
| t | -0.139 | ||||
| p | 0.555 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.998 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.867 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.998 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.868 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.114 | ||||
| Upside Potential Ratio | 0.658 | ||||
| Upside part of mean | 0.094 | ||||
| Downside part of mean | -0.110 | ||||
| Upside SD | 0.197 | ||||
| Downside SD | 0.143 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.391 | ||||
| Mean of criterion | -0.016 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 0.246 | ||||
| Covariance | -0.001 | ||||
| r | -0.019 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | -0.009 | ||||
| Mean Square Error | 0.061 | ||||
| DF error | 51.000 | ||||
| t(b) | -0.138 | ||||
| p(b) | 0.555 | ||||
| t(a) | -0.068 | ||||
| p(a) | 0.527 | ||||
| Lowerbound of 95% confidence interval for beta | -0.292 | ||||
| Upperbound of 95% confidence interval for beta | 0.254 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.269 | ||||
| Upperbound of 95% confidence interval for alpha | 0.251 | ||||
| Treynor index (mean / b) | 0.861 | ||||
| Jensen alpha (a) | -0.009 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.237 | ||||
| Sharpe ratio (Glass type estimate) | -0.185 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.183 | ||||
| df | 52.000 | ||||
| t | -0.390 | ||||
| p | 0.651 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.118 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.749 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.116 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.750 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.261 | ||||
| Upside Potential Ratio | 0.465 | ||||
| Upside part of mean | 0.078 | ||||
| Downside part of mean | -0.122 | ||||
| Upside SD | 0.164 | ||||
| Downside SD | 0.168 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.354 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 0.237 | ||||
| Covariance | 0.000 | ||||
| r | 0.008 | ||||
| b (slope, estimate of beta) | 0.007 | ||||
| a (intercept, estimate of alpha) | -0.047 | ||||
| Mean Square Error | 0.057 | ||||
| DF error | 51.000 | ||||
| t(b) | 0.055 | ||||
| p(b) | 0.478 | ||||
| t(a) | -0.377 | ||||
| p(a) | 0.646 | ||||
| Lowerbound of 95% confidence interval for beta | -0.267 | ||||
| Upperbound of 95% confidence interval for beta | 0.282 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.295 | ||||
| Upperbound of 95% confidence interval for alpha | 0.202 | ||||
| Treynor index (mean / b) | -5.891 | ||||
| Jensen alpha (a) | -0.047 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.110 | ||||
| Expected Shortfall on VaR | 0.135 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.069 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 53.000 | ||||
| Minimum | 0.705 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.418 | ||||
| Mean of quarter 1 | 0.979 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.032 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.038 | ||||
| Mean of outliers low | 0.852 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.139 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.295 | ||||
| Quartile 1 | 0.295 | ||||
| Median | 0.295 | ||||
| Quartile 3 | 0.295 | ||||
| Maximum | 0.295 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.021 | ||||
| SD | 0.232 | ||||
| Sharpe ratio (Glass type estimate) | -0.091 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.091 | ||||
| df | 1178.000 | ||||
| t | -0.193 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.015 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.833 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.015 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.833 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.204 | ||||
| Upside Potential Ratio | 1.335 | ||||
| Upside part of mean | 0.138 | ||||
| Downside part of mean | -0.159 | ||||
| Upside SD | 0.207 | ||||
| Downside SD | 0.104 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 1170.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1179.000 | ||||
| Mean of predictor | 0.420 | ||||
| Mean of criterion | -0.021 | ||||
| SD of predictor | 0.326 | ||||
| SD of criterion | 0.232 | ||||
| Covariance | -0.004 | ||||
| r | -0.052 | ||||
| b (slope, estimate of beta) | -0.037 | ||||
| a (intercept, estimate of alpha) | -0.006 | ||||
| Mean Square Error | 0.054 | ||||
| DF error | 1177.000 | ||||
| t(b) | -1.776 | ||||
| p(b) | 0.533 | ||||
| t(a) | -0.052 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | -0.077 | ||||
| Upperbound of 95% confidence interval for beta | 0.004 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.221 | ||||
| Upperbound of 95% confidence interval for alpha | 0.209 | ||||
| Treynor index (mean / b) | 0.574 | ||||
| Jensen alpha (a) | -0.006 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.206 | ||||
| Sharpe ratio (Glass type estimate) | -0.213 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.213 | ||||
| df | 1178.000 | ||||
| t | -0.452 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.137 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.711 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.137 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.711 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.396 | ||||
| Upside Potential Ratio | 1.092 | ||||
| Upside part of mean | 0.121 | ||||
| Downside part of mean | -0.165 | ||||
| Upside SD | 0.174 | ||||
| Downside SD | 0.111 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 1170.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1179.000 | ||||
| Mean of predictor | 0.366 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.206 | ||||
| Covariance | -0.003 | ||||
| r | -0.047 | ||||
| b (slope, estimate of beta) | -0.029 | ||||
| a (intercept, estimate of alpha) | -0.033 | ||||
| Mean Square Error | 0.043 | ||||
| DF error | 1177.000 | ||||
| t(b) | -1.602 | ||||
| p(b) | 0.530 | ||||
| t(a) | -0.341 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | -0.065 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.224 | ||||
| Upperbound of 95% confidence interval for alpha | 0.158 | ||||
| Treynor index (mean / b) | 1.499 | ||||
| Jensen alpha (a) | -0.033 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1179.000 | ||||
| Minimum | 0.846 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.431 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 22.000 | ||||
| Percentage of outliers low | 0.019 | ||||
| Mean of outliers low | 0.976 | ||||
| Number of outliers high | 16.000 | ||||
| Percentage of outliers high | 0.014 | ||||
| Mean of outliers high | 1.039 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.268 | ||||
| VaR(95%) (moments method) | -0.292 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.491 | ||||
| VaR(95%) (regression method) | -0.010 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.016 | ||||
| Quartile 1 | 0.024 | ||||
| Median | 0.040 | ||||
| Quartile 3 | 0.125 | ||||
| Maximum | 0.335 | ||||
| Mean of quarter 1 | 0.016 | ||||
| Mean of quarter 2 | 0.026 | ||||
| Mean of quarter 3 | 0.055 | ||||
| Mean of quarter 4 | 0.335 | ||||
| Inter Quartile Range | 0.102 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 0.335 | ||||
| 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) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 0.990 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.388 | ||||
| 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 | 0.913 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.389 | ||||
| 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) | -8707782920389353.000 | ||||
| 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) | -136960068843270626664430002241536.000 | ||||
| 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 | ||||