Advanced Statistics: System 26583686
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 | -0.129 | ||||
| SD | 0.265 | ||||
| Sharpe ratio (Glass type estimate) | -0.487 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.482 | ||||
| df | 77.000 | ||||
| t | -1.240 | ||||
| p | 0.891 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.258 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.288 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.254 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.291 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.534 | ||||
| Upside Potential Ratio | 0.253 | ||||
| Upside part of mean | 0.061 | ||||
| Downside part of mean | -0.190 | ||||
| Upside SD | 0.111 | ||||
| Downside SD | 0.241 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 78.000 | ||||
| Mean of predictor | 0.224 | ||||
| Mean of criterion | -0.129 | ||||
| SD of predictor | 0.275 | ||||
| SD of criterion | 0.265 | ||||
| Covariance | 0.002 | ||||
| r | 0.024 | ||||
| b (slope, estimate of beta) | 0.023 | ||||
| a (intercept, estimate of alpha) | -0.134 | ||||
| Mean Square Error | 0.071 | ||||
| DF error | 76.000 | ||||
| t(b) | 0.210 | ||||
| p(b) | 0.417 | ||||
| t(a) | -1.248 | ||||
| p(a) | 0.892 | ||||
| Lowerbound of 95% confidence interval for beta | -0.197 | ||||
| Upperbound of 95% confidence interval for beta | 0.243 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.348 | ||||
| Upperbound of 95% confidence interval for alpha | 0.080 | ||||
| Treynor index (mean / b) | -5.562 | ||||
| Jensen alpha (a) | -0.134 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.178 | ||||
| SD | 0.346 | ||||
| Sharpe ratio (Glass type estimate) | -0.514 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.509 | ||||
| df | 77.000 | ||||
| t | -1.311 | ||||
| p | 0.903 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.286 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.260 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.282 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.264 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.534 | ||||
| Upside Potential Ratio | 0.167 | ||||
| Upside part of mean | 0.056 | ||||
| Downside part of mean | -0.233 | ||||
| Upside SD | 0.099 | ||||
| Downside SD | 0.333 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 78.000 | ||||
| Mean of predictor | 0.185 | ||||
| Mean of criterion | -0.178 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.346 | ||||
| Covariance | 0.002 | ||||
| r | 0.026 | ||||
| b (slope, estimate of beta) | 0.033 | ||||
| a (intercept, estimate of alpha) | -0.184 | ||||
| Mean Square Error | 0.121 | ||||
| DF error | 76.000 | ||||
| t(b) | 0.225 | ||||
| p(b) | 0.411 | ||||
| t(a) | -1.322 | ||||
| p(a) | 0.905 | ||||
| Lowerbound of 95% confidence interval for beta | -0.257 | ||||
| Upperbound of 95% confidence interval for beta | 0.323 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.461 | ||||
| Upperbound of 95% confidence interval for alpha | 0.093 | ||||
| Treynor index (mean / b) | -5.435 | ||||
| Jensen alpha (a) | -0.184 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.164 | ||||
| Expected Shortfall on VaR | 0.198 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.050 | ||||
| Expected Shortfall on VaR | 0.112 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 78.000 | ||||
| Minimum | 0.454 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.279 | ||||
| Mean of quarter 1 | 0.951 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.141 | ||||
| Mean of outliers low | 0.910 | ||||
| Number of outliers high | 14.000 | ||||
| Percentage of outliers high | 0.179 | ||||
| Mean of outliers high | 1.031 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.160 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.759 | ||||
| VaR(95%) (regression method) | 0.025 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.144 | ||||
| Quartile 1 | 0.272 | ||||
| Median | 0.401 | ||||
| Quartile 3 | 0.530 | ||||
| Maximum | 0.658 | ||||
| Mean of quarter 1 | 0.144 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.658 | ||||
| Inter Quartile Range | 0.257 | ||||
| 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) | -0.089 | ||||
| Compounded annual return (geometric extrapolation) | -0.125 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.190 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.190 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.634 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.028 | ||||
| SD | 0.748 | ||||
| Sharpe ratio (Glass type estimate) | 0.037 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.037 | ||||
| df | 1717.000 | ||||
| t | 0.095 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.728 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.803 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.728 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.803 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.078 | ||||
| Upside Potential Ratio | 2.185 | ||||
| Upside part of mean | 0.778 | ||||
| Downside part of mean | -0.750 | ||||
| Upside SD | 0.658 | ||||
| Downside SD | 0.356 | ||||
| N nonnegative terms | 194.000 | ||||
| N negative terms | 1524.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1718.000 | ||||
| Mean of predictor | 0.396 | ||||
| Mean of criterion | 0.028 | ||||
| SD of predictor | 0.631 | ||||
| SD of criterion | 0.748 | ||||
| Covariance | 0.107 | ||||
| r | 0.227 | ||||
| b (slope, estimate of beta) | 0.269 | ||||
| a (intercept, estimate of alpha) | -0.079 | ||||
| Mean Square Error | 0.532 | ||||
| DF error | 1716.000 | ||||
| t(b) | 9.638 | ||||
| p(b) | 0.387 | ||||
| t(a) | -0.276 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | 0.214 | ||||
| Upperbound of 95% confidence interval for beta | 0.323 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.638 | ||||
| Upperbound of 95% confidence interval for alpha | 0.480 | ||||
| Treynor index (mean / b) | 0.104 | ||||
| Jensen alpha (a) | -0.079 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.177 | ||||
| SD | 0.614 | ||||
| Sharpe ratio (Glass type estimate) | -0.288 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.288 | ||||
| df | 1717.000 | ||||
| t | -0.738 | ||||
| p | 0.511 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.053 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.477 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.053 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.478 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.405 | ||||
| Upside Potential Ratio | 1.503 | ||||
| Upside part of mean | 0.655 | ||||
| Downside part of mean | -0.832 | ||||
| Upside SD | 0.432 | ||||
| Downside SD | 0.436 | ||||
| N nonnegative terms | 194.000 | ||||
| N negative terms | 1524.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1718.000 | ||||
| Mean of predictor | 0.200 | ||||
| Mean of criterion | -0.177 | ||||
| SD of predictor | 0.626 | ||||
| SD of criterion | 0.614 | ||||
| Covariance | 0.078 | ||||
| r | 0.203 | ||||
| b (slope, estimate of beta) | 0.199 | ||||
| a (intercept, estimate of alpha) | -0.216 | ||||
| Mean Square Error | 0.361 | ||||
| DF error | 1716.000 | ||||
| t(b) | 8.576 | ||||
| p(b) | 0.399 | ||||
| t(a) | -0.922 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | 0.153 | ||||
| Upperbound of 95% confidence interval for beta | 0.244 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.677 | ||||
| Upperbound of 95% confidence interval for alpha | 0.244 | ||||
| Treynor index (mean / b) | -0.890 | ||||
| Jensen alpha (a) | -0.216 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.061 | ||||
| Expected Shortfall on VaR | 0.076 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1718.000 | ||||
| Minimum | 0.482 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.546 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.012 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 199.000 | ||||
| Percentage of outliers low | 0.116 | ||||
| Mean of outliers low | 0.977 | ||||
| Number of outliers high | 236.000 | ||||
| Percentage of outliers high | 0.137 | ||||
| Mean of outliers high | 1.022 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.918 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.292 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.120 | ||||
| Quartile 1 | 0.222 | ||||
| Median | 0.334 | ||||
| Quartile 3 | 0.626 | ||||
| Maximum | 0.671 | ||||
| Mean of quarter 1 | 0.171 | ||||
| Mean of quarter 2 | 0.334 | ||||
| Mean of quarter 3 | 0.626 | ||||
| Mean of quarter 4 | 0.671 | ||||
| Inter Quartile Range | 0.404 | ||||
| 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) | -0.089 | ||||
| Compounded annual return (geometric extrapolation) | -0.124 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.185 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.185 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.641 | ||||
| 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 | 1.021 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.495 | ||||
| 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 | 0.900 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.487 | ||||
| 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) | -8742528018583704.000 | ||||
| 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) | 983194909185386730019334307971072.000 | ||||
| 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 | ||||