Advanced Statistics: System 39940733
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 | -0.217 | ||||
| SD | 1.581 | ||||
| Sharpe ratio (Glass type estimate) | -0.137 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.136 | ||||
| df | 56.000 | ||||
| t | -0.300 | ||||
| p | 0.617 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.037 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.763 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.035 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.764 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.237 | ||||
| Upside Potential Ratio | 1.293 | ||||
| Upside part of mean | 1.185 | ||||
| Downside part of mean | -1.402 | ||||
| Upside SD | 1.273 | ||||
| Downside SD | 0.916 | ||||
| N nonnegative terms | 16.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 57.000 | ||||
| Mean of predictor | 0.422 | ||||
| Mean of criterion | -0.217 | ||||
| SD of predictor | 0.258 | ||||
| SD of criterion | 1.581 | ||||
| Covariance | -0.036 | ||||
| r | -0.088 | ||||
| b (slope, estimate of beta) | -0.540 | ||||
| a (intercept, estimate of alpha) | 0.011 | ||||
| Mean Square Error | 2.524 | ||||
| DF error | 55.000 | ||||
| t(b) | -0.656 | ||||
| p(b) | 0.743 | ||||
| t(a) | 0.014 | ||||
| p(a) | 0.495 | ||||
| Lowerbound of 95% confidence interval for beta | -2.191 | ||||
| Upperbound of 95% confidence interval for beta | 1.110 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.608 | ||||
| Upperbound of 95% confidence interval for alpha | 1.630 | ||||
| Treynor index (mean / b) | 0.402 | ||||
| Jensen alpha (a) | 0.011 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.796 | ||||
| SD | 3.877 | ||||
| Sharpe ratio (Glass type estimate) | -0.721 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.711 | ||||
| df | 56.000 | ||||
| t | -1.572 | ||||
| p | 0.939 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.627 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.191 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.620 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.197 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.725 | ||||
| Upside Potential Ratio | 0.206 | ||||
| Upside part of mean | 0.794 | ||||
| Downside part of mean | -3.590 | ||||
| Upside SD | 0.739 | ||||
| Downside SD | 3.857 | ||||
| N nonnegative terms | 16.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 57.000 | ||||
| Mean of predictor | 0.384 | ||||
| Mean of criterion | -2.796 | ||||
| SD of predictor | 0.246 | ||||
| SD of criterion | 3.877 | ||||
| Covariance | -0.182 | ||||
| r | -0.190 | ||||
| b (slope, estimate of beta) | -2.993 | ||||
| a (intercept, estimate of alpha) | -1.648 | ||||
| Mean Square Error | 14.753 | ||||
| DF error | 55.000 | ||||
| t(b) | -1.437 | ||||
| p(b) | 0.922 | ||||
| t(a) | -0.852 | ||||
| p(a) | 0.801 | ||||
| Lowerbound of 95% confidence interval for beta | -7.168 | ||||
| Upperbound of 95% confidence interval for beta | 1.182 | ||||
| Lowerbound of 95% confidence interval for alpha | -5.526 | ||||
| Upperbound of 95% confidence interval for alpha | 2.230 | ||||
| Treynor index (mean / b) | 0.934 | ||||
| Jensen alpha (a) | -1.648 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.874 | ||||
| Expected Shortfall on VaR | 0.915 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.334 | ||||
| Expected Shortfall on VaR | 0.655 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 57.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.894 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 3.317 | ||||
| Mean of quarter 1 | 0.570 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.406 | ||||
| Inter Quartile Range | 0.111 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.158 | ||||
| Mean of outliers low | 0.408 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.123 | ||||
| Mean of outliers high | 1.743 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.569 | ||||
| VaR(95%) (moments method) | 0.328 | ||||
| Expected Shortfall (moments method) | 0.382 | ||||
| Extreme Value Index (regression method) | -0.344 | ||||
| VaR(95%) (regression method) | 0.573 | ||||
| Expected Shortfall (regression method) | 0.730 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.027 | ||||
| Quartile 1 | 0.156 | ||||
| Median | 0.285 | ||||
| Quartile 3 | 0.642 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.027 | ||||
| Mean of quarter 2 | 0.285 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.486 | ||||
| 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) | -0.211 | ||||
| Compounded annual return (geometric extrapolation) | -0.936 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.936 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.936 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.023 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.980 | ||||
| SD | 5.937 | ||||
| Sharpe ratio (Glass type estimate) | 0.334 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.333 | ||||
| df | 1251.000 | ||||
| t | 0.729 | ||||
| p | 0.487 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.563 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.230 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.563 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.230 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.766 | ||||
| Upside Potential Ratio | 6.156 | ||||
| Upside part of mean | 6.903 | ||||
| Downside part of mean | -4.923 | ||||
| Upside SD | 5.829 | ||||
| Downside SD | 1.121 | ||||
| N nonnegative terms | 280.000 | ||||
| N negative terms | 972.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1252.000 | ||||
| Mean of predictor | 0.455 | ||||
| Mean of criterion | 1.980 | ||||
| SD of predictor | 0.330 | ||||
| SD of criterion | 5.937 | ||||
| Covariance | 0.180 | ||||
| r | 0.092 | ||||
| b (slope, estimate of beta) | 1.653 | ||||
| a (intercept, estimate of alpha) | 1.228 | ||||
| Mean Square Error | 34.981 | ||||
| DF error | 1250.000 | ||||
| t(b) | 3.260 | ||||
| p(b) | 0.454 | ||||
| t(a) | 0.452 | ||||
| p(a) | 0.494 | ||||
| Lowerbound of 95% confidence interval for beta | 0.658 | ||||
| Upperbound of 95% confidence interval for beta | 2.647 | ||||
| Lowerbound of 95% confidence interval for alpha | -4.099 | ||||
| Upperbound of 95% confidence interval for alpha | 6.555 | ||||
| Treynor index (mean / b) | 1.198 | ||||
| Jensen alpha (a) | 1.228 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.780 | ||||
| SD | 4.055 | ||||
| Sharpe ratio (Glass type estimate) | -0.685 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.685 | ||||
| df | 1251.000 | ||||
| t | -1.498 | ||||
| p | 0.527 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.582 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.212 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.582 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.212 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.736 | ||||
| Upside Potential Ratio | 1.160 | ||||
| Upside part of mean | 4.384 | ||||
| Downside part of mean | -7.163 | ||||
| Upside SD | 1.478 | ||||
| Downside SD | 3.778 | ||||
| N nonnegative terms | 280.000 | ||||
| N negative terms | 972.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1252.000 | ||||
| Mean of predictor | 0.400 | ||||
| Mean of criterion | -2.780 | ||||
| SD of predictor | 0.331 | ||||
| SD of criterion | 4.055 | ||||
| Covariance | 0.149 | ||||
| r | 0.111 | ||||
| b (slope, estimate of beta) | 1.354 | ||||
| a (intercept, estimate of alpha) | -3.321 | ||||
| Mean Square Error | 16.254 | ||||
| DF error | 1250.000 | ||||
| t(b) | 3.937 | ||||
| p(b) | 0.445 | ||||
| t(a) | -1.796 | ||||
| p(a) | 0.525 | ||||
| Lowerbound of 95% confidence interval for beta | 0.679 | ||||
| Upperbound of 95% confidence interval for beta | 2.028 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.950 | ||||
| Upperbound of 95% confidence interval for alpha | 0.307 | ||||
| Treynor index (mean / b) | -2.053 | ||||
| Jensen alpha (a) | -3.321 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.345 | ||||
| Expected Shortfall on VaR | 0.407 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.056 | ||||
| Expected Shortfall on VaR | 0.122 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1252.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 13.509 | ||||
| Mean of quarter 1 | 0.925 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.106 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 275.000 | ||||
| Percentage of outliers low | 0.220 | ||||
| Mean of outliers low | 0.916 | ||||
| Number of outliers high | 257.000 | ||||
| Percentage of outliers high | 0.205 | ||||
| Mean of outliers high | 1.128 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.849 | ||||
| VaR(95%) (moments method) | 0.025 | ||||
| Expected Shortfall (moments method) | 0.195 | ||||
| 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 | 14.000 | ||||
| Minimum | 0.035 | ||||
| Quartile 1 | 0.093 | ||||
| Median | 0.204 | ||||
| Quartile 3 | 0.302 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.053 | ||||
| Mean of quarter 2 | 0.176 | ||||
| Mean of quarter 3 | 0.220 | ||||
| Mean of quarter 4 | 0.530 | ||||
| Inter Quartile Range | 0.209 | ||||
| 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 | 0.071 | ||||
| Mean of outliers high | 1.000 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.388 | ||||
| VaR(95%) (moments method) | 0.645 | ||||
| Expected Shortfall (moments method) | 1.115 | ||||
| Extreme Value Index (regression method) | 2.060 | ||||
| VaR(95%) (regression method) | 0.862 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.209 | ||||
| Compounded annual return (geometric extrapolation) | -0.935 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.935 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.764 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.295 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.043 | ||||
| SD | 1.413 | ||||
| Sharpe ratio (Glass type estimate) | -1.445 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.437 | ||||
| df | 130.000 | ||||
| t | -1.022 | ||||
| p | 0.545 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.220 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.335 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.214 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.340 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.445 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -2.043 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 1.414 | ||||
| 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 | 1.189 | ||||
| Mean of criterion | -2.043 | ||||
| SD of predictor | 0.503 | ||||
| SD of criterion | 1.413 | ||||
| Covariance | 0.082 | ||||
| r | 0.116 | ||||
| b (slope, estimate of beta) | 0.326 | ||||
| a (intercept, estimate of alpha) | -2.431 | ||||
| Mean Square Error | 1.986 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.327 | ||||
| p(b) | 0.426 | ||||
| t(a) | -1.207 | ||||
| p(a) | 0.567 | ||||
| Lowerbound of 95% confidence interval for beta | -0.160 | ||||
| Upperbound of 95% confidence interval for beta | 0.813 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.417 | ||||
| Upperbound of 95% confidence interval for alpha | 1.554 | ||||
| Treynor index (mean / b) | -6.259 | ||||
| Jensen alpha (a) | -2.431 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -15.083 | ||||
| SD | 10.634 | ||||
| Sharpe ratio (Glass type estimate) | -1.418 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.410 | ||||
| df | 130.000 | ||||
| t | -1.003 | ||||
| p | 0.544 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.193 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.361 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.187 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.367 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.418 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -15.083 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 10.635 | ||||
| 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 | 1.060 | ||||
| Mean of criterion | -15.083 | ||||
| SD of predictor | 0.506 | ||||
| SD of criterion | 10.634 | ||||
| Covariance | 0.623 | ||||
| r | 0.116 | ||||
| b (slope, estimate of beta) | 2.432 | ||||
| a (intercept, estimate of alpha) | -17.662 | ||||
| Mean Square Error | 112.441 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.324 | ||||
| p(b) | 0.426 | ||||
| t(a) | -1.168 | ||||
| p(a) | 0.565 | ||||
| Lowerbound of 95% confidence interval for beta | -1.203 | ||||
| Upperbound of 95% confidence interval for beta | 6.067 | ||||
| Lowerbound of 95% confidence interval for alpha | -47.581 | ||||
| Upperbound of 95% confidence interval for alpha | 12.257 | ||||
| Treynor index (mean / b) | -6.202 | ||||
| Jensen alpha (a) | -17.662 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.680 | ||||
| Expected Shortfall on VaR | 0.750 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.970 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.001 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.999 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 0.999 | ||||
| Quartile 3 | 0.999 | ||||
| Maximum | 0.999 | ||||
| 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) | -1.999 | ||||
| Compounded annual return (geometric extrapolation) | -1.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.001 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.333 | ||||