Advanced Statistics: SEMM Conqueror
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 0.405 | ||||
| Sharpe ratio (Glass type estimate) | -0.064 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.063 | ||||
| df | 70.000 | ||||
| t | -0.155 | ||||
| p | 0.562 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.870 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.742 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.869 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.743 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.105 | ||||
| Upside Potential Ratio | 0.761 | ||||
| Upside part of mean | 0.188 | ||||
| Downside part of mean | -0.213 | ||||
| Upside SD | 0.318 | ||||
| Downside SD | 0.246 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.253 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.321 | ||||
| SD of criterion | 0.405 | ||||
| Covariance | -0.021 | ||||
| r | -0.161 | ||||
| b (slope, estimate of beta) | -0.204 | ||||
| a (intercept, estimate of alpha) | 0.026 | ||||
| Mean Square Error | 0.162 | ||||
| DF error | 69.000 | ||||
| t(b) | -1.357 | ||||
| p(b) | 0.910 | ||||
| t(a) | 0.150 | ||||
| p(a) | 0.440 | ||||
| Lowerbound of 95% confidence interval for beta | -0.503 | ||||
| Upperbound of 95% confidence interval for beta | 0.096 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.313 | ||||
| Upperbound of 95% confidence interval for alpha | 0.364 | ||||
| Treynor index (mean / b) | 0.127 | ||||
| Jensen alpha (a) | 0.026 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.102 | ||||
| SD | 0.396 | ||||
| Sharpe ratio (Glass type estimate) | -0.259 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.256 | ||||
| df | 70.000 | ||||
| t | -0.630 | ||||
| p | 0.735 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.065 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.549 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.063 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.551 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.336 | ||||
| Upside Potential Ratio | 0.493 | ||||
| Upside part of mean | 0.150 | ||||
| Downside part of mean | -0.253 | ||||
| Upside SD | 0.249 | ||||
| Downside SD | 0.305 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.202 | ||||
| Mean of criterion | -0.102 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.396 | ||||
| Covariance | -0.015 | ||||
| r | -0.125 | ||||
| b (slope, estimate of beta) | -0.161 | ||||
| a (intercept, estimate of alpha) | -0.070 | ||||
| Mean Square Error | 0.156 | ||||
| DF error | 69.000 | ||||
| t(b) | -1.050 | ||||
| p(b) | 0.851 | ||||
| t(a) | -0.423 | ||||
| p(a) | 0.663 | ||||
| Lowerbound of 95% confidence interval for beta | -0.466 | ||||
| Upperbound of 95% confidence interval for beta | 0.145 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.400 | ||||
| Upperbound of 95% confidence interval for alpha | 0.260 | ||||
| Treynor index (mean / b) | 0.637 | ||||
| Jensen alpha (a) | -0.070 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.178 | ||||
| Expected Shortfall on VaR | 0.216 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.060 | ||||
| Expected Shortfall on VaR | 0.131 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 71.000 | ||||
| Minimum | 0.584 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.679 | ||||
| Mean of quarter 1 | 0.944 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.062 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.070 | ||||
| Mean of outliers low | 0.797 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.099 | ||||
| Mean of outliers high | 1.160 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1212.910 | ||||
| VaR(95%) (moments method) | -51250548042449313108452767235487095033374322301542553528603020043473913896121831260160.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -1.476 | ||||
| VaR(95%) (regression method) | 0.044 | ||||
| Expected Shortfall (regression method) | 0.199 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.712 | ||||
| Quartile 1 | 0.712 | ||||
| Median | 0.712 | ||||
| Quartile 3 | 0.712 | ||||
| Maximum | 0.712 | ||||
| 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) | -0.049 | ||||
| Compounded annual return (geometric extrapolation) | -0.057 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.080 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.263 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.763 | ||||
| SD | 1.481 | ||||
| Sharpe ratio (Glass type estimate) | 0.515 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.515 | ||||
| df | 1568.000 | ||||
| t | 1.261 | ||||
| p | 0.484 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.286 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.316 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.286 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.316 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.087 | ||||
| Upside Potential Ratio | 3.327 | ||||
| Upside part of mean | 2.334 | ||||
| Downside part of mean | -1.571 | ||||
| Upside SD | 1.304 | ||||
| Downside SD | 0.702 | ||||
| N nonnegative terms | 55.000 | ||||
| N negative terms | 1514.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1569.000 | ||||
| Mean of predictor | 0.361 | ||||
| Mean of criterion | 0.763 | ||||
| SD of predictor | 0.507 | ||||
| SD of criterion | 1.481 | ||||
| Covariance | -0.171 | ||||
| r | -0.228 | ||||
| b (slope, estimate of beta) | -0.666 | ||||
| a (intercept, estimate of alpha) | 1.004 | ||||
| Mean Square Error | 2.081 | ||||
| DF error | 1567.000 | ||||
| t(b) | -9.269 | ||||
| p(b) | 0.644 | ||||
| t(a) | 1.701 | ||||
| p(a) | 0.473 | ||||
| Lowerbound of 95% confidence interval for beta | -0.807 | ||||
| Upperbound of 95% confidence interval for beta | -0.525 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.154 | ||||
| Upperbound of 95% confidence interval for alpha | 2.161 | ||||
| Treynor index (mean / b) | -1.145 | ||||
| Jensen alpha (a) | 1.004 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.102 | ||||
| SD | 1.290 | ||||
| Sharpe ratio (Glass type estimate) | -0.079 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.079 | ||||
| df | 1568.000 | ||||
| t | -0.193 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.880 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.722 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.880 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.722 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.109 | ||||
| Upside Potential Ratio | 1.964 | ||||
| Upside part of mean | 1.825 | ||||
| Downside part of mean | -1.927 | ||||
| Upside SD | 0.895 | ||||
| Downside SD | 0.929 | ||||
| N nonnegative terms | 55.000 | ||||
| N negative terms | 1514.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1569.000 | ||||
| Mean of predictor | 0.234 | ||||
| Mean of criterion | -0.102 | ||||
| SD of predictor | 0.504 | ||||
| SD of criterion | 1.290 | ||||
| Covariance | -0.150 | ||||
| r | -0.231 | ||||
| b (slope, estimate of beta) | -0.593 | ||||
| a (intercept, estimate of alpha) | 0.037 | ||||
| Mean Square Error | 1.576 | ||||
| DF error | 1567.000 | ||||
| t(b) | -9.412 | ||||
| p(b) | 0.646 | ||||
| t(a) | 0.072 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | -0.716 | ||||
| Upperbound of 95% confidence interval for beta | -0.469 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.970 | ||||
| Upperbound of 95% confidence interval for alpha | 1.044 | ||||
| Treynor index (mean / b) | 0.172 | ||||
| Jensen alpha (a) | 0.037 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.123 | ||||
| Expected Shortfall on VaR | 0.152 | ||||
| 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 | 1569.000 | ||||
| Minimum | 0.383 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.822 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.036 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 78.000 | ||||
| Percentage of outliers low | 0.050 | ||||
| Mean of outliers low | 0.883 | ||||
| Number of outliers high | 77.000 | ||||
| Percentage of outliers high | 0.049 | ||||
| Mean of outliers high | 1.182 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.936 | ||||
| VaR(95%) (moments method) | -0.007 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.025 | ||||
| VaR(95%) (regression method) | -0.036 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.367 | ||||
| Quartile 1 | 0.483 | ||||
| Median | 0.600 | ||||
| Quartile 3 | 0.716 | ||||
| Maximum | 0.832 | ||||
| Mean of quarter 1 | 0.367 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.832 | ||||
| Inter Quartile Range | 0.232 | ||||
| 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) | -0.049 | ||||
| Compounded annual return (geometric extrapolation) | -0.056 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.067 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.067 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.370 | ||||
| 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 | 2.261 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.593 | ||||
| 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 | 2.081 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.585 | ||||
| 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) | -8593272200231857.000 | ||||
| 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) | 90976226403512990954493810049024.000 | ||||
| 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 | ||||