Advanced Statistics: Euro 30
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 | 1.122 | ||||
| SD | 2.408 | ||||
| Sharpe ratio (Glass type estimate) | 0.466 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.458 | ||||
| df | 46.000 | ||||
| t | 0.922 | ||||
| p | 0.181 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.531 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.458 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.537 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.453 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.221 | ||||
| Upside Potential Ratio | 3.030 | ||||
| Upside part of mean | 2.784 | ||||
| Downside part of mean | -1.662 | ||||
| Upside SD | 2.221 | ||||
| Downside SD | 0.919 | ||||
| N nonnegative terms | 21.000 | ||||
| N negative terms | 26.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 47.000 | ||||
| Mean of predictor | 0.417 | ||||
| Mean of criterion | 1.122 | ||||
| SD of predictor | 0.284 | ||||
| SD of criterion | 2.408 | ||||
| Covariance | -0.033 | ||||
| r | -0.049 | ||||
| b (slope, estimate of beta) | -0.411 | ||||
| a (intercept, estimate of alpha) | 1.293 | ||||
| Mean Square Error | 5.911 | ||||
| DF error | 45.000 | ||||
| t(b) | -0.326 | ||||
| p(b) | 0.627 | ||||
| t(a) | 0.968 | ||||
| p(a) | 0.169 | ||||
| Lowerbound of 95% confidence interval for beta | -2.950 | ||||
| Upperbound of 95% confidence interval for beta | 2.128 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.398 | ||||
| Upperbound of 95% confidence interval for alpha | 3.984 | ||||
| Treynor index (mean / b) | -2.730 | ||||
| Jensen alpha (a) | 1.293 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.088 | ||||
| SD | 4.261 | ||||
| Sharpe ratio (Glass type estimate) | -0.490 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.482 | ||||
| df | 46.000 | ||||
| t | -0.970 | ||||
| p | 0.831 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.483 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.508 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.477 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.513 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.509 | ||||
| Upside Potential Ratio | 0.435 | ||||
| Upside part of mean | 1.785 | ||||
| Downside part of mean | -3.873 | ||||
| Upside SD | 1.147 | ||||
| Downside SD | 4.101 | ||||
| N nonnegative terms | 21.000 | ||||
| N negative terms | 26.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 47.000 | ||||
| Mean of predictor | 0.372 | ||||
| Mean of criterion | -2.088 | ||||
| SD of predictor | 0.272 | ||||
| SD of criterion | 4.261 | ||||
| Covariance | 0.305 | ||||
| r | 0.263 | ||||
| b (slope, estimate of beta) | 4.119 | ||||
| a (intercept, estimate of alpha) | -3.619 | ||||
| Mean Square Error | 17.272 | ||||
| DF error | 45.000 | ||||
| t(b) | 1.831 | ||||
| p(b) | 0.037 | ||||
| t(a) | -1.601 | ||||
| p(a) | 0.942 | ||||
| Lowerbound of 95% confidence interval for beta | -0.413 | ||||
| Upperbound of 95% confidence interval for beta | 8.651 | ||||
| Lowerbound of 95% confidence interval for alpha | -8.171 | ||||
| Upperbound of 95% confidence interval for alpha | 0.934 | ||||
| Treynor index (mean / b) | -0.507 | ||||
| Jensen alpha (a) | -3.619 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.889 | ||||
| Expected Shortfall on VaR | 0.928 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.341 | ||||
| Expected Shortfall on VaR | 0.635 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 47.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.808 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.132 | ||||
| Maximum | 4.752 | ||||
| Mean of quarter 1 | 0.540 | ||||
| Mean of quarter 2 | 0.925 | ||||
| Mean of quarter 3 | 1.056 | ||||
| Mean of quarter 4 | 1.864 | ||||
| Inter Quartile Range | 0.324 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.043 | ||||
| Mean of outliers low | 0.157 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.149 | ||||
| Mean of outliers high | 2.272 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.339 | ||||
| VaR(95%) (moments method) | 0.458 | ||||
| Expected Shortfall (moments method) | 0.550 | ||||
| Extreme Value Index (regression method) | -0.187 | ||||
| VaR(95%) (regression method) | 0.422 | ||||
| Expected Shortfall (regression method) | 0.518 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.103 | ||||
| Quartile 1 | 0.327 | ||||
| Median | 0.551 | ||||
| Quartile 3 | 0.776 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.103 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.448 | ||||
| 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) | -0.255 | ||||
| Compounded annual return (geometric extrapolation) | -0.870 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.871 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.871 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.938 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2.957 | ||||
| SD | 6.012 | ||||
| Sharpe ratio (Glass type estimate) | 0.492 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.491 | ||||
| df | 1037.000 | ||||
| t | 0.979 | ||||
| p | 0.481 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.493 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.477 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.493 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.476 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.399 | ||||
| Upside Potential Ratio | 8.410 | ||||
| Upside part of mean | 10.369 | ||||
| Downside part of mean | -7.412 | ||||
| Upside SD | 5.885 | ||||
| Downside SD | 1.233 | ||||
| N nonnegative terms | 443.000 | ||||
| N negative terms | 595.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1038.000 | ||||
| Mean of predictor | 0.421 | ||||
| Mean of criterion | 2.957 | ||||
| SD of predictor | 0.319 | ||||
| SD of criterion | 6.012 | ||||
| Covariance | -0.127 | ||||
| r | -0.066 | ||||
| b (slope, estimate of beta) | -1.252 | ||||
| a (intercept, estimate of alpha) | 3.484 | ||||
| Mean Square Error | 36.025 | ||||
| DF error | 1036.000 | ||||
| t(b) | -2.139 | ||||
| p(b) | 0.533 | ||||
| t(a) | 1.151 | ||||
| p(a) | 0.482 | ||||
| Lowerbound of 95% confidence interval for beta | -2.400 | ||||
| Upperbound of 95% confidence interval for beta | -0.103 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.453 | ||||
| Upperbound of 95% confidence interval for alpha | 9.420 | ||||
| Treynor index (mean / b) | -2.363 | ||||
| Jensen alpha (a) | 3.484 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.065 | ||||
| SD | 3.530 | ||||
| Sharpe ratio (Glass type estimate) | -0.585 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.584 | ||||
| df | 1037.000 | ||||
| t | -1.164 | ||||
| p | 0.523 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.570 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.400 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.569 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.401 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.670 | ||||
| Upside Potential Ratio | 2.378 | ||||
| Upside part of mean | 7.329 | ||||
| Downside part of mean | -9.394 | ||||
| Upside SD | 1.724 | ||||
| Downside SD | 3.081 | ||||
| N nonnegative terms | 443.000 | ||||
| N negative terms | 595.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1038.000 | ||||
| Mean of predictor | 0.369 | ||||
| Mean of criterion | -2.065 | ||||
| SD of predictor | 0.323 | ||||
| SD of criterion | 3.530 | ||||
| Covariance | -0.084 | ||||
| r | -0.074 | ||||
| b (slope, estimate of beta) | -0.804 | ||||
| a (intercept, estimate of alpha) | -1.768 | ||||
| Mean Square Error | 12.406 | ||||
| DF error | 1036.000 | ||||
| t(b) | -2.375 | ||||
| p(b) | 0.537 | ||||
| t(a) | -0.997 | ||||
| p(a) | 0.515 | ||||
| Lowerbound of 95% confidence interval for beta | -1.469 | ||||
| Upperbound of 95% confidence interval for beta | -0.140 | ||||
| Lowerbound of 95% confidence interval for alpha | -5.249 | ||||
| Upperbound of 95% confidence interval for alpha | 1.713 | ||||
| Treynor index (mean / b) | 2.567 | ||||
| Jensen alpha (a) | -1.768 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.307 | ||||
| Expected Shortfall on VaR | 0.365 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.070 | ||||
| Expected Shortfall on VaR | 0.149 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1038.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.973 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.021 | ||||
| Maximum | 12.292 | ||||
| Mean of quarter 1 | 0.895 | ||||
| Mean of quarter 2 | 0.992 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.152 | ||||
| Inter Quartile Range | 0.048 | ||||
| Number outliers low | 91.000 | ||||
| Percentage of outliers low | 0.088 | ||||
| Mean of outliers low | 0.801 | ||||
| Number of outliers high | 90.000 | ||||
| Percentage of outliers high | 0.087 | ||||
| Mean of outliers high | 1.347 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.452 | ||||
| VaR(95%) (moments method) | 0.094 | ||||
| Expected Shortfall (moments method) | 0.202 | ||||
| Extreme Value Index (regression method) | 0.254 | ||||
| VaR(95%) (regression method) | 0.097 | ||||
| Expected Shortfall (regression method) | 0.169 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 18.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.045 | ||||
| Median | 0.071 | ||||
| Quartile 3 | 0.184 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.025 | ||||
| Mean of quarter 2 | 0.053 | ||||
| Mean of quarter 3 | 0.136 | ||||
| Mean of quarter 4 | 0.376 | ||||
| Inter Quartile Range | 0.139 | ||||
| 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 | 0.056 | ||||
| Mean of outliers high | 1.000 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.697 | ||||
| VaR(95%) (moments method) | 0.464 | ||||
| Expected Shortfall (moments method) | 1.447 | ||||
| Extreme Value Index (regression method) | 2.889 | ||||
| VaR(95%) (regression method) | 0.540 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.252 | ||||
| Compounded annual return (geometric extrapolation) | -0.867 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.867 | ||||
| Compounded annual return / average of 25% largest draw downs | -2.310 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.375 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -5.317 | ||||
| SD | 1.748 | ||||
| Sharpe ratio (Glass type estimate) | -3.041 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.023 | ||||
| df | 130.000 | ||||
| t | -2.150 | ||||
| p | 0.593 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.832 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.239 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.819 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.227 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.000 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -5.317 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 1.773 | ||||
| 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 | 0.915 | ||||
| Mean of criterion | -5.317 | ||||
| SD of predictor | 0.464 | ||||
| SD of criterion | 1.748 | ||||
| Covariance | 0.040 | ||||
| r | 0.049 | ||||
| b (slope, estimate of beta) | 0.186 | ||||
| a (intercept, estimate of alpha) | -5.488 | ||||
| Mean Square Error | 3.073 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.563 | ||||
| p(b) | 0.469 | ||||
| t(a) | -2.197 | ||||
| p(a) | 0.620 | ||||
| Lowerbound of 95% confidence interval for beta | -0.469 | ||||
| Upperbound of 95% confidence interval for beta | 0.842 | ||||
| Lowerbound of 95% confidence interval for alpha | -10.429 | ||||
| Upperbound of 95% confidence interval for alpha | -0.546 | ||||
| Treynor index (mean / b) | -28.522 | ||||
| Jensen alpha (a) | -5.488 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -14.974 | ||||
| SD | 7.773 | ||||
| Sharpe ratio (Glass type estimate) | -1.926 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.915 | ||||
| df | 130.000 | ||||
| t | -1.362 | ||||
| p | 0.559 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.705 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.859 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.697 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.866 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.920 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -14.974 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 7.798 | ||||
| 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 | 0.807 | ||||
| Mean of criterion | -14.974 | ||||
| SD of predictor | 0.464 | ||||
| SD of criterion | 7.773 | ||||
| Covariance | 0.080 | ||||
| r | 0.022 | ||||
| b (slope, estimate of beta) | 0.373 | ||||
| a (intercept, estimate of alpha) | -15.275 | ||||
| Mean Square Error | 60.854 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.253 | ||||
| p(b) | 0.486 | ||||
| t(a) | -1.377 | ||||
| p(a) | 0.576 | ||||
| Lowerbound of 95% confidence interval for beta | -2.542 | ||||
| Upperbound of 95% confidence interval for beta | 3.289 | ||||
| Lowerbound of 95% confidence interval for alpha | -37.229 | ||||
| Upperbound of 95% confidence interval for alpha | 6.678 | ||||
| Treynor index (mean / b) | -40.110 | ||||
| Jensen alpha (a) | -15.275 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.571 | ||||
| Expected Shortfall on VaR | 0.644 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.071 | ||||
| Expected Shortfall on VaR | 0.157 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.920 | ||||
| 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 | 6.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.561 | ||||
| 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) | 0.104 | ||||
| VaR(95%) (regression method) | 0.013 | ||||
| Expected Shortfall (regression method) | 0.259 | ||||
| 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 | -1.553 | ||||