Advanced Statistics: Holly DAX
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 | 0.061 | ||||
| SD | 0.641 | ||||
| Sharpe ratio (Glass type estimate) | 0.096 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.095 | ||||
| df | 66.000 | ||||
| t | 0.226 | ||||
| p | 0.411 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.734 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.925 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.735 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.924 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.130 | ||||
| Upside Potential Ratio | 0.903 | ||||
| Upside part of mean | 0.425 | ||||
| Downside part of mean | -0.363 | ||||
| Upside SD | 0.429 | ||||
| Downside SD | 0.470 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 67.000 | ||||
| Mean of predictor | 0.189 | ||||
| Mean of criterion | 0.061 | ||||
| SD of predictor | 0.249 | ||||
| SD of criterion | 0.641 | ||||
| Covariance | 0.019 | ||||
| r | 0.117 | ||||
| b (slope, estimate of beta) | 0.301 | ||||
| a (intercept, estimate of alpha) | 0.004 | ||||
| Mean Square Error | 0.411 | ||||
| DF error | 65.000 | ||||
| t(b) | 0.950 | ||||
| p(b) | 0.173 | ||||
| t(a) | 0.015 | ||||
| p(a) | 0.494 | ||||
| Lowerbound of 95% confidence interval for beta | -0.332 | ||||
| Upperbound of 95% confidence interval for beta | 0.935 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.551 | ||||
| Upperbound of 95% confidence interval for alpha | 0.559 | ||||
| Treynor index (mean / b) | 0.203 | ||||
| Jensen alpha (a) | 0.004 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.267 | ||||
| SD | 0.972 | ||||
| Sharpe ratio (Glass type estimate) | -0.274 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.271 | ||||
| df | 66.000 | ||||
| t | -0.648 | ||||
| p | 0.740 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.104 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.557 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.102 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.560 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.294 | ||||
| Upside Potential Ratio | 0.394 | ||||
| Upside part of mean | 0.358 | ||||
| Downside part of mean | -0.624 | ||||
| Upside SD | 0.334 | ||||
| Downside SD | 0.908 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 67.000 | ||||
| Mean of predictor | 0.157 | ||||
| Mean of criterion | -0.267 | ||||
| SD of predictor | 0.251 | ||||
| SD of criterion | 0.972 | ||||
| Covariance | 0.037 | ||||
| r | 0.153 | ||||
| b (slope, estimate of beta) | 0.592 | ||||
| a (intercept, estimate of alpha) | -0.359 | ||||
| Mean Square Error | 0.937 | ||||
| DF error | 65.000 | ||||
| t(b) | 1.246 | ||||
| p(b) | 0.109 | ||||
| t(a) | -0.863 | ||||
| p(a) | 0.804 | ||||
| Lowerbound of 95% confidence interval for beta | -0.357 | ||||
| Upperbound of 95% confidence interval for beta | 1.541 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.191 | ||||
| Upperbound of 95% confidence interval for alpha | 0.472 | ||||
| Treynor index (mean / b) | -0.450 | ||||
| Jensen alpha (a) | -0.359 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.384 | ||||
| Expected Shortfall on VaR | 0.449 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.093 | ||||
| Expected Shortfall on VaR | 0.207 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 67.000 | ||||
| Minimum | 0.173 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.836 | ||||
| Mean of quarter 1 | 0.893 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.142 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.075 | ||||
| Mean of outliers low | 0.635 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.194 | ||||
| Mean of outliers high | 1.186 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -25.343 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | -0.185 | ||||
| VaR(95%) (regression method) | 0.092 | ||||
| Expected Shortfall (regression method) | 0.286 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.948 | ||||
| Quartile 1 | 0.948 | ||||
| Median | 0.948 | ||||
| Quartile 3 | 0.948 | ||||
| Maximum | 0.948 | ||||
| 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) | -0.127 | ||||
| Compounded annual return (geometric extrapolation) | -0.200 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.210 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.445 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 36.898 | ||||
| SD | 25.197 | ||||
| Sharpe ratio (Glass type estimate) | 1.464 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.464 | ||||
| df | 1469.000 | ||||
| t | 3.469 | ||||
| p | 0.443 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.635 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.293 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.635 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.293 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 23.585 | ||||
| Upside Potential Ratio | 25.712 | ||||
| Upside part of mean | 40.227 | ||||
| Downside part of mean | -3.329 | ||||
| Upside SD | 25.243 | ||||
| Downside SD | 1.565 | ||||
| N nonnegative terms | 174.000 | ||||
| N negative terms | 1296.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1470.000 | ||||
| Mean of predictor | 0.373 | ||||
| Mean of criterion | 36.898 | ||||
| SD of predictor | 0.602 | ||||
| SD of criterion | 25.197 | ||||
| Covariance | 3.377 | ||||
| r | 0.223 | ||||
| b (slope, estimate of beta) | 9.319 | ||||
| a (intercept, estimate of alpha) | 33.422 | ||||
| Mean Square Error | 603.822 | ||||
| DF error | 1468.000 | ||||
| t(b) | 8.750 | ||||
| p(b) | 0.389 | ||||
| t(a) | 3.219 | ||||
| p(a) | 0.458 | ||||
| Lowerbound of 95% confidence interval for beta | 7.230 | ||||
| Upperbound of 95% confidence interval for beta | 11.408 | ||||
| Lowerbound of 95% confidence interval for alpha | 13.058 | ||||
| Upperbound of 95% confidence interval for alpha | 53.786 | ||||
| Treynor index (mean / b) | 3.960 | ||||
| Jensen alpha (a) | 33.422 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.266 | ||||
| SD | 6.343 | ||||
| Sharpe ratio (Glass type estimate) | -0.042 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.042 | ||||
| df | 1469.000 | ||||
| t | -0.099 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.869 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.786 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.869 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.786 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.059 | ||||
| Upside Potential Ratio | 1.761 | ||||
| Upside part of mean | 7.949 | ||||
| Downside part of mean | -8.215 | ||||
| Upside SD | 4.455 | ||||
| Downside SD | 4.513 | ||||
| N nonnegative terms | 174.000 | ||||
| N negative terms | 1296.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1470.000 | ||||
| Mean of predictor | 0.194 | ||||
| Mean of criterion | -0.266 | ||||
| SD of predictor | 0.598 | ||||
| SD of criterion | 6.343 | ||||
| Covariance | 1.085 | ||||
| r | 0.286 | ||||
| b (slope, estimate of beta) | 3.036 | ||||
| a (intercept, estimate of alpha) | -0.855 | ||||
| Mean Square Error | 36.971 | ||||
| DF error | 1468.000 | ||||
| t(b) | 11.438 | ||||
| p(b) | 0.357 | ||||
| t(a) | -0.333 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | 2.515 | ||||
| Upperbound of 95% confidence interval for beta | 3.557 | ||||
| Lowerbound of 95% confidence interval for alpha | -5.891 | ||||
| Upperbound of 95% confidence interval for alpha | 4.181 | ||||
| Treynor index (mean / b) | -0.087 | ||||
| Jensen alpha (a) | -0.855 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.476 | ||||
| Expected Shortfall on VaR | 0.550 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.041 | ||||
| Expected Shortfall on VaR | 0.093 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1470.000 | ||||
| Minimum | 0.051 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 19.306 | ||||
| Mean of quarter 1 | 0.950 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.613 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 149.000 | ||||
| Percentage of outliers low | 0.101 | ||||
| Mean of outliers low | 0.876 | ||||
| Number of outliers high | 174.000 | ||||
| Percentage of outliers high | 0.118 | ||||
| Mean of outliers high | 2.297 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.835 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| 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 | 5.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.943 | ||||
| Quartile 3 | 0.945 | ||||
| Maximum | 0.949 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.943 | ||||
| Mean of quarter 3 | 0.945 | ||||
| Mean of quarter 4 | 0.949 | ||||
| Inter Quartile Range | 0.936 | ||||
| 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) | -0.127 | ||||
| Compounded annual return (geometric extrapolation) | -0.199 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.209 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.209 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.361 | ||||
| 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 | 1.584 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.667 | ||||
| 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 | 1.362 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.664 | ||||
| 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) | -8729463616207533.000 | ||||
| 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) | -799621779457619043853378682617856.000 | ||||
| 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 | ||||