Advanced Statistics: German BUND Sprinter
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 | 0.180 | ||||
| SD | 0.543 | ||||
| Sharpe ratio (Glass type estimate) | 0.332 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.326 | ||||
| df | 43.000 | ||||
| t | 0.636 | ||||
| p | 0.264 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.696 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.356 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.699 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.352 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.802 | ||||
| Upside Potential Ratio | 2.047 | ||||
| Upside part of mean | 0.461 | ||||
| Downside part of mean | -0.280 | ||||
| Upside SD | 0.490 | ||||
| Downside SD | 0.225 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 44.000 | ||||
| Mean of predictor | 0.437 | ||||
| Mean of criterion | 0.180 | ||||
| SD of predictor | 0.313 | ||||
| SD of criterion | 0.543 | ||||
| Covariance | -0.017 | ||||
| r | -0.100 | ||||
| b (slope, estimate of beta) | -0.173 | ||||
| a (intercept, estimate of alpha) | 0.256 | ||||
| Mean Square Error | 0.299 | ||||
| DF error | 42.000 | ||||
| t(b) | -0.650 | ||||
| p(b) | 0.740 | ||||
| t(a) | 0.830 | ||||
| p(a) | 0.206 | ||||
| Lowerbound of 95% confidence interval for beta | -0.711 | ||||
| Upperbound of 95% confidence interval for beta | 0.365 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.366 | ||||
| Upperbound of 95% confidence interval for alpha | 0.878 | ||||
| Treynor index (mean / b) | -1.042 | ||||
| Jensen alpha (a) | 0.256 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.069 | ||||
| SD | 0.450 | ||||
| Sharpe ratio (Glass type estimate) | 0.154 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.152 | ||||
| df | 43.000 | ||||
| t | 0.296 | ||||
| p | 0.384 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.870 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.178 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.872 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.176 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.271 | ||||
| Upside Potential Ratio | 1.476 | ||||
| Upside part of mean | 0.379 | ||||
| Downside part of mean | -0.309 | ||||
| Upside SD | 0.364 | ||||
| Downside SD | 0.257 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 44.000 | ||||
| Mean of predictor | 0.384 | ||||
| Mean of criterion | 0.069 | ||||
| SD of predictor | 0.294 | ||||
| SD of criterion | 0.450 | ||||
| Covariance | -0.011 | ||||
| r | -0.084 | ||||
| b (slope, estimate of beta) | -0.128 | ||||
| a (intercept, estimate of alpha) | 0.119 | ||||
| Mean Square Error | 0.206 | ||||
| DF error | 42.000 | ||||
| t(b) | -0.545 | ||||
| p(b) | 0.706 | ||||
| t(a) | 0.469 | ||||
| p(a) | 0.321 | ||||
| Lowerbound of 95% confidence interval for beta | -0.603 | ||||
| Upperbound of 95% confidence interval for beta | 0.347 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.393 | ||||
| Upperbound of 95% confidence interval for alpha | 0.631 | ||||
| Treynor index (mean / b) | -0.542 | ||||
| Jensen alpha (a) | 0.119 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.188 | ||||
| Expected Shortfall on VaR | 0.230 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.068 | ||||
| Expected Shortfall on VaR | 0.142 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 44.000 | ||||
| Minimum | 0.724 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.888 | ||||
| Mean of quarter 1 | 0.919 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.157 | ||||
| Inter Quartile Range | 0.006 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.159 | ||||
| Mean of outliers low | 0.876 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.205 | ||||
| Mean of outliers high | 1.191 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.600 | ||||
| VaR(95%) (moments method) | 0.056 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.115 | ||||
| VaR(95%) (regression method) | 0.053 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.038 | ||||
| Quartile 1 | 0.138 | ||||
| Median | 0.237 | ||||
| Quartile 3 | 0.322 | ||||
| Maximum | 0.408 | ||||
| Mean of quarter 1 | 0.038 | ||||
| Mean of quarter 2 | 0.237 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.408 | ||||
| Inter Quartile Range | 0.185 | ||||
| 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) | 0.141 | ||||
| Compounded annual return (geometric extrapolation) | 0.120 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.295 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.295 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.523 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.133 | ||||
| SD | 0.374 | ||||
| Sharpe ratio (Glass type estimate) | 0.357 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.357 | ||||
| df | 964.000 | ||||
| t | 0.685 | ||||
| p | 0.247 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.665 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.378 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.665 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.378 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.677 | ||||
| Upside Potential Ratio | 5.344 | ||||
| Upside part of mean | 1.053 | ||||
| Downside part of mean | -0.920 | ||||
| Upside SD | 0.318 | ||||
| Downside SD | 0.197 | ||||
| N nonnegative terms | 246.000 | ||||
| N negative terms | 719.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 965.000 | ||||
| Mean of predictor | 0.453 | ||||
| Mean of criterion | 0.133 | ||||
| SD of predictor | 0.289 | ||||
| SD of criterion | 0.374 | ||||
| Covariance | -0.006 | ||||
| r | -0.058 | ||||
| b (slope, estimate of beta) | -0.075 | ||||
| a (intercept, estimate of alpha) | 0.167 | ||||
| Mean Square Error | 0.139 | ||||
| DF error | 963.000 | ||||
| t(b) | -1.809 | ||||
| p(b) | 0.965 | ||||
| t(a) | 0.857 | ||||
| p(a) | 0.196 | ||||
| Lowerbound of 95% confidence interval for beta | -0.157 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.216 | ||||
| Upperbound of 95% confidence interval for alpha | 0.551 | ||||
| Treynor index (mean / b) | -1.771 | ||||
| Jensen alpha (a) | 0.167 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.069 | ||||
| SD | 0.353 | ||||
| Sharpe ratio (Glass type estimate) | 0.196 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.195 | ||||
| df | 964.000 | ||||
| t | 0.375 | ||||
| p | 0.354 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.826 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.217 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.826 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.217 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.333 | ||||
| Upside Potential Ratio | 4.873 | ||||
| Upside part of mean | 1.009 | ||||
| Downside part of mean | -0.940 | ||||
| Upside SD | 0.285 | ||||
| Downside SD | 0.207 | ||||
| N nonnegative terms | 246.000 | ||||
| N negative terms | 719.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 965.000 | ||||
| Mean of predictor | 0.410 | ||||
| Mean of criterion | 0.069 | ||||
| SD of predictor | 0.291 | ||||
| SD of criterion | 0.353 | ||||
| Covariance | -0.006 | ||||
| r | -0.059 | ||||
| b (slope, estimate of beta) | -0.072 | ||||
| a (intercept, estimate of alpha) | 0.098 | ||||
| Mean Square Error | 0.124 | ||||
| DF error | 963.000 | ||||
| t(b) | -1.836 | ||||
| p(b) | 0.967 | ||||
| t(a) | 0.534 | ||||
| p(a) | 0.297 | ||||
| Lowerbound of 95% confidence interval for beta | -0.148 | ||||
| Upperbound of 95% confidence interval for beta | 0.005 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.263 | ||||
| Upperbound of 95% confidence interval for alpha | 0.460 | ||||
| Treynor index (mean / b) | -0.964 | ||||
| Jensen alpha (a) | 0.098 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.044 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.022 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 965.000 | ||||
| Minimum | 0.800 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.413 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 179.000 | ||||
| Percentage of outliers low | 0.185 | ||||
| Mean of outliers low | 0.982 | ||||
| Number of outliers high | 184.000 | ||||
| Percentage of outliers high | 0.191 | ||||
| Mean of outliers high | 1.021 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.137 | ||||
| VaR(95%) (moments method) | 0.008 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.369 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.023 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.034 | ||||
| Quartile 3 | 0.055 | ||||
| Maximum | 0.460 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.019 | ||||
| Mean of quarter 3 | 0.044 | ||||
| Mean of quarter 4 | 0.314 | ||||
| Inter Quartile Range | 0.049 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.167 | ||||
| Mean of outliers high | 0.429 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -252.440 | ||||
| VaR(95%) (moments method) | 0.220 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -3.342 | ||||
| VaR(95%) (regression method) | 0.808 | ||||
| Expected Shortfall (regression method) | 0.812 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.140 | ||||
| Compounded annual return (geometric extrapolation) | 0.120 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.260 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.381 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.739 | ||||
| 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 | 1.013 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.446 | ||||
| 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 | 0.912 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.448 | ||||
| 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) | -8730438590860116.000 | ||||
| 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) | 153296804453015361056099790749696.000 | ||||
| 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 | ||||