Advanced Statistics: EUR Scalper
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 | 0.227 | ||||
| SD | 0.228 | ||||
| Sharpe ratio (Glass type estimate) | 0.993 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.984 | ||||
| df | 80.000 | ||||
| t | 2.579 | ||||
| p | 0.006 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.220 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.760 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.214 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.753 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.321 | ||||
| Upside Potential Ratio | 3.542 | ||||
| Upside part of mean | 0.346 | ||||
| Downside part of mean | -0.119 | ||||
| Upside SD | 0.215 | ||||
| Downside SD | 0.098 | ||||
| N nonnegative terms | 34.000 | ||||
| N negative terms | 47.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 81.000 | ||||
| Mean of predictor | 0.262 | ||||
| Mean of criterion | 0.227 | ||||
| SD of predictor | 0.206 | ||||
| SD of criterion | 0.228 | ||||
| Covariance | 0.001 | ||||
| r | 0.026 | ||||
| b (slope, estimate of beta) | 0.029 | ||||
| a (intercept, estimate of alpha) | 0.219 | ||||
| Mean Square Error | 0.053 | ||||
| DF error | 79.000 | ||||
| t(b) | 0.235 | ||||
| p(b) | 0.407 | ||||
| t(a) | 2.324 | ||||
| p(a) | 0.011 | ||||
| Lowerbound of 95% confidence interval for beta | -0.219 | ||||
| Upperbound of 95% confidence interval for beta | 0.277 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.031 | ||||
| Upperbound of 95% confidence interval for alpha | 0.407 | ||||
| Treynor index (mean / b) | 7.727 | ||||
| Jensen alpha (a) | 0.219 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.200 | ||||
| SD | 0.217 | ||||
| Sharpe ratio (Glass type estimate) | 0.923 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.914 | ||||
| df | 80.000 | ||||
| t | 2.397 | ||||
| p | 0.009 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.152 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.688 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.146 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.682 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.916 | ||||
| Upside Potential Ratio | 3.103 | ||||
| Upside part of mean | 0.324 | ||||
| Downside part of mean | -0.124 | ||||
| Upside SD | 0.197 | ||||
| Downside SD | 0.105 | ||||
| N nonnegative terms | 34.000 | ||||
| N negative terms | 47.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 81.000 | ||||
| Mean of predictor | 0.239 | ||||
| Mean of criterion | 0.200 | ||||
| SD of predictor | 0.199 | ||||
| SD of criterion | 0.217 | ||||
| Covariance | 0.002 | ||||
| r | 0.049 | ||||
| b (slope, estimate of beta) | 0.053 | ||||
| a (intercept, estimate of alpha) | 0.187 | ||||
| Mean Square Error | 0.048 | ||||
| DF error | 79.000 | ||||
| t(b) | 0.437 | ||||
| p(b) | 0.332 | ||||
| t(a) | 2.109 | ||||
| p(a) | 0.019 | ||||
| Lowerbound of 95% confidence interval for beta | -0.190 | ||||
| Upperbound of 95% confidence interval for beta | 0.297 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.011 | ||||
| Upperbound of 95% confidence interval for alpha | 0.364 | ||||
| Treynor index (mean / b) | 3.742 | ||||
| Jensen alpha (a) | 0.187 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.083 | ||||
| Expected Shortfall on VaR | 0.106 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 81.000 | ||||
| Minimum | 0.825 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.038 | ||||
| Maximum | 1.266 | ||||
| Mean of quarter 1 | 0.970 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.016 | ||||
| Mean of quarter 4 | 1.108 | ||||
| Inter Quartile Range | 0.038 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.049 | ||||
| Mean of outliers low | 0.891 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.111 | ||||
| Mean of outliers high | 1.168 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.320 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.010 | ||||
| Extreme Value Index (regression method) | 0.764 | ||||
| VaR(95%) (regression method) | 0.029 | ||||
| Expected Shortfall (regression method) | 0.168 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.040 | ||||
| Quartile 3 | 0.089 | ||||
| Maximum | 0.239 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.028 | ||||
| Mean of quarter 3 | 0.054 | ||||
| Mean of quarter 4 | 0.149 | ||||
| Inter Quartile Range | 0.081 | ||||
| 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 | 0.100 | ||||
| Mean of outliers high | 0.239 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.093 | ||||
| VaR(95%) (moments method) | 0.171 | ||||
| Expected Shortfall (moments method) | 0.234 | ||||
| Extreme Value Index (regression method) | 2.151 | ||||
| VaR(95%) (regression method) | 0.306 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.622 | ||||
| Compounded annual return (geometric extrapolation) | 0.277 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.159 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.858 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.605 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.251 | ||||
| SD | 0.321 | ||||
| Sharpe ratio (Glass type estimate) | 0.783 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.782 | ||||
| df | 1770.000 | ||||
| t | 2.035 | ||||
| p | 0.476 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.028 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.537 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.028 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.537 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.147 | ||||
| Upside Potential Ratio | 5.223 | ||||
| Upside part of mean | 1.145 | ||||
| Downside part of mean | -0.893 | ||||
| Upside SD | 0.235 | ||||
| Downside SD | 0.219 | ||||
| N nonnegative terms | 554.000 | ||||
| N negative terms | 1217.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1771.000 | ||||
| Mean of predictor | 0.272 | ||||
| Mean of criterion | 0.251 | ||||
| SD of predictor | 0.276 | ||||
| SD of criterion | 0.321 | ||||
| Covariance | 0.018 | ||||
| r | 0.207 | ||||
| b (slope, estimate of beta) | 0.241 | ||||
| a (intercept, estimate of alpha) | 0.186 | ||||
| Mean Square Error | 0.099 | ||||
| DF error | 1769.000 | ||||
| t(b) | 8.908 | ||||
| p(b) | 0.369 | ||||
| t(a) | 1.535 | ||||
| p(a) | 0.477 | ||||
| Lowerbound of 95% confidence interval for beta | 0.188 | ||||
| Upperbound of 95% confidence interval for beta | 0.294 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.052 | ||||
| Upperbound of 95% confidence interval for alpha | 0.423 | ||||
| Treynor index (mean / b) | 1.042 | ||||
| Jensen alpha (a) | 0.186 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.200 | ||||
| SD | 0.321 | ||||
| Sharpe ratio (Glass type estimate) | 0.623 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.623 | ||||
| df | 1770.000 | ||||
| t | 1.620 | ||||
| p | 0.481 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.131 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.377 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.131 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.377 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.872 | ||||
| Upside Potential Ratio | 4.883 | ||||
| Upside part of mean | 1.119 | ||||
| Downside part of mean | -0.919 | ||||
| Upside SD | 0.225 | ||||
| Downside SD | 0.229 | ||||
| N nonnegative terms | 554.000 | ||||
| N negative terms | 1217.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1771.000 | ||||
| Mean of predictor | 0.233 | ||||
| Mean of criterion | 0.200 | ||||
| SD of predictor | 0.278 | ||||
| SD of criterion | 0.321 | ||||
| Covariance | 0.018 | ||||
| r | 0.203 | ||||
| b (slope, estimate of beta) | 0.234 | ||||
| a (intercept, estimate of alpha) | 0.145 | ||||
| Mean Square Error | 0.099 | ||||
| DF error | 1769.000 | ||||
| t(b) | 8.715 | ||||
| p(b) | 0.372 | ||||
| t(a) | 1.200 | ||||
| p(a) | 0.482 | ||||
| Lowerbound of 95% confidence interval for beta | 0.182 | ||||
| Upperbound of 95% confidence interval for beta | 0.287 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.092 | ||||
| Upperbound of 95% confidence interval for alpha | 0.382 | ||||
| Treynor index (mean / b) | 0.853 | ||||
| Jensen alpha (a) | 0.145 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1771.000 | ||||
| Minimum | 0.845 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.183 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 216.000 | ||||
| Percentage of outliers low | 0.122 | ||||
| Mean of outliers low | 0.974 | ||||
| Number of outliers high | 311.000 | ||||
| Percentage of outliers high | 0.176 | ||||
| Mean of outliers high | 1.023 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.997 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 2.141 | ||||
| Extreme Value Index (regression method) | 0.298 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.026 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 51.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.033 | ||||
| Quartile 3 | 0.083 | ||||
| Maximum | 0.324 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.023 | ||||
| Mean of quarter 3 | 0.058 | ||||
| Mean of quarter 4 | 0.141 | ||||
| Inter Quartile Range | 0.075 | ||||
| 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 | 0.039 | ||||
| Mean of outliers high | 0.267 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.042 | ||||
| VaR(95%) (moments method) | 0.148 | ||||
| Expected Shortfall (moments method) | 0.186 | ||||
| Extreme Value Index (regression method) | 0.536 | ||||
| VaR(95%) (regression method) | 0.135 | ||||
| Expected Shortfall (regression method) | 0.234 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.621 | ||||
| Compounded annual return (geometric extrapolation) | 0.276 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.853 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.955 | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.030 | ||||
| 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 | 0.857 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.458 | ||||
| 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 | 0.750 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.465 | ||||
| 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) | -8756036844158426.000 | ||||
| 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) | -180315094161456986274734440185856.000 | ||||
| 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 | ||||