Advanced Statistics: Daily E-Mini Hedge
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 | 0.115 | ||||
| SD | 0.292 | ||||
| Sharpe ratio (Glass type estimate) | 0.394 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.389 | ||||
| df | 60.000 | ||||
| t | 0.887 | ||||
| p | 0.189 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.480 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.264 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.483 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.261 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.089 | ||||
| Upside Potential Ratio | 2.325 | ||||
| Upside part of mean | 0.245 | ||||
| Downside part of mean | -0.130 | ||||
| Upside SD | 0.272 | ||||
| Downside SD | 0.106 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 51.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.349 | ||||
| Mean of criterion | 0.115 | ||||
| SD of predictor | 0.360 | ||||
| SD of criterion | 0.292 | ||||
| Covariance | -0.000 | ||||
| r | -0.003 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | 0.116 | ||||
| Mean Square Error | 0.087 | ||||
| DF error | 59.000 | ||||
| t(b) | -0.021 | ||||
| p(b) | 0.509 | ||||
| t(a) | 0.853 | ||||
| p(a) | 0.199 | ||||
| Lowerbound of 95% confidence interval for beta | -0.214 | ||||
| Upperbound of 95% confidence interval for beta | 0.209 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.156 | ||||
| Upperbound of 95% confidence interval for alpha | 0.387 | ||||
| Treynor index (mean / b) | -50.697 | ||||
| Jensen alpha (a) | 0.116 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.080 | ||||
| SD | 0.253 | ||||
| Sharpe ratio (Glass type estimate) | 0.315 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.311 | ||||
| df | 60.000 | ||||
| t | 0.711 | ||||
| p | 0.240 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.557 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.185 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.560 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.183 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.705 | ||||
| Upside Potential Ratio | 1.906 | ||||
| Upside part of mean | 0.216 | ||||
| Downside part of mean | -0.136 | ||||
| Upside SD | 0.225 | ||||
| Downside SD | 0.113 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 51.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.284 | ||||
| Mean of criterion | 0.080 | ||||
| SD of predictor | 0.345 | ||||
| SD of criterion | 0.253 | ||||
| Covariance | 0.001 | ||||
| r | 0.011 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | 0.078 | ||||
| Mean Square Error | 0.065 | ||||
| DF error | 59.000 | ||||
| t(b) | 0.082 | ||||
| p(b) | 0.468 | ||||
| t(a) | 0.667 | ||||
| p(a) | 0.254 | ||||
| Lowerbound of 95% confidence interval for beta | -0.183 | ||||
| Upperbound of 95% confidence interval for beta | 0.199 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.155 | ||||
| Upperbound of 95% confidence interval for alpha | 0.310 | ||||
| Treynor index (mean / b) | 10.244 | ||||
| Jensen alpha (a) | 0.078 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.107 | ||||
| Expected Shortfall on VaR | 0.134 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.070 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.829 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.546 | ||||
| Mean of quarter 1 | 0.970 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.086 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.131 | ||||
| Mean of outliers low | 0.940 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.180 | ||||
| Mean of outliers high | 1.117 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -11.405 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.051 | ||||
| VaR(95%) (regression method) | 0.041 | ||||
| Expected Shortfall (regression method) | 0.081 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.048 | ||||
| Quartile 1 | 0.085 | ||||
| Median | 0.122 | ||||
| Quartile 3 | 0.178 | ||||
| Maximum | 0.235 | ||||
| Mean of quarter 1 | 0.048 | ||||
| Mean of quarter 2 | 0.122 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.235 | ||||
| Inter Quartile Range | 0.094 | ||||
| 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) | 0.172 | ||||
| Compounded annual return (geometric extrapolation) | 0.132 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.561 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.561 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.985 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.451 | ||||
| SD | 0.884 | ||||
| Sharpe ratio (Glass type estimate) | 0.511 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.510 | ||||
| df | 1337.000 | ||||
| t | 1.154 | ||||
| p | 0.480 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.357 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.378 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.357 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.378 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.896 | ||||
| Upside Potential Ratio | 3.538 | ||||
| Upside part of mean | 1.782 | ||||
| Downside part of mean | -1.331 | ||||
| Upside SD | 0.726 | ||||
| Downside SD | 0.504 | ||||
| N nonnegative terms | 115.000 | ||||
| N negative terms | 1223.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1338.000 | ||||
| Mean of predictor | 0.532 | ||||
| Mean of criterion | 0.451 | ||||
| SD of predictor | 0.698 | ||||
| SD of criterion | 0.884 | ||||
| Covariance | -0.027 | ||||
| r | -0.044 | ||||
| b (slope, estimate of beta) | -0.055 | ||||
| a (intercept, estimate of alpha) | 0.481 | ||||
| Mean Square Error | 0.780 | ||||
| DF error | 1336.000 | ||||
| t(b) | -1.598 | ||||
| p(b) | 0.522 | ||||
| t(a) | 1.229 | ||||
| p(a) | 0.483 | ||||
| Lowerbound of 95% confidence interval for beta | -0.123 | ||||
| Upperbound of 95% confidence interval for beta | 0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.287 | ||||
| Upperbound of 95% confidence interval for alpha | 1.249 | ||||
| Treynor index (mean / b) | -8.167 | ||||
| Jensen alpha (a) | 0.481 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.079 | ||||
| SD | 0.864 | ||||
| Sharpe ratio (Glass type estimate) | 0.092 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.092 | ||||
| df | 1337.000 | ||||
| t | 0.207 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.776 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.959 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.776 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.959 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.129 | ||||
| Upside Potential Ratio | 2.571 | ||||
| Upside part of mean | 1.574 | ||||
| Downside part of mean | -1.494 | ||||
| Upside SD | 0.609 | ||||
| Downside SD | 0.612 | ||||
| N nonnegative terms | 115.000 | ||||
| N negative terms | 1223.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1338.000 | ||||
| Mean of predictor | 0.297 | ||||
| Mean of criterion | 0.079 | ||||
| SD of predictor | 0.683 | ||||
| SD of criterion | 0.864 | ||||
| Covariance | -0.030 | ||||
| r | -0.052 | ||||
| b (slope, estimate of beta) | -0.065 | ||||
| a (intercept, estimate of alpha) | 0.099 | ||||
| Mean Square Error | 0.745 | ||||
| DF error | 1336.000 | ||||
| t(b) | -1.892 | ||||
| p(b) | 0.526 | ||||
| t(a) | 0.258 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -0.133 | ||||
| Upperbound of 95% confidence interval for beta | 0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.651 | ||||
| Upperbound of 95% confidence interval for alpha | 0.848 | ||||
| Treynor index (mean / b) | -1.212 | ||||
| Jensen alpha (a) | 0.099 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.084 | ||||
| Expected Shortfall on VaR | 0.104 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1338.000 | ||||
| Minimum | 0.500 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.652 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.027 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 141.000 | ||||
| Percentage of outliers low | 0.105 | ||||
| Mean of outliers low | 0.953 | ||||
| Number of outliers high | 136.000 | ||||
| Percentage of outliers high | 0.102 | ||||
| Mean of outliers high | 1.067 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.760 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.023 | ||||
| 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 | 13.000 | ||||
| Minimum | 0.034 | ||||
| Quartile 1 | 0.116 | ||||
| Median | 0.267 | ||||
| Quartile 3 | 0.310 | ||||
| Maximum | 0.512 | ||||
| Mean of quarter 1 | 0.082 | ||||
| Mean of quarter 2 | 0.231 | ||||
| Mean of quarter 3 | 0.294 | ||||
| Mean of quarter 4 | 0.434 | ||||
| Inter Quartile Range | 0.193 | ||||
| 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) | -1.814 | ||||
| VaR(95%) (moments method) | 0.457 | ||||
| Expected Shortfall (moments method) | 0.463 | ||||
| Extreme Value Index (regression method) | -0.574 | ||||
| VaR(95%) (regression method) | 0.518 | ||||
| Expected Shortfall (regression method) | 0.562 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.172 | ||||
| Compounded annual return (geometric extrapolation) | 0.131 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.256 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.302 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.264 | ||||
| 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 | 1.996 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.678 | ||||
| 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 | 1.765 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.668 | ||||
| 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) | -8684064812669457.000 | ||||
| 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) | 656734982606693040711454261510144.000 | ||||
| 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 | ||||