Advanced Statistics: ES Bomber
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 | -0.163 | ||||
| SD | 0.156 | ||||
| Sharpe ratio (Glass type estimate) | -1.048 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.020 | ||||
| df | 29.000 | ||||
| t | -1.657 | ||||
| p | 0.946 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.307 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.229 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.287 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.247 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.019 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.163 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.160 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 30.000 | ||||
| Mean of predictor | 0.638 | ||||
| Mean of criterion | -0.163 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.156 | ||||
| Covariance | -0.001 | ||||
| r | -0.017 | ||||
| b (slope, estimate of beta) | -0.008 | ||||
| a (intercept, estimate of alpha) | -0.158 | ||||
| Mean Square Error | 0.025 | ||||
| DF error | 28.000 | ||||
| t(b) | -0.089 | ||||
| p(b) | 0.535 | ||||
| t(a) | -1.360 | ||||
| p(a) | 0.908 | ||||
| Lowerbound of 95% confidence interval for beta | -0.197 | ||||
| Upperbound of 95% confidence interval for beta | 0.180 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.396 | ||||
| Upperbound of 95% confidence interval for alpha | 0.080 | ||||
| Treynor index (mean / b) | 19.893 | ||||
| Jensen alpha (a) | -0.158 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.178 | ||||
| SD | 0.178 | ||||
| Sharpe ratio (Glass type estimate) | -1.001 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.975 | ||||
| df | 29.000 | ||||
| t | -1.583 | ||||
| p | 0.938 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.259 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.273 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.240 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.290 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.977 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.178 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.182 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 30.000 | ||||
| Mean of predictor | 0.578 | ||||
| Mean of criterion | -0.178 | ||||
| SD of predictor | 0.289 | ||||
| SD of criterion | 0.178 | ||||
| Covariance | -0.001 | ||||
| r | -0.028 | ||||
| b (slope, estimate of beta) | -0.017 | ||||
| a (intercept, estimate of alpha) | -0.168 | ||||
| Mean Square Error | 0.033 | ||||
| DF error | 28.000 | ||||
| t(b) | -0.151 | ||||
| p(b) | 0.559 | ||||
| t(a) | -1.266 | ||||
| p(a) | 0.892 | ||||
| Lowerbound of 95% confidence interval for beta | -0.255 | ||||
| Upperbound of 95% confidence interval for beta | 0.220 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.439 | ||||
| Upperbound of 95% confidence interval for alpha | 0.104 | ||||
| Treynor index (mean / b) | 10.178 | ||||
| Jensen alpha (a) | -0.168 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.094 | ||||
| Expected Shortfall on VaR | 0.113 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.047 | ||||
| Expected Shortfall on VaR | 0.100 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 30.000 | ||||
| Minimum | 0.758 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.963 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers low | 0.067 | ||||
| Mean of outliers low | 0.851 | ||||
| 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) | 0.729 | ||||
| VaR(95%) (regression method) | 0.071 | ||||
| Expected Shortfall (regression method) | 0.569 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.284 | ||||
| Quartile 1 | 0.284 | ||||
| Median | 0.284 | ||||
| Quartile 3 | 0.284 | ||||
| Maximum | 0.284 | ||||
| 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) | -0.114 | ||||
| Compounded annual return (geometric extrapolation) | -0.125 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.441 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.104 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.163 | ||||
| SD | 0.152 | ||||
| Sharpe ratio (Glass type estimate) | -1.068 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.067 | ||||
| df | 669.000 | ||||
| t | -1.708 | ||||
| p | 0.956 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.295 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.159 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.294 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.160 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.252 | ||||
| Upside Potential Ratio | 1.372 | ||||
| Upside part of mean | 0.178 | ||||
| Downside part of mean | -0.341 | ||||
| Upside SD | 0.080 | ||||
| Downside SD | 0.130 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 650.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 670.000 | ||||
| Mean of predictor | 0.647 | ||||
| Mean of criterion | -0.163 | ||||
| SD of predictor | 0.386 | ||||
| SD of criterion | 0.152 | ||||
| Covariance | -0.006 | ||||
| r | -0.102 | ||||
| b (slope, estimate of beta) | -0.040 | ||||
| a (intercept, estimate of alpha) | -0.137 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 668.000 | ||||
| t(b) | -2.643 | ||||
| p(b) | 0.996 | ||||
| t(a) | -1.435 | ||||
| p(a) | 0.924 | ||||
| Lowerbound of 95% confidence interval for beta | -0.070 | ||||
| Upperbound of 95% confidence interval for beta | -0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.324 | ||||
| Upperbound of 95% confidence interval for alpha | 0.050 | ||||
| Treynor index (mean / b) | 4.052 | ||||
| Jensen alpha (a) | -0.137 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.175 | ||||
| SD | 0.156 | ||||
| Sharpe ratio (Glass type estimate) | -1.121 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.120 | ||||
| df | 669.000 | ||||
| t | -1.792 | ||||
| p | 0.963 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.348 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.107 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.347 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.108 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.293 | ||||
| Upside Potential Ratio | 1.296 | ||||
| Upside part of mean | 0.175 | ||||
| Downside part of mean | -0.350 | ||||
| Upside SD | 0.078 | ||||
| Downside SD | 0.135 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 650.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 670.000 | ||||
| Mean of predictor | 0.574 | ||||
| Mean of criterion | -0.175 | ||||
| SD of predictor | 0.375 | ||||
| SD of criterion | 0.156 | ||||
| Covariance | -0.006 | ||||
| r | -0.104 | ||||
| b (slope, estimate of beta) | -0.043 | ||||
| a (intercept, estimate of alpha) | -0.150 | ||||
| Mean Square Error | 0.024 | ||||
| DF error | 668.000 | ||||
| t(b) | -2.710 | ||||
| p(b) | 0.997 | ||||
| t(a) | -1.538 | ||||
| p(a) | 0.938 | ||||
| Lowerbound of 95% confidence interval for beta | -0.075 | ||||
| Upperbound of 95% confidence interval for beta | -0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.341 | ||||
| Upperbound of 95% confidence interval for alpha | 0.042 | ||||
| Treynor index (mean / b) | 4.035 | ||||
| Jensen alpha (a) | -0.150 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 670.000 | ||||
| Minimum | 0.899 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.063 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 23.000 | ||||
| Percentage of outliers low | 0.034 | ||||
| Mean of outliers low | 0.967 | ||||
| Number of outliers high | 20.000 | ||||
| Percentage of outliers high | 0.030 | ||||
| Mean of outliers high | 1.023 | ||||
| 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) | -0.302 | ||||
| VaR(95%) (regression method) | -0.009 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.040 | ||||
| Quartile 1 | 0.114 | ||||
| Median | 0.187 | ||||
| Quartile 3 | 0.261 | ||||
| Maximum | 0.334 | ||||
| Mean of quarter 1 | 0.040 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.334 | ||||
| Inter Quartile Range | 0.147 | ||||
| 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) | -0.111 | ||||
| Compounded annual return (geometric extrapolation) | -0.123 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.367 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.367 | ||||
| Compounded annual return / Expected Shortfall lognormal | -6.032 | ||||
| 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 | 0.812 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.459 | ||||
| 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 | 0.706 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.458 | ||||
| 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) | -8759897823524449.000 | ||||
| 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) | -125798292405256544858620586622976.000 | ||||
| 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 | ||||