Advanced Statistics: MORE Futures
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 | -0.476 | ||||
| SD | 0.555 | ||||
| Sharpe ratio (Glass type estimate) | -0.859 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.840 | ||||
| df | 34.000 | ||||
| t | -1.467 | ||||
| p | 0.924 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.018 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.313 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.005 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.325 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.849 | ||||
| Upside Potential Ratio | 0.052 | ||||
| Upside part of mean | 0.029 | ||||
| Downside part of mean | -0.506 | ||||
| Upside SD | 0.050 | ||||
| Downside SD | 0.561 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.511 | ||||
| Mean of criterion | -0.476 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.555 | ||||
| Covariance | 0.031 | ||||
| r | 0.213 | ||||
| b (slope, estimate of beta) | 0.449 | ||||
| a (intercept, estimate of alpha) | -0.706 | ||||
| Mean Square Error | 0.302 | ||||
| DF error | 33.000 | ||||
| t(b) | 1.252 | ||||
| p(b) | 0.110 | ||||
| t(a) | -1.905 | ||||
| p(a) | 0.967 | ||||
| Lowerbound of 95% confidence interval for beta | -0.281 | ||||
| Upperbound of 95% confidence interval for beta | 1.179 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.460 | ||||
| Upperbound of 95% confidence interval for alpha | 0.048 | ||||
| Treynor index (mean / b) | -1.060 | ||||
| Jensen alpha (a) | -0.706 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.067 | ||||
| SD | 1.535 | ||||
| Sharpe ratio (Glass type estimate) | -0.695 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.680 | ||||
| df | 34.000 | ||||
| t | -1.188 | ||||
| p | 0.878 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.850 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.469 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.839 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.479 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.692 | ||||
| Upside Potential Ratio | 0.018 | ||||
| Upside part of mean | 0.028 | ||||
| Downside part of mean | -1.095 | ||||
| Upside SD | 0.048 | ||||
| Downside SD | 1.543 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.468 | ||||
| Mean of criterion | -1.067 | ||||
| SD of predictor | 0.248 | ||||
| SD of criterion | 1.535 | ||||
| Covariance | 0.067 | ||||
| r | 0.175 | ||||
| b (slope, estimate of beta) | 1.082 | ||||
| a (intercept, estimate of alpha) | -1.574 | ||||
| Mean Square Error | 2.353 | ||||
| DF error | 33.000 | ||||
| t(b) | 1.020 | ||||
| p(b) | 0.158 | ||||
| t(a) | -1.533 | ||||
| p(a) | 0.933 | ||||
| Lowerbound of 95% confidence interval for beta | -1.076 | ||||
| Upperbound of 95% confidence interval for beta | 3.240 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.662 | ||||
| Upperbound of 95% confidence interval for alpha | 0.514 | ||||
| Treynor index (mean / b) | -0.986 | ||||
| Jensen alpha (a) | -1.574 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.559 | ||||
| Expected Shortfall on VaR | 0.629 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.144 | ||||
| Expected Shortfall on VaR | 0.311 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.073 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.089 | ||||
| Mean of quarter 1 | 0.850 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.171 | ||||
| Mean of outliers low | 0.775 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.029 | ||||
| Mean of outliers high | 1.089 | ||||
| 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) | 1.500 | ||||
| VaR(95%) (regression method) | 0.133 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.949 | ||||
| Quartile 1 | 0.949 | ||||
| Median | 0.949 | ||||
| Quartile 3 | 0.949 | ||||
| Maximum | 0.949 | ||||
| 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) | -0.326 | ||||
| Compounded annual return (geometric extrapolation) | -0.641 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.675 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.019 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.695 | ||||
| SD | 0.603 | ||||
| Sharpe ratio (Glass type estimate) | -1.153 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.152 | ||||
| df | 782.000 | ||||
| t | -1.993 | ||||
| p | 0.977 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.288 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.017 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.287 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.016 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.175 | ||||
| Upside Potential Ratio | 0.638 | ||||
| Upside part of mean | 0.378 | ||||
| Downside part of mean | -1.073 | ||||
| Upside SD | 0.122 | ||||
| Downside SD | 0.592 | ||||
| N nonnegative terms | 54.000 | ||||
| N negative terms | 729.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 783.000 | ||||
| Mean of predictor | 0.562 | ||||
| Mean of criterion | -0.695 | ||||
| SD of predictor | 0.359 | ||||
| SD of criterion | 0.603 | ||||
| Covariance | 0.005 | ||||
| r | 0.023 | ||||
| b (slope, estimate of beta) | 0.039 | ||||
| a (intercept, estimate of alpha) | -0.717 | ||||
| Mean Square Error | 0.364 | ||||
| DF error | 781.000 | ||||
| t(b) | 0.646 | ||||
| p(b) | 0.259 | ||||
| t(a) | -2.045 | ||||
| p(a) | 0.979 | ||||
| Lowerbound of 95% confidence interval for beta | -0.079 | ||||
| Upperbound of 95% confidence interval for beta | 0.157 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.405 | ||||
| Upperbound of 95% confidence interval for alpha | -0.029 | ||||
| Treynor index (mean / b) | -17.913 | ||||
| Jensen alpha (a) | -0.717 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.043 | ||||
| SD | 0.987 | ||||
| Sharpe ratio (Glass type estimate) | -1.056 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.055 | ||||
| df | 782.000 | ||||
| t | -1.826 | ||||
| p | 0.966 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.191 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.079 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.190 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.079 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.063 | ||||
| Upside Potential Ratio | 0.377 | ||||
| Upside part of mean | 0.370 | ||||
| Downside part of mean | -1.413 | ||||
| Upside SD | 0.119 | ||||
| Downside SD | 0.981 | ||||
| N nonnegative terms | 54.000 | ||||
| N negative terms | 729.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 783.000 | ||||
| Mean of predictor | 0.497 | ||||
| Mean of criterion | -1.043 | ||||
| SD of predictor | 0.357 | ||||
| SD of criterion | 0.987 | ||||
| Covariance | 0.006 | ||||
| r | 0.018 | ||||
| b (slope, estimate of beta) | 0.050 | ||||
| a (intercept, estimate of alpha) | -1.068 | ||||
| Mean Square Error | 0.975 | ||||
| DF error | 781.000 | ||||
| t(b) | 0.504 | ||||
| p(b) | 0.307 | ||||
| t(a) | -1.862 | ||||
| p(a) | 0.969 | ||||
| Lowerbound of 95% confidence interval for beta | -0.144 | ||||
| Upperbound of 95% confidence interval for beta | 0.244 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.193 | ||||
| Upperbound of 95% confidence interval for alpha | 0.058 | ||||
| Treynor index (mean / b) | -20.891 | ||||
| Jensen alpha (a) | -1.068 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.099 | ||||
| Expected Shortfall on VaR | 0.121 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 783.000 | ||||
| Minimum | 0.272 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.088 | ||||
| Mean of quarter 1 | 0.984 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 57.000 | ||||
| Percentage of outliers low | 0.073 | ||||
| Mean of outliers low | 0.946 | ||||
| Number of outliers high | 54.000 | ||||
| Percentage of outliers high | 0.069 | ||||
| Mean of outliers high | 1.021 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.062 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 0.350 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.026 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.949 | ||||
| Quartile 1 | 0.949 | ||||
| Median | 0.949 | ||||
| Quartile 3 | 0.949 | ||||
| Maximum | 0.949 | ||||
| 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) | -0.318 | ||||
| Compounded annual return (geometric extrapolation) | -0.632 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.665 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -5.200 | ||||
| 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 | 0.969 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.489 | ||||
| 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 | 0.848 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.493 | ||||
| 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) | -8750184465147522.000 | ||||
| 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) | -882086574847441506954590623367168.000 | ||||
| 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 | ||||