Advanced Statistics: bmrtrading
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 | -0.199 | ||||
| SD | 0.389 | ||||
| Sharpe ratio (Glass type estimate) | -0.510 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.500 | ||||
| df | 37.000 | ||||
| t | -0.908 | ||||
| p | 0.815 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.614 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.601 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.607 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.608 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.533 | ||||
| Upside Potential Ratio | 0.347 | ||||
| Upside part of mean | 0.129 | ||||
| Downside part of mean | -0.328 | ||||
| Upside SD | 0.109 | ||||
| Downside SD | 0.373 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.560 | ||||
| Mean of criterion | -0.199 | ||||
| SD of predictor | 0.306 | ||||
| SD of criterion | 0.389 | ||||
| Covariance | -0.003 | ||||
| r | -0.029 | ||||
| b (slope, estimate of beta) | -0.037 | ||||
| a (intercept, estimate of alpha) | -0.178 | ||||
| Mean Square Error | 0.156 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.176 | ||||
| p(b) | 0.569 | ||||
| t(a) | -0.707 | ||||
| p(a) | 0.758 | ||||
| Lowerbound of 95% confidence interval for beta | -0.467 | ||||
| Upperbound of 95% confidence interval for beta | 0.392 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.688 | ||||
| Upperbound of 95% confidence interval for alpha | 0.332 | ||||
| Treynor index (mean / b) | 5.337 | ||||
| Jensen alpha (a) | -0.178 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.326 | ||||
| SD | 0.581 | ||||
| Sharpe ratio (Glass type estimate) | -0.560 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.549 | ||||
| df | 37.000 | ||||
| t | -0.997 | ||||
| p | 0.837 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.665 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.552 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.657 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.560 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.569 | ||||
| Upside Potential Ratio | 0.216 | ||||
| Upside part of mean | 0.123 | ||||
| Downside part of mean | -0.449 | ||||
| Upside SD | 0.104 | ||||
| Downside SD | 0.572 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.503 | ||||
| Mean of criterion | -0.326 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 0.581 | ||||
| Covariance | -0.002 | ||||
| r | -0.013 | ||||
| b (slope, estimate of beta) | -0.025 | ||||
| a (intercept, estimate of alpha) | -0.313 | ||||
| Mean Square Error | 0.347 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.076 | ||||
| p(b) | 0.530 | ||||
| t(a) | -0.846 | ||||
| p(a) | 0.798 | ||||
| Lowerbound of 95% confidence interval for beta | -0.690 | ||||
| Upperbound of 95% confidence interval for beta | 0.641 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.063 | ||||
| Upperbound of 95% confidence interval for alpha | 0.437 | ||||
| Treynor index (mean / b) | 13.094 | ||||
| Jensen alpha (a) | -0.313 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.261 | ||||
| Expected Shortfall on VaR | 0.310 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.087 | ||||
| Expected Shortfall on VaR | 0.190 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 38.000 | ||||
| Minimum | 0.372 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.125 | ||||
| Mean of quarter 1 | 0.908 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.043 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.105 | ||||
| Mean of outliers low | 0.771 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.132 | ||||
| Mean of outliers high | 1.086 | ||||
| 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) | 0.924 | ||||
| VaR(95%) (regression method) | 0.141 | ||||
| Expected Shortfall (regression method) | 3.105 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.035 | ||||
| Quartile 1 | 0.206 | ||||
| Median | 0.376 | ||||
| Quartile 3 | 0.547 | ||||
| Maximum | 0.718 | ||||
| Mean of quarter 1 | 0.035 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.718 | ||||
| Inter Quartile Range | 0.341 | ||||
| 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) | -0.186 | ||||
| Compounded annual return (geometric extrapolation) | -0.245 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.342 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.342 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.791 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.240 | ||||
| SD | 0.394 | ||||
| Sharpe ratio (Glass type estimate) | -0.609 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.608 | ||||
| df | 830.000 | ||||
| t | -1.084 | ||||
| p | 0.861 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.710 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.492 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.709 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.493 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.732 | ||||
| Upside Potential Ratio | 1.739 | ||||
| Upside part of mean | 0.570 | ||||
| Downside part of mean | -0.810 | ||||
| Upside SD | 0.219 | ||||
| Downside SD | 0.328 | ||||
| N nonnegative terms | 91.000 | ||||
| N negative terms | 740.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 831.000 | ||||
| Mean of predictor | 0.579 | ||||
| Mean of criterion | -0.240 | ||||
| SD of predictor | 0.358 | ||||
| SD of criterion | 0.394 | ||||
| Covariance | -0.002 | ||||
| r | -0.013 | ||||
| b (slope, estimate of beta) | -0.015 | ||||
| a (intercept, estimate of alpha) | -0.232 | ||||
| Mean Square Error | 0.156 | ||||
| DF error | 829.000 | ||||
| t(b) | -0.387 | ||||
| p(b) | 0.650 | ||||
| t(a) | -1.040 | ||||
| p(a) | 0.851 | ||||
| Lowerbound of 95% confidence interval for beta | -0.090 | ||||
| Upperbound of 95% confidence interval for beta | 0.060 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.669 | ||||
| Upperbound of 95% confidence interval for alpha | 0.205 | ||||
| Treynor index (mean / b) | 16.231 | ||||
| Jensen alpha (a) | -0.232 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.325 | ||||
| SD | 0.423 | ||||
| Sharpe ratio (Glass type estimate) | -0.769 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.769 | ||||
| df | 830.000 | ||||
| t | -1.370 | ||||
| p | 0.914 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.870 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.332 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.870 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.333 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.880 | ||||
| Upside Potential Ratio | 1.483 | ||||
| Upside part of mean | 0.548 | ||||
| Downside part of mean | -0.873 | ||||
| Upside SD | 0.205 | ||||
| Downside SD | 0.370 | ||||
| N nonnegative terms | 91.000 | ||||
| N negative terms | 740.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 831.000 | ||||
| Mean of predictor | 0.511 | ||||
| Mean of criterion | -0.325 | ||||
| SD of predictor | 0.373 | ||||
| SD of criterion | 0.423 | ||||
| Covariance | -0.002 | ||||
| r | -0.012 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | -0.318 | ||||
| Mean Square Error | 0.179 | ||||
| DF error | 829.000 | ||||
| t(b) | -0.351 | ||||
| p(b) | 0.637 | ||||
| t(a) | -1.335 | ||||
| p(a) | 0.909 | ||||
| Lowerbound of 95% confidence interval for beta | -0.091 | ||||
| Upperbound of 95% confidence interval for beta | 0.063 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.786 | ||||
| Upperbound of 95% confidence interval for alpha | 0.150 | ||||
| Treynor index (mean / b) | 23.557 | ||||
| Jensen alpha (a) | -0.318 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.043 | ||||
| Expected Shortfall on VaR | 0.054 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 831.000 | ||||
| Minimum | 0.692 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.221 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 62.000 | ||||
| Percentage of outliers low | 0.075 | ||||
| Mean of outliers low | 0.961 | ||||
| Number of outliers high | 91.000 | ||||
| Percentage of outliers high | 0.110 | ||||
| Mean of outliers high | 1.020 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.736 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.850 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.082 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 20.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.048 | ||||
| Maximum | 0.720 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.017 | ||||
| Mean of quarter 4 | 0.245 | ||||
| Inter Quartile Range | 0.046 | ||||
| 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 | 0.100 | ||||
| Mean of outliers high | 0.469 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.703 | ||||
| VaR(95%) (moments method) | 0.254 | ||||
| Expected Shortfall (moments method) | 0.926 | ||||
| Extreme Value Index (regression method) | 2.092 | ||||
| VaR(95%) (regression method) | 0.263 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.186 | ||||
| Compounded annual return (geometric extrapolation) | -0.245 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.340 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.999 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.575 | ||||
| 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 | 1.057 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.505 | ||||
| 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 | 0.927 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.510 | ||||
| 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) | -8744439956089298.000 | ||||
| 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) | -77097603714330544082642788155392.000 | ||||
| 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 | ||||