Advanced Statistics: Swing
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 | 1582.536 | ||||
| SD | 1810.252 | ||||
| Sharpe ratio (Glass type estimate) | 0.874 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.864 | ||||
| df | 67.000 | ||||
| t | 2.081 | ||||
| p | 0.021 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.035 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.708 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.028 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.701 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1337.652 | ||||
| Upside Potential Ratio | 1339.161 | ||||
| Upside part of mean | 1584.320 | ||||
| Downside part of mean | -1.784 | ||||
| Upside SD | 1854.056 | ||||
| Downside SD | 1.183 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 54.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.278 | ||||
| Mean of criterion | 1582.536 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 1810.252 | ||||
| Covariance | 104.220 | ||||
| r | 0.213 | ||||
| b (slope, estimate of beta) | 1430.110 | ||||
| a (intercept, estimate of alpha) | 1184.608 | ||||
| Mean Square Error | 3175360.135 | ||||
| DF error | 66.000 | ||||
| t(b) | 1.773 | ||||
| p(b) | 0.040 | ||||
| t(a) | 1.516 | ||||
| p(a) | 0.067 | ||||
| Lowerbound of 95% confidence interval for beta | -179.982 | ||||
| Upperbound of 95% confidence interval for beta | 3040.202 | ||||
| Lowerbound of 95% confidence interval for alpha | -375.664 | ||||
| Upperbound of 95% confidence interval for alpha | 2744.880 | ||||
| Treynor index (mean / b) | 1.107 | ||||
| Jensen alpha (a) | 1184.608 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.673 | ||||
| SD | 10.588 | ||||
| Sharpe ratio (Glass type estimate) | -0.158 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.156 | ||||
| df | 67.000 | ||||
| t | -0.376 | ||||
| p | 0.646 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.981 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.666 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.980 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.668 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.212 | ||||
| Upside Potential Ratio | 0.934 | ||||
| Upside part of mean | 7.353 | ||||
| Downside part of mean | -9.026 | ||||
| Upside SD | 6.977 | ||||
| Downside SD | 7.874 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 54.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.239 | ||||
| Mean of criterion | -1.673 | ||||
| SD of predictor | 0.267 | ||||
| SD of criterion | 10.588 | ||||
| Covariance | 0.917 | ||||
| r | 0.324 | ||||
| b (slope, estimate of beta) | 12.847 | ||||
| a (intercept, estimate of alpha) | -4.748 | ||||
| Mean Square Error | 101.844 | ||||
| DF error | 66.000 | ||||
| t(b) | 2.783 | ||||
| p(b) | 0.004 | ||||
| t(a) | -1.084 | ||||
| p(a) | 0.859 | ||||
| Lowerbound of 95% confidence interval for beta | 3.632 | ||||
| Upperbound of 95% confidence interval for beta | 22.062 | ||||
| Lowerbound of 95% confidence interval for alpha | -13.495 | ||||
| Upperbound of 95% confidence interval for alpha | 3.999 | ||||
| Treynor index (mean / b) | -0.130 | ||||
| Jensen alpha (a) | -4.748 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.994 | ||||
| Expected Shortfall on VaR | 0.998 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.451 | ||||
| Expected Shortfall on VaR | 0.880 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 68.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.938 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2713.000 | ||||
| Mean of quarter 1 | 0.422 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 529.110 | ||||
| Inter Quartile Range | 0.062 | ||||
| Number outliers low | 16.000 | ||||
| Percentage of outliers low | 0.235 | ||||
| Mean of outliers low | 0.390 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.176 | ||||
| Mean of outliers high | 749.149 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.915 | ||||
| VaR(95%) (moments method) | 0.262 | ||||
| Expected Shortfall (moments method) | 0.269 | ||||
| Extreme Value Index (regression method) | -3.777 | ||||
| VaR(95%) (regression method) | 0.594 | ||||
| Expected Shortfall (regression method) | 0.595 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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) | -0.176 | ||||
| Compounded annual return (geometric extrapolation) | -0.804 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.804 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.806 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 4790.484 | ||||
| SD | 3812.864 | ||||
| Sharpe ratio (Glass type estimate) | 1.256 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.256 | ||||
| df | 1491.000 | ||||
| t | 2.998 | ||||
| p | 0.451 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.434 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.079 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.433 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.078 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1720.577 | ||||
| Upside Potential Ratio | 1725.398 | ||||
| Upside part of mean | 4803.909 | ||||
| Downside part of mean | -13.424 | ||||
| Upside SD | 3823.058 | ||||
| Downside SD | 2.784 | ||||
| N nonnegative terms | 328.000 | ||||
| N negative terms | 1164.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1492.000 | ||||
| Mean of predictor | 0.376 | ||||
| Mean of criterion | 4790.484 | ||||
| SD of predictor | 0.536 | ||||
| SD of criterion | 3812.864 | ||||
| Covariance | 819.725 | ||||
| r | 0.401 | ||||
| b (slope, estimate of beta) | 2856.329 | ||||
| a (intercept, estimate of alpha) | 3716.458 | ||||
| Mean Square Error | 12204716.638 | ||||
| DF error | 1490.000 | ||||
| t(b) | 16.913 | ||||
| p(b) | 0.299 | ||||
| t(a) | 2.536 | ||||
| p(a) | 0.467 | ||||
| Lowerbound of 95% confidence interval for beta | 2525.048 | ||||
| Upperbound of 95% confidence interval for beta | 3187.610 | ||||
| Lowerbound of 95% confidence interval for alpha | 842.110 | ||||
| Upperbound of 95% confidence interval for alpha | 6590.806 | ||||
| Treynor index (mean / b) | 1.677 | ||||
| Jensen alpha (a) | 3716.458 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.665 | ||||
| SD | 19.281 | ||||
| Sharpe ratio (Glass type estimate) | -0.086 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.086 | ||||
| df | 1491.000 | ||||
| t | -0.206 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.908 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.735 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.908 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.735 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.122 | ||||
| Upside Potential Ratio | 2.772 | ||||
| Upside part of mean | 37.921 | ||||
| Downside part of mean | -39.586 | ||||
| Upside SD | 13.578 | ||||
| Downside SD | 13.680 | ||||
| N nonnegative terms | 328.000 | ||||
| N negative terms | 1164.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1492.000 | ||||
| Mean of predictor | 0.234 | ||||
| Mean of criterion | -1.665 | ||||
| SD of predictor | 0.534 | ||||
| SD of criterion | 19.281 | ||||
| Covariance | 4.153 | ||||
| r | 0.404 | ||||
| b (slope, estimate of beta) | 14.591 | ||||
| a (intercept, estimate of alpha) | -5.075 | ||||
| Mean Square Error | 311.352 | ||||
| DF error | 1490.000 | ||||
| t(b) | 17.036 | ||||
| p(b) | 0.298 | ||||
| t(a) | -0.686 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | 12.911 | ||||
| Upperbound of 95% confidence interval for beta | 16.272 | ||||
| Lowerbound of 95% confidence interval for alpha | -19.584 | ||||
| Upperbound of 95% confidence interval for alpha | 9.435 | ||||
| Treynor index (mean / b) | -0.114 | ||||
| Jensen alpha (a) | -5.075 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.860 | ||||
| Expected Shortfall on VaR | 0.908 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.153 | ||||
| Expected Shortfall on VaR | 0.330 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1492.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 6092.000 | ||||
| Mean of quarter 1 | 0.796 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 74.342 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 348.000 | ||||
| Percentage of outliers low | 0.233 | ||||
| Mean of outliers low | 0.781 | ||||
| Number of outliers high | 329.000 | ||||
| Percentage of outliers high | 0.221 | ||||
| Mean of outliers high | 84.151 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.463 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| Extreme Value Index (regression method) | -0.502 | ||||
| VaR(95%) (regression method) | 0.148 | ||||
| Expected Shortfall (regression method) | 0.190 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.036 | ||||
| Quartile 1 | 0.445 | ||||
| Median | 0.853 | ||||
| Quartile 3 | 0.927 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.036 | ||||
| Mean of quarter 2 | 0.853 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.482 | ||||
| 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) | -0.176 | ||||
| Compounded annual return (geometric extrapolation) | -0.802 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.802 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.802 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.884 | ||||
| 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 | 0.754 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.462 | ||||
| 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 | 0.645 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.469 | ||||
| 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) | -8767923385614539.000 | ||||
| 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) | 607151333247835952817699249192960.000 | ||||
| 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 | ||||