Advanced Statistics: Easy Button
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 | 4269.517 | ||||
| SD | 9782.263 | ||||
| Sharpe ratio (Glass type estimate) | 0.436 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.431 | ||||
| df | 62.000 | ||||
| t | 1.000 | ||||
| p | 0.161 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.424 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.294 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.428 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.290 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 9354.099 | ||||
| Upside Potential Ratio | 9354.790 | ||||
| Upside part of mean | 4269.832 | ||||
| Downside part of mean | -0.315 | ||||
| Upside SD | 9782.270 | ||||
| Downside SD | 0.456 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 48.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.342 | ||||
| Mean of criterion | 4269.517 | ||||
| SD of predictor | 0.336 | ||||
| SD of criterion | 9782.263 | ||||
| Covariance | -582.878 | ||||
| r | -0.177 | ||||
| b (slope, estimate of beta) | -5171.294 | ||||
| a (intercept, estimate of alpha) | 6038.735 | ||||
| Mean Square Error | 94197759.295 | ||||
| DF error | 61.000 | ||||
| t(b) | -1.409 | ||||
| p(b) | 0.918 | ||||
| t(a) | 1.367 | ||||
| p(a) | 0.088 | ||||
| Lowerbound of 95% confidence interval for beta | -12512.773 | ||||
| Upperbound of 95% confidence interval for beta | 2170.185 | ||||
| Lowerbound of 95% confidence interval for alpha | -2795.930 | ||||
| Upperbound of 95% confidence interval for alpha | 14873.400 | ||||
| Treynor index (mean / b) | -0.826 | ||||
| Jensen alpha (a) | 6038.735 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.483 | ||||
| SD | 5.934 | ||||
| Sharpe ratio (Glass type estimate) | 0.081 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.080 | ||||
| df | 62.000 | ||||
| t | 0.187 | ||||
| p | 0.426 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.774 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.937 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.775 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.936 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.123 | ||||
| Upside Potential Ratio | 0.593 | ||||
| Upside part of mean | 2.330 | ||||
| Downside part of mean | -1.847 | ||||
| Upside SD | 4.385 | ||||
| Downside SD | 3.930 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 48.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.283 | ||||
| Mean of criterion | 0.483 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 5.934 | ||||
| Covariance | -0.075 | ||||
| r | -0.038 | ||||
| b (slope, estimate of beta) | -0.691 | ||||
| a (intercept, estimate of alpha) | 0.679 | ||||
| Mean Square Error | 35.737 | ||||
| DF error | 61.000 | ||||
| t(b) | -0.300 | ||||
| p(b) | 0.617 | ||||
| t(a) | 0.252 | ||||
| p(a) | 0.401 | ||||
| Lowerbound of 95% confidence interval for beta | -5.300 | ||||
| Upperbound of 95% confidence interval for beta | 3.918 | ||||
| Lowerbound of 95% confidence interval for alpha | -4.699 | ||||
| Upperbound of 95% confidence interval for alpha | 6.057 | ||||
| Treynor index (mean / b) | -0.699 | ||||
| Jensen alpha (a) | 0.679 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.938 | ||||
| Expected Shortfall on VaR | 0.965 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.077 | ||||
| Expected Shortfall on VaR | 0.174 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 63.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 22415.000 | ||||
| Mean of quarter 1 | 0.908 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1402.042 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.127 | ||||
| Mean of outliers low | 0.815 | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.238 | ||||
| Mean of outliers high | 1495.445 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.003 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | 1.487 | ||||
| VaR(95%) (regression method) | 0.029 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.013 | ||||
| Median | 0.036 | ||||
| Quartile 3 | 0.157 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.035 | ||||
| Mean of quarter 3 | 0.037 | ||||
| Mean of quarter 4 | 0.599 | ||||
| Inter Quartile Range | 0.144 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.167 | ||||
| Mean of outliers high | 1.000 | ||||
| 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) | 2.841 | ||||
| Compounded annual return (geometric extrapolation) | 0.694 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.694 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.159 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.720 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 5719.334 | ||||
| SD | 10318.265 | ||||
| Sharpe ratio (Glass type estimate) | 0.554 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.554 | ||||
| df | 1391.000 | ||||
| t | 1.278 | ||||
| p | 0.478 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.296 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.405 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.297 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.405 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 6335.117 | ||||
| Upside Potential Ratio | 6337.590 | ||||
| Upside part of mean | 5721.567 | ||||
| Downside part of mean | -2.232 | ||||
| Upside SD | 10320.608 | ||||
| Downside SD | 0.903 | ||||
| N nonnegative terms | 263.000 | ||||
| N negative terms | 1129.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1392.000 | ||||
| Mean of predictor | 0.434 | ||||
| Mean of criterion | 5719.334 | ||||
| SD of predictor | 0.535 | ||||
| SD of criterion | 10318.265 | ||||
| Covariance | -2.877 | ||||
| r | -0.001 | ||||
| b (slope, estimate of beta) | -10.036 | ||||
| a (intercept, estimate of alpha) | 5723.693 | ||||
| Mean Square Error | 106543148.991 | ||||
| DF error | 1390.000 | ||||
| t(b) | -0.019 | ||||
| p(b) | 0.500 | ||||
| t(a) | 1.277 | ||||
| p(a) | 0.483 | ||||
| Lowerbound of 95% confidence interval for beta | -1024.046 | ||||
| Upperbound of 95% confidence interval for beta | 1003.975 | ||||
| Lowerbound of 95% confidence interval for alpha | -3071.903 | ||||
| Upperbound of 95% confidence interval for alpha | 14519.288 | ||||
| Treynor index (mean / b) | -569.899 | ||||
| Jensen alpha (a) | 5723.693 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.477 | ||||
| SD | 7.967 | ||||
| Sharpe ratio (Glass type estimate) | 0.060 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.060 | ||||
| df | 1391.000 | ||||
| t | 0.138 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.790 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.910 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.790 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.910 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.089 | ||||
| Upside Potential Ratio | 1.098 | ||||
| Upside part of mean | 5.881 | ||||
| Downside part of mean | -5.404 | ||||
| Upside SD | 5.894 | ||||
| Downside SD | 5.356 | ||||
| N nonnegative terms | 263.000 | ||||
| N negative terms | 1129.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1392.000 | ||||
| Mean of predictor | 0.290 | ||||
| Mean of criterion | 0.477 | ||||
| SD of predictor | 0.539 | ||||
| SD of criterion | 7.967 | ||||
| Covariance | 0.128 | ||||
| r | 0.030 | ||||
| b (slope, estimate of beta) | 0.442 | ||||
| a (intercept, estimate of alpha) | 0.349 | ||||
| Mean Square Error | 63.458 | ||||
| DF error | 1390.000 | ||||
| t(b) | 1.115 | ||||
| p(b) | 0.485 | ||||
| t(a) | 0.101 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | -0.336 | ||||
| Upperbound of 95% confidence interval for beta | 1.220 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.435 | ||||
| Upperbound of 95% confidence interval for alpha | 7.132 | ||||
| Treynor index (mean / b) | 1.078 | ||||
| Jensen alpha (a) | 0.349 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.554 | ||||
| Expected Shortfall on VaR | 0.631 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.059 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1392.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 22415.000 | ||||
| Mean of quarter 1 | 0.966 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 88.352 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 166.000 | ||||
| Percentage of outliers low | 0.119 | ||||
| Mean of outliers low | 0.930 | ||||
| Number of outliers high | 265.000 | ||||
| Percentage of outliers high | 0.190 | ||||
| Mean of outliers high | 115.712 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.465 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.601 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.079 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 14.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.011 | ||||
| Median | 0.061 | ||||
| Quartile 3 | 0.393 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.029 | ||||
| Mean of quarter 3 | 0.169 | ||||
| Mean of quarter 4 | 0.623 | ||||
| Inter Quartile Range | 0.382 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.071 | ||||
| Mean of outliers high | 1.000 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.038 | ||||
| VaR(95%) (moments method) | 0.695 | ||||
| Expected Shortfall (moments method) | 0.873 | ||||
| Extreme Value Index (regression method) | 0.932 | ||||
| VaR(95%) (regression method) | 0.896 | ||||
| Expected Shortfall (regression method) | 9.111 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 2.807 | ||||
| Compounded annual return (geometric extrapolation) | 0.683 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.684 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.097 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.082 | ||||
| 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 | 0.987 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.463 | ||||
| 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 | 0.879 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.463 | ||||
| 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) | -8739546147855019.000 | ||||
| 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) | 143259392406179655899625115615232.000 | ||||
| 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 | ||||