Advanced Statistics: Libertad
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 | -0.081 | ||||
| SD | 0.118 | ||||
| Sharpe ratio (Glass type estimate) | -0.682 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.666 | ||||
| df | 31.000 | ||||
| t | -1.114 | ||||
| p | 0.863 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.889 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.535 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.877 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.546 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.734 | ||||
| Upside Potential Ratio | 0.251 | ||||
| Upside part of mean | 0.028 | ||||
| Downside part of mean | -0.108 | ||||
| Upside SD | 0.045 | ||||
| Downside SD | 0.110 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.577 | ||||
| Mean of criterion | -0.081 | ||||
| SD of predictor | 0.314 | ||||
| SD of criterion | 0.118 | ||||
| Covariance | -0.004 | ||||
| r | -0.094 | ||||
| b (slope, estimate of beta) | -0.036 | ||||
| a (intercept, estimate of alpha) | -0.060 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.519 | ||||
| p(b) | 0.696 | ||||
| t(a) | -0.722 | ||||
| p(a) | 0.762 | ||||
| Lowerbound of 95% confidence interval for beta | -0.175 | ||||
| Upperbound of 95% confidence interval for beta | 0.104 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.230 | ||||
| Upperbound of 95% confidence interval for alpha | 0.110 | ||||
| Treynor index (mean / b) | 2.268 | ||||
| Jensen alpha (a) | -0.060 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.088 | ||||
| SD | 0.127 | ||||
| Sharpe ratio (Glass type estimate) | -0.692 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.675 | ||||
| df | 31.000 | ||||
| t | -1.130 | ||||
| p | 0.866 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.899 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.526 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.887 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.537 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.732 | ||||
| Upside Potential Ratio | 0.220 | ||||
| Upside part of mean | 0.026 | ||||
| Downside part of mean | -0.115 | ||||
| Upside SD | 0.043 | ||||
| Downside SD | 0.120 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.518 | ||||
| Mean of criterion | -0.088 | ||||
| SD of predictor | 0.300 | ||||
| SD of criterion | 0.127 | ||||
| Covariance | -0.004 | ||||
| r | -0.093 | ||||
| b (slope, estimate of beta) | -0.040 | ||||
| a (intercept, estimate of alpha) | -0.068 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.514 | ||||
| p(b) | 0.694 | ||||
| t(a) | -0.764 | ||||
| p(a) | 0.775 | ||||
| Lowerbound of 95% confidence interval for beta | -0.197 | ||||
| Upperbound of 95% confidence interval for beta | 0.118 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.248 | ||||
| Upperbound of 95% confidence interval for alpha | 0.113 | ||||
| Treynor index (mean / b) | 2.222 | ||||
| Jensen alpha (a) | -0.068 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.066 | ||||
| Expected Shortfall on VaR | 0.080 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.066 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.825 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.077 | ||||
| Mean of quarter 1 | 0.978 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.825 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.077 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.175 | ||||
| Quartile 1 | 0.175 | ||||
| Median | 0.175 | ||||
| Quartile 3 | 0.175 | ||||
| Maximum | 0.175 | ||||
| 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) | -0.042 | ||||
| Compounded annual return (geometric extrapolation) | -0.043 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.247 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.541 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.080 | ||||
| SD | 0.111 | ||||
| Sharpe ratio (Glass type estimate) | -0.721 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.721 | ||||
| df | 716.000 | ||||
| t | -1.193 | ||||
| p | 0.883 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.907 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.464 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.906 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.465 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.779 | ||||
| Upside Potential Ratio | 0.687 | ||||
| Upside part of mean | 0.071 | ||||
| Downside part of mean | -0.151 | ||||
| Upside SD | 0.042 | ||||
| Downside SD | 0.103 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 706.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 717.000 | ||||
| Mean of predictor | 0.642 | ||||
| Mean of criterion | -0.080 | ||||
| SD of predictor | 0.391 | ||||
| SD of criterion | 0.111 | ||||
| Covariance | -0.001 | ||||
| r | -0.017 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | -0.077 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 715.000 | ||||
| t(b) | -0.453 | ||||
| p(b) | 0.675 | ||||
| t(a) | -1.141 | ||||
| p(a) | 0.873 | ||||
| Lowerbound of 95% confidence interval for beta | -0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.210 | ||||
| Upperbound of 95% confidence interval for alpha | 0.056 | ||||
| Treynor index (mean / b) | 16.655 | ||||
| Jensen alpha (a) | -0.077 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.087 | ||||
| SD | 0.117 | ||||
| Sharpe ratio (Glass type estimate) | -0.744 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.744 | ||||
| df | 716.000 | ||||
| t | -1.231 | ||||
| p | 0.891 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.930 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.441 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.929 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.442 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.796 | ||||
| Upside Potential Ratio | 0.640 | ||||
| Upside part of mean | 0.070 | ||||
| Downside part of mean | -0.157 | ||||
| Upside SD | 0.042 | ||||
| Downside SD | 0.109 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 706.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 717.000 | ||||
| Mean of predictor | 0.562 | ||||
| Mean of criterion | -0.087 | ||||
| SD of predictor | 0.404 | ||||
| SD of criterion | 0.117 | ||||
| Covariance | -0.001 | ||||
| r | -0.016 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | -0.084 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 715.000 | ||||
| t(b) | -0.433 | ||||
| p(b) | 0.667 | ||||
| t(a) | -1.189 | ||||
| p(a) | 0.883 | ||||
| Lowerbound of 95% confidence interval for beta | -0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.017 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.224 | ||||
| Upperbound of 95% confidence interval for alpha | 0.055 | ||||
| Treynor index (mean / b) | 18.555 | ||||
| Jensen alpha (a) | -0.084 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 717.000 | ||||
| Minimum | 0.880 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.039 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.951 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.018 | ||||
| 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) | 0.282 | ||||
| VaR(95%) (regression method) | -0.027 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.006 | ||||
| Quartile 3 | 0.070 | ||||
| Maximum | 0.256 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.008 | ||||
| Mean of quarter 4 | 0.256 | ||||
| Inter Quartile Range | 0.065 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 0.256 | ||||
| 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) | -0.041 | ||||
| Compounded annual return (geometric extrapolation) | -0.042 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.164 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.164 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.784 | ||||
| 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 | 1.023 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.500 | ||||
| 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 | 0.900 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.492 | ||||
| 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) | -8743597917024508.000 | ||||
| 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) | -7014679604623942266750439711047680.000 | ||||
| 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 | ||||