Advanced Statistics: drbfly
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 | -0.010 | ||||
| SD | 0.120 | ||||
| Sharpe ratio (Glass type estimate) | -0.087 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.086 | ||||
| df | 78.000 | ||||
| t | -0.223 | ||||
| p | 0.588 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.851 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.677 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.850 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.678 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.351 | ||||
| Upside Potential Ratio | 1.518 | ||||
| Upside part of mean | 0.045 | ||||
| Downside part of mean | -0.056 | ||||
| Upside SD | 0.116 | ||||
| Downside SD | 0.030 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 79.000 | ||||
| Mean of predictor | 0.283 | ||||
| Mean of criterion | -0.010 | ||||
| SD of predictor | 0.249 | ||||
| SD of criterion | 0.120 | ||||
| Covariance | 0.005 | ||||
| r | 0.159 | ||||
| b (slope, estimate of beta) | 0.077 | ||||
| a (intercept, estimate of alpha) | -0.032 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 77.000 | ||||
| t(b) | 1.417 | ||||
| p(b) | 0.080 | ||||
| t(a) | -0.657 | ||||
| p(a) | 0.744 | ||||
| Lowerbound of 95% confidence interval for beta | -0.031 | ||||
| Upperbound of 95% confidence interval for beta | 0.185 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.130 | ||||
| Upperbound of 95% confidence interval for alpha | 0.066 | ||||
| Treynor index (mean / b) | -0.136 | ||||
| Jensen alpha (a) | -0.032 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.016 | ||||
| SD | 0.106 | ||||
| Sharpe ratio (Glass type estimate) | -0.155 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.154 | ||||
| df | 78.000 | ||||
| t | -0.398 | ||||
| p | 0.654 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.919 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.610 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.918 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.611 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.541 | ||||
| Upside Potential Ratio | 1.294 | ||||
| Upside part of mean | 0.039 | ||||
| Downside part of mean | -0.056 | ||||
| Upside SD | 0.101 | ||||
| Downside SD | 0.030 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 79.000 | ||||
| Mean of predictor | 0.250 | ||||
| Mean of criterion | -0.016 | ||||
| SD of predictor | 0.242 | ||||
| SD of criterion | 0.106 | ||||
| Covariance | 0.004 | ||||
| r | 0.160 | ||||
| b (slope, estimate of beta) | 0.070 | ||||
| a (intercept, estimate of alpha) | -0.034 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 77.000 | ||||
| t(b) | 1.420 | ||||
| p(b) | 0.080 | ||||
| t(a) | -0.792 | ||||
| p(a) | 0.785 | ||||
| Lowerbound of 95% confidence interval for beta | -0.028 | ||||
| Upperbound of 95% confidence interval for beta | 0.168 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.120 | ||||
| Upperbound of 95% confidence interval for alpha | 0.052 | ||||
| Treynor index (mean / b) | -0.235 | ||||
| Jensen alpha (a) | -0.034 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.050 | ||||
| Expected Shortfall on VaR | 0.063 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 79.000 | ||||
| Minimum | 0.938 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.301 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.025 | ||||
| Mean of outliers low | 0.960 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.025 | ||||
| Mean of outliers high | 1.151 | ||||
| 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) | 0.358 | ||||
| VaR(95%) (regression method) | -0.008 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.079 | ||||
| Quartile 1 | 0.079 | ||||
| Median | 0.079 | ||||
| Quartile 3 | 0.079 | ||||
| Maximum | 0.079 | ||||
| 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) | 0.030 | ||||
| Compounded annual return (geometric extrapolation) | 0.028 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.354 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.447 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.010 | ||||
| SD | 0.240 | ||||
| Sharpe ratio (Glass type estimate) | 0.043 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.043 | ||||
| df | 1743.000 | ||||
| t | 0.111 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.717 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.803 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.717 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.803 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.075 | ||||
| Upside Potential Ratio | 1.505 | ||||
| Upside part of mean | 0.206 | ||||
| Downside part of mean | -0.196 | ||||
| Upside SD | 0.197 | ||||
| Downside SD | 0.137 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 1727.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1744.000 | ||||
| Mean of predictor | 0.340 | ||||
| Mean of criterion | 0.010 | ||||
| SD of predictor | 0.366 | ||||
| SD of criterion | 0.240 | ||||
| Covariance | 0.016 | ||||
| r | 0.179 | ||||
| b (slope, estimate of beta) | 0.118 | ||||
| a (intercept, estimate of alpha) | -0.030 | ||||
| Mean Square Error | 0.056 | ||||
| DF error | 1742.000 | ||||
| t(b) | 7.609 | ||||
| p(b) | 0.410 | ||||
| t(a) | -0.323 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | 0.087 | ||||
| Upperbound of 95% confidence interval for beta | 0.148 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.209 | ||||
| Upperbound of 95% confidence interval for alpha | 0.150 | ||||
| Treynor index (mean / b) | 0.088 | ||||
| Jensen alpha (a) | -0.030 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.017 | ||||
| SD | 0.230 | ||||
| Sharpe ratio (Glass type estimate) | -0.073 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.073 | ||||
| df | 1743.000 | ||||
| t | -0.188 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.833 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.687 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.833 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.687 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.113 | ||||
| Upside Potential Ratio | 1.278 | ||||
| Upside part of mean | 0.189 | ||||
| Downside part of mean | -0.206 | ||||
| Upside SD | 0.176 | ||||
| Downside SD | 0.148 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 1727.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1744.000 | ||||
| Mean of predictor | 0.273 | ||||
| Mean of criterion | -0.017 | ||||
| SD of predictor | 0.365 | ||||
| SD of criterion | 0.230 | ||||
| Covariance | 0.015 | ||||
| r | 0.180 | ||||
| b (slope, estimate of beta) | 0.113 | ||||
| a (intercept, estimate of alpha) | -0.048 | ||||
| Mean Square Error | 0.051 | ||||
| DF error | 1742.000 | ||||
| t(b) | 7.624 | ||||
| p(b) | 0.410 | ||||
| t(a) | -0.543 | ||||
| p(a) | 0.507 | ||||
| Lowerbound of 95% confidence interval for beta | 0.084 | ||||
| Upperbound of 95% confidence interval for beta | 0.143 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.220 | ||||
| Upperbound of 95% confidence interval for alpha | 0.125 | ||||
| Treynor index (mean / b) | -0.148 | ||||
| Jensen alpha (a) | -0.048 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1744.000 | ||||
| Minimum | 0.809 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.317 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 16.000 | ||||
| Percentage of outliers low | 0.009 | ||||
| Mean of outliers low | 0.937 | ||||
| Number of outliers high | 18.000 | ||||
| Percentage of outliers high | 0.010 | ||||
| Mean of outliers high | 1.076 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.827 | ||||
| VaR(95%) (moments method) | -0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.003 | ||||
| VaR(95%) (regression method) | -0.066 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.032 | ||||
| Quartile 1 | 0.060 | ||||
| Median | 0.137 | ||||
| Quartile 3 | 0.159 | ||||
| Maximum | 0.301 | ||||
| Mean of quarter 1 | 0.036 | ||||
| Mean of quarter 2 | 0.121 | ||||
| Mean of quarter 3 | 0.153 | ||||
| Mean of quarter 4 | 0.231 | ||||
| Inter Quartile Range | 0.099 | ||||
| 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) | 0.030 | ||||
| Compounded annual return (geometric extrapolation) | 0.028 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.092 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.119 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.954 | ||||
| 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 | 1.157 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.476 | ||||
| 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 | 1.042 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.476 | ||||
| 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) | -8719666304615695.000 | ||||
| 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) | 81364569647048940255442995511296.000 | ||||
| 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 | ||||