Advanced Statistics: ETF GLOBAL TIMER
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 | 0.013 | ||||
| SD | 0.131 | ||||
| Sharpe ratio (Glass type estimate) | 0.099 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.098 | ||||
| df | 97.000 | ||||
| t | 0.282 | ||||
| p | 0.389 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.588 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.784 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.588 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.784 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.191 | ||||
| Upside Potential Ratio | 1.587 | ||||
| Upside part of mean | 0.107 | ||||
| Downside part of mean | -0.094 | ||||
| Upside SD | 0.111 | ||||
| Downside SD | 0.067 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 81.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 98.000 | ||||
| Mean of predictor | 0.171 | ||||
| Mean of criterion | 0.013 | ||||
| SD of predictor | 0.195 | ||||
| SD of criterion | 0.131 | ||||
| Covariance | 0.003 | ||||
| r | 0.106 | ||||
| b (slope, estimate of beta) | 0.071 | ||||
| a (intercept, estimate of alpha) | 0.001 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 96.000 | ||||
| t(b) | 1.040 | ||||
| p(b) | 0.150 | ||||
| t(a) | 0.017 | ||||
| p(a) | 0.493 | ||||
| Lowerbound of 95% confidence interval for beta | -0.064 | ||||
| Upperbound of 95% confidence interval for beta | 0.206 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.093 | ||||
| Upperbound of 95% confidence interval for alpha | 0.094 | ||||
| Treynor index (mean / b) | 0.182 | ||||
| Jensen alpha (a) | 0.001 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.005 | ||||
| SD | 0.125 | ||||
| Sharpe ratio (Glass type estimate) | 0.039 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.039 | ||||
| df | 97.000 | ||||
| t | 0.112 | ||||
| p | 0.455 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.647 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.725 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.647 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.725 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.069 | ||||
| Upside Potential Ratio | 1.429 | ||||
| Upside part of mean | 0.101 | ||||
| Downside part of mean | -0.096 | ||||
| Upside SD | 0.102 | ||||
| Downside SD | 0.071 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 81.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 98.000 | ||||
| Mean of predictor | 0.152 | ||||
| Mean of criterion | 0.005 | ||||
| SD of predictor | 0.186 | ||||
| SD of criterion | 0.125 | ||||
| Covariance | 0.002 | ||||
| r | 0.102 | ||||
| b (slope, estimate of beta) | 0.068 | ||||
| a (intercept, estimate of alpha) | -0.005 | ||||
| Mean Square Error | 0.016 | ||||
| DF error | 96.000 | ||||
| t(b) | 1.003 | ||||
| p(b) | 0.159 | ||||
| t(a) | -0.122 | ||||
| p(a) | 0.548 | ||||
| Lowerbound of 95% confidence interval for beta | -0.067 | ||||
| Upperbound of 95% confidence interval for beta | 0.204 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.095 | ||||
| Upperbound of 95% confidence interval for alpha | 0.084 | ||||
| Treynor index (mean / b) | 0.072 | ||||
| Jensen alpha (a) | -0.005 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.057 | ||||
| Expected Shortfall on VaR | 0.071 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.049 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 98.000 | ||||
| Minimum | 0.867 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.242 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.038 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 17.000 | ||||
| Percentage of outliers low | 0.173 | ||||
| Mean of outliers low | 0.972 | ||||
| Number of outliers high | 22.000 | ||||
| Percentage of outliers high | 0.224 | ||||
| Mean of outliers high | 1.043 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.173 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.351 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.054 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.009 | ||||
| Quartile 1 | 0.023 | ||||
| Median | 0.058 | ||||
| Quartile 3 | 0.096 | ||||
| Maximum | 0.133 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.031 | ||||
| Mean of quarter 3 | 0.086 | ||||
| Mean of quarter 4 | 0.116 | ||||
| Inter Quartile Range | 0.072 | ||||
| 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) | 0.060 | ||||
| Compounded annual return (geometric extrapolation) | 0.050 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.377 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.432 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.703 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.011 | ||||
| SD | 0.111 | ||||
| Sharpe ratio (Glass type estimate) | 0.096 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.096 | ||||
| df | 2156.000 | ||||
| t | 0.275 | ||||
| p | 0.392 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.587 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.779 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.587 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.779 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.146 | ||||
| Upside Potential Ratio | 4.656 | ||||
| Upside part of mean | 0.340 | ||||
| Downside part of mean | -0.329 | ||||
| Upside SD | 0.084 | ||||
| Downside SD | 0.073 | ||||
| N nonnegative terms | 385.000 | ||||
| N negative terms | 1772.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2157.000 | ||||
| Mean of predictor | 0.193 | ||||
| Mean of criterion | 0.011 | ||||
| SD of predictor | 0.221 | ||||
| SD of criterion | 0.111 | ||||
| Covariance | 0.002 | ||||
| r | 0.089 | ||||
| b (slope, estimate of beta) | 0.045 | ||||
| a (intercept, estimate of alpha) | 0.002 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 2155.000 | ||||
| t(b) | 4.140 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.053 | ||||
| p(a) | 0.479 | ||||
| Lowerbound of 95% confidence interval for beta | 0.024 | ||||
| Upperbound of 95% confidence interval for beta | 0.066 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.074 | ||||
| Upperbound of 95% confidence interval for alpha | 0.078 | ||||
| Treynor index (mean / b) | 0.239 | ||||
| Jensen alpha (a) | 0.002 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.005 | ||||
| SD | 0.111 | ||||
| Sharpe ratio (Glass type estimate) | 0.041 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.041 | ||||
| df | 2156.000 | ||||
| t | 0.117 | ||||
| p | 0.454 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.642 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.724 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.642 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.724 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.061 | ||||
| Upside Potential Ratio | 4.528 | ||||
| Upside part of mean | 0.336 | ||||
| Downside part of mean | -0.332 | ||||
| Upside SD | 0.082 | ||||
| Downside SD | 0.074 | ||||
| N nonnegative terms | 385.000 | ||||
| N negative terms | 1772.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2157.000 | ||||
| Mean of predictor | 0.168 | ||||
| Mean of criterion | 0.005 | ||||
| SD of predictor | 0.223 | ||||
| SD of criterion | 0.111 | ||||
| Covariance | 0.002 | ||||
| r | 0.089 | ||||
| b (slope, estimate of beta) | 0.044 | ||||
| a (intercept, estimate of alpha) | -0.003 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 2155.000 | ||||
| t(b) | 4.130 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.074 | ||||
| p(a) | 0.530 | ||||
| Lowerbound of 95% confidence interval for beta | 0.023 | ||||
| Upperbound of 95% confidence interval for beta | 0.065 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.078 | ||||
| Upperbound of 95% confidence interval for alpha | 0.073 | ||||
| Treynor index (mean / b) | 0.103 | ||||
| Jensen alpha (a) | -0.003 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2157.000 | ||||
| Minimum | 0.928 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.070 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 399.000 | ||||
| Percentage of outliers low | 0.185 | ||||
| Mean of outliers low | 0.994 | ||||
| Number of outliers high | 405.000 | ||||
| Percentage of outliers high | 0.188 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.536 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.009 | ||||
| Extreme Value Index (regression method) | 0.434 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.009 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 26.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.017 | ||||
| Quartile 3 | 0.057 | ||||
| Maximum | 0.169 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.012 | ||||
| Mean of quarter 3 | 0.028 | ||||
| Mean of quarter 4 | 0.114 | ||||
| Inter Quartile Range | 0.048 | ||||
| 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 | 0.077 | ||||
| Mean of outliers high | 0.169 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.926 | ||||
| VaR(95%) (moments method) | 0.123 | ||||
| Expected Shortfall (moments method) | 0.133 | ||||
| Extreme Value Index (regression method) | -1.836 | ||||
| VaR(95%) (regression method) | 0.142 | ||||
| Expected Shortfall (regression method) | 0.145 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.060 | ||||
| Compounded annual return (geometric extrapolation) | 0.050 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.294 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.438 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.548 | ||||
| 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 | 1.054 | ||||
| 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 | 0.938 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.481 | ||||
| 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) | -8736033308046887.000 | ||||
| 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) | -315573830821471736723248051650560.000 | ||||
| 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 | ||||