Advanced Statistics: VeePo ES Custom
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 | 0.289 | ||||
| Sharpe ratio (Glass type estimate) | -0.044 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.043 | ||||
| df | 72.000 | ||||
| t | -0.107 | ||||
| p | 0.543 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.838 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.751 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.838 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.752 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.053 | ||||
| Upside Potential Ratio | 1.024 | ||||
| Upside part of mean | 0.245 | ||||
| Downside part of mean | -0.257 | ||||
| Upside SD | 0.159 | ||||
| Downside SD | 0.239 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.249 | ||||
| Mean of criterion | -0.013 | ||||
| SD of predictor | 0.225 | ||||
| SD of criterion | 0.289 | ||||
| Covariance | -0.008 | ||||
| r | -0.116 | ||||
| b (slope, estimate of beta) | -0.149 | ||||
| a (intercept, estimate of alpha) | 0.024 | ||||
| Mean Square Error | 0.084 | ||||
| DF error | 71.000 | ||||
| t(b) | -0.981 | ||||
| p(b) | 0.835 | ||||
| t(a) | 0.198 | ||||
| p(a) | 0.422 | ||||
| Lowerbound of 95% confidence interval for beta | -0.451 | ||||
| Upperbound of 95% confidence interval for beta | 0.154 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.221 | ||||
| Upperbound of 95% confidence interval for alpha | 0.270 | ||||
| Treynor index (mean / b) | 0.085 | ||||
| Jensen alpha (a) | 0.024 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.065 | ||||
| SD | 0.351 | ||||
| Sharpe ratio (Glass type estimate) | -0.186 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.184 | ||||
| df | 72.000 | ||||
| t | -0.458 | ||||
| p | 0.676 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.980 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.610 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.979 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.611 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.206 | ||||
| Upside Potential Ratio | 0.735 | ||||
| Upside part of mean | 0.232 | ||||
| Downside part of mean | -0.298 | ||||
| Upside SD | 0.148 | ||||
| Downside SD | 0.316 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.223 | ||||
| Mean of criterion | -0.065 | ||||
| SD of predictor | 0.210 | ||||
| SD of criterion | 0.351 | ||||
| Covariance | -0.009 | ||||
| r | -0.116 | ||||
| b (slope, estimate of beta) | -0.194 | ||||
| a (intercept, estimate of alpha) | -0.022 | ||||
| Mean Square Error | 0.123 | ||||
| DF error | 71.000 | ||||
| t(b) | -0.986 | ||||
| p(b) | 0.836 | ||||
| t(a) | -0.147 | ||||
| p(a) | 0.558 | ||||
| Lowerbound of 95% confidence interval for beta | -0.586 | ||||
| Upperbound of 95% confidence interval for beta | 0.198 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.319 | ||||
| Upperbound of 95% confidence interval for alpha | 0.275 | ||||
| Treynor index (mean / b) | 0.336 | ||||
| Jensen alpha (a) | -0.022 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.158 | ||||
| Expected Shortfall on VaR | 0.193 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.121 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 73.000 | ||||
| Minimum | 0.489 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.031 | ||||
| Maximum | 1.242 | ||||
| Mean of quarter 1 | 0.926 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.010 | ||||
| Mean of quarter 4 | 1.079 | ||||
| Inter Quartile Range | 0.033 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.110 | ||||
| Mean of outliers low | 0.857 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.068 | ||||
| Mean of outliers high | 1.148 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.685 | ||||
| VaR(95%) (moments method) | 0.020 | ||||
| Expected Shortfall (moments method) | 0.080 | ||||
| Extreme Value Index (regression method) | 0.717 | ||||
| VaR(95%) (regression method) | 0.053 | ||||
| Expected Shortfall (regression method) | 0.239 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.019 | ||||
| Median | 0.137 | ||||
| Quartile 3 | 0.147 | ||||
| Maximum | 0.646 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | 0.137 | ||||
| Mean of quarter 3 | 0.147 | ||||
| Mean of quarter 4 | 0.646 | ||||
| Inter Quartile Range | 0.128 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.646 | ||||
| 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) | -0.020 | ||||
| Compounded annual return (geometric extrapolation) | -0.021 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.032 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.032 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.109 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.029 | ||||
| SD | 0.269 | ||||
| Sharpe ratio (Glass type estimate) | -0.106 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.106 | ||||
| df | 1614.000 | ||||
| t | -0.263 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.896 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.683 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.896 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.683 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.150 | ||||
| Upside Potential Ratio | 4.284 | ||||
| Upside part of mean | 0.818 | ||||
| Downside part of mean | -0.847 | ||||
| Upside SD | 0.189 | ||||
| Downside SD | 0.191 | ||||
| N nonnegative terms | 484.000 | ||||
| N negative terms | 1131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1615.000 | ||||
| Mean of predictor | 0.278 | ||||
| Mean of criterion | -0.029 | ||||
| SD of predictor | 0.249 | ||||
| SD of criterion | 0.269 | ||||
| Covariance | -0.001 | ||||
| r | -0.022 | ||||
| b (slope, estimate of beta) | -0.024 | ||||
| a (intercept, estimate of alpha) | -0.022 | ||||
| Mean Square Error | 0.072 | ||||
| DF error | 1613.000 | ||||
| t(b) | -0.884 | ||||
| p(b) | 0.514 | ||||
| t(a) | -0.202 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | -0.077 | ||||
| Upperbound of 95% confidence interval for beta | 0.029 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.235 | ||||
| Upperbound of 95% confidence interval for alpha | 0.191 | ||||
| Treynor index (mean / b) | 1.198 | ||||
| Jensen alpha (a) | -0.022 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.065 | ||||
| SD | 0.270 | ||||
| Sharpe ratio (Glass type estimate) | -0.240 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.240 | ||||
| df | 1614.000 | ||||
| t | -0.596 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.030 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.549 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.029 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.549 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.322 | ||||
| Upside Potential Ratio | 3.977 | ||||
| Upside part of mean | 0.801 | ||||
| Downside part of mean | -0.866 | ||||
| Upside SD | 0.180 | ||||
| Downside SD | 0.202 | ||||
| N nonnegative terms | 484.000 | ||||
| N negative terms | 1131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1615.000 | ||||
| Mean of predictor | 0.246 | ||||
| Mean of criterion | -0.065 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 0.270 | ||||
| Covariance | -0.001 | ||||
| r | -0.021 | ||||
| b (slope, estimate of beta) | -0.022 | ||||
| a (intercept, estimate of alpha) | -0.059 | ||||
| Mean Square Error | 0.073 | ||||
| DF error | 1613.000 | ||||
| t(b) | -0.836 | ||||
| p(b) | 0.513 | ||||
| t(a) | -0.545 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | -0.074 | ||||
| Upperbound of 95% confidence interval for beta | 0.030 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.274 | ||||
| Upperbound of 95% confidence interval for alpha | 0.155 | ||||
| Treynor index (mean / b) | 2.923 | ||||
| Jensen alpha (a) | -0.059 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1615.000 | ||||
| Minimum | 0.815 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.173 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 253.000 | ||||
| Percentage of outliers low | 0.157 | ||||
| Mean of outliers low | 0.982 | ||||
| Number of outliers high | 254.000 | ||||
| Percentage of outliers high | 0.157 | ||||
| Mean of outliers high | 1.018 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.697 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.026 | ||||
| Extreme Value Index (regression method) | 0.406 | ||||
| VaR(95%) (regression method) | 0.009 | ||||
| Expected Shortfall (regression method) | 0.022 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 55.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.011 | ||||
| Quartile 3 | 0.031 | ||||
| Maximum | 0.754 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.021 | ||||
| Mean of quarter 4 | 0.117 | ||||
| Inter Quartile Range | 0.029 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.073 | ||||
| Mean of outliers high | 0.305 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.898 | ||||
| VaR(95%) (moments method) | 0.117 | ||||
| Expected Shortfall (moments method) | 1.119 | ||||
| Extreme Value Index (regression method) | 1.563 | ||||
| VaR(95%) (regression method) | 0.083 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.020 | ||||
| Compounded annual return (geometric extrapolation) | -0.021 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.027 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.177 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.607 | ||||
| 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 | 1.238 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.399 | ||||
| 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 | 1.156 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.397 | ||||
| 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) | -8659884705823633.000 | ||||
| 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) | 114588880060657895498896302407680.000 | ||||
| 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 | ||||