Advanced Statistics: VW trading
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 | 0.064 | ||||
| SD | 0.505 | ||||
| Sharpe ratio (Glass type estimate) | 0.127 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.126 | ||||
| df | 73.000 | ||||
| t | 0.316 | ||||
| p | 0.376 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.663 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.916 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.664 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.915 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.202 | ||||
| Upside Potential Ratio | 1.725 | ||||
| Upside part of mean | 0.549 | ||||
| Downside part of mean | -0.485 | ||||
| Upside SD | 0.388 | ||||
| Downside SD | 0.318 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 74.000 | ||||
| Mean of predictor | 0.290 | ||||
| Mean of criterion | 0.064 | ||||
| SD of predictor | 0.360 | ||||
| SD of criterion | 0.505 | ||||
| Covariance | -0.008 | ||||
| r | -0.044 | ||||
| b (slope, estimate of beta) | -0.062 | ||||
| a (intercept, estimate of alpha) | 0.082 | ||||
| Mean Square Error | 0.258 | ||||
| DF error | 72.000 | ||||
| t(b) | -0.377 | ||||
| p(b) | 0.646 | ||||
| t(a) | 0.392 | ||||
| p(a) | 0.348 | ||||
| Lowerbound of 95% confidence interval for beta | -0.391 | ||||
| Upperbound of 95% confidence interval for beta | 0.267 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.337 | ||||
| Upperbound of 95% confidence interval for alpha | 0.501 | ||||
| Treynor index (mean / b) | -1.034 | ||||
| Jensen alpha (a) | 0.082 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.060 | ||||
| SD | 0.505 | ||||
| Sharpe ratio (Glass type estimate) | -0.119 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.118 | ||||
| df | 73.000 | ||||
| t | -0.295 | ||||
| p | 0.616 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.908 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.671 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.907 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.672 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.161 | ||||
| Upside Potential Ratio | 1.299 | ||||
| Upside part of mean | 0.486 | ||||
| Downside part of mean | -0.546 | ||||
| Upside SD | 0.335 | ||||
| Downside SD | 0.374 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 74.000 | ||||
| Mean of predictor | 0.230 | ||||
| Mean of criterion | -0.060 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.505 | ||||
| Covariance | -0.007 | ||||
| r | -0.045 | ||||
| b (slope, estimate of beta) | -0.069 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.258 | ||||
| DF error | 72.000 | ||||
| t(b) | -0.381 | ||||
| p(b) | 0.648 | ||||
| t(a) | -0.211 | ||||
| p(a) | 0.583 | ||||
| Lowerbound of 95% confidence interval for beta | -0.430 | ||||
| Upperbound of 95% confidence interval for beta | 0.292 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.460 | ||||
| Upperbound of 95% confidence interval for alpha | 0.372 | ||||
| Treynor index (mean / b) | 0.868 | ||||
| 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%) | 0.217 | ||||
| Expected Shortfall on VaR | 0.262 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.118 | ||||
| Expected Shortfall on VaR | 0.231 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 74.000 | ||||
| Minimum | 0.602 | ||||
| Quartile 1 | 0.975 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.015 | ||||
| Maximum | 1.541 | ||||
| Mean of quarter 1 | 0.856 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.182 | ||||
| Inter Quartile Range | 0.040 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.149 | ||||
| Mean of outliers low | 0.786 | ||||
| Number of outliers high | 14.000 | ||||
| Percentage of outliers high | 0.189 | ||||
| Mean of outliers high | 1.232 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.116 | ||||
| VaR(95%) (moments method) | 0.092 | ||||
| Expected Shortfall (moments method) | 0.144 | ||||
| Extreme Value Index (regression method) | -0.154 | ||||
| VaR(95%) (regression method) | 0.126 | ||||
| Expected Shortfall (regression method) | 0.173 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.040 | ||||
| Quartile 1 | 0.040 | ||||
| Median | 0.041 | ||||
| Quartile 3 | 0.414 | ||||
| Maximum | 0.788 | ||||
| Mean of quarter 1 | 0.040 | ||||
| Mean of quarter 2 | 0.041 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.788 | ||||
| Inter Quartile Range | 0.374 | ||||
| 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) | -0.015 | ||||
| Compounded annual return (geometric extrapolation) | -0.016 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.020 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.020 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.060 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.281 | ||||
| SD | 0.851 | ||||
| Sharpe ratio (Glass type estimate) | 0.330 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.330 | ||||
| df | 1621.000 | ||||
| t | 0.822 | ||||
| p | 0.487 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.457 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.118 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.458 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.118 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.564 | ||||
| Upside Potential Ratio | 5.738 | ||||
| Upside part of mean | 2.863 | ||||
| Downside part of mean | -2.581 | ||||
| Upside SD | 0.690 | ||||
| Downside SD | 0.499 | ||||
| N nonnegative terms | 397.000 | ||||
| N negative terms | 1225.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1622.000 | ||||
| Mean of predictor | 0.409 | ||||
| Mean of criterion | 0.281 | ||||
| SD of predictor | 0.577 | ||||
| SD of criterion | 0.851 | ||||
| Covariance | -0.014 | ||||
| r | -0.029 | ||||
| b (slope, estimate of beta) | -0.043 | ||||
| a (intercept, estimate of alpha) | 0.299 | ||||
| Mean Square Error | 0.724 | ||||
| DF error | 1620.000 | ||||
| t(b) | -1.182 | ||||
| p(b) | 0.515 | ||||
| t(a) | 0.873 | ||||
| p(a) | 0.489 | ||||
| Lowerbound of 95% confidence interval for beta | -0.115 | ||||
| Upperbound of 95% confidence interval for beta | 0.029 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.373 | ||||
| Upperbound of 95% confidence interval for alpha | 0.971 | ||||
| Treynor index (mean / b) | -6.488 | ||||
| Jensen alpha (a) | 0.299 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.060 | ||||
| SD | 0.819 | ||||
| Sharpe ratio (Glass type estimate) | -0.073 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.073 | ||||
| df | 1621.000 | ||||
| t | -0.182 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.861 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.715 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.861 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.715 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.108 | ||||
| Upside Potential Ratio | 4.808 | ||||
| Upside part of mean | 2.664 | ||||
| Downside part of mean | -2.724 | ||||
| Upside SD | 0.603 | ||||
| Downside SD | 0.554 | ||||
| N nonnegative terms | 397.000 | ||||
| N negative terms | 1225.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1622.000 | ||||
| Mean of predictor | 0.246 | ||||
| Mean of criterion | -0.060 | ||||
| SD of predictor | 0.571 | ||||
| SD of criterion | 0.819 | ||||
| Covariance | -0.014 | ||||
| r | -0.029 | ||||
| b (slope, estimate of beta) | -0.042 | ||||
| a (intercept, estimate of alpha) | -0.050 | ||||
| Mean Square Error | 0.671 | ||||
| DF error | 1620.000 | ||||
| t(b) | -1.178 | ||||
| p(b) | 0.515 | ||||
| t(a) | -0.151 | ||||
| p(a) | 0.502 | ||||
| Lowerbound of 95% confidence interval for beta | -0.112 | ||||
| Upperbound of 95% confidence interval for beta | 0.028 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.696 | ||||
| Upperbound of 95% confidence interval for alpha | 0.596 | ||||
| Treynor index (mean / b) | 1.427 | ||||
| Jensen alpha (a) | -0.050 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.080 | ||||
| Expected Shortfall on VaR | 0.099 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1622.000 | ||||
| Minimum | 0.595 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.621 | ||||
| Mean of quarter 1 | 0.961 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.044 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 357.000 | ||||
| Percentage of outliers low | 0.220 | ||||
| Mean of outliers low | 0.957 | ||||
| Number of outliers high | 343.000 | ||||
| Percentage of outliers high | 0.211 | ||||
| Mean of outliers high | 1.052 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.481 | ||||
| VaR(95%) (moments method) | 0.016 | ||||
| Expected Shortfall (moments method) | 0.038 | ||||
| Extreme Value Index (regression method) | 0.361 | ||||
| VaR(95%) (regression method) | 0.032 | ||||
| Expected Shortfall (regression method) | 0.069 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 17.000 | ||||
| Minimum | 0.031 | ||||
| Quartile 1 | 0.067 | ||||
| Median | 0.103 | ||||
| Quartile 3 | 0.176 | ||||
| Maximum | 0.809 | ||||
| Mean of quarter 1 | 0.044 | ||||
| Mean of quarter 2 | 0.084 | ||||
| Mean of quarter 3 | 0.152 | ||||
| Mean of quarter 4 | 0.412 | ||||
| Inter Quartile Range | 0.109 | ||||
| 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 | 0.118 | ||||
| Mean of outliers high | 0.604 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.425 | ||||
| VaR(95%) (moments method) | 0.441 | ||||
| Expected Shortfall (moments method) | 0.848 | ||||
| Extreme Value Index (regression method) | 1.638 | ||||
| VaR(95%) (regression method) | 0.581 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.015 | ||||
| Compounded annual return (geometric extrapolation) | -0.016 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.020 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.038 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.159 | ||||
| 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 | 2.125 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.669 | ||||
| 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 | 1.900 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.660 | ||||
| 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) | -8662960898405598.000 | ||||
| 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) | -324436263966231371932800632487936.000 | ||||
| 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 | ||||