Advanced Statistics: EWP plus
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 | 0.384 | ||||
| SD | 0.533 | ||||
| Sharpe ratio (Glass type estimate) | 0.722 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.714 | ||||
| df | 69.000 | ||||
| t | 1.743 | ||||
| p | 0.043 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.101 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.540 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.106 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.534 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.836 | ||||
| Upside Potential Ratio | 3.412 | ||||
| Upside part of mean | 0.714 | ||||
| Downside part of mean | -0.330 | ||||
| Upside SD | 0.498 | ||||
| Downside SD | 0.209 | ||||
| N nonnegative terms | 27.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.202 | ||||
| Mean of criterion | 0.384 | ||||
| SD of predictor | 0.249 | ||||
| SD of criterion | 0.533 | ||||
| Covariance | -0.040 | ||||
| r | -0.298 | ||||
| b (slope, estimate of beta) | -0.636 | ||||
| a (intercept, estimate of alpha) | 0.513 | ||||
| Mean Square Error | 0.262 | ||||
| DF error | 68.000 | ||||
| t(b) | -2.574 | ||||
| p(b) | 0.994 | ||||
| t(a) | 2.354 | ||||
| p(a) | 0.011 | ||||
| Lowerbound of 95% confidence interval for beta | -1.129 | ||||
| Upperbound of 95% confidence interval for beta | -0.143 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.078 | ||||
| Upperbound of 95% confidence interval for alpha | 0.947 | ||||
| Treynor index (mean / b) | -0.604 | ||||
| Jensen alpha (a) | 0.513 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.265 | ||||
| SD | 0.460 | ||||
| Sharpe ratio (Glass type estimate) | 0.576 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.570 | ||||
| df | 69.000 | ||||
| t | 1.392 | ||||
| p | 0.084 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.243 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.391 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.247 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.387 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.173 | ||||
| Upside Potential Ratio | 2.735 | ||||
| Upside part of mean | 0.618 | ||||
| Downside part of mean | -0.353 | ||||
| Upside SD | 0.405 | ||||
| Downside SD | 0.226 | ||||
| N nonnegative terms | 27.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.170 | ||||
| Mean of criterion | 0.265 | ||||
| SD of predictor | 0.246 | ||||
| SD of criterion | 0.460 | ||||
| Covariance | -0.035 | ||||
| r | -0.308 | ||||
| b (slope, estimate of beta) | -0.577 | ||||
| a (intercept, estimate of alpha) | 0.363 | ||||
| Mean Square Error | 0.195 | ||||
| DF error | 68.000 | ||||
| t(b) | -2.672 | ||||
| p(b) | 0.995 | ||||
| t(a) | 1.949 | ||||
| p(a) | 0.028 | ||||
| Lowerbound of 95% confidence interval for beta | -1.008 | ||||
| Upperbound of 95% confidence interval for beta | -0.146 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.009 | ||||
| Upperbound of 95% confidence interval for alpha | 0.735 | ||||
| Treynor index (mean / b) | -0.460 | ||||
| Jensen alpha (a) | 0.363 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.178 | ||||
| Expected Shortfall on VaR | 0.222 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.072 | ||||
| Expected Shortfall on VaR | 0.141 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 70.000 | ||||
| Minimum | 0.819 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.065 | ||||
| Maximum | 1.749 | ||||
| Mean of quarter 1 | 0.902 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.015 | ||||
| Mean of quarter 4 | 1.223 | ||||
| Inter Quartile Range | 0.065 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.143 | ||||
| Mean of outliers low | 0.854 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.129 | ||||
| Mean of outliers high | 1.329 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -67.559 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -1.842 | ||||
| VaR(95%) (regression method) | 0.111 | ||||
| Expected Shortfall (regression method) | 0.116 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.065 | ||||
| Quartile 1 | 0.119 | ||||
| Median | 0.196 | ||||
| Quartile 3 | 0.315 | ||||
| Maximum | 0.399 | ||||
| Mean of quarter 1 | 0.088 | ||||
| Mean of quarter 2 | 0.143 | ||||
| Mean of quarter 3 | 0.248 | ||||
| Mean of quarter 4 | 0.368 | ||||
| Inter Quartile Range | 0.196 | ||||
| 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) | 0.870 | ||||
| Compounded annual return (geometric extrapolation) | 0.363 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.909 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.985 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.634 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.710 | ||||
| SD | 1.905 | ||||
| Sharpe ratio (Glass type estimate) | 0.898 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.898 | ||||
| df | 1539.000 | ||||
| t | 2.177 | ||||
| p | 0.465 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.089 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.707 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.088 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.707 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.952 | ||||
| Upside Potential Ratio | 6.274 | ||||
| Upside part of mean | 5.498 | ||||
| Downside part of mean | -3.788 | ||||
| Upside SD | 1.694 | ||||
| Downside SD | 0.876 | ||||
| N nonnegative terms | 400.000 | ||||
| N negative terms | 1140.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1540.000 | ||||
| Mean of predictor | 0.391 | ||||
| Mean of criterion | 1.710 | ||||
| SD of predictor | 0.549 | ||||
| SD of criterion | 1.905 | ||||
| Covariance | -0.409 | ||||
| r | -0.391 | ||||
| b (slope, estimate of beta) | -1.354 | ||||
| a (intercept, estimate of alpha) | 2.240 | ||||
| Mean Square Error | 3.076 | ||||
| DF error | 1538.000 | ||||
| t(b) | -16.645 | ||||
| p(b) | 0.695 | ||||
| t(a) | 3.093 | ||||
| p(a) | 0.461 | ||||
| Lowerbound of 95% confidence interval for beta | -1.514 | ||||
| Upperbound of 95% confidence interval for beta | -1.195 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.820 | ||||
| Upperbound of 95% confidence interval for alpha | 3.660 | ||||
| Treynor index (mean / b) | -1.263 | ||||
| Jensen alpha (a) | 2.240 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.263 | ||||
| SD | 1.675 | ||||
| Sharpe ratio (Glass type estimate) | 0.157 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.157 | ||||
| df | 1539.000 | ||||
| t | 0.381 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.651 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.965 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.651 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.965 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.224 | ||||
| Upside Potential Ratio | 3.931 | ||||
| Upside part of mean | 4.607 | ||||
| Downside part of mean | -4.344 | ||||
| Upside SD | 1.195 | ||||
| Downside SD | 1.172 | ||||
| N nonnegative terms | 400.000 | ||||
| N negative terms | 1140.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1540.000 | ||||
| Mean of predictor | 0.238 | ||||
| Mean of criterion | 0.263 | ||||
| SD of predictor | 0.556 | ||||
| SD of criterion | 1.675 | ||||
| Covariance | -0.359 | ||||
| r | -0.385 | ||||
| b (slope, estimate of beta) | -1.161 | ||||
| a (intercept, estimate of alpha) | 0.540 | ||||
| Mean Square Error | 2.389 | ||||
| DF error | 1538.000 | ||||
| t(b) | -16.378 | ||||
| p(b) | 0.693 | ||||
| t(a) | 0.846 | ||||
| p(a) | 0.489 | ||||
| Lowerbound of 95% confidence interval for beta | -1.300 | ||||
| Upperbound of 95% confidence interval for beta | -1.022 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.711 | ||||
| Upperbound of 95% confidence interval for alpha | 1.791 | ||||
| Treynor index (mean / b) | -0.226 | ||||
| Jensen alpha (a) | 0.540 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.156 | ||||
| Expected Shortfall on VaR | 0.191 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.092 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1540.000 | ||||
| Minimum | 0.258 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 2.962 | ||||
| Mean of quarter 1 | 0.943 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.084 | ||||
| Inter Quartile Range | 0.004 | ||||
| Number outliers low | 305.000 | ||||
| Percentage of outliers low | 0.198 | ||||
| Mean of outliers low | 0.929 | ||||
| Number of outliers high | 332.000 | ||||
| Percentage of outliers high | 0.216 | ||||
| Mean of outliers high | 1.097 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.908 | ||||
| VaR(95%) (moments method) | 0.027 | ||||
| Expected Shortfall (moments method) | 0.336 | ||||
| Extreme Value Index (regression method) | 0.520 | ||||
| VaR(95%) (regression method) | 0.042 | ||||
| Expected Shortfall (regression method) | 0.116 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.030 | ||||
| Median | 0.097 | ||||
| Quartile 3 | 0.219 | ||||
| Maximum | 0.742 | ||||
| Mean of quarter 1 | 0.014 | ||||
| Mean of quarter 2 | 0.060 | ||||
| Mean of quarter 3 | 0.117 | ||||
| Mean of quarter 4 | 0.531 | ||||
| Inter Quartile Range | 0.188 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.147 | ||||
| Mean of outliers high | 0.654 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -4.723 | ||||
| VaR(95%) (moments method) | 0.487 | ||||
| Expected Shortfall (moments method) | 0.487 | ||||
| Extreme Value Index (regression method) | -1.311 | ||||
| VaR(95%) (regression method) | 0.679 | ||||
| Expected Shortfall (regression method) | 0.711 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.864 | ||||
| Compounded annual return (geometric extrapolation) | 0.359 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.484 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.677 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.884 | ||||
| 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 | 2.196 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.766 | ||||
| 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 | 1.870 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.821 | ||||
| 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) | -8713348107372027.000 | ||||
| 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) | 890283298286820588622625353236480.000 | ||||
| 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 | ||||