Advanced Statistics: EPS Signal
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 | 0.470 | ||||
| SD | 0.414 | ||||
| Sharpe ratio (Glass type estimate) | 1.136 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.110 | ||||
| df | 33.000 | ||||
| t | 1.913 | ||||
| p | 0.032 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.068 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.324 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.085 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.305 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.378 | ||||
| Upside Potential Ratio | 3.994 | ||||
| Upside part of mean | 0.790 | ||||
| Downside part of mean | -0.320 | ||||
| Upside SD | 0.381 | ||||
| Downside SD | 0.198 | ||||
| N nonnegative terms | 23.000 | ||||
| N negative terms | 11.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.573 | ||||
| Mean of criterion | 0.470 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.414 | ||||
| Covariance | 0.102 | ||||
| r | 0.752 | ||||
| b (slope, estimate of beta) | 0.949 | ||||
| a (intercept, estimate of alpha) | -0.074 | ||||
| Mean Square Error | 0.077 | ||||
| DF error | 32.000 | ||||
| t(b) | 6.457 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.402 | ||||
| p(a) | 0.655 | ||||
| Lowerbound of 95% confidence interval for beta | 0.650 | ||||
| Upperbound of 95% confidence interval for beta | 1.249 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.451 | ||||
| Upperbound of 95% confidence interval for alpha | 0.302 | ||||
| Treynor index (mean / b) | 0.495 | ||||
| Jensen alpha (a) | -0.074 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.385 | ||||
| SD | 0.391 | ||||
| Sharpe ratio (Glass type estimate) | 0.985 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.963 | ||||
| df | 33.000 | ||||
| t | 1.658 | ||||
| p | 0.053 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.210 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.166 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.225 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.150 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.815 | ||||
| Upside Potential Ratio | 3.417 | ||||
| Upside part of mean | 0.725 | ||||
| Downside part of mean | -0.340 | ||||
| Upside SD | 0.340 | ||||
| Downside SD | 0.212 | ||||
| N nonnegative terms | 23.000 | ||||
| N negative terms | 11.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.511 | ||||
| Mean of criterion | 0.385 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 0.391 | ||||
| Covariance | 0.091 | ||||
| r | 0.751 | ||||
| b (slope, estimate of beta) | 0.945 | ||||
| a (intercept, estimate of alpha) | -0.098 | ||||
| Mean Square Error | 0.069 | ||||
| DF error | 32.000 | ||||
| t(b) | 6.438 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.569 | ||||
| p(a) | 0.713 | ||||
| Lowerbound of 95% confidence interval for beta | 0.646 | ||||
| Upperbound of 95% confidence interval for beta | 1.244 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.450 | ||||
| Upperbound of 95% confidence interval for alpha | 0.253 | ||||
| Treynor index (mean / b) | 0.407 | ||||
| Jensen alpha (a) | -0.098 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.142 | ||||
| Expected Shortfall on VaR | 0.181 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.045 | ||||
| Expected Shortfall on VaR | 0.098 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.834 | ||||
| Quartile 1 | 0.986 | ||||
| Median | 1.040 | ||||
| Quartile 3 | 1.076 | ||||
| Maximum | 1.366 | ||||
| Mean of quarter 1 | 0.905 | ||||
| Mean of quarter 2 | 1.018 | ||||
| Mean of quarter 3 | 1.061 | ||||
| Mean of quarter 4 | 1.186 | ||||
| Inter Quartile Range | 0.090 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.834 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.118 | ||||
| Mean of outliers high | 1.279 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.616 | ||||
| VaR(95%) (moments method) | 0.049 | ||||
| Expected Shortfall (moments method) | 0.049 | ||||
| Extreme Value Index (regression method) | -1.284 | ||||
| VaR(95%) (regression method) | 0.137 | ||||
| Expected Shortfall (regression method) | 0.146 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.014 | ||||
| Quartile 1 | 0.071 | ||||
| Median | 0.125 | ||||
| Quartile 3 | 0.183 | ||||
| Maximum | 0.202 | ||||
| Mean of quarter 1 | 0.037 | ||||
| Mean of quarter 2 | 0.108 | ||||
| Mean of quarter 3 | 0.142 | ||||
| Mean of quarter 4 | 0.199 | ||||
| Inter Quartile Range | 0.111 | ||||
| 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) | 0.837 | ||||
| Compounded annual return (geometric extrapolation) | 0.536 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.650 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.689 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.959 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.445 | ||||
| SD | 0.437 | ||||
| Sharpe ratio (Glass type estimate) | 1.020 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.019 | ||||
| df | 743.000 | ||||
| t | 1.719 | ||||
| p | 0.043 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.145 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.184 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.145 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.183 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.433 | ||||
| Upside Potential Ratio | 7.894 | ||||
| Upside part of mean | 2.453 | ||||
| Downside part of mean | -2.007 | ||||
| Upside SD | 0.307 | ||||
| Downside SD | 0.311 | ||||
| N nonnegative terms | 399.000 | ||||
| N negative terms | 345.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 744.000 | ||||
| Mean of predictor | 0.612 | ||||
| Mean of criterion | 0.445 | ||||
| SD of predictor | 0.358 | ||||
| SD of criterion | 0.437 | ||||
| Covariance | 0.096 | ||||
| r | 0.615 | ||||
| b (slope, estimate of beta) | 0.750 | ||||
| a (intercept, estimate of alpha) | -0.013 | ||||
| Mean Square Error | 0.119 | ||||
| DF error | 742.000 | ||||
| t(b) | 21.251 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.065 | ||||
| p(a) | 0.526 | ||||
| Lowerbound of 95% confidence interval for beta | 0.681 | ||||
| Upperbound of 95% confidence interval for beta | 0.819 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.417 | ||||
| Upperbound of 95% confidence interval for alpha | 0.390 | ||||
| Treynor index (mean / b) | 0.594 | ||||
| Jensen alpha (a) | -0.013 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.348 | ||||
| SD | 0.443 | ||||
| Sharpe ratio (Glass type estimate) | 0.786 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.785 | ||||
| df | 743.000 | ||||
| t | 1.324 | ||||
| p | 0.093 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.378 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.950 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.379 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.949 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.061 | ||||
| Upside Potential Ratio | 7.339 | ||||
| Upside part of mean | 2.407 | ||||
| Downside part of mean | -2.059 | ||||
| Upside SD | 0.298 | ||||
| Downside SD | 0.328 | ||||
| N nonnegative terms | 399.000 | ||||
| N negative terms | 345.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 744.000 | ||||
| Mean of predictor | 0.547 | ||||
| Mean of criterion | 0.348 | ||||
| SD of predictor | 0.358 | ||||
| SD of criterion | 0.443 | ||||
| Covariance | 0.097 | ||||
| r | 0.614 | ||||
| b (slope, estimate of beta) | 0.761 | ||||
| a (intercept, estimate of alpha) | -0.068 | ||||
| Mean Square Error | 0.122 | ||||
| DF error | 742.000 | ||||
| t(b) | 21.197 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.326 | ||||
| p(a) | 0.628 | ||||
| Lowerbound of 95% confidence interval for beta | 0.690 | ||||
| Upperbound of 95% confidence interval for beta | 0.831 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.477 | ||||
| Upperbound of 95% confidence interval for alpha | 0.341 | ||||
| Treynor index (mean / b) | 0.458 | ||||
| Jensen alpha (a) | -0.068 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.043 | ||||
| Expected Shortfall on VaR | 0.054 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 744.000 | ||||
| Minimum | 0.774 | ||||
| Quartile 1 | 0.992 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.013 | ||||
| Maximum | 1.143 | ||||
| Mean of quarter 1 | 0.972 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.031 | ||||
| Inter Quartile Range | 0.022 | ||||
| Number outliers low | 26.000 | ||||
| Percentage of outliers low | 0.035 | ||||
| Mean of outliers low | 0.923 | ||||
| Number of outliers high | 27.000 | ||||
| Percentage of outliers high | 0.036 | ||||
| Mean of outliers high | 1.070 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.336 | ||||
| VaR(95%) (moments method) | 0.026 | ||||
| Expected Shortfall (moments method) | 0.046 | ||||
| Extreme Value Index (regression method) | 0.236 | ||||
| VaR(95%) (regression method) | 0.025 | ||||
| Expected Shortfall (regression method) | 0.041 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 46.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.026 | ||||
| Quartile 3 | 0.071 | ||||
| Maximum | 0.358 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.019 | ||||
| Mean of quarter 3 | 0.053 | ||||
| Mean of quarter 4 | 0.168 | ||||
| Inter Quartile Range | 0.063 | ||||
| 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 | 0.109 | ||||
| Mean of outliers high | 0.263 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.219 | ||||
| VaR(95%) (moments method) | 0.175 | ||||
| Expected Shortfall (moments method) | 0.274 | ||||
| Extreme Value Index (regression method) | 0.204 | ||||
| VaR(95%) (regression method) | 0.173 | ||||
| Expected Shortfall (regression method) | 0.264 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.720 | ||||
| Compounded annual return (geometric extrapolation) | 0.480 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.339 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.857 | ||||
| Compounded annual return / Expected Shortfall lognormal | 8.962 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.558 | ||||
| SD | 0.693 | ||||
| Sharpe ratio (Glass type estimate) | 0.806 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.801 | ||||
| df | 130.000 | ||||
| t | 0.570 | ||||
| p | 0.475 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.969 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.578 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.972 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.575 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.154 | ||||
| Upside Potential Ratio | 8.760 | ||||
| Upside part of mean | 4.240 | ||||
| Downside part of mean | -3.682 | ||||
| Upside SD | 0.493 | ||||
| Downside SD | 0.484 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 63.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.366 | ||||
| Mean of criterion | 0.558 | ||||
| SD of predictor | 0.576 | ||||
| SD of criterion | 0.693 | ||||
| Covariance | 0.219 | ||||
| r | 0.549 | ||||
| b (slope, estimate of beta) | 0.660 | ||||
| a (intercept, estimate of alpha) | -0.343 | ||||
| Mean Square Error | 0.338 | ||||
| DF error | 129.000 | ||||
| t(b) | 7.451 | ||||
| p(b) | 0.169 | ||||
| t(a) | -0.413 | ||||
| p(a) | 0.523 | ||||
| Lowerbound of 95% confidence interval for beta | 0.485 | ||||
| Upperbound of 95% confidence interval for beta | 0.835 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.988 | ||||
| Upperbound of 95% confidence interval for alpha | 1.302 | ||||
| Treynor index (mean / b) | 0.846 | ||||
| Jensen alpha (a) | -0.343 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.318 | ||||
| SD | 0.697 | ||||
| Sharpe ratio (Glass type estimate) | 0.456 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.453 | ||||
| df | 130.000 | ||||
| t | 0.322 | ||||
| p | 0.486 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.317 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.228 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.319 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.226 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.626 | ||||
| Upside Potential Ratio | 8.122 | ||||
| Upside part of mean | 4.124 | ||||
| Downside part of mean | -3.806 | ||||
| Upside SD | 0.474 | ||||
| Downside SD | 0.508 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 63.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.200 | ||||
| Mean of criterion | 0.318 | ||||
| SD of predictor | 0.571 | ||||
| SD of criterion | 0.697 | ||||
| Covariance | 0.222 | ||||
| r | 0.557 | ||||
| b (slope, estimate of beta) | 0.680 | ||||
| a (intercept, estimate of alpha) | -0.498 | ||||
| Mean Square Error | 0.338 | ||||
| DF error | 129.000 | ||||
| t(b) | 7.615 | ||||
| p(b) | 0.165 | ||||
| t(a) | -0.600 | ||||
| p(a) | 0.534 | ||||
| Lowerbound of 95% confidence interval for beta | 0.503 | ||||
| Upperbound of 95% confidence interval for beta | 0.856 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.138 | ||||
| Upperbound of 95% confidence interval for alpha | 1.143 | ||||
| Treynor index (mean / b) | 0.468 | ||||
| Jensen alpha (a) | -0.498 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.067 | ||||
| Expected Shortfall on VaR | 0.084 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.063 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.864 | ||||
| Quartile 1 | 0.980 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.026 | ||||
| Maximum | 1.143 | ||||
| Mean of quarter 1 | 0.952 | ||||
| Mean of quarter 2 | 0.993 | ||||
| Mean of quarter 3 | 1.013 | ||||
| Mean of quarter 4 | 1.052 | ||||
| Inter Quartile Range | 0.046 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.038 | ||||
| Mean of outliers low | 0.885 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.119 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.527 | ||||
| VaR(95%) (moments method) | 0.055 | ||||
| Expected Shortfall (moments method) | 0.123 | ||||
| Extreme Value Index (regression method) | 0.426 | ||||
| VaR(95%) (regression method) | 0.044 | ||||
| Expected Shortfall (regression method) | 0.080 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.061 | ||||
| Quartile 3 | 0.142 | ||||
| Maximum | 0.317 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.033 | ||||
| Mean of quarter 3 | 0.094 | ||||
| Mean of quarter 4 | 0.258 | ||||
| Inter Quartile Range | 0.133 | ||||
| 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) | 0.397 | ||||
| Compounded annual return (geometric extrapolation) | 0.436 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.377 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.691 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.205 | ||||