Advanced Statistics: Sector 1 Funds
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 | 0.308 | ||||
| SD | 0.328 | ||||
| Sharpe ratio (Glass type estimate) | 0.940 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.919 | ||||
| df | 35.000 | ||||
| t | 1.627 | ||||
| p | 0.056 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.219 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.086 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.233 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.071 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.742 | ||||
| Upside Potential Ratio | 3.440 | ||||
| Upside part of mean | 0.609 | ||||
| Downside part of mean | -0.301 | ||||
| Upside SD | 0.285 | ||||
| Downside SD | 0.177 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 14.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.513 | ||||
| Mean of criterion | 0.308 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.328 | ||||
| Covariance | 0.024 | ||||
| r | 0.270 | ||||
| b (slope, estimate of beta) | 0.325 | ||||
| a (intercept, estimate of alpha) | 0.142 | ||||
| Mean Square Error | 0.103 | ||||
| DF error | 34.000 | ||||
| t(b) | 1.637 | ||||
| p(b) | 0.055 | ||||
| t(a) | 0.672 | ||||
| p(a) | 0.253 | ||||
| Lowerbound of 95% confidence interval for beta | -0.078 | ||||
| Upperbound of 95% confidence interval for beta | 0.728 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.287 | ||||
| Upperbound of 95% confidence interval for alpha | 0.571 | ||||
| Treynor index (mean / b) | 0.950 | ||||
| Jensen alpha (a) | 0.142 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.254 | ||||
| SD | 0.320 | ||||
| Sharpe ratio (Glass type estimate) | 0.793 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.776 | ||||
| df | 35.000 | ||||
| t | 1.374 | ||||
| p | 0.089 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.359 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.934 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.370 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.922 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.340 | ||||
| Upside Potential Ratio | 3.013 | ||||
| Upside part of mean | 0.571 | ||||
| Downside part of mean | -0.317 | ||||
| Upside SD | 0.263 | ||||
| Downside SD | 0.189 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 14.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.468 | ||||
| Mean of criterion | 0.254 | ||||
| SD of predictor | 0.257 | ||||
| SD of criterion | 0.320 | ||||
| Covariance | 0.021 | ||||
| r | 0.255 | ||||
| b (slope, estimate of beta) | 0.318 | ||||
| a (intercept, estimate of alpha) | 0.105 | ||||
| Mean Square Error | 0.099 | ||||
| DF error | 34.000 | ||||
| t(b) | 1.536 | ||||
| p(b) | 0.067 | ||||
| t(a) | 0.511 | ||||
| p(a) | 0.306 | ||||
| Lowerbound of 95% confidence interval for beta | -0.103 | ||||
| Upperbound of 95% confidence interval for beta | 0.738 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.313 | ||||
| Upperbound of 95% confidence interval for alpha | 0.523 | ||||
| Treynor index (mean / b) | 0.799 | ||||
| Jensen alpha (a) | 0.105 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.123 | ||||
| Expected Shortfall on VaR | 0.155 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.049 | ||||
| Expected Shortfall on VaR | 0.100 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.813 | ||||
| Quartile 1 | 0.961 | ||||
| Median | 1.025 | ||||
| Quartile 3 | 1.075 | ||||
| Maximum | 1.246 | ||||
| Mean of quarter 1 | 0.912 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.057 | ||||
| Mean of quarter 4 | 1.149 | ||||
| Inter Quartile Range | 0.113 | ||||
| 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 | 0.028 | ||||
| Mean of outliers high | 1.246 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.400 | ||||
| VaR(95%) (moments method) | 0.089 | ||||
| Expected Shortfall (moments method) | 0.105 | ||||
| Extreme Value Index (regression method) | 0.072 | ||||
| VaR(95%) (regression method) | 0.100 | ||||
| Expected Shortfall (regression method) | 0.143 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.038 | ||||
| Quartile 1 | 0.046 | ||||
| Median | 0.056 | ||||
| Quartile 3 | 0.170 | ||||
| Maximum | 0.341 | ||||
| Mean of quarter 1 | 0.042 | ||||
| Mean of quarter 2 | 0.056 | ||||
| Mean of quarter 3 | 0.170 | ||||
| Mean of quarter 4 | 0.341 | ||||
| Inter Quartile Range | 0.124 | ||||
| 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) | 0.481 | ||||
| Compounded annual return (geometric extrapolation) | 0.347 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.017 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.017 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.233 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.207 | ||||
| SD | 0.387 | ||||
| Sharpe ratio (Glass type estimate) | 0.534 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.533 | ||||
| df | 798.000 | ||||
| t | 0.932 | ||||
| p | 0.176 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.589 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.656 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.589 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.656 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.727 | ||||
| Upside Potential Ratio | 6.720 | ||||
| Upside part of mean | 1.910 | ||||
| Downside part of mean | -1.703 | ||||
| Upside SD | 0.263 | ||||
| Downside SD | 0.284 | ||||
| N nonnegative terms | 411.000 | ||||
| N negative terms | 388.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 799.000 | ||||
| Mean of predictor | 0.563 | ||||
| Mean of criterion | 0.207 | ||||
| SD of predictor | 0.341 | ||||
| SD of criterion | 0.387 | ||||
| Covariance | 0.052 | ||||
| r | 0.393 | ||||
| b (slope, estimate of beta) | 0.446 | ||||
| a (intercept, estimate of alpha) | -0.045 | ||||
| Mean Square Error | 0.127 | ||||
| DF error | 797.000 | ||||
| t(b) | 12.081 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.217 | ||||
| p(a) | 0.586 | ||||
| Lowerbound of 95% confidence interval for beta | 0.374 | ||||
| Upperbound of 95% confidence interval for beta | 0.519 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.447 | ||||
| Upperbound of 95% confidence interval for alpha | 0.358 | ||||
| Treynor index (mean / b) | 0.463 | ||||
| Jensen alpha (a) | -0.045 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.130 | ||||
| SD | 0.396 | ||||
| Sharpe ratio (Glass type estimate) | 0.328 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.328 | ||||
| df | 798.000 | ||||
| t | 0.573 | ||||
| p | 0.284 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.795 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.450 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.795 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.450 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.429 | ||||
| Upside Potential Ratio | 6.205 | ||||
| Upside part of mean | 1.877 | ||||
| Downside part of mean | -1.747 | ||||
| Upside SD | 0.255 | ||||
| Downside SD | 0.302 | ||||
| N nonnegative terms | 411.000 | ||||
| N negative terms | 388.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 799.000 | ||||
| Mean of predictor | 0.504 | ||||
| Mean of criterion | 0.130 | ||||
| SD of predictor | 0.344 | ||||
| SD of criterion | 0.396 | ||||
| Covariance | 0.052 | ||||
| r | 0.382 | ||||
| b (slope, estimate of beta) | 0.440 | ||||
| a (intercept, estimate of alpha) | -0.092 | ||||
| Mean Square Error | 0.134 | ||||
| DF error | 797.000 | ||||
| t(b) | 11.674 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.437 | ||||
| p(a) | 0.669 | ||||
| Lowerbound of 95% confidence interval for beta | 0.366 | ||||
| Upperbound of 95% confidence interval for beta | 0.514 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.505 | ||||
| Upperbound of 95% confidence interval for alpha | 0.321 | ||||
| Treynor index (mean / b) | 0.295 | ||||
| Jensen alpha (a) | -0.092 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.039 | ||||
| Expected Shortfall on VaR | 0.049 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 799.000 | ||||
| Minimum | 0.760 | ||||
| Quartile 1 | 0.994 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.009 | ||||
| Maximum | 1.141 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.025 | ||||
| Inter Quartile Range | 0.016 | ||||
| Number outliers low | 36.000 | ||||
| Percentage of outliers low | 0.045 | ||||
| Mean of outliers low | 0.938 | ||||
| Number of outliers high | 38.000 | ||||
| Percentage of outliers high | 0.048 | ||||
| Mean of outliers high | 1.057 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.507 | ||||
| VaR(95%) (moments method) | 0.022 | ||||
| Expected Shortfall (moments method) | 0.052 | ||||
| Extreme Value Index (regression method) | 0.328 | ||||
| VaR(95%) (regression method) | 0.019 | ||||
| Expected Shortfall (regression method) | 0.034 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.021 | ||||
| Quartile 3 | 0.047 | ||||
| Maximum | 0.394 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.014 | ||||
| Mean of quarter 3 | 0.031 | ||||
| Mean of quarter 4 | 0.147 | ||||
| Inter Quartile Range | 0.039 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.086 | ||||
| Mean of outliers high | 0.312 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.730 | ||||
| VaR(95%) (moments method) | 0.169 | ||||
| Expected Shortfall (moments method) | 0.643 | ||||
| Extreme Value Index (regression method) | 0.785 | ||||
| VaR(95%) (regression method) | 0.125 | ||||
| Expected Shortfall (regression method) | 0.498 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.229 | ||||
| Compounded annual return (geometric extrapolation) | 0.190 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.482 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.289 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.900 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.603 | ||||
| SD | 0.692 | ||||
| Sharpe ratio (Glass type estimate) | -0.872 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.867 | ||||
| df | 130.000 | ||||
| t | -0.616 | ||||
| p | 0.527 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.644 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.904 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.641 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.907 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.064 | ||||
| Upside Potential Ratio | 5.761 | ||||
| Upside part of mean | 3.265 | ||||
| Downside part of mean | -3.868 | ||||
| Upside SD | 0.394 | ||||
| Downside SD | 0.567 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.064 | ||||
| Mean of criterion | -0.603 | ||||
| SD of predictor | 0.513 | ||||
| SD of criterion | 0.692 | ||||
| Covariance | 0.160 | ||||
| r | 0.449 | ||||
| b (slope, estimate of beta) | 0.605 | ||||
| a (intercept, estimate of alpha) | -1.247 | ||||
| Mean Square Error | 0.385 | ||||
| DF error | 129.000 | ||||
| t(b) | 5.714 | ||||
| p(b) | 0.224 | ||||
| t(a) | -1.411 | ||||
| p(a) | 0.578 | ||||
| Lowerbound of 95% confidence interval for beta | 0.396 | ||||
| Upperbound of 95% confidence interval for beta | 0.815 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.997 | ||||
| Upperbound of 95% confidence interval for alpha | 0.502 | ||||
| Treynor index (mean / b) | -0.996 | ||||
| Jensen alpha (a) | -1.247 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.855 | ||||
| SD | 0.723 | ||||
| Sharpe ratio (Glass type estimate) | -1.182 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.176 | ||||
| df | 130.000 | ||||
| t | -0.836 | ||||
| p | 0.537 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.956 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.595 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.951 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.600 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.392 | ||||
| Upside Potential Ratio | 5.192 | ||||
| Upside part of mean | 3.190 | ||||
| Downside part of mean | -4.046 | ||||
| Upside SD | 0.380 | ||||
| Downside SD | 0.614 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.930 | ||||
| Mean of criterion | -0.855 | ||||
| SD of predictor | 0.518 | ||||
| SD of criterion | 0.723 | ||||
| Covariance | 0.166 | ||||
| r | 0.443 | ||||
| b (slope, estimate of beta) | 0.619 | ||||
| a (intercept, estimate of alpha) | -1.431 | ||||
| Mean Square Error | 0.424 | ||||
| DF error | 129.000 | ||||
| t(b) | 5.608 | ||||
| p(b) | 0.228 | ||||
| t(a) | -1.544 | ||||
| p(a) | 0.585 | ||||
| Lowerbound of 95% confidence interval for beta | 0.400 | ||||
| Upperbound of 95% confidence interval for beta | 0.837 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.264 | ||||
| Upperbound of 95% confidence interval for alpha | 0.403 | ||||
| Treynor index (mean / b) | -1.383 | ||||
| Jensen alpha (a) | -1.431 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.074 | ||||
| Expected Shortfall on VaR | 0.091 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.070 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.760 | ||||
| Quartile 1 | 0.982 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.020 | ||||
| Maximum | 1.119 | ||||
| Mean of quarter 1 | 0.948 | ||||
| Mean of quarter 2 | 0.994 | ||||
| Mean of quarter 3 | 1.009 | ||||
| Mean of quarter 4 | 1.041 | ||||
| Inter Quartile Range | 0.038 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.038 | ||||
| Mean of outliers low | 0.859 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.107 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.447 | ||||
| VaR(95%) (moments method) | 0.054 | ||||
| Expected Shortfall (moments method) | 0.110 | ||||
| Extreme Value Index (regression method) | 0.444 | ||||
| VaR(95%) (regression method) | 0.047 | ||||
| Expected Shortfall (regression method) | 0.091 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.013 | ||||
| Quartile 1 | 0.108 | ||||
| Median | 0.203 | ||||
| Quartile 3 | 0.298 | ||||
| Maximum | 0.394 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.394 | ||||
| Inter Quartile Range | 0.190 | ||||
| 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) | -0.667 | ||||
| Compounded annual return (geometric extrapolation) | -0.556 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.412 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.412 | ||||
| Compounded annual return / Expected Shortfall lognormal | -6.113 | ||||