Advanced Statistics: Spectre Composite (S-Eq/S-Cr/S-Fx/L-Co)
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 | 0.281 | ||||
| SD | 0.862 | ||||
| Sharpe ratio (Glass type estimate) | 0.326 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.323 | ||||
| df | 81.000 | ||||
| t | 0.853 | ||||
| p | 0.198 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.426 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.077 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.428 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.075 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.644 | ||||
| Upside Potential Ratio | 2.668 | ||||
| Upside part of mean | 1.164 | ||||
| Downside part of mean | -0.883 | ||||
| Upside SD | 0.742 | ||||
| Downside SD | 0.436 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 82.000 | ||||
| Mean of predictor | 0.211 | ||||
| Mean of criterion | 0.281 | ||||
| SD of predictor | 0.272 | ||||
| SD of criterion | 0.862 | ||||
| Covariance | -0.078 | ||||
| r | -0.332 | ||||
| b (slope, estimate of beta) | -1.051 | ||||
| a (intercept, estimate of alpha) | 0.503 | ||||
| Mean Square Error | 0.669 | ||||
| DF error | 80.000 | ||||
| t(b) | -3.148 | ||||
| p(b) | 0.999 | ||||
| t(a) | 1.568 | ||||
| p(a) | 0.060 | ||||
| Lowerbound of 95% confidence interval for beta | -1.716 | ||||
| Upperbound of 95% confidence interval for beta | -0.387 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.136 | ||||
| Upperbound of 95% confidence interval for alpha | 1.141 | ||||
| Treynor index (mean / b) | -0.267 | ||||
| Jensen alpha (a) | 0.503 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 0.765 | ||||
| Sharpe ratio (Glass type estimate) | -0.033 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.033 | ||||
| df | 81.000 | ||||
| t | -0.087 | ||||
| p | 0.535 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.783 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.716 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.783 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.717 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.050 | ||||
| Upside Potential Ratio | 1.908 | ||||
| Upside part of mean | 0.970 | ||||
| Downside part of mean | -0.996 | ||||
| Upside SD | 0.565 | ||||
| Downside SD | 0.509 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 82.000 | ||||
| Mean of predictor | 0.172 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.272 | ||||
| SD of criterion | 0.765 | ||||
| Covariance | -0.065 | ||||
| r | -0.312 | ||||
| b (slope, estimate of beta) | -0.876 | ||||
| a (intercept, estimate of alpha) | 0.125 | ||||
| Mean Square Error | 0.534 | ||||
| DF error | 80.000 | ||||
| t(b) | -2.937 | ||||
| p(b) | 0.998 | ||||
| t(a) | 0.441 | ||||
| p(a) | 0.330 | ||||
| Lowerbound of 95% confidence interval for beta | -1.470 | ||||
| Upperbound of 95% confidence interval for beta | -0.282 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.440 | ||||
| Upperbound of 95% confidence interval for alpha | 0.691 | ||||
| Treynor index (mean / b) | 0.029 | ||||
| Jensen alpha (a) | 0.125 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.306 | ||||
| Expected Shortfall on VaR | 0.365 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.181 | ||||
| Expected Shortfall on VaR | 0.312 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 82.000 | ||||
| Minimum | 0.625 | ||||
| Quartile 1 | 0.887 | ||||
| Median | 0.987 | ||||
| Quartile 3 | 1.127 | ||||
| Maximum | 2.205 | ||||
| Mean of quarter 1 | 0.780 | ||||
| Mean of quarter 2 | 0.939 | ||||
| Mean of quarter 3 | 1.052 | ||||
| Mean of quarter 4 | 1.334 | ||||
| Inter Quartile Range | 0.240 | ||||
| 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 | 0.049 | ||||
| Mean of outliers high | 1.760 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.551 | ||||
| VaR(95%) (moments method) | 0.231 | ||||
| Expected Shortfall (moments method) | 0.260 | ||||
| Extreme Value Index (regression method) | -0.560 | ||||
| VaR(95%) (regression method) | 0.217 | ||||
| Expected Shortfall (regression method) | 0.241 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.094 | ||||
| Quartile 1 | 0.213 | ||||
| Median | 0.438 | ||||
| Quartile 3 | 0.570 | ||||
| Maximum | 0.722 | ||||
| Mean of quarter 1 | 0.105 | ||||
| Mean of quarter 2 | 0.373 | ||||
| Mean of quarter 3 | 0.498 | ||||
| Mean of quarter 4 | 0.682 | ||||
| Inter Quartile Range | 0.358 | ||||
| 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) | 0.020 | ||||
| Compounded annual return (geometric extrapolation) | 0.019 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.026 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.027 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.051 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.336 | ||||
| SD | 1.836 | ||||
| Sharpe ratio (Glass type estimate) | 0.728 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.727 | ||||
| df | 1808.000 | ||||
| t | 1.912 | ||||
| p | 0.478 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.019 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.474 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.019 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.474 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.487 | ||||
| Upside Potential Ratio | 7.370 | ||||
| Upside part of mean | 6.621 | ||||
| Downside part of mean | -5.286 | ||||
| Upside SD | 1.603 | ||||
| Downside SD | 0.898 | ||||
| N nonnegative terms | 891.000 | ||||
| N negative terms | 918.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1809.000 | ||||
| Mean of predictor | 0.351 | ||||
| Mean of criterion | 1.336 | ||||
| SD of predictor | 0.559 | ||||
| SD of criterion | 1.836 | ||||
| Covariance | -0.302 | ||||
| r | -0.294 | ||||
| b (slope, estimate of beta) | -0.964 | ||||
| a (intercept, estimate of alpha) | 1.674 | ||||
| Mean Square Error | 3.081 | ||||
| DF error | 1807.000 | ||||
| t(b) | -13.070 | ||||
| p(b) | 0.684 | ||||
| t(a) | 2.504 | ||||
| p(a) | 0.463 | ||||
| Lowerbound of 95% confidence interval for beta | -1.109 | ||||
| Upperbound of 95% confidence interval for beta | -0.820 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.363 | ||||
| Upperbound of 95% confidence interval for alpha | 2.985 | ||||
| Treynor index (mean / b) | -1.385 | ||||
| Jensen alpha (a) | 1.674 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.027 | ||||
| SD | 1.618 | ||||
| Sharpe ratio (Glass type estimate) | -0.017 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.017 | ||||
| df | 1808.000 | ||||
| t | -0.045 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.763 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.729 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.763 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.729 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.024 | ||||
| Upside Potential Ratio | 5.114 | ||||
| Upside part of mean | 5.803 | ||||
| Downside part of mean | -5.830 | ||||
| Upside SD | 1.153 | ||||
| Downside SD | 1.135 | ||||
| N nonnegative terms | 891.000 | ||||
| N negative terms | 918.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1809.000 | ||||
| Mean of predictor | 0.197 | ||||
| Mean of criterion | -0.027 | ||||
| SD of predictor | 0.553 | ||||
| SD of criterion | 1.618 | ||||
| Covariance | -0.278 | ||||
| r | -0.310 | ||||
| b (slope, estimate of beta) | -0.908 | ||||
| a (intercept, estimate of alpha) | 0.152 | ||||
| Mean Square Error | 2.368 | ||||
| DF error | 1807.000 | ||||
| t(b) | -13.884 | ||||
| p(b) | 0.694 | ||||
| t(a) | 0.259 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -1.036 | ||||
| Upperbound of 95% confidence interval for beta | -0.780 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.997 | ||||
| Upperbound of 95% confidence interval for alpha | 1.301 | ||||
| Treynor index (mean / b) | 0.030 | ||||
| Jensen alpha (a) | 0.152 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.152 | ||||
| Expected Shortfall on VaR | 0.186 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.100 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1809.000 | ||||
| Minimum | 0.354 | ||||
| Quartile 1 | 0.979 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.022 | ||||
| Maximum | 2.933 | ||||
| Mean of quarter 1 | 0.929 | ||||
| Mean of quarter 2 | 0.991 | ||||
| Mean of quarter 3 | 1.011 | ||||
| Mean of quarter 4 | 1.091 | ||||
| Inter Quartile Range | 0.043 | ||||
| Number outliers low | 86.000 | ||||
| Percentage of outliers low | 0.048 | ||||
| Mean of outliers low | 0.804 | ||||
| Number of outliers high | 90.000 | ||||
| Percentage of outliers high | 0.050 | ||||
| Mean of outliers high | 1.288 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.620 | ||||
| VaR(95%) (moments method) | 0.072 | ||||
| Expected Shortfall (moments method) | 0.205 | ||||
| Extreme Value Index (regression method) | 0.528 | ||||
| VaR(95%) (regression method) | 0.058 | ||||
| Expected Shortfall (regression method) | 0.130 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 14.000 | ||||
| Minimum | 0.021 | ||||
| Quartile 1 | 0.093 | ||||
| Median | 0.250 | ||||
| Quartile 3 | 0.474 | ||||
| Maximum | 0.802 | ||||
| Mean of quarter 1 | 0.058 | ||||
| Mean of quarter 2 | 0.141 | ||||
| Mean of quarter 3 | 0.367 | ||||
| Mean of quarter 4 | 0.635 | ||||
| Inter Quartile Range | 0.381 | ||||
| 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) | -0.677 | ||||
| VaR(95%) (moments method) | 0.734 | ||||
| Expected Shortfall (moments method) | 0.796 | ||||
| Extreme Value Index (regression method) | -0.899 | ||||
| VaR(95%) (regression method) | 0.716 | ||||
| Expected Shortfall (regression method) | 0.748 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.018 | ||||
| Compounded annual return (geometric extrapolation) | 0.017 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.021 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.026 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.090 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.581 | ||||
| SD | 0.631 | ||||
| Sharpe ratio (Glass type estimate) | -0.920 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.915 | ||||
| df | 130.000 | ||||
| t | -0.651 | ||||
| p | 0.528 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.693 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.855 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.689 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.859 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.244 | ||||
| Upside Potential Ratio | 6.811 | ||||
| Upside part of mean | 3.181 | ||||
| Downside part of mean | -3.762 | ||||
| Upside SD | 0.422 | ||||
| Downside SD | 0.467 | ||||
| N nonnegative terms | 51.000 | ||||
| N negative terms | 80.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.062 | ||||
| Mean of criterion | -0.581 | ||||
| SD of predictor | 0.421 | ||||
| SD of criterion | 0.631 | ||||
| Covariance | -0.073 | ||||
| r | -0.276 | ||||
| b (slope, estimate of beta) | -0.414 | ||||
| a (intercept, estimate of alpha) | -0.141 | ||||
| Mean Square Error | 0.371 | ||||
| DF error | 129.000 | ||||
| t(b) | -3.263 | ||||
| p(b) | 0.674 | ||||
| t(a) | -0.162 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | -0.665 | ||||
| Upperbound of 95% confidence interval for beta | -0.163 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.866 | ||||
| Upperbound of 95% confidence interval for alpha | 1.583 | ||||
| Treynor index (mean / b) | 1.403 | ||||
| Jensen alpha (a) | -0.141 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.780 | ||||
| SD | 0.634 | ||||
| Sharpe ratio (Glass type estimate) | -1.230 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.223 | ||||
| df | 130.000 | ||||
| t | -0.870 | ||||
| p | 0.538 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.004 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.548 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.999 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.553 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.605 | ||||
| Upside Potential Ratio | 6.365 | ||||
| Upside part of mean | 3.096 | ||||
| Downside part of mean | -3.876 | ||||
| Upside SD | 0.406 | ||||
| Downside SD | 0.486 | ||||
| N nonnegative terms | 51.000 | ||||
| N negative terms | 80.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.971 | ||||
| Mean of criterion | -0.780 | ||||
| SD of predictor | 0.422 | ||||
| SD of criterion | 0.634 | ||||
| Covariance | -0.074 | ||||
| r | -0.277 | ||||
| b (slope, estimate of beta) | -0.416 | ||||
| a (intercept, estimate of alpha) | -0.376 | ||||
| Mean Square Error | 0.374 | ||||
| DF error | 129.000 | ||||
| t(b) | -3.274 | ||||
| p(b) | 0.674 | ||||
| t(a) | -0.430 | ||||
| p(a) | 0.524 | ||||
| Lowerbound of 95% confidence interval for beta | -0.668 | ||||
| Upperbound of 95% confidence interval for beta | -0.165 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.105 | ||||
| Upperbound of 95% confidence interval for alpha | 1.354 | ||||
| Treynor index (mean / b) | 1.874 | ||||
| Jensen alpha (a) | -0.376 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.065 | ||||
| Expected Shortfall on VaR | 0.080 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.071 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.879 | ||||
| Quartile 1 | 0.979 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.017 | ||||
| Maximum | 1.141 | ||||
| Mean of quarter 1 | 0.950 | ||||
| Mean of quarter 2 | 0.993 | ||||
| Mean of quarter 3 | 1.005 | ||||
| Mean of quarter 4 | 1.044 | ||||
| Inter Quartile Range | 0.038 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.053 | ||||
| Mean of outliers low | 0.904 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.105 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.023 | ||||
| VaR(95%) (moments method) | 0.047 | ||||
| Expected Shortfall (moments method) | 0.063 | ||||
| Extreme Value Index (regression method) | 0.175 | ||||
| VaR(95%) (regression method) | 0.045 | ||||
| Expected Shortfall (regression method) | 0.065 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.021 | ||||
| Quartile 1 | 0.031 | ||||
| Median | 0.061 | ||||
| Quartile 3 | 0.064 | ||||
| Maximum | 0.511 | ||||
| Mean of quarter 1 | 0.026 | ||||
| Mean of quarter 2 | 0.061 | ||||
| Mean of quarter 3 | 0.064 | ||||
| Mean of quarter 4 | 0.511 | ||||
| Inter Quartile Range | 0.033 | ||||
| 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 | 0.511 | ||||
| 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) | -0.616 | ||||
| Compounded annual return (geometric extrapolation) | -0.521 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.020 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.020 | ||||
| Compounded annual return / Expected Shortfall lognormal | -6.490 | ||||