Advanced Statistics: system
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 | 1458.220 | ||||
| SD | 2977.119 | ||||
| Sharpe ratio (Glass type estimate) | 0.490 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.482 | ||||
| df | 49.000 | ||||
| t | 1.000 | ||||
| p | 0.161 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.478 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.452 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.483 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.447 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1601.934 | ||||
| Upside Potential Ratio | 1603.521 | ||||
| Upside part of mean | 1459.665 | ||||
| Downside part of mean | -1.445 | ||||
| Upside SD | 2977.108 | ||||
| Downside SD | 0.910 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 28.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 50.000 | ||||
| Mean of predictor | 0.367 | ||||
| Mean of criterion | 1458.220 | ||||
| SD of predictor | 0.255 | ||||
| SD of criterion | 2977.119 | ||||
| Covariance | -57.198 | ||||
| r | -0.075 | ||||
| b (slope, estimate of beta) | -882.990 | ||||
| a (intercept, estimate of alpha) | 1782.671 | ||||
| Mean Square Error | 8996332.146 | ||||
| DF error | 48.000 | ||||
| t(b) | -0.524 | ||||
| p(b) | 0.699 | ||||
| t(a) | 1.118 | ||||
| p(a) | 0.135 | ||||
| Lowerbound of 95% confidence interval for beta | -4267.956 | ||||
| Upperbound of 95% confidence interval for beta | 2501.975 | ||||
| Lowerbound of 95% confidence interval for alpha | -1422.885 | ||||
| Upperbound of 95% confidence interval for alpha | 4988.228 | ||||
| Treynor index (mean / b) | -1.651 | ||||
| Jensen alpha (a) | 1782.671 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.807 | ||||
| SD | 7.862 | ||||
| Sharpe ratio (Glass type estimate) | -0.357 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.352 | ||||
| df | 49.000 | ||||
| t | -0.729 | ||||
| p | 0.765 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.318 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.607 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.314 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.611 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.430 | ||||
| Upside Potential Ratio | 0.447 | ||||
| Upside part of mean | 2.918 | ||||
| Downside part of mean | -5.725 | ||||
| Upside SD | 4.322 | ||||
| Downside SD | 6.523 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 28.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 50.000 | ||||
| Mean of predictor | 0.331 | ||||
| Mean of criterion | -2.807 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 7.862 | ||||
| Covariance | -0.919 | ||||
| r | -0.480 | ||||
| b (slope, estimate of beta) | -15.509 | ||||
| a (intercept, estimate of alpha) | 2.333 | ||||
| Mean Square Error | 48.548 | ||||
| DF error | 48.000 | ||||
| t(b) | -3.793 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.635 | ||||
| p(a) | 0.264 | ||||
| Lowerbound of 95% confidence interval for beta | -23.731 | ||||
| Upperbound of 95% confidence interval for beta | -7.287 | ||||
| Lowerbound of 95% confidence interval for alpha | -5.052 | ||||
| Upperbound of 95% confidence interval for alpha | 9.717 | ||||
| Treynor index (mean / b) | 0.181 | ||||
| Jensen alpha (a) | 2.333 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.981 | ||||
| Expected Shortfall on VaR | 0.991 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.296 | ||||
| Expected Shortfall on VaR | 0.589 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 50.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.902 | ||||
| Median | 0.980 | ||||
| Quartile 3 | 1.065 | ||||
| Maximum | 6078.000 | ||||
| Mean of quarter 1 | 0.594 | ||||
| Mean of quarter 2 | 0.950 | ||||
| Mean of quarter 3 | 1.025 | ||||
| Mean of quarter 4 | 468.821 | ||||
| Inter Quartile Range | 0.163 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.100 | ||||
| Mean of outliers low | 0.251 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.060 | ||||
| Mean of outliers high | 2027.648 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.250 | ||||
| VaR(95%) (moments method) | 0.336 | ||||
| Expected Shortfall (moments method) | 0.576 | ||||
| Extreme Value Index (regression method) | -2.369 | ||||
| VaR(95%) (regression method) | 0.561 | ||||
| Expected Shortfall (regression method) | 0.568 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.047 | ||||
| Quartile 1 | 0.075 | ||||
| Median | 0.102 | ||||
| Quartile 3 | 0.551 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.047 | ||||
| Mean of quarter 2 | 0.102 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.476 | ||||
| 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) | -0.240 | ||||
| Compounded annual return (geometric extrapolation) | -0.937 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.937 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.937 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.946 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2370.393 | ||||
| SD | 2413.762 | ||||
| Sharpe ratio (Glass type estimate) | 0.982 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.981 | ||||
| df | 1109.000 | ||||
| t | 2.021 | ||||
| p | 0.461 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.029 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.935 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.028 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.934 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1382.000 | ||||
| Upside Potential Ratio | 1386.319 | ||||
| Upside part of mean | 2377.800 | ||||
| Downside part of mean | -7.408 | ||||
| Upside SD | 2417.114 | ||||
| Downside SD | 1.715 | ||||
| N nonnegative terms | 470.000 | ||||
| N negative terms | 640.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1110.000 | ||||
| Mean of predictor | 0.399 | ||||
| Mean of criterion | 2370.393 | ||||
| SD of predictor | 0.294 | ||||
| SD of criterion | 2413.762 | ||||
| Covariance | 29.868 | ||||
| r | 0.042 | ||||
| b (slope, estimate of beta) | 346.497 | ||||
| a (intercept, estimate of alpha) | 2231.982 | ||||
| Mean Square Error | 5821146.912 | ||||
| DF error | 1108.000 | ||||
| t(b) | 1.404 | ||||
| p(b) | 0.479 | ||||
| t(a) | 1.897 | ||||
| p(a) | 0.472 | ||||
| Lowerbound of 95% confidence interval for beta | -137.681 | ||||
| Upperbound of 95% confidence interval for beta | 830.676 | ||||
| Lowerbound of 95% confidence interval for alpha | -76.074 | ||||
| Upperbound of 95% confidence interval for alpha | 4540.038 | ||||
| Treynor index (mean / b) | 6.841 | ||||
| Jensen alpha (a) | 2231.982 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.761 | ||||
| SD | 12.690 | ||||
| Sharpe ratio (Glass type estimate) | -0.218 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.217 | ||||
| df | 1109.000 | ||||
| t | -0.448 | ||||
| p | 0.509 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.170 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.735 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.170 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.735 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.292 | ||||
| Upside Potential Ratio | 1.641 | ||||
| Upside part of mean | 15.506 | ||||
| Downside part of mean | -18.268 | ||||
| Upside SD | 8.465 | ||||
| Downside SD | 9.448 | ||||
| N nonnegative terms | 470.000 | ||||
| N negative terms | 640.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1110.000 | ||||
| Mean of predictor | 0.356 | ||||
| Mean of criterion | -2.761 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 12.690 | ||||
| Covariance | -0.088 | ||||
| r | -0.024 | ||||
| b (slope, estimate of beta) | -1.019 | ||||
| a (intercept, estimate of alpha) | -2.399 | ||||
| Mean Square Error | 161.102 | ||||
| DF error | 1108.000 | ||||
| t(b) | -0.787 | ||||
| p(b) | 0.512 | ||||
| t(a) | -0.388 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | -3.558 | ||||
| Upperbound of 95% confidence interval for beta | 1.520 | ||||
| Lowerbound of 95% confidence interval for alpha | -14.532 | ||||
| Upperbound of 95% confidence interval for alpha | 9.734 | ||||
| Treynor index (mean / b) | 2.710 | ||||
| Jensen alpha (a) | -2.399 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.728 | ||||
| Expected Shortfall on VaR | 0.796 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.069 | ||||
| Expected Shortfall on VaR | 0.156 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1110.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.982 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.013 | ||||
| Maximum | 2977.000 | ||||
| Mean of quarter 1 | 0.895 | ||||
| Mean of quarter 2 | 0.992 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 37.233 | ||||
| Inter Quartile Range | 0.031 | ||||
| Number outliers low | 83.000 | ||||
| Percentage of outliers low | 0.075 | ||||
| Mean of outliers low | 0.728 | ||||
| Number of outliers high | 77.000 | ||||
| Percentage of outliers high | 0.069 | ||||
| Mean of outliers high | 131.744 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.961 | ||||
| VaR(95%) (moments method) | 0.094 | ||||
| Expected Shortfall (moments method) | 2.479 | ||||
| Extreme Value Index (regression method) | 0.427 | ||||
| VaR(95%) (regression method) | 0.065 | ||||
| Expected Shortfall (regression method) | 0.136 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.051 | ||||
| Quartile 3 | 0.110 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | 0.029 | ||||
| Mean of quarter 3 | 0.067 | ||||
| Mean of quarter 4 | 0.427 | ||||
| Inter Quartile Range | 0.096 | ||||
| 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 | 0.100 | ||||
| Mean of outliers high | 1.000 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.834 | ||||
| VaR(95%) (moments method) | 0.500 | ||||
| Expected Shortfall (moments method) | 3.279 | ||||
| Extreme Value Index (regression method) | 3.375 | ||||
| VaR(95%) (regression method) | 1.983 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.236 | ||||
| Compounded annual return (geometric extrapolation) | -0.934 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.934 | ||||
| Compounded annual return / average of 25% largest draw downs | -2.185 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.173 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 7895.828 | ||||
| SD | 4410.856 | ||||
| Sharpe ratio (Glass type estimate) | 1.790 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.780 | ||||
| df | 130.000 | ||||
| t | 1.266 | ||||
| p | 0.445 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.994 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.567 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.560 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2384.030 | ||||
| Upside Potential Ratio | 2390.268 | ||||
| Upside part of mean | 7916.487 | ||||
| Downside part of mean | -20.658 | ||||
| Upside SD | 4420.982 | ||||
| Downside SD | 3.312 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 96.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.946 | ||||
| Mean of criterion | 7895.828 | ||||
| SD of predictor | 0.508 | ||||
| SD of criterion | 4410.856 | ||||
| Covariance | 85.276 | ||||
| r | 0.038 | ||||
| b (slope, estimate of beta) | 330.393 | ||||
| a (intercept, estimate of alpha) | 7583.140 | ||||
| Mean Square Error | 19578076.363 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.433 | ||||
| p(b) | 0.476 | ||||
| t(a) | 1.204 | ||||
| p(a) | 0.433 | ||||
| Lowerbound of 95% confidence interval for beta | -1180.931 | ||||
| Upperbound of 95% confidence interval for beta | 1841.717 | ||||
| Lowerbound of 95% confidence interval for alpha | -4879.804 | ||||
| Upperbound of 95% confidence interval for alpha | 20046.083 | ||||
| Treynor index (mean / b) | 23.898 | ||||
| Jensen alpha (a) | 7583.140 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -15.726 | ||||
| SD | 26.237 | ||||
| Sharpe ratio (Glass type estimate) | -0.599 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.596 | ||||
| df | 130.000 | ||||
| t | -0.424 | ||||
| p | 0.519 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.371 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.174 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.369 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.177 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.754 | ||||
| Upside Potential Ratio | 2.571 | ||||
| Upside part of mean | 53.625 | ||||
| Downside part of mean | -69.351 | ||||
| Upside SD | 15.784 | ||||
| Downside SD | 20.855 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 96.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.815 | ||||
| Mean of criterion | -15.726 | ||||
| SD of predictor | 0.512 | ||||
| SD of criterion | 26.237 | ||||
| Covariance | -0.088 | ||||
| r | -0.007 | ||||
| b (slope, estimate of beta) | -0.337 | ||||
| a (intercept, estimate of alpha) | -15.452 | ||||
| Mean Square Error | 693.675 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.075 | ||||
| p(b) | 0.504 | ||||
| t(a) | -0.413 | ||||
| p(a) | 0.523 | ||||
| Lowerbound of 95% confidence interval for beta | -9.261 | ||||
| Upperbound of 95% confidence interval for beta | 8.587 | ||||
| Lowerbound of 95% confidence interval for alpha | -89.504 | ||||
| Upperbound of 95% confidence interval for alpha | 58.601 | ||||
| Treynor index (mean / b) | 46.685 | ||||
| Jensen alpha (a) | -15.452 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.935 | ||||
| Expected Shortfall on VaR | 0.962 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.228 | ||||
| Expected Shortfall on VaR | 0.466 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.941 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.028 | ||||
| Maximum | 2977.000 | ||||
| Mean of quarter 1 | 0.698 | ||||
| Mean of quarter 2 | 0.990 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 120.946 | ||||
| Inter Quartile Range | 0.086 | ||||
| Number outliers low | 17.000 | ||||
| Percentage of outliers low | 0.130 | ||||
| Mean of outliers low | 0.528 | ||||
| Number of outliers high | 18.000 | ||||
| Percentage of outliers high | 0.137 | ||||
| Mean of outliers high | 220.841 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.154 | ||||
| VaR(95%) (moments method) | 0.204 | ||||
| Expected Shortfall (moments method) | 0.326 | ||||
| Extreme Value Index (regression method) | -1.103 | ||||
| VaR(95%) (regression method) | 0.284 | ||||
| Expected Shortfall (regression method) | 0.308 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.204 | ||||
| Quartile 1 | 0.413 | ||||
| Median | 0.421 | ||||
| Quartile 3 | 0.909 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.309 | ||||
| Mean of quarter 2 | 0.421 | ||||
| Mean of quarter 3 | 0.909 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.496 | ||||
| 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) | -1.999 | ||||
| Compounded annual return (geometric extrapolation) | -1.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.000 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.040 | ||||