Advanced Statistics: LibertyFX test
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 | 1702.975 | ||||
| SD | 3408.701 | ||||
| Sharpe ratio (Glass type estimate) | 0.500 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.492 | ||||
| df | 52.000 | ||||
| t | 1.050 | ||||
| p | 0.149 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.440 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.435 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.445 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.430 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1579.216 | ||||
| Upside Potential Ratio | 1580.918 | ||||
| Upside part of mean | 1704.810 | ||||
| Downside part of mean | -1.835 | ||||
| Upside SD | 3411.991 | ||||
| Downside SD | 1.078 | ||||
| N nonnegative terms | 30.000 | ||||
| N negative terms | 23.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.364 | ||||
| Mean of criterion | 1702.975 | ||||
| SD of predictor | 0.228 | ||||
| SD of criterion | 3408.701 | ||||
| Covariance | 45.557 | ||||
| r | 0.059 | ||||
| b (slope, estimate of beta) | 877.465 | ||||
| a (intercept, estimate of alpha) | 1383.290 | ||||
| Mean Square Error | 11806310.740 | ||||
| DF error | 51.000 | ||||
| t(b) | 0.420 | ||||
| p(b) | 0.338 | ||||
| t(a) | 0.767 | ||||
| p(a) | 0.223 | ||||
| Lowerbound of 95% confidence interval for beta | -3320.790 | ||||
| Upperbound of 95% confidence interval for beta | 5075.720 | ||||
| Lowerbound of 95% confidence interval for alpha | -2237.931 | ||||
| Upperbound of 95% confidence interval for alpha | 5004.512 | ||||
| Treynor index (mean / b) | 1.941 | ||||
| Jensen alpha (a) | 1383.290 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.073 | ||||
| SD | 7.352 | ||||
| Sharpe ratio (Glass type estimate) | 0.010 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.010 | ||||
| df | 52.000 | ||||
| t | 0.021 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.923 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.943 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.923 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.942 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.014 | ||||
| Upside Potential Ratio | 1.078 | ||||
| Upside part of mean | 5.458 | ||||
| Downside part of mean | -5.384 | ||||
| Upside SD | 5.235 | ||||
| Downside SD | 5.063 | ||||
| N nonnegative terms | 30.000 | ||||
| N negative terms | 23.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.335 | ||||
| Mean of criterion | 0.073 | ||||
| SD of predictor | 0.213 | ||||
| SD of criterion | 7.352 | ||||
| Covariance | 0.294 | ||||
| r | 0.187 | ||||
| b (slope, estimate of beta) | 6.456 | ||||
| a (intercept, estimate of alpha) | -2.088 | ||||
| Mean Square Error | 53.182 | ||||
| DF error | 51.000 | ||||
| t(b) | 1.363 | ||||
| p(b) | 0.089 | ||||
| t(a) | -0.547 | ||||
| p(a) | 0.707 | ||||
| Lowerbound of 95% confidence interval for beta | -3.055 | ||||
| Upperbound of 95% confidence interval for beta | 15.968 | ||||
| Lowerbound of 95% confidence interval for alpha | -9.748 | ||||
| Upperbound of 95% confidence interval for alpha | 5.571 | ||||
| Treynor index (mean / b) | 0.011 | ||||
| Jensen alpha (a) | -2.088 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.969 | ||||
| Expected Shortfall on VaR | 0.984 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.322 | ||||
| Expected Shortfall on VaR | 0.642 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 53.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.779 | ||||
| Median | 1.041 | ||||
| Quartile 3 | 1.363 | ||||
| Maximum | 7163.000 | ||||
| Mean of quarter 1 | 0.480 | ||||
| Mean of quarter 2 | 0.950 | ||||
| Mean of quarter 3 | 1.189 | ||||
| Mean of quarter 4 | 580.010 | ||||
| Inter Quartile Range | 0.584 | ||||
| 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 | 0.075 | ||||
| Mean of outliers high | 1881.553 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.324 | ||||
| VaR(95%) (moments method) | 0.566 | ||||
| Expected Shortfall (moments method) | 0.976 | ||||
| Extreme Value Index (regression method) | -0.666 | ||||
| VaR(95%) (regression method) | 0.494 | ||||
| Expected Shortfall (regression method) | 0.548 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.024 | ||||
| Quartile 1 | 0.239 | ||||
| Median | 0.521 | ||||
| Quartile 3 | 0.622 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.132 | ||||
| Mean of quarter 2 | 0.521 | ||||
| Mean of quarter 3 | 0.622 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.383 | ||||
| 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) | 0.154 | ||||
| Compounded annual return (geometric extrapolation) | 0.125 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.125 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.125 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.127 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1760.613 | ||||
| SD | 1839.653 | ||||
| Sharpe ratio (Glass type estimate) | 0.957 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.956 | ||||
| df | 1160.000 | ||||
| t | 2.015 | ||||
| p | 0.470 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.025 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.889 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.025 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.888 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 834.291 | ||||
| Upside Potential Ratio | 839.221 | ||||
| Upside part of mean | 1771.018 | ||||
| Downside part of mean | -10.404 | ||||
| Upside SD | 1842.073 | ||||
| Downside SD | 2.110 | ||||
| N nonnegative terms | 521.000 | ||||
| N negative terms | 640.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1161.000 | ||||
| Mean of predictor | 0.389 | ||||
| Mean of criterion | 1760.613 | ||||
| SD of predictor | 0.254 | ||||
| SD of criterion | 1839.653 | ||||
| Covariance | 19.037 | ||||
| r | 0.041 | ||||
| b (slope, estimate of beta) | 295.968 | ||||
| a (intercept, estimate of alpha) | 1645.415 | ||||
| Mean Square Error | 3381603.698 | ||||
| DF error | 1159.000 | ||||
| t(b) | 1.390 | ||||
| p(b) | 0.474 | ||||
| t(a) | 1.875 | ||||
| p(a) | 0.465 | ||||
| Lowerbound of 95% confidence interval for beta | -121.722 | ||||
| Upperbound of 95% confidence interval for beta | 713.657 | ||||
| Lowerbound of 95% confidence interval for alpha | -76.227 | ||||
| Upperbound of 95% confidence interval for alpha | 3367.057 | ||||
| Treynor index (mean / b) | 5.949 | ||||
| Jensen alpha (a) | 1645.415 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.073 | ||||
| SD | 13.076 | ||||
| Sharpe ratio (Glass type estimate) | 0.006 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.006 | ||||
| df | 1160.000 | ||||
| t | 0.012 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.925 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.937 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.925 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.937 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.008 | ||||
| Upside Potential Ratio | 2.497 | ||||
| Upside part of mean | 23.120 | ||||
| Downside part of mean | -23.047 | ||||
| Upside SD | 9.226 | ||||
| Downside SD | 9.258 | ||||
| N nonnegative terms | 521.000 | ||||
| N negative terms | 640.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1161.000 | ||||
| Mean of predictor | 0.356 | ||||
| Mean of criterion | 0.073 | ||||
| SD of predictor | 0.256 | ||||
| SD of criterion | 13.076 | ||||
| Covariance | 0.284 | ||||
| r | 0.085 | ||||
| b (slope, estimate of beta) | 4.348 | ||||
| a (intercept, estimate of alpha) | -1.477 | ||||
| Mean Square Error | 169.884 | ||||
| DF error | 1159.000 | ||||
| t(b) | 2.903 | ||||
| p(b) | 0.446 | ||||
| t(a) | -0.238 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | 1.410 | ||||
| Upperbound of 95% confidence interval for beta | 7.286 | ||||
| Lowerbound of 95% confidence interval for alpha | -13.670 | ||||
| Upperbound of 95% confidence interval for alpha | 10.716 | ||||
| Treynor index (mean / b) | 0.017 | ||||
| Jensen alpha (a) | -1.477 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.735 | ||||
| Expected Shortfall on VaR | 0.803 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.094 | ||||
| Expected Shortfall on VaR | 0.211 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1161.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.980 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.026 | ||||
| Maximum | 3187.000 | ||||
| Mean of quarter 1 | 0.848 | ||||
| Mean of quarter 2 | 0.994 | ||||
| Mean of quarter 3 | 1.008 | ||||
| Mean of quarter 4 | 28.054 | ||||
| Inter Quartile Range | 0.045 | ||||
| Number outliers low | 125.000 | ||||
| Percentage of outliers low | 0.108 | ||||
| Mean of outliers low | 0.704 | ||||
| Number of outliers high | 120.000 | ||||
| Percentage of outliers high | 0.103 | ||||
| Mean of outliers high | 66.306 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.961 | ||||
| VaR(95%) (moments method) | 0.128 | ||||
| Expected Shortfall (moments method) | 3.544 | ||||
| Extreme Value Index (regression method) | 0.200 | ||||
| VaR(95%) (regression method) | 0.098 | ||||
| Expected Shortfall (regression method) | 0.170 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 20.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.048 | ||||
| Quartile 3 | 0.106 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.034 | ||||
| Mean of quarter 3 | 0.068 | ||||
| Mean of quarter 4 | 0.550 | ||||
| Inter Quartile Range | 0.085 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.648 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.645 | ||||
| VaR(95%) (moments method) | 0.433 | ||||
| Expected Shortfall (moments method) | 0.438 | ||||
| Extreme Value Index (regression method) | -0.704 | ||||
| VaR(95%) (regression method) | 0.789 | ||||
| Expected Shortfall (regression method) | 0.920 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.153 | ||||
| Compounded annual return (geometric extrapolation) | 0.124 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.124 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.226 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.155 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 3.657 | ||||
| SD | 1.915 | ||||
| Sharpe ratio (Glass type estimate) | 1.910 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.899 | ||||
| df | 130.000 | ||||
| t | 1.351 | ||||
| p | 0.441 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.875 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.688 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.882 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.681 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.567 | ||||
| Upside Potential Ratio | 10.358 | ||||
| Upside part of mean | 10.619 | ||||
| Downside part of mean | -6.962 | ||||
| Upside SD | 1.624 | ||||
| Downside SD | 1.025 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.218 | ||||
| Mean of criterion | 3.657 | ||||
| SD of predictor | 0.413 | ||||
| SD of criterion | 1.915 | ||||
| Covariance | 0.288 | ||||
| r | 0.364 | ||||
| b (slope, estimate of beta) | 1.687 | ||||
| a (intercept, estimate of alpha) | 1.602 | ||||
| Mean Square Error | 3.203 | ||||
| DF error | 129.000 | ||||
| t(b) | 4.445 | ||||
| p(b) | 0.273 | ||||
| t(a) | 0.623 | ||||
| p(a) | 0.465 | ||||
| Lowerbound of 95% confidence interval for beta | 0.936 | ||||
| Upperbound of 95% confidence interval for beta | 2.438 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.488 | ||||
| Upperbound of 95% confidence interval for alpha | 6.693 | ||||
| Treynor index (mean / b) | 2.167 | ||||
| Jensen alpha (a) | 1.602 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.996 | ||||
| SD | 1.798 | ||||
| Sharpe ratio (Glass type estimate) | 1.110 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.103 | ||||
| df | 130.000 | ||||
| t | 0.785 | ||||
| p | 0.466 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.667 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.883 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.672 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.879 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.687 | ||||
| Upside Potential Ratio | 8.107 | ||||
| Upside part of mean | 9.590 | ||||
| Downside part of mean | -7.595 | ||||
| Upside SD | 1.351 | ||||
| Downside SD | 1.183 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.129 | ||||
| Mean of criterion | 1.996 | ||||
| SD of predictor | 0.416 | ||||
| SD of criterion | 1.798 | ||||
| Covariance | 0.273 | ||||
| r | 0.365 | ||||
| b (slope, estimate of beta) | 1.577 | ||||
| a (intercept, estimate of alpha) | 0.215 | ||||
| Mean Square Error | 2.824 | ||||
| DF error | 129.000 | ||||
| t(b) | 4.454 | ||||
| p(b) | 0.273 | ||||
| t(a) | 0.089 | ||||
| p(a) | 0.495 | ||||
| Lowerbound of 95% confidence interval for beta | 0.876 | ||||
| Upperbound of 95% confidence interval for beta | 2.277 | ||||
| Lowerbound of 95% confidence interval for alpha | -4.553 | ||||
| Upperbound of 95% confidence interval for alpha | 4.983 | ||||
| Treynor index (mean / b) | 1.266 | ||||
| Jensen alpha (a) | 0.215 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.161 | ||||
| Expected Shortfall on VaR | 0.198 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.064 | ||||
| Expected Shortfall on VaR | 0.132 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.606 | ||||
| Quartile 1 | 0.973 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.054 | ||||
| Maximum | 1.778 | ||||
| Mean of quarter 1 | 0.903 | ||||
| Mean of quarter 2 | 0.992 | ||||
| Mean of quarter 3 | 1.018 | ||||
| Mean of quarter 4 | 1.144 | ||||
| Inter Quartile Range | 0.081 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.038 | ||||
| Mean of outliers low | 0.742 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.366 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.391 | ||||
| VaR(95%) (moments method) | 0.092 | ||||
| Expected Shortfall (moments method) | 0.179 | ||||
| Extreme Value Index (regression method) | 0.182 | ||||
| VaR(95%) (regression method) | 0.101 | ||||
| Expected Shortfall (regression method) | 0.163 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.033 | ||||
| Median | 0.090 | ||||
| Quartile 3 | 0.122 | ||||
| Maximum | 0.622 | ||||
| Mean of quarter 1 | 0.021 | ||||
| Mean of quarter 2 | 0.066 | ||||
| Mean of quarter 3 | 0.117 | ||||
| Mean of quarter 4 | 0.516 | ||||
| Inter Quartile Range | 0.089 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.222 | ||||
| Mean of outliers high | 0.516 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -21.552 | ||||
| VaR(95%) (moments method) | 0.303 | ||||
| Expected Shortfall (moments method) | 0.303 | ||||
| Extreme Value Index (regression method) | -1.449 | ||||
| VaR(95%) (regression method) | 0.786 | ||||
| Expected Shortfall (regression method) | 0.818 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 3.546 | ||||
| Compounded annual return (geometric extrapolation) | 6.689 | ||||
| Calmar ratio (compounded annual return / max draw down) | 10.748 | ||||
| Compounded annual return / average of 25% largest draw downs | 12.951 | ||||
| Compounded annual return / Expected Shortfall lognormal | 33.776 | ||||