Advanced Statistics: EURUSD and Oil futures
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 | -0.575 | ||||
| SD | 0.663 | ||||
| Sharpe ratio (Glass type estimate) | -0.868 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.849 | ||||
| df | 35.000 | ||||
| t | -1.503 | ||||
| p | 0.929 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.011 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.288 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.998 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.300 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.853 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.575 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.674 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.548 | ||||
| Mean of criterion | -0.575 | ||||
| SD of predictor | 0.333 | ||||
| SD of criterion | 0.663 | ||||
| Covariance | 0.062 | ||||
| r | 0.284 | ||||
| b (slope, estimate of beta) | 0.565 | ||||
| a (intercept, estimate of alpha) | -0.885 | ||||
| Mean Square Error | 0.416 | ||||
| DF error | 34.000 | ||||
| t(b) | 1.724 | ||||
| p(b) | 0.047 | ||||
| t(a) | -2.141 | ||||
| p(a) | 0.980 | ||||
| Lowerbound of 95% confidence interval for beta | -0.101 | ||||
| Upperbound of 95% confidence interval for beta | 1.231 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.725 | ||||
| Upperbound of 95% confidence interval for alpha | -0.045 | ||||
| Treynor index (mean / b) | -1.017 | ||||
| Jensen alpha (a) | -0.885 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.651 | ||||
| SD | 5.737 | ||||
| Sharpe ratio (Glass type estimate) | -0.636 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.623 | ||||
| df | 35.000 | ||||
| t | -1.102 | ||||
| p | 0.861 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.773 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.509 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.763 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.518 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.634 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -3.651 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 5.754 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.488 | ||||
| Mean of criterion | -3.651 | ||||
| SD of predictor | 0.303 | ||||
| SD of criterion | 5.737 | ||||
| Covariance | 0.425 | ||||
| r | 0.244 | ||||
| b (slope, estimate of beta) | 4.614 | ||||
| a (intercept, estimate of alpha) | -5.904 | ||||
| Mean Square Error | 31.868 | ||||
| DF error | 34.000 | ||||
| t(b) | 1.467 | ||||
| p(b) | 0.076 | ||||
| t(a) | -1.639 | ||||
| p(a) | 0.945 | ||||
| Lowerbound of 95% confidence interval for beta | -1.777 | ||||
| Upperbound of 95% confidence interval for beta | 11.004 | ||||
| Lowerbound of 95% confidence interval for alpha | -13.226 | ||||
| Upperbound of 95% confidence interval for alpha | 1.418 | ||||
| Treynor index (mean / b) | -0.791 | ||||
| Jensen alpha (a) | -5.904 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.952 | ||||
| Expected Shortfall on VaR | 0.972 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.167 | ||||
| Expected Shortfall on VaR | 0.361 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.823 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.056 | ||||
| Mean of outliers low | 0.204 | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates for a one-period unit investment (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) | -1.539 | ||||
| VaR(95%) (regression method) | 0.754 | ||||
| Expected Shortfall (regression method) | 1.168 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| 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) | -0.333 | ||||
| Compounded annual return (geometric extrapolation) | -0.973 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.973 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.001 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.635 | ||||
| SD | 0.949 | ||||
| Sharpe ratio (Glass type estimate) | -0.669 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.669 | ||||
| df | 793.000 | ||||
| t | -1.165 | ||||
| p | 0.878 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.795 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.457 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.795 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.458 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.797 | ||||
| Upside Potential Ratio | 0.722 | ||||
| Upside part of mean | 0.575 | ||||
| Downside part of mean | -1.210 | ||||
| Upside SD | 0.516 | ||||
| Downside SD | 0.797 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 786.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 794.000 | ||||
| Mean of predictor | 0.564 | ||||
| Mean of criterion | -0.635 | ||||
| SD of predictor | 0.370 | ||||
| SD of criterion | 0.949 | ||||
| Covariance | 0.019 | ||||
| r | 0.055 | ||||
| b (slope, estimate of beta) | 0.141 | ||||
| a (intercept, estimate of alpha) | -0.714 | ||||
| Mean Square Error | 0.898 | ||||
| DF error | 792.000 | ||||
| t(b) | 1.545 | ||||
| p(b) | 0.061 | ||||
| t(a) | -1.306 | ||||
| p(a) | 0.904 | ||||
| Lowerbound of 95% confidence interval for beta | -0.038 | ||||
| Upperbound of 95% confidence interval for beta | 0.319 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.788 | ||||
| Upperbound of 95% confidence interval for alpha | 0.359 | ||||
| Treynor index (mean / b) | -4.516 | ||||
| Jensen alpha (a) | -0.714 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.614 | ||||
| SD | 5.272 | ||||
| Sharpe ratio (Glass type estimate) | -0.686 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.685 | ||||
| df | 793.000 | ||||
| t | -1.193 | ||||
| p | 0.883 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.812 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.441 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.811 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.441 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.687 | ||||
| Upside Potential Ratio | 0.091 | ||||
| Upside part of mean | 0.480 | ||||
| Downside part of mean | -4.094 | ||||
| Upside SD | 0.403 | ||||
| Downside SD | 5.258 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 786.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 794.000 | ||||
| Mean of predictor | 0.496 | ||||
| Mean of criterion | -3.614 | ||||
| SD of predictor | 0.366 | ||||
| SD of criterion | 5.272 | ||||
| Covariance | 0.033 | ||||
| r | 0.017 | ||||
| b (slope, estimate of beta) | 0.246 | ||||
| a (intercept, estimate of alpha) | -3.737 | ||||
| Mean Square Error | 27.821 | ||||
| DF error | 792.000 | ||||
| t(b) | 0.482 | ||||
| p(b) | 0.315 | ||||
| t(a) | -1.229 | ||||
| p(a) | 0.890 | ||||
| Lowerbound of 95% confidence interval for beta | -0.757 | ||||
| Upperbound of 95% confidence interval for beta | 1.250 | ||||
| Lowerbound of 95% confidence interval for alpha | -9.705 | ||||
| Upperbound of 95% confidence interval for alpha | 2.232 | ||||
| Treynor index (mean / b) | -14.672 | ||||
| Jensen alpha (a) | -3.737 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.423 | ||||
| Expected Shortfall on VaR | 0.493 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 794.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.778 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.016 | ||||
| Mean of outliers low | 0.728 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.010 | ||||
| Mean of outliers high | 1.218 | ||||
| Risk estimates for a one-period unit investment (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) | 0.404 | ||||
| VaR(95%) (regression method) | -0.091 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| 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) | -0.330 | ||||
| Compounded annual return (geometric extrapolation) | -0.972 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.972 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.972 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.934 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.450 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.832 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.450 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.000 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8742378296813852.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | 146747567740221984655886841282560.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| 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 for a one-period unit investment (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 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||