Advanced Statistics: EUR Macro
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 | -0.066 | ||||
| SD | 0.037 | ||||
| Sharpe ratio (Glass type estimate) | -1.793 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.752 | ||||
| df | 33.000 | ||||
| t | -3.018 | ||||
| p | 0.998 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.022 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.539 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.990 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.513 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.611 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.066 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.606 | ||||
| Mean of criterion | -0.066 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 0.037 | ||||
| Covariance | 0.000 | ||||
| r | 0.003 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.066 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.017 | ||||
| p(b) | 0.493 | ||||
| t(a) | -2.495 | ||||
| p(a) | 0.991 | ||||
| Lowerbound of 95% confidence interval for beta | -0.048 | ||||
| Upperbound of 95% confidence interval for beta | 0.049 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.120 | ||||
| Upperbound of 95% confidence interval for alpha | -0.012 | ||||
| Treynor index (mean / b) | -163.019 | ||||
| Jensen alpha (a) | -0.066 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.067 | ||||
| SD | 0.038 | ||||
| Sharpe ratio (Glass type estimate) | -1.753 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.713 | ||||
| df | 33.000 | ||||
| t | -2.951 | ||||
| p | 0.997 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.980 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.503 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.949 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.477 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.583 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.067 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.558 | ||||
| Mean of criterion | -0.067 | ||||
| SD of predictor | 0.251 | ||||
| SD of criterion | 0.038 | ||||
| Covariance | -0.000 | ||||
| r | -0.003 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.066 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 32.000 | ||||
| t(b) | -0.018 | ||||
| p(b) | 0.507 | ||||
| t(a) | -2.424 | ||||
| p(a) | 0.989 | ||||
| Lowerbound of 95% confidence interval for beta | -0.055 | ||||
| Upperbound of 95% confidence interval for beta | 0.054 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.122 | ||||
| Upperbound of 95% confidence interval for alpha | -0.011 | ||||
| Treynor index (mean / b) | 135.419 | ||||
| Jensen alpha (a) | -0.066 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.938 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.993 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.938 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.062 | ||||
| Quartile 1 | 0.062 | ||||
| Median | 0.062 | ||||
| Quartile 3 | 0.062 | ||||
| Maximum | 0.062 | ||||
| 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) | -0.022 | ||||
| Compounded annual return (geometric extrapolation) | -0.022 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.360 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.804 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.065 | ||||
| SD | 0.043 | ||||
| Sharpe ratio (Glass type estimate) | -1.506 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.504 | ||||
| df | 750.000 | ||||
| t | -2.549 | ||||
| p | 0.995 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.665 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.345 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.664 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.344 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.655 | ||||
| Upside Potential Ratio | 0.455 | ||||
| Upside part of mean | 0.018 | ||||
| Downside part of mean | -0.083 | ||||
| Upside SD | 0.018 | ||||
| Downside SD | 0.039 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 747.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 751.000 | ||||
| Mean of predictor | 0.643 | ||||
| Mean of criterion | -0.065 | ||||
| SD of predictor | 0.340 | ||||
| SD of criterion | 0.043 | ||||
| Covariance | 0.000 | ||||
| r | 0.003 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.066 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 749.000 | ||||
| t(b) | 0.071 | ||||
| p(b) | 0.472 | ||||
| t(a) | -2.538 | ||||
| p(a) | 0.994 | ||||
| Lowerbound of 95% confidence interval for beta | -0.009 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.116 | ||||
| Upperbound of 95% confidence interval for alpha | -0.015 | ||||
| Treynor index (mean / b) | -196.854 | ||||
| Jensen alpha (a) | -0.066 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.066 | ||||
| SD | 0.044 | ||||
| Sharpe ratio (Glass type estimate) | -1.498 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.497 | ||||
| df | 750.000 | ||||
| t | -2.537 | ||||
| p | 0.994 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.658 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.338 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.657 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.337 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.637 | ||||
| Upside Potential Ratio | 0.439 | ||||
| Upside part of mean | 0.018 | ||||
| Downside part of mean | -0.084 | ||||
| Upside SD | 0.018 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 747.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 751.000 | ||||
| Mean of predictor | 0.584 | ||||
| Mean of criterion | -0.066 | ||||
| SD of predictor | 0.343 | ||||
| SD of criterion | 0.044 | ||||
| Covariance | 0.000 | ||||
| r | 0.002 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.066 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 749.000 | ||||
| t(b) | 0.061 | ||||
| p(b) | 0.476 | ||||
| t(a) | -2.528 | ||||
| p(a) | 0.994 | ||||
| Lowerbound of 95% confidence interval for beta | -0.009 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.118 | ||||
| Upperbound of 95% confidence interval for alpha | -0.015 | ||||
| Treynor index (mean / b) | -229.179 | ||||
| Jensen alpha (a) | -0.066 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 751.000 | ||||
| Minimum | 0.942 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.026 | ||||
| Mean of quarter 1 | 0.999 | ||||
| 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 | 6.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.981 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.005 | ||||
| Mean of outliers high | 1.013 | ||||
| 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) | 0.571 | ||||
| VaR(95%) (regression method) | -0.006 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.008 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.055 | ||||
| Quartile 3 | 0.078 | ||||
| Maximum | 0.102 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.102 | ||||
| Inter Quartile Range | 0.047 | ||||
| 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) | -0.022 | ||||
| Compounded annual return (geometric extrapolation) | -0.022 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.217 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.217 | ||||
| Compounded annual return / Expected Shortfall lognormal | -3.753 | ||||
| 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 | 1.059 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.518 | ||||
| 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 | 0.923 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.522 | ||||
| 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) | -8747369919163451.000 | ||||
| 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) | 208118462656863565357972971323392.000 | ||||
| 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 | ||||