Advanced Statistics: German Forex - EUR/USD -
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 | -0.140 | ||||
| SD | 0.114 | ||||
| Sharpe ratio (Glass type estimate) | -1.225 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.197 | ||||
| df | 33.000 | ||||
| t | -2.062 | ||||
| p | 0.976 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.417 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.015 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.397 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.003 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.206 | ||||
| Upside Potential Ratio | 0.200 | ||||
| Upside part of mean | 0.023 | ||||
| Downside part of mean | -0.163 | ||||
| Upside SD | 0.029 | ||||
| Downside SD | 0.116 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.569 | ||||
| Mean of criterion | -0.140 | ||||
| SD of predictor | 0.305 | ||||
| SD of criterion | 0.114 | ||||
| Covariance | 0.001 | ||||
| r | 0.035 | ||||
| b (slope, estimate of beta) | 0.013 | ||||
| a (intercept, estimate of alpha) | -0.148 | ||||
| Mean Square Error | 0.013 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.198 | ||||
| p(b) | 0.422 | ||||
| t(a) | -1.878 | ||||
| p(a) | 0.965 | ||||
| Lowerbound of 95% confidence interval for beta | -0.122 | ||||
| Upperbound of 95% confidence interval for beta | 0.148 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.308 | ||||
| Upperbound of 95% confidence interval for alpha | 0.013 | ||||
| Treynor index (mean / b) | -10.659 | ||||
| Jensen alpha (a) | -0.148 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.147 | ||||
| SD | 0.121 | ||||
| Sharpe ratio (Glass type estimate) | -1.217 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.189 | ||||
| df | 33.000 | ||||
| t | -2.049 | ||||
| p | 0.976 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.409 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.008 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.389 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.010 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.194 | ||||
| Upside Potential Ratio | 0.184 | ||||
| Upside part of mean | 0.023 | ||||
| Downside part of mean | -0.170 | ||||
| Upside SD | 0.028 | ||||
| Downside SD | 0.123 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.514 | ||||
| Mean of criterion | -0.147 | ||||
| SD of predictor | 0.286 | ||||
| SD of criterion | 0.121 | ||||
| Covariance | 0.001 | ||||
| r | 0.032 | ||||
| b (slope, estimate of beta) | 0.014 | ||||
| a (intercept, estimate of alpha) | -0.154 | ||||
| Mean Square Error | 0.015 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.182 | ||||
| p(b) | 0.428 | ||||
| t(a) | -1.870 | ||||
| p(a) | 0.965 | ||||
| Lowerbound of 95% confidence interval for beta | -0.139 | ||||
| Upperbound of 95% confidence interval for beta | 0.166 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.322 | ||||
| Upperbound of 95% confidence interval for alpha | 0.014 | ||||
| Treynor index (mean / b) | -10.830 | ||||
| Jensen alpha (a) | -0.154 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.067 | ||||
| Expected Shortfall on VaR | 0.081 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.045 | ||||
| Expected Shortfall on VaR | 0.088 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.852 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.049 | ||||
| Mean of quarter 1 | 0.961 | ||||
| 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 | 5.000 | ||||
| Percentage of outliers low | 0.147 | ||||
| Mean of outliers low | 0.930 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.206 | ||||
| Mean of outliers high | 1.011 | ||||
| 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) | -0.111 | ||||
| VaR(95%) (regression method) | 0.075 | ||||
| Expected Shortfall (regression method) | 0.126 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.275 | ||||
| Quartile 1 | 0.275 | ||||
| Median | 0.275 | ||||
| Quartile 3 | 0.275 | ||||
| Maximum | 0.275 | ||||
| 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) | -0.089 | ||||
| Compounded annual return (geometric extrapolation) | -0.098 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.357 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.214 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.141 | ||||
| SD | 0.092 | ||||
| Sharpe ratio (Glass type estimate) | -1.525 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.524 | ||||
| df | 756.000 | ||||
| t | -2.593 | ||||
| p | 0.995 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.680 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.369 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.679 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.368 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.768 | ||||
| Upside Potential Ratio | 1.513 | ||||
| Upside part of mean | 0.121 | ||||
| Downside part of mean | -0.261 | ||||
| Upside SD | 0.047 | ||||
| Downside SD | 0.080 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 722.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 757.000 | ||||
| Mean of predictor | 0.603 | ||||
| Mean of criterion | -0.141 | ||||
| SD of predictor | 0.370 | ||||
| SD of criterion | 0.092 | ||||
| Covariance | -0.001 | ||||
| r | -0.016 | ||||
| b (slope, estimate of beta) | -0.004 | ||||
| a (intercept, estimate of alpha) | -0.138 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 755.000 | ||||
| t(b) | -0.447 | ||||
| p(b) | 0.673 | ||||
| t(a) | -2.533 | ||||
| p(a) | 0.994 | ||||
| Lowerbound of 95% confidence interval for beta | -0.022 | ||||
| Upperbound of 95% confidence interval for beta | 0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.246 | ||||
| Upperbound of 95% confidence interval for alpha | -0.031 | ||||
| Treynor index (mean / b) | 34.657 | ||||
| Jensen alpha (a) | -0.138 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.145 | ||||
| SD | 0.094 | ||||
| Sharpe ratio (Glass type estimate) | -1.550 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.548 | ||||
| df | 756.000 | ||||
| t | -2.634 | ||||
| p | 0.996 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.705 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.394 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.704 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.393 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.780 | ||||
| Upside Potential Ratio | 1.463 | ||||
| Upside part of mean | 0.119 | ||||
| Downside part of mean | -0.265 | ||||
| Upside SD | 0.047 | ||||
| Downside SD | 0.082 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 722.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 757.000 | ||||
| Mean of predictor | 0.531 | ||||
| Mean of criterion | -0.145 | ||||
| SD of predictor | 0.384 | ||||
| SD of criterion | 0.094 | ||||
| Covariance | -0.001 | ||||
| r | -0.016 | ||||
| b (slope, estimate of beta) | -0.004 | ||||
| a (intercept, estimate of alpha) | -0.143 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 755.000 | ||||
| t(b) | -0.440 | ||||
| p(b) | 0.670 | ||||
| t(a) | -2.586 | ||||
| p(a) | 0.995 | ||||
| Lowerbound of 95% confidence interval for beta | -0.021 | ||||
| Upperbound of 95% confidence interval for beta | 0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.252 | ||||
| Upperbound of 95% confidence interval for alpha | -0.034 | ||||
| Treynor index (mean / b) | 37.153 | ||||
| Jensen alpha (a) | -0.143 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 757.000 | ||||
| Minimum | 0.918 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.043 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 60.000 | ||||
| Percentage of outliers low | 0.079 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 54.000 | ||||
| Percentage of outliers high | 0.071 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.442 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | -0.005 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | 0.011 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.072 | ||||
| Median | 0.142 | ||||
| Quartile 3 | 0.213 | ||||
| Maximum | 0.283 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.283 | ||||
| Inter Quartile Range | 0.141 | ||||
| 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) | -0.088 | ||||
| Compounded annual return (geometric extrapolation) | -0.096 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.340 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.340 | ||||
| Compounded annual return / Expected Shortfall lognormal | -7.753 | ||||
| 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 | 0.992 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.477 | ||||
| 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 | 0.878 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.475 | ||||
| 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) | -8742644254916121.000 | ||||
| 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) | NA | ||||
| 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 | ||||