Advanced Statistics: positive forex
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 | -0.129 | ||||
| SD | 0.526 | ||||
| Sharpe ratio (Glass type estimate) | -0.246 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.244 | ||||
| df | 88.000 | ||||
| t | -0.670 | ||||
| p | 0.748 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.966 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.475 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.964 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.477 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.298 | ||||
| Upside Potential Ratio | 0.607 | ||||
| Upside part of mean | 0.263 | ||||
| Downside part of mean | -0.392 | ||||
| Upside SD | 0.295 | ||||
| Downside SD | 0.434 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 89.000 | ||||
| Mean of predictor | 0.208 | ||||
| Mean of criterion | -0.129 | ||||
| SD of predictor | 0.306 | ||||
| SD of criterion | 0.526 | ||||
| Covariance | 0.030 | ||||
| r | 0.189 | ||||
| b (slope, estimate of beta) | 0.325 | ||||
| a (intercept, estimate of alpha) | -0.197 | ||||
| Mean Square Error | 0.270 | ||||
| DF error | 87.000 | ||||
| t(b) | 1.792 | ||||
| p(b) | 0.038 | ||||
| t(a) | -1.013 | ||||
| p(a) | 0.843 | ||||
| Lowerbound of 95% confidence interval for beta | -0.035 | ||||
| Upperbound of 95% confidence interval for beta | 0.685 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.584 | ||||
| Upperbound of 95% confidence interval for alpha | 0.190 | ||||
| Treynor index (mean / b) | -0.398 | ||||
| Jensen alpha (a) | -0.197 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.333 | ||||
| SD | 0.721 | ||||
| Sharpe ratio (Glass type estimate) | -0.461 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.457 | ||||
| df | 88.000 | ||||
| t | -1.256 | ||||
| p | 0.894 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.183 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.263 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.180 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.266 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.488 | ||||
| Upside Potential Ratio | 0.335 | ||||
| Upside part of mean | 0.229 | ||||
| Downside part of mean | -0.561 | ||||
| Upside SD | 0.243 | ||||
| Downside SD | 0.682 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 89.000 | ||||
| Mean of predictor | 0.162 | ||||
| Mean of criterion | -0.333 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.721 | ||||
| Covariance | 0.044 | ||||
| r | 0.203 | ||||
| b (slope, estimate of beta) | 0.490 | ||||
| a (intercept, estimate of alpha) | -0.412 | ||||
| Mean Square Error | 0.505 | ||||
| DF error | 87.000 | ||||
| t(b) | 1.937 | ||||
| p(b) | 0.028 | ||||
| t(a) | -1.560 | ||||
| p(a) | 0.939 | ||||
| Lowerbound of 95% confidence interval for beta | -0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.993 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.937 | ||||
| Upperbound of 95% confidence interval for alpha | 0.113 | ||||
| Treynor index (mean / b) | -0.679 | ||||
| Jensen alpha (a) | -0.412 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.309 | ||||
| Expected Shortfall on VaR | 0.365 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.104 | ||||
| Expected Shortfall on VaR | 0.227 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 89.000 | ||||
| Minimum | 0.306 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.593 | ||||
| Mean of quarter 1 | 0.886 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.091 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 14.000 | ||||
| Percentage of outliers low | 0.157 | ||||
| Mean of outliers low | 0.812 | ||||
| Number of outliers high | 16.000 | ||||
| Percentage of outliers high | 0.180 | ||||
| Mean of outliers high | 1.125 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.064 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.221 | ||||
| Quartile 1 | 0.405 | ||||
| Median | 0.589 | ||||
| Quartile 3 | 0.773 | ||||
| Maximum | 0.957 | ||||
| Mean of quarter 1 | 0.221 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.957 | ||||
| Inter Quartile Range | 0.368 | ||||
| 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) | -0.119 | ||||
| Compounded annual return (geometric extrapolation) | -0.251 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.262 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.262 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.687 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 4.258 | ||||
| SD | 5.496 | ||||
| Sharpe ratio (Glass type estimate) | 0.775 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.774 | ||||
| df | 1959.000 | ||||
| t | 2.119 | ||||
| p | 0.470 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.058 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.492 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.057 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.491 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.978 | ||||
| Upside Potential Ratio | 6.663 | ||||
| Upside part of mean | 7.133 | ||||
| Downside part of mean | -2.875 | ||||
| Upside SD | 5.396 | ||||
| Downside SD | 1.071 | ||||
| N nonnegative terms | 273.000 | ||||
| N negative terms | 1687.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1960.000 | ||||
| Mean of predictor | 0.365 | ||||
| Mean of criterion | 4.258 | ||||
| SD of predictor | 0.620 | ||||
| SD of criterion | 5.496 | ||||
| Covariance | 0.584 | ||||
| r | 0.171 | ||||
| b (slope, estimate of beta) | 1.518 | ||||
| a (intercept, estimate of alpha) | 3.705 | ||||
| Mean Square Error | 29.336 | ||||
| DF error | 1958.000 | ||||
| t(b) | 7.692 | ||||
| p(b) | 0.414 | ||||
| t(a) | 1.870 | ||||
| p(a) | 0.479 | ||||
| Lowerbound of 95% confidence interval for beta | 1.131 | ||||
| Upperbound of 95% confidence interval for beta | 1.905 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.181 | ||||
| Upperbound of 95% confidence interval for alpha | 7.591 | ||||
| Treynor index (mean / b) | 2.806 | ||||
| Jensen alpha (a) | 3.705 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.330 | ||||
| SD | 2.686 | ||||
| Sharpe ratio (Glass type estimate) | -0.123 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.123 | ||||
| df | 1959.000 | ||||
| t | -0.336 | ||||
| p | 0.505 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.840 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.594 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.840 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.594 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.172 | ||||
| Upside Potential Ratio | 1.954 | ||||
| Upside part of mean | 3.746 | ||||
| Downside part of mean | -4.076 | ||||
| Upside SD | 1.881 | ||||
| Downside SD | 1.917 | ||||
| N nonnegative terms | 273.000 | ||||
| N negative terms | 1687.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1960.000 | ||||
| Mean of predictor | 0.175 | ||||
| Mean of criterion | -0.330 | ||||
| SD of predictor | 0.616 | ||||
| SD of criterion | 2.686 | ||||
| Covariance | 0.270 | ||||
| r | 0.163 | ||||
| b (slope, estimate of beta) | 0.712 | ||||
| a (intercept, estimate of alpha) | -0.455 | ||||
| Mean Square Error | 7.025 | ||||
| DF error | 1958.000 | ||||
| t(b) | 7.329 | ||||
| p(b) | 0.418 | ||||
| t(a) | -0.469 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | 0.522 | ||||
| Upperbound of 95% confidence interval for beta | 0.903 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.356 | ||||
| Upperbound of 95% confidence interval for alpha | 1.446 | ||||
| Treynor index (mean / b) | -0.464 | ||||
| Jensen alpha (a) | -0.455 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.240 | ||||
| Expected Shortfall on VaR | 0.289 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.078 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1960.000 | ||||
| Minimum | 0.084 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 11.928 | ||||
| Mean of quarter 1 | 0.957 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.109 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 239.000 | ||||
| Percentage of outliers low | 0.122 | ||||
| Mean of outliers low | 0.911 | ||||
| Number of outliers high | 290.000 | ||||
| Percentage of outliers high | 0.148 | ||||
| Mean of outliers high | 1.184 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.915 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| 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 | 10.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.012 | ||||
| Median | 0.041 | ||||
| Quartile 3 | 0.284 | ||||
| Maximum | 0.976 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | 0.017 | ||||
| Mean of quarter 3 | 0.070 | ||||
| Mean of quarter 4 | 0.753 | ||||
| Inter Quartile Range | 0.272 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.954 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -914.629 | ||||
| VaR(95%) (moments method) | 0.703 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -4.706 | ||||
| VaR(95%) (regression method) | 2.012 | ||||
| Expected Shortfall (regression method) | 2.012 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.118 | ||||
| Compounded annual return (geometric extrapolation) | -0.249 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.255 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.331 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.860 | ||||
| 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 | 1.051 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.528 | ||||
| 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 | 0.909 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.534 | ||||
| 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) | -8751152881993862.000 | ||||
| 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) | 98434155577660262826208856637440.000 | ||||
| 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 | ||||