Advanced Statistics: FX HE-MAN
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 | 0.103 | ||||
| SD | 0.652 | ||||
| Sharpe ratio (Glass type estimate) | 0.158 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.155 | ||||
| df | 42.000 | ||||
| t | 0.300 | ||||
| p | 0.383 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.879 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.193 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.881 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.191 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.234 | ||||
| Upside Potential Ratio | 1.905 | ||||
| Upside part of mean | 0.840 | ||||
| Downside part of mean | -0.736 | ||||
| Upside SD | 0.472 | ||||
| Downside SD | 0.441 | ||||
| N nonnegative terms | 24.000 | ||||
| N negative terms | 19.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 43.000 | ||||
| Mean of predictor | 0.456 | ||||
| Mean of criterion | 0.103 | ||||
| SD of predictor | 0.277 | ||||
| SD of criterion | 0.652 | ||||
| Covariance | 0.082 | ||||
| r | 0.452 | ||||
| b (slope, estimate of beta) | 1.064 | ||||
| a (intercept, estimate of alpha) | -0.382 | ||||
| Mean Square Error | 0.347 | ||||
| DF error | 41.000 | ||||
| t(b) | 3.245 | ||||
| p(b) | 0.001 | ||||
| t(a) | -1.106 | ||||
| p(a) | 0.862 | ||||
| Lowerbound of 95% confidence interval for beta | 0.402 | ||||
| Upperbound of 95% confidence interval for beta | 1.727 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.079 | ||||
| Upperbound of 95% confidence interval for alpha | 0.315 | ||||
| Treynor index (mean / b) | 0.097 | ||||
| Jensen alpha (a) | -0.382 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.115 | ||||
| SD | 0.685 | ||||
| Sharpe ratio (Glass type estimate) | -0.168 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.165 | ||||
| df | 42.000 | ||||
| t | -0.319 | ||||
| p | 0.624 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.203 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.869 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.201 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.871 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.212 | ||||
| Upside Potential Ratio | 1.374 | ||||
| Upside part of mean | 0.746 | ||||
| Downside part of mean | -0.861 | ||||
| Upside SD | 0.406 | ||||
| Downside SD | 0.543 | ||||
| N nonnegative terms | 24.000 | ||||
| N negative terms | 19.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 43.000 | ||||
| Mean of predictor | 0.411 | ||||
| Mean of criterion | -0.115 | ||||
| SD of predictor | 0.267 | ||||
| SD of criterion | 0.685 | ||||
| Covariance | 0.084 | ||||
| r | 0.460 | ||||
| b (slope, estimate of beta) | 1.182 | ||||
| a (intercept, estimate of alpha) | -0.601 | ||||
| Mean Square Error | 0.379 | ||||
| DF error | 41.000 | ||||
| t(b) | 3.317 | ||||
| p(b) | 0.001 | ||||
| t(a) | -1.685 | ||||
| p(a) | 0.950 | ||||
| Lowerbound of 95% confidence interval for beta | 0.462 | ||||
| Upperbound of 95% confidence interval for beta | 1.901 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.321 | ||||
| Upperbound of 95% confidence interval for alpha | 0.119 | ||||
| Treynor index (mean / b) | -0.098 | ||||
| Jensen alpha (a) | -0.601 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.285 | ||||
| Expected Shortfall on VaR | 0.340 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.130 | ||||
| Expected Shortfall on VaR | 0.262 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 43.000 | ||||
| Minimum | 0.520 | ||||
| Quartile 1 | 0.929 | ||||
| Median | 1.011 | ||||
| Quartile 3 | 1.097 | ||||
| Maximum | 1.437 | ||||
| Mean of quarter 1 | 0.787 | ||||
| Mean of quarter 2 | 0.981 | ||||
| Mean of quarter 3 | 1.046 | ||||
| Mean of quarter 4 | 1.238 | ||||
| Inter Quartile Range | 0.168 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.520 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.070 | ||||
| Mean of outliers high | 1.424 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.089 | ||||
| VaR(95%) (moments method) | 0.188 | ||||
| Expected Shortfall (moments method) | 0.251 | ||||
| Extreme Value Index (regression method) | -0.427 | ||||
| VaR(95%) (regression method) | 0.208 | ||||
| Expected Shortfall (regression method) | 0.247 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.073 | ||||
| Median | 0.145 | ||||
| Quartile 3 | 0.448 | ||||
| Maximum | 0.751 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.145 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.751 | ||||
| Inter Quartile Range | 0.375 | ||||
| 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) | -0.063 | ||||
| Compounded annual return (geometric extrapolation) | -0.069 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.092 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.092 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.203 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 6138.038 | ||||
| SD | 11669.302 | ||||
| Sharpe ratio (Glass type estimate) | 0.526 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.526 | ||||
| df | 946.000 | ||||
| t | 1.000 | ||||
| p | 0.159 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.505 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.557 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.506 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.557 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 7528.988 | ||||
| Upside Potential Ratio | 7534.406 | ||||
| Upside part of mean | 6142.455 | ||||
| Downside part of mean | -4.417 | ||||
| Upside SD | 11669.302 | ||||
| Downside SD | 0.815 | ||||
| N nonnegative terms | 434.000 | ||||
| N negative terms | 513.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 947.000 | ||||
| Mean of predictor | 0.471 | ||||
| Mean of criterion | 6138.038 | ||||
| SD of predictor | 0.306 | ||||
| SD of criterion | 11669.302 | ||||
| Covariance | 203.638 | ||||
| r | 0.057 | ||||
| b (slope, estimate of beta) | 2175.946 | ||||
| a (intercept, estimate of alpha) | 5113.871 | ||||
| Mean Square Error | 135873123.933 | ||||
| DF error | 945.000 | ||||
| t(b) | 1.756 | ||||
| p(b) | 0.040 | ||||
| t(a) | 0.830 | ||||
| p(a) | 0.203 | ||||
| Lowerbound of 95% confidence interval for beta | -255.251 | ||||
| Upperbound of 95% confidence interval for beta | 4607.144 | ||||
| Lowerbound of 95% confidence interval for alpha | -6972.679 | ||||
| Upperbound of 95% confidence interval for alpha | 17200.421 | ||||
| Treynor index (mean / b) | 2.821 | ||||
| Jensen alpha (a) | 5113.871 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.115 | ||||
| SD | 7.575 | ||||
| Sharpe ratio (Glass type estimate) | -0.015 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.015 | ||||
| df | 946.000 | ||||
| t | -0.029 | ||||
| p | 0.511 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.046 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.016 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.046 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.016 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.021 | ||||
| Upside Potential Ratio | 1.308 | ||||
| Upside part of mean | 7.061 | ||||
| Downside part of mean | -7.176 | ||||
| Upside SD | 5.308 | ||||
| Downside SD | 5.399 | ||||
| N nonnegative terms | 434.000 | ||||
| N negative terms | 513.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 947.000 | ||||
| Mean of predictor | 0.423 | ||||
| Mean of criterion | -0.115 | ||||
| SD of predictor | 0.307 | ||||
| SD of criterion | 7.575 | ||||
| Covariance | 0.497 | ||||
| r | 0.214 | ||||
| b (slope, estimate of beta) | 5.272 | ||||
| a (intercept, estimate of alpha) | -2.346 | ||||
| Mean Square Error | 54.817 | ||||
| DF error | 945.000 | ||||
| t(b) | 6.727 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.600 | ||||
| p(a) | 0.726 | ||||
| Lowerbound of 95% confidence interval for beta | 3.734 | ||||
| Upperbound of 95% confidence interval for beta | 6.810 | ||||
| Lowerbound of 95% confidence interval for alpha | -10.017 | ||||
| Upperbound of 95% confidence interval for alpha | 5.324 | ||||
| Treynor index (mean / b) | -0.022 | ||||
| Jensen alpha (a) | -2.346 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.537 | ||||
| Expected Shortfall on VaR | 0.614 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.040 | ||||
| Expected Shortfall on VaR | 0.088 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 947.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.985 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.015 | ||||
| Maximum | 22186.500 | ||||
| Mean of quarter 1 | 0.937 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.005 | ||||
| Mean of quarter 4 | 94.674 | ||||
| Inter Quartile Range | 0.030 | ||||
| Number outliers low | 86.000 | ||||
| Percentage of outliers low | 0.091 | ||||
| Mean of outliers low | 0.884 | ||||
| Number of outliers high | 79.000 | ||||
| Percentage of outliers high | 0.083 | ||||
| Mean of outliers high | 281.959 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.360 | ||||
| VaR(95%) (moments method) | 0.052 | ||||
| Expected Shortfall (moments method) | 0.100 | ||||
| Extreme Value Index (regression method) | 0.203 | ||||
| VaR(95%) (regression method) | 0.054 | ||||
| Expected Shortfall (regression method) | 0.089 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 15.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.058 | ||||
| Quartile 3 | 0.095 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.041 | ||||
| Mean of quarter 3 | 0.075 | ||||
| Mean of quarter 4 | 0.359 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.067 | ||||
| Mean of outliers high | 1.000 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.768 | ||||
| VaR(95%) (moments method) | 0.376 | ||||
| Expected Shortfall (moments method) | 1.759 | ||||
| Extreme Value Index (regression method) | 1.789 | ||||
| VaR(95%) (regression method) | 0.508 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.062 | ||||
| Compounded annual return (geometric extrapolation) | -0.068 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.068 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.190 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.111 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 44370.824 | ||||
| SD | 31375.036 | ||||
| Sharpe ratio (Glass type estimate) | 1.414 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.406 | ||||
| df | 130.000 | ||||
| t | 1.000 | ||||
| p | 0.456 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.366 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.189 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.371 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.183 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 25050.757 | ||||
| Upside Potential Ratio | 25056.563 | ||||
| Upside part of mean | 44381.107 | ||||
| Downside part of mean | -10.283 | ||||
| Upside SD | 31375.035 | ||||
| Downside SD | 1.771 | ||||
| N nonnegative terms | 54.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.132 | ||||
| Mean of criterion | 44370.824 | ||||
| SD of predictor | 0.505 | ||||
| SD of criterion | 31375.036 | ||||
| Covariance | 1368.702 | ||||
| r | 0.086 | ||||
| b (slope, estimate of beta) | 5369.306 | ||||
| a (intercept, estimate of alpha) | 38293.332 | ||||
| Mean Square Error | 984617872.727 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.985 | ||||
| p(b) | 0.445 | ||||
| t(a) | 0.855 | ||||
| p(a) | 0.452 | ||||
| Lowerbound of 95% confidence interval for beta | -5415.398 | ||||
| Upperbound of 95% confidence interval for beta | 16154.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -50350.370 | ||||
| Upperbound of 95% confidence interval for alpha | 126937.034 | ||||
| Treynor index (mean / b) | 8.264 | ||||
| Jensen alpha (a) | 38293.332 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.060 | ||||
| SD | 20.342 | ||||
| Sharpe ratio (Glass type estimate) | -0.003 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.003 | ||||
| df | 130.000 | ||||
| t | -0.002 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.775 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.769 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.775 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.769 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.004 | ||||
| Upside Potential Ratio | 2.025 | ||||
| Upside part of mean | 29.258 | ||||
| Downside part of mean | -29.317 | ||||
| Upside SD | 14.208 | ||||
| Downside SD | 14.449 | ||||
| N nonnegative terms | 54.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.003 | ||||
| Mean of criterion | -0.060 | ||||
| SD of predictor | 0.505 | ||||
| SD of criterion | 20.342 | ||||
| Covariance | 3.292 | ||||
| r | 0.321 | ||||
| b (slope, estimate of beta) | 12.915 | ||||
| a (intercept, estimate of alpha) | -13.016 | ||||
| Mean Square Error | 374.154 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.843 | ||||
| p(b) | 0.299 | ||||
| t(a) | -0.472 | ||||
| p(a) | 0.526 | ||||
| Lowerbound of 95% confidence interval for beta | 6.267 | ||||
| Upperbound of 95% confidence interval for beta | 19.563 | ||||
| Lowerbound of 95% confidence interval for alpha | -67.548 | ||||
| Upperbound of 95% confidence interval for alpha | 41.516 | ||||
| Treynor index (mean / b) | -0.005 | ||||
| Jensen alpha (a) | -13.016 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.873 | ||||
| Expected Shortfall on VaR | 0.918 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.098 | ||||
| Expected Shortfall on VaR | 0.210 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.950 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.043 | ||||
| Maximum | 22186.500 | ||||
| Mean of quarter 1 | 0.861 | ||||
| Mean of quarter 2 | 0.983 | ||||
| Mean of quarter 3 | 1.014 | ||||
| Mean of quarter 4 | 673.427 | ||||
| Inter Quartile Range | 0.094 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.038 | ||||
| Mean of outliers low | 0.592 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.053 | ||||
| Mean of outliers high | 3170.646 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.456 | ||||
| VaR(95%) (moments method) | 0.142 | ||||
| Expected Shortfall (moments method) | 0.287 | ||||
| Extreme Value Index (regression method) | 0.458 | ||||
| VaR(95%) (regression method) | 0.120 | ||||
| Expected Shortfall (regression method) | 0.230 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.111 | ||||
| Quartile 1 | 0.333 | ||||
| Median | 0.555 | ||||
| Quartile 3 | 0.778 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.111 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.445 | ||||
| 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) | -0.016 | ||||
| Compounded annual return (geometric extrapolation) | -0.015 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.015 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.015 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.017 | ||||