Advanced Statistics: Relax 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 | 0.221 | ||||
| SD | 0.857 | ||||
| Sharpe ratio (Glass type estimate) | 0.257 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.254 | ||||
| df | 60.000 | ||||
| t | 0.580 | ||||
| p | 0.282 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.614 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.127 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.616 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.124 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.461 | ||||
| Upside Potential Ratio | 2.556 | ||||
| Upside part of mean | 1.222 | ||||
| Downside part of mean | -1.001 | ||||
| Upside SD | 0.706 | ||||
| Downside SD | 0.478 | ||||
| N nonnegative terms | 30.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.339 | ||||
| Mean of criterion | 0.221 | ||||
| SD of predictor | 0.244 | ||||
| SD of criterion | 0.857 | ||||
| Covariance | -0.012 | ||||
| r | -0.058 | ||||
| b (slope, estimate of beta) | -0.203 | ||||
| a (intercept, estimate of alpha) | 0.289 | ||||
| Mean Square Error | 0.745 | ||||
| DF error | 59.000 | ||||
| t(b) | -0.444 | ||||
| p(b) | 0.671 | ||||
| t(a) | 0.700 | ||||
| p(a) | 0.243 | ||||
| Lowerbound of 95% confidence interval for beta | -1.118 | ||||
| Upperbound of 95% confidence interval for beta | 0.712 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.537 | ||||
| Upperbound of 95% confidence interval for alpha | 1.116 | ||||
| Treynor index (mean / b) | -1.087 | ||||
| Jensen alpha (a) | 0.289 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.102 | ||||
| SD | 0.798 | ||||
| Sharpe ratio (Glass type estimate) | -0.128 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.127 | ||||
| df | 60.000 | ||||
| t | -0.289 | ||||
| p | 0.613 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.997 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.742 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.996 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.743 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.183 | ||||
| Upside Potential Ratio | 1.850 | ||||
| Upside part of mean | 1.036 | ||||
| Downside part of mean | -1.138 | ||||
| Upside SD | 0.560 | ||||
| Downside SD | 0.560 | ||||
| N nonnegative terms | 30.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.305 | ||||
| Mean of criterion | -0.102 | ||||
| SD of predictor | 0.237 | ||||
| SD of criterion | 0.798 | ||||
| Covariance | -0.008 | ||||
| r | -0.040 | ||||
| b (slope, estimate of beta) | -0.134 | ||||
| a (intercept, estimate of alpha) | -0.061 | ||||
| Mean Square Error | 0.646 | ||||
| DF error | 59.000 | ||||
| t(b) | -0.307 | ||||
| p(b) | 0.620 | ||||
| t(a) | -0.161 | ||||
| p(a) | 0.564 | ||||
| Lowerbound of 95% confidence interval for beta | -1.009 | ||||
| Upperbound of 95% confidence interval for beta | 0.740 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.823 | ||||
| Upperbound of 95% confidence interval for alpha | 0.700 | ||||
| Treynor index (mean / b) | 0.762 | ||||
| Jensen alpha (a) | -0.061 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.321 | ||||
| Expected Shortfall on VaR | 0.381 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.197 | ||||
| Expected Shortfall on VaR | 0.333 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.572 | ||||
| Quartile 1 | 0.844 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.161 | ||||
| Maximum | 1.983 | ||||
| Mean of quarter 1 | 0.757 | ||||
| Mean of quarter 2 | 0.927 | ||||
| Mean of quarter 3 | 1.071 | ||||
| Mean of quarter 4 | 1.350 | ||||
| Inter Quartile Range | 0.317 | ||||
| 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 | 0.016 | ||||
| Mean of outliers high | 1.983 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.718 | ||||
| VaR(95%) (moments method) | 0.267 | ||||
| Expected Shortfall (moments method) | 0.288 | ||||
| Extreme Value Index (regression method) | 0.170 | ||||
| VaR(95%) (regression method) | 0.224 | ||||
| Expected Shortfall (regression method) | 0.280 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.110 | ||||
| Quartile 1 | 0.112 | ||||
| Median | 0.116 | ||||
| Quartile 3 | 0.378 | ||||
| Maximum | 0.897 | ||||
| Mean of quarter 1 | 0.111 | ||||
| Mean of quarter 2 | 0.116 | ||||
| Mean of quarter 3 | 0.378 | ||||
| Mean of quarter 4 | 0.897 | ||||
| Inter Quartile Range | 0.265 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.897 | ||||
| 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) | -0.050 | ||||
| Compounded annual return (geometric extrapolation) | -0.057 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.063 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.063 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.148 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.535 | ||||
| SD | 1.165 | ||||
| Sharpe ratio (Glass type estimate) | 0.459 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.459 | ||||
| df | 1348.000 | ||||
| t | 1.041 | ||||
| p | 0.486 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.405 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.323 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.405 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.322 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.763 | ||||
| Upside Potential Ratio | 7.555 | ||||
| Upside part of mean | 5.291 | ||||
| Downside part of mean | -4.757 | ||||
| Upside SD | 0.931 | ||||
| Downside SD | 0.700 | ||||
| N nonnegative terms | 653.000 | ||||
| N negative terms | 696.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1349.000 | ||||
| Mean of predictor | 0.371 | ||||
| Mean of criterion | 0.535 | ||||
| SD of predictor | 0.285 | ||||
| SD of criterion | 1.165 | ||||
| Covariance | -0.034 | ||||
| r | -0.103 | ||||
| b (slope, estimate of beta) | -0.422 | ||||
| a (intercept, estimate of alpha) | 0.691 | ||||
| Mean Square Error | 1.344 | ||||
| DF error | 1347.000 | ||||
| t(b) | -3.805 | ||||
| p(b) | 0.566 | ||||
| t(a) | 1.348 | ||||
| p(a) | 0.477 | ||||
| Lowerbound of 95% confidence interval for beta | -0.639 | ||||
| Upperbound of 95% confidence interval for beta | -0.204 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.315 | ||||
| Upperbound of 95% confidence interval for alpha | 1.696 | ||||
| Treynor index (mean / b) | -1.267 | ||||
| Jensen alpha (a) | 0.691 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.102 | ||||
| SD | 1.123 | ||||
| Sharpe ratio (Glass type estimate) | -0.090 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.090 | ||||
| df | 1348.000 | ||||
| t | -0.205 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.954 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.773 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.954 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.773 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.126 | ||||
| Upside Potential Ratio | 6.140 | ||||
| Upside part of mean | 4.949 | ||||
| Downside part of mean | -5.051 | ||||
| Upside SD | 0.782 | ||||
| Downside SD | 0.806 | ||||
| N nonnegative terms | 653.000 | ||||
| N negative terms | 696.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1349.000 | ||||
| Mean of predictor | 0.330 | ||||
| Mean of criterion | -0.102 | ||||
| SD of predictor | 0.286 | ||||
| SD of criterion | 1.123 | ||||
| Covariance | -0.036 | ||||
| r | -0.113 | ||||
| b (slope, estimate of beta) | -0.445 | ||||
| a (intercept, estimate of alpha) | 0.045 | ||||
| Mean Square Error | 1.246 | ||||
| DF error | 1347.000 | ||||
| t(b) | -4.185 | ||||
| p(b) | 0.572 | ||||
| t(a) | 0.092 | ||||
| p(a) | 0.498 | ||||
| Lowerbound of 95% confidence interval for beta | -0.654 | ||||
| Upperbound of 95% confidence interval for beta | -0.236 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.922 | ||||
| Upperbound of 95% confidence interval for alpha | 1.013 | ||||
| Treynor index (mean / b) | 0.228 | ||||
| Jensen alpha (a) | 0.045 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.108 | ||||
| Expected Shortfall on VaR | 0.133 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.088 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1349.000 | ||||
| Minimum | 0.559 | ||||
| Quartile 1 | 0.976 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.026 | ||||
| Maximum | 1.895 | ||||
| Mean of quarter 1 | 0.939 | ||||
| Mean of quarter 2 | 0.989 | ||||
| Mean of quarter 3 | 1.011 | ||||
| Mean of quarter 4 | 1.071 | ||||
| Inter Quartile Range | 0.050 | ||||
| Number outliers low | 41.000 | ||||
| Percentage of outliers low | 0.030 | ||||
| Mean of outliers low | 0.817 | ||||
| Number of outliers high | 41.000 | ||||
| Percentage of outliers high | 0.030 | ||||
| Mean of outliers high | 1.228 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.480 | ||||
| VaR(95%) (moments method) | 0.065 | ||||
| Expected Shortfall (moments method) | 0.137 | ||||
| Extreme Value Index (regression method) | 0.362 | ||||
| VaR(95%) (regression method) | 0.053 | ||||
| Expected Shortfall (regression method) | 0.092 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 17.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.026 | ||||
| Median | 0.075 | ||||
| Quartile 3 | 0.168 | ||||
| Maximum | 0.955 | ||||
| Mean of quarter 1 | 0.016 | ||||
| Mean of quarter 2 | 0.054 | ||||
| Mean of quarter 3 | 0.135 | ||||
| Mean of quarter 4 | 0.453 | ||||
| Inter Quartile Range | 0.142 | ||||
| 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 | 0.118 | ||||
| Mean of outliers high | 0.698 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.573 | ||||
| VaR(95%) (moments method) | 0.492 | ||||
| Expected Shortfall (moments method) | 1.229 | ||||
| Extreme Value Index (regression method) | 2.532 | ||||
| VaR(95%) (regression method) | 0.681 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.050 | ||||
| Compounded annual return (geometric extrapolation) | -0.056 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.059 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.123 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.419 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.055 | ||||
| SD | 0.668 | ||||
| Sharpe ratio (Glass type estimate) | 0.082 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.081 | ||||
| df | 130.000 | ||||
| t | 0.058 | ||||
| p | 0.497 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.690 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.854 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.690 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.853 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.118 | ||||
| Upside Potential Ratio | 8.145 | ||||
| Upside part of mean | 3.769 | ||||
| Downside part of mean | -3.714 | ||||
| Upside SD | 0.478 | ||||
| Downside SD | 0.463 | ||||
| N nonnegative terms | 55.000 | ||||
| N negative terms | 76.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.034 | ||||
| Mean of criterion | 0.055 | ||||
| SD of predictor | 0.486 | ||||
| SD of criterion | 0.668 | ||||
| Covariance | -0.088 | ||||
| r | -0.272 | ||||
| b (slope, estimate of beta) | -0.373 | ||||
| a (intercept, estimate of alpha) | 0.440 | ||||
| Mean Square Error | 0.416 | ||||
| DF error | 129.000 | ||||
| t(b) | -3.205 | ||||
| p(b) | 0.671 | ||||
| t(a) | 0.478 | ||||
| p(a) | 0.473 | ||||
| Lowerbound of 95% confidence interval for beta | -0.603 | ||||
| Upperbound of 95% confidence interval for beta | -0.143 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.380 | ||||
| Upperbound of 95% confidence interval for alpha | 2.261 | ||||
| Treynor index (mean / b) | -0.147 | ||||
| Jensen alpha (a) | 0.440 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.167 | ||||
| SD | 0.669 | ||||
| Sharpe ratio (Glass type estimate) | -0.250 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.248 | ||||
| df | 130.000 | ||||
| t | -0.176 | ||||
| p | 0.508 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.021 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.523 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.020 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.524 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.346 | ||||
| Upside Potential Ratio | 7.590 | ||||
| Upside part of mean | 3.660 | ||||
| Downside part of mean | -3.827 | ||||
| Upside SD | 0.460 | ||||
| Downside SD | 0.482 | ||||
| N nonnegative terms | 55.000 | ||||
| N negative terms | 76.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.914 | ||||
| Mean of criterion | -0.167 | ||||
| SD of predictor | 0.489 | ||||
| SD of criterion | 0.669 | ||||
| Covariance | -0.087 | ||||
| r | -0.265 | ||||
| b (slope, estimate of beta) | -0.363 | ||||
| a (intercept, estimate of alpha) | 0.164 | ||||
| Mean Square Error | 0.419 | ||||
| DF error | 129.000 | ||||
| t(b) | -3.121 | ||||
| p(b) | 0.667 | ||||
| t(a) | 0.178 | ||||
| p(a) | 0.490 | ||||
| Lowerbound of 95% confidence interval for beta | -0.593 | ||||
| Upperbound of 95% confidence interval for beta | -0.133 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.660 | ||||
| Upperbound of 95% confidence interval for alpha | 1.989 | ||||
| Treynor index (mean / b) | 0.460 | ||||
| Jensen alpha (a) | 0.164 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.066 | ||||
| Expected Shortfall on VaR | 0.082 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.875 | ||||
| Quartile 1 | 0.979 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.018 | ||||
| Maximum | 1.109 | ||||
| Mean of quarter 1 | 0.952 | ||||
| Mean of quarter 2 | 0.992 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.052 | ||||
| Inter Quartile Range | 0.039 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.038 | ||||
| Mean of outliers low | 0.897 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.038 | ||||
| Mean of outliers high | 1.104 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.319 | ||||
| VaR(95%) (moments method) | 0.052 | ||||
| Expected Shortfall (moments method) | 0.088 | ||||
| Extreme Value Index (regression method) | 0.145 | ||||
| VaR(95%) (regression method) | 0.050 | ||||
| Expected Shortfall (regression method) | 0.073 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.026 | ||||
| Median | 0.035 | ||||
| Quartile 3 | 0.067 | ||||
| Maximum | 0.478 | ||||
| Mean of quarter 1 | 0.020 | ||||
| Mean of quarter 2 | 0.031 | ||||
| Mean of quarter 3 | 0.065 | ||||
| Mean of quarter 4 | 0.274 | ||||
| Inter Quartile Range | 0.042 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.478 | ||||
| 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) | -0.116 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.242 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.423 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.407 | ||||