Advanced Statistics: Special 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 | 0.716 | ||||
| SD | 1.509 | ||||
| Sharpe ratio (Glass type estimate) | 0.474 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.470 | ||||
| df | 77.000 | ||||
| t | 1.209 | ||||
| p | 0.115 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.300 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.245 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.303 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.242 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.150 | ||||
| Upside Potential Ratio | 3.449 | ||||
| Upside part of mean | 1.148 | ||||
| Downside part of mean | -0.433 | ||||
| Upside SD | 1.477 | ||||
| Downside SD | 0.333 | ||||
| N nonnegative terms | 47.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 78.000 | ||||
| Mean of predictor | 0.269 | ||||
| Mean of criterion | 0.716 | ||||
| SD of predictor | 0.229 | ||||
| SD of criterion | 1.509 | ||||
| Covariance | -0.006 | ||||
| r | -0.018 | ||||
| b (slope, estimate of beta) | -0.122 | ||||
| a (intercept, estimate of alpha) | 0.749 | ||||
| Mean Square Error | 2.307 | ||||
| DF error | 76.000 | ||||
| t(b) | -0.161 | ||||
| p(b) | 0.564 | ||||
| t(a) | 1.189 | ||||
| p(a) | 0.119 | ||||
| Lowerbound of 95% confidence interval for beta | -1.629 | ||||
| Upperbound of 95% confidence interval for beta | 1.385 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.505 | ||||
| Upperbound of 95% confidence interval for alpha | 2.003 | ||||
| Treynor index (mean / b) | -5.878 | ||||
| Jensen alpha (a) | 0.749 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.258 | ||||
| SD | 0.803 | ||||
| Sharpe ratio (Glass type estimate) | 0.321 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.318 | ||||
| df | 77.000 | ||||
| t | 0.818 | ||||
| p | 0.208 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.451 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.090 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.453 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.088 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.619 | ||||
| Upside Potential Ratio | 1.833 | ||||
| Upside part of mean | 0.763 | ||||
| Downside part of mean | -0.505 | ||||
| Upside SD | 0.685 | ||||
| Downside SD | 0.416 | ||||
| N nonnegative terms | 47.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 78.000 | ||||
| Mean of predictor | 0.242 | ||||
| Mean of criterion | 0.258 | ||||
| SD of predictor | 0.217 | ||||
| SD of criterion | 0.803 | ||||
| Covariance | -0.005 | ||||
| r | -0.030 | ||||
| b (slope, estimate of beta) | -0.112 | ||||
| a (intercept, estimate of alpha) | 0.285 | ||||
| Mean Square Error | 0.653 | ||||
| DF error | 76.000 | ||||
| t(b) | -0.264 | ||||
| p(b) | 0.604 | ||||
| t(a) | 0.855 | ||||
| p(a) | 0.198 | ||||
| Lowerbound of 95% confidence interval for beta | -0.957 | ||||
| Upperbound of 95% confidence interval for beta | 0.733 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.379 | ||||
| Upperbound of 95% confidence interval for alpha | 0.948 | ||||
| Treynor index (mean / b) | -2.302 | ||||
| Jensen alpha (a) | 0.285 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.302 | ||||
| Expected Shortfall on VaR | 0.364 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.069 | ||||
| Expected Shortfall on VaR | 0.155 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 78.000 | ||||
| Minimum | 0.512 | ||||
| Quartile 1 | 0.979 | ||||
| Median | 1.017 | ||||
| Quartile 3 | 1.048 | ||||
| Maximum | 4.640 | ||||
| Mean of quarter 1 | 0.868 | ||||
| Mean of quarter 2 | 1.002 | ||||
| Mean of quarter 3 | 1.028 | ||||
| Mean of quarter 4 | 1.350 | ||||
| Inter Quartile Range | 0.069 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.103 | ||||
| Mean of outliers low | 0.736 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.128 | ||||
| Mean of outliers high | 1.635 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.793 | ||||
| VaR(95%) (moments method) | 0.121 | ||||
| Expected Shortfall (moments method) | 0.647 | ||||
| Extreme Value Index (regression method) | 0.694 | ||||
| VaR(95%) (regression method) | 0.103 | ||||
| Expected Shortfall (regression method) | 0.374 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.094 | ||||
| Quartile 1 | 0.095 | ||||
| Median | 0.232 | ||||
| Quartile 3 | 0.385 | ||||
| Maximum | 0.828 | ||||
| Mean of quarter 1 | 0.095 | ||||
| Mean of quarter 2 | 0.232 | ||||
| Mean of quarter 3 | 0.385 | ||||
| Mean of quarter 4 | 0.828 | ||||
| Inter Quartile Range | 0.290 | ||||
| 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 | 0.828 | ||||
| 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) | 0.939 | ||||
| Compounded annual return (geometric extrapolation) | 0.352 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.425 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.425 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.967 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.472 | ||||
| SD | 0.669 | ||||
| Sharpe ratio (Glass type estimate) | 0.705 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.705 | ||||
| df | 1713.000 | ||||
| t | 1.803 | ||||
| p | 0.472 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.062 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.472 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.062 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.471 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.172 | ||||
| Upside Potential Ratio | 6.579 | ||||
| Upside part of mean | 2.646 | ||||
| Downside part of mean | -2.174 | ||||
| Upside SD | 0.535 | ||||
| Downside SD | 0.402 | ||||
| N nonnegative terms | 681.000 | ||||
| N negative terms | 1033.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1714.000 | ||||
| Mean of predictor | 0.295 | ||||
| Mean of criterion | 0.472 | ||||
| SD of predictor | 0.262 | ||||
| SD of criterion | 0.669 | ||||
| Covariance | -0.017 | ||||
| r | -0.099 | ||||
| b (slope, estimate of beta) | -0.251 | ||||
| a (intercept, estimate of alpha) | 0.546 | ||||
| Mean Square Error | 0.443 | ||||
| DF error | 1712.000 | ||||
| t(b) | -4.099 | ||||
| p(b) | 0.549 | ||||
| t(a) | 2.092 | ||||
| p(a) | 0.475 | ||||
| Lowerbound of 95% confidence interval for beta | -0.371 | ||||
| Upperbound of 95% confidence interval for beta | -0.131 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.034 | ||||
| Upperbound of 95% confidence interval for alpha | 1.057 | ||||
| Treynor index (mean / b) | -1.877 | ||||
| Jensen alpha (a) | 0.546 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.256 | ||||
| SD | 0.653 | ||||
| Sharpe ratio (Glass type estimate) | 0.392 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.392 | ||||
| df | 1713.000 | ||||
| t | 1.002 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.375 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.158 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.375 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.158 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.591 | ||||
| Upside Potential Ratio | 5.823 | ||||
| Upside part of mean | 2.519 | ||||
| Downside part of mean | -2.263 | ||||
| Upside SD | 0.489 | ||||
| Downside SD | 0.432 | ||||
| N nonnegative terms | 681.000 | ||||
| N negative terms | 1033.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1714.000 | ||||
| Mean of predictor | 0.260 | ||||
| Mean of criterion | 0.256 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.653 | ||||
| Covariance | -0.018 | ||||
| r | -0.101 | ||||
| b (slope, estimate of beta) | -0.248 | ||||
| a (intercept, estimate of alpha) | 0.320 | ||||
| Mean Square Error | 0.422 | ||||
| DF error | 1712.000 | ||||
| t(b) | -4.207 | ||||
| p(b) | 0.551 | ||||
| t(a) | 1.259 | ||||
| p(a) | 0.485 | ||||
| Lowerbound of 95% confidence interval for beta | -0.364 | ||||
| Upperbound of 95% confidence interval for beta | -0.133 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.179 | ||||
| Upperbound of 95% confidence interval for alpha | 0.819 | ||||
| Treynor index (mean / b) | -1.030 | ||||
| Jensen alpha (a) | 0.320 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.063 | ||||
| Expected Shortfall on VaR | 0.079 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.046 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1714.000 | ||||
| Minimum | 0.709 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.004 | ||||
| Maximum | 1.500 | ||||
| Mean of quarter 1 | 0.968 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.039 | ||||
| Inter Quartile Range | 0.007 | ||||
| Number outliers low | 252.000 | ||||
| Percentage of outliers low | 0.147 | ||||
| Mean of outliers low | 0.950 | ||||
| Number of outliers high | 244.000 | ||||
| Percentage of outliers high | 0.142 | ||||
| Mean of outliers high | 1.063 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.751 | ||||
| VaR(95%) (moments method) | 0.021 | ||||
| Expected Shortfall (moments method) | 0.096 | ||||
| Extreme Value Index (regression method) | 0.340 | ||||
| VaR(95%) (regression method) | 0.028 | ||||
| Expected Shortfall (regression method) | 0.058 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 85.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.011 | ||||
| Quartile 3 | 0.052 | ||||
| Maximum | 0.858 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.025 | ||||
| Mean of quarter 4 | 0.209 | ||||
| Inter Quartile Range | 0.050 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.106 | ||||
| Mean of outliers high | 0.366 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.489 | ||||
| VaR(95%) (moments method) | 0.189 | ||||
| Expected Shortfall (moments method) | 0.430 | ||||
| Extreme Value Index (regression method) | 0.432 | ||||
| VaR(95%) (regression method) | 0.223 | ||||
| Expected Shortfall (regression method) | 0.479 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.933 | ||||
| Compounded annual return (geometric extrapolation) | 0.350 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.407 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.672 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.434 | ||||
| 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 | 1.056 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.471 | ||||
| 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 | 0.944 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.471 | ||||
| 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) | -8732684973147783.000 | ||||
| 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) | 1171846249862166804178762142318592.000 | ||||
| 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 | ||||