Advanced Statistics: Professional 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 | 0.088 | ||||
| SD | 0.340 | ||||
| Sharpe ratio (Glass type estimate) | 0.257 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.255 | ||||
| df | 80.000 | ||||
| t | 0.668 | ||||
| p | 0.253 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.499 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.012 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.501 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.010 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.470 | ||||
| Upside Potential Ratio | 2.066 | ||||
| Upside part of mean | 0.385 | ||||
| Downside part of mean | -0.297 | ||||
| Upside SD | 0.283 | ||||
| Downside SD | 0.186 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 81.000 | ||||
| Mean of predictor | 0.270 | ||||
| Mean of criterion | 0.088 | ||||
| SD of predictor | 0.215 | ||||
| SD of criterion | 0.340 | ||||
| Covariance | -0.009 | ||||
| r | -0.128 | ||||
| b (slope, estimate of beta) | -0.204 | ||||
| a (intercept, estimate of alpha) | 0.143 | ||||
| Mean Square Error | 0.115 | ||||
| DF error | 79.000 | ||||
| t(b) | -1.151 | ||||
| p(b) | 0.873 | ||||
| t(a) | 1.025 | ||||
| p(a) | 0.154 | ||||
| Lowerbound of 95% confidence interval for beta | -0.556 | ||||
| Upperbound of 95% confidence interval for beta | 0.148 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.134 | ||||
| Upperbound of 95% confidence interval for alpha | 0.420 | ||||
| Treynor index (mean / b) | -0.430 | ||||
| Jensen alpha (a) | 0.143 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.034 | ||||
| SD | 0.323 | ||||
| Sharpe ratio (Glass type estimate) | 0.106 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.105 | ||||
| df | 80.000 | ||||
| t | 0.275 | ||||
| p | 0.392 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.649 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.860 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.650 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.859 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.170 | ||||
| Upside Potential Ratio | 1.733 | ||||
| Upside part of mean | 0.349 | ||||
| Downside part of mean | -0.315 | ||||
| Upside SD | 0.250 | ||||
| Downside SD | 0.202 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 81.000 | ||||
| Mean of predictor | 0.246 | ||||
| Mean of criterion | 0.034 | ||||
| SD of predictor | 0.203 | ||||
| SD of criterion | 0.323 | ||||
| Covariance | -0.007 | ||||
| r | -0.113 | ||||
| b (slope, estimate of beta) | -0.179 | ||||
| a (intercept, estimate of alpha) | 0.078 | ||||
| Mean Square Error | 0.104 | ||||
| DF error | 79.000 | ||||
| t(b) | -1.011 | ||||
| p(b) | 0.842 | ||||
| t(a) | 0.594 | ||||
| p(a) | 0.277 | ||||
| Lowerbound of 95% confidence interval for beta | -0.533 | ||||
| Upperbound of 95% confidence interval for beta | 0.174 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.184 | ||||
| Upperbound of 95% confidence interval for alpha | 0.340 | ||||
| Treynor index (mean / b) | -0.190 | ||||
| Jensen alpha (a) | 0.078 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.140 | ||||
| Expected Shortfall on VaR | 0.172 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.071 | ||||
| Expected Shortfall on VaR | 0.137 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 81.000 | ||||
| Minimum | 0.805 | ||||
| Quartile 1 | 0.984 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.023 | ||||
| Maximum | 1.427 | ||||
| Mean of quarter 1 | 0.916 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.132 | ||||
| Inter Quartile Range | 0.040 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.123 | ||||
| Mean of outliers low | 0.865 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.136 | ||||
| Mean of outliers high | 1.199 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.115 | ||||
| VaR(95%) (moments method) | 0.057 | ||||
| Expected Shortfall (moments method) | 0.088 | ||||
| Extreme Value Index (regression method) | -0.457 | ||||
| VaR(95%) (regression method) | 0.097 | ||||
| Expected Shortfall (regression method) | 0.120 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.033 | ||||
| Quartile 1 | 0.036 | ||||
| Median | 0.049 | ||||
| Quartile 3 | 0.081 | ||||
| Maximum | 0.601 | ||||
| Mean of quarter 1 | 0.034 | ||||
| Mean of quarter 2 | 0.039 | ||||
| Mean of quarter 3 | 0.059 | ||||
| Mean of quarter 4 | 0.344 | ||||
| Inter Quartile Range | 0.044 | ||||
| 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 | 0.167 | ||||
| Mean of outliers high | 0.601 | ||||
| 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) | 0.103 | ||||
| Compounded annual return (geometric extrapolation) | 0.081 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.135 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.236 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.473 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.102 | ||||
| SD | 0.369 | ||||
| Sharpe ratio (Glass type estimate) | 0.275 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.275 | ||||
| df | 1771.000 | ||||
| t | 0.716 | ||||
| p | 0.489 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.478 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.029 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.478 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.029 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.415 | ||||
| Upside Potential Ratio | 6.283 | ||||
| Upside part of mean | 1.538 | ||||
| Downside part of mean | -1.437 | ||||
| Upside SD | 0.276 | ||||
| Downside SD | 0.245 | ||||
| N nonnegative terms | 524.000 | ||||
| N negative terms | 1248.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1772.000 | ||||
| Mean of predictor | 0.310 | ||||
| Mean of criterion | 0.102 | ||||
| SD of predictor | 0.294 | ||||
| SD of criterion | 0.369 | ||||
| Covariance | 0.009 | ||||
| r | 0.087 | ||||
| b (slope, estimate of beta) | 0.110 | ||||
| a (intercept, estimate of alpha) | 0.068 | ||||
| Mean Square Error | 0.135 | ||||
| DF error | 1770.000 | ||||
| t(b) | 3.695 | ||||
| p(b) | 0.456 | ||||
| t(a) | 0.477 | ||||
| p(a) | 0.494 | ||||
| Lowerbound of 95% confidence interval for beta | 0.052 | ||||
| Upperbound of 95% confidence interval for beta | 0.168 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.210 | ||||
| Upperbound of 95% confidence interval for alpha | 0.345 | ||||
| Treynor index (mean / b) | 0.924 | ||||
| Jensen alpha (a) | 0.068 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.034 | ||||
| SD | 0.368 | ||||
| Sharpe ratio (Glass type estimate) | 0.093 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.093 | ||||
| df | 1771.000 | ||||
| t | 0.241 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.661 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.846 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.661 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.846 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.133 | ||||
| Upside Potential Ratio | 5.866 | ||||
| Upside part of mean | 1.502 | ||||
| Downside part of mean | -1.468 | ||||
| Upside SD | 0.263 | ||||
| Downside SD | 0.256 | ||||
| N nonnegative terms | 524.000 | ||||
| N negative terms | 1248.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1772.000 | ||||
| Mean of predictor | 0.267 | ||||
| Mean of criterion | 0.034 | ||||
| SD of predictor | 0.291 | ||||
| SD of criterion | 0.368 | ||||
| Covariance | 0.009 | ||||
| r | 0.088 | ||||
| b (slope, estimate of beta) | 0.111 | ||||
| a (intercept, estimate of alpha) | 0.004 | ||||
| Mean Square Error | 0.134 | ||||
| DF error | 1770.000 | ||||
| t(b) | 3.702 | ||||
| p(b) | 0.456 | ||||
| t(a) | 0.031 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | 0.052 | ||||
| Upperbound of 95% confidence interval for beta | 0.169 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.272 | ||||
| Upperbound of 95% confidence interval for alpha | 0.281 | ||||
| Treynor index (mean / b) | 0.307 | ||||
| Jensen alpha (a) | 0.004 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.046 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.032 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1772.000 | ||||
| Minimum | 0.823 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.225 | ||||
| Mean of quarter 1 | 0.979 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.023 | ||||
| Inter Quartile Range | 0.007 | ||||
| Number outliers low | 245.000 | ||||
| Percentage of outliers low | 0.138 | ||||
| Mean of outliers low | 0.969 | ||||
| Number of outliers high | 260.000 | ||||
| Percentage of outliers high | 0.147 | ||||
| Mean of outliers high | 1.034 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.144 | ||||
| VaR(95%) (moments method) | 0.013 | ||||
| Expected Shortfall (moments method) | 0.021 | ||||
| Extreme Value Index (regression method) | 0.167 | ||||
| VaR(95%) (regression method) | 0.019 | ||||
| Expected Shortfall (regression method) | 0.033 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 37.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.083 | ||||
| Quartile 3 | 0.135 | ||||
| Maximum | 0.602 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.048 | ||||
| Mean of quarter 3 | 0.111 | ||||
| Mean of quarter 4 | 0.208 | ||||
| Inter Quartile Range | 0.114 | ||||
| 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 | 0.027 | ||||
| Mean of outliers high | 0.602 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.549 | ||||
| VaR(95%) (moments method) | 0.239 | ||||
| Expected Shortfall (moments method) | 0.457 | ||||
| Extreme Value Index (regression method) | 0.543 | ||||
| VaR(95%) (regression method) | 0.184 | ||||
| Expected Shortfall (regression method) | 0.283 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.103 | ||||
| Compounded annual return (geometric extrapolation) | 0.081 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.135 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.391 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.780 | ||||
| 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 | 1.059 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.485 | ||||
| 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 | 0.941 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.483 | ||||
| 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) | -8736255408124534.000 | ||||
| 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) | -466657914374630437035729049616384.000 | ||||
| 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 | ||||