Advanced Statistics: Seleukos Intraday Currency System
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.066 | ||||
| SD | 0.280 | ||||
| Sharpe ratio (Glass type estimate) | -0.236 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.234 | ||||
| df | 84.000 | ||||
| t | -0.629 | ||||
| p | 0.734 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.973 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.502 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.971 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.503 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.332 | ||||
| Upside Potential Ratio | 1.156 | ||||
| Upside part of mean | 0.231 | ||||
| Downside part of mean | -0.297 | ||||
| Upside SD | 0.195 | ||||
| Downside SD | 0.200 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 85.000 | ||||
| Mean of predictor | 0.131 | ||||
| Mean of criterion | -0.066 | ||||
| SD of predictor | 0.230 | ||||
| SD of criterion | 0.280 | ||||
| Covariance | -0.003 | ||||
| r | -0.045 | ||||
| b (slope, estimate of beta) | -0.055 | ||||
| a (intercept, estimate of alpha) | -0.059 | ||||
| Mean Square Error | 0.079 | ||||
| DF error | 83.000 | ||||
| t(b) | -0.411 | ||||
| p(b) | 0.659 | ||||
| t(a) | -0.550 | ||||
| p(a) | 0.708 | ||||
| Lowerbound of 95% confidence interval for beta | -0.320 | ||||
| Upperbound of 95% confidence interval for beta | 0.210 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.272 | ||||
| Upperbound of 95% confidence interval for alpha | 0.154 | ||||
| Treynor index (mean / b) | 1.207 | ||||
| Jensen alpha (a) | -0.059 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.106 | ||||
| SD | 0.287 | ||||
| Sharpe ratio (Glass type estimate) | -0.369 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.366 | ||||
| df | 84.000 | ||||
| t | -0.983 | ||||
| p | 0.836 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.107 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.370 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.104 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.373 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.466 | ||||
| Upside Potential Ratio | 0.940 | ||||
| Upside part of mean | 0.213 | ||||
| Downside part of mean | -0.319 | ||||
| Upside SD | 0.175 | ||||
| Downside SD | 0.227 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 85.000 | ||||
| Mean of predictor | 0.104 | ||||
| Mean of criterion | -0.106 | ||||
| SD of predictor | 0.235 | ||||
| SD of criterion | 0.287 | ||||
| Covariance | -0.001 | ||||
| r | -0.018 | ||||
| b (slope, estimate of beta) | -0.022 | ||||
| a (intercept, estimate of alpha) | -0.104 | ||||
| Mean Square Error | 0.083 | ||||
| DF error | 83.000 | ||||
| t(b) | -0.167 | ||||
| p(b) | 0.566 | ||||
| t(a) | -0.948 | ||||
| p(a) | 0.827 | ||||
| Lowerbound of 95% confidence interval for beta | -0.288 | ||||
| Upperbound of 95% confidence interval for beta | 0.244 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.321 | ||||
| Upperbound of 95% confidence interval for alpha | 0.114 | ||||
| Treynor index (mean / b) | 4.749 | ||||
| Jensen alpha (a) | -0.104 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.135 | ||||
| Expected Shortfall on VaR | 0.164 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.073 | ||||
| Expected Shortfall on VaR | 0.144 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 85.000 | ||||
| Minimum | 0.655 | ||||
| Quartile 1 | 0.984 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.316 | ||||
| Mean of quarter 1 | 0.917 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.081 | ||||
| Inter Quartile Range | 0.016 | ||||
| Number outliers low | 15.000 | ||||
| Percentage of outliers low | 0.176 | ||||
| Mean of outliers low | 0.892 | ||||
| Number of outliers high | 18.000 | ||||
| Percentage of outliers high | 0.212 | ||||
| Mean of outliers high | 1.093 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.117 | ||||
| VaR(95%) (moments method) | 0.052 | ||||
| Expected Shortfall (moments method) | 0.070 | ||||
| Extreme Value Index (regression method) | 0.276 | ||||
| VaR(95%) (regression method) | 0.102 | ||||
| Expected Shortfall (regression method) | 0.192 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.400 | ||||
| Quartile 1 | 0.422 | ||||
| Median | 0.445 | ||||
| Quartile 3 | 0.468 | ||||
| Maximum | 0.491 | ||||
| Mean of quarter 1 | 0.400 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.491 | ||||
| Inter Quartile Range | 0.045 | ||||
| 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) | -0.050 | ||||
| Compounded annual return (geometric extrapolation) | -0.060 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.122 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.122 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.366 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.232 | ||||
| SD | 0.848 | ||||
| Sharpe ratio (Glass type estimate) | 0.274 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.274 | ||||
| df | 1873.000 | ||||
| t | 0.733 | ||||
| p | 0.489 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.459 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.007 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.459 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.007 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.458 | ||||
| Upside Potential Ratio | 4.351 | ||||
| Upside part of mean | 2.206 | ||||
| Downside part of mean | -1.974 | ||||
| Upside SD | 0.679 | ||||
| Downside SD | 0.507 | ||||
| N nonnegative terms | 505.000 | ||||
| N negative terms | 1369.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1874.000 | ||||
| Mean of predictor | 0.258 | ||||
| Mean of criterion | 0.232 | ||||
| SD of predictor | 0.570 | ||||
| SD of criterion | 0.848 | ||||
| Covariance | 0.012 | ||||
| r | 0.025 | ||||
| b (slope, estimate of beta) | 0.038 | ||||
| a (intercept, estimate of alpha) | 0.223 | ||||
| Mean Square Error | 0.718 | ||||
| DF error | 1872.000 | ||||
| t(b) | 1.099 | ||||
| p(b) | 0.487 | ||||
| t(a) | 0.702 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | -0.030 | ||||
| Upperbound of 95% confidence interval for beta | 0.105 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.399 | ||||
| Upperbound of 95% confidence interval for alpha | 0.844 | ||||
| Treynor index (mean / b) | 6.153 | ||||
| Jensen alpha (a) | 0.223 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.105 | ||||
| SD | 0.819 | ||||
| Sharpe ratio (Glass type estimate) | -0.128 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.128 | ||||
| df | 1873.000 | ||||
| t | -0.344 | ||||
| p | 0.505 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.861 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.604 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.861 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.604 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.178 | ||||
| Upside Potential Ratio | 3.432 | ||||
| Upside part of mean | 2.025 | ||||
| Downside part of mean | -2.130 | ||||
| Upside SD | 0.568 | ||||
| Downside SD | 0.590 | ||||
| N nonnegative terms | 505.000 | ||||
| N negative terms | 1369.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1874.000 | ||||
| Mean of predictor | 0.097 | ||||
| Mean of criterion | -0.105 | ||||
| SD of predictor | 0.570 | ||||
| SD of criterion | 0.819 | ||||
| Covariance | 0.008 | ||||
| r | 0.018 | ||||
| b (slope, estimate of beta) | 0.026 | ||||
| a (intercept, estimate of alpha) | -0.108 | ||||
| Mean Square Error | 0.671 | ||||
| DF error | 1872.000 | ||||
| t(b) | 0.784 | ||||
| p(b) | 0.491 | ||||
| t(a) | -0.352 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | -0.039 | ||||
| Upperbound of 95% confidence interval for beta | 0.091 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.709 | ||||
| Upperbound of 95% confidence interval for alpha | 0.493 | ||||
| Treynor index (mean / b) | -4.043 | ||||
| Jensen alpha (a) | -0.108 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.080 | ||||
| Expected Shortfall on VaR | 0.099 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.048 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1874.000 | ||||
| Minimum | 0.540 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.833 | ||||
| Mean of quarter 1 | 0.970 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.034 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 360.000 | ||||
| Percentage of outliers low | 0.192 | ||||
| Mean of outliers low | 0.963 | ||||
| Number of outliers high | 333.000 | ||||
| Percentage of outliers high | 0.178 | ||||
| Mean of outliers high | 1.046 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.043 | ||||
| VaR(95%) (moments method) | 0.015 | ||||
| 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 | 0.000 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.018 | ||||
| Quartile 3 | 0.262 | ||||
| Maximum | 0.512 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.012 | ||||
| Mean of quarter 3 | 0.079 | ||||
| Mean of quarter 4 | 0.425 | ||||
| Inter Quartile Range | 0.253 | ||||
| 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) | -36.643 | ||||
| VaR(95%) (moments method) | 0.450 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -2.574 | ||||
| VaR(95%) (regression method) | 0.643 | ||||
| Expected Shortfall (regression method) | 0.646 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.050 | ||||
| Compounded annual return (geometric extrapolation) | -0.059 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.116 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.140 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.598 | ||||
| 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 | 0.832 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.665 | ||||
| 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 | 0.587 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.720 | ||||
| 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) | -8788572277427192.000 | ||||
| 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) | -2152703621584037669329671787905024.000 | ||||
| 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 | ||||