Advanced Statistics: STS Currency
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 | -0.041 | ||||
| SD | 0.006 | ||||
| Sharpe ratio (Glass type estimate) | -6.303 | ||||
| Sharpe ratio (Hedges UMVUE) | -6.144 | ||||
| df | 30.000 | ||||
| t | -10.131 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -4.281 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -8.120 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.168 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.203 | ||||
| Upside Potential Ratio | 0.201 | ||||
| Upside part of mean | 0.003 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.004 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 31.000 | ||||
| Mean of predictor | 0.680 | ||||
| Mean of criterion | -0.041 | ||||
| SD of predictor | 0.344 | ||||
| SD of criterion | 0.006 | ||||
| Covariance | 0.000 | ||||
| r | 0.013 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.041 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 29.000 | ||||
| t(b) | 0.067 | ||||
| p(b) | 0.473 | ||||
| t(a) | -8.650 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.050 | ||||
| Upperbound of 95% confidence interval for alpha | -0.031 | ||||
| Treynor index (mean / b) | -172.991 | ||||
| Jensen alpha (a) | -0.041 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.040 | ||||
| SD | 0.006 | ||||
| Sharpe ratio (Glass type estimate) | -6.326 | ||||
| Sharpe ratio (Hedges UMVUE) | -6.166 | ||||
| df | 30.000 | ||||
| t | -10.167 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -4.299 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -8.146 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.186 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.204 | ||||
| Upside Potential Ratio | 0.200 | ||||
| Upside part of mean | 0.003 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.004 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 31.000 | ||||
| Mean of predictor | 0.610 | ||||
| Mean of criterion | -0.040 | ||||
| SD of predictor | 0.315 | ||||
| SD of criterion | 0.006 | ||||
| Covariance | 0.000 | ||||
| r | 0.020 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.041 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 29.000 | ||||
| t(b) | 0.110 | ||||
| p(b) | 0.456 | ||||
| t(a) | -8.744 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.050 | ||||
| Upperbound of 95% confidence interval for alpha | -0.031 | ||||
| Treynor index (mean / b) | -97.144 | ||||
| Jensen alpha (a) | -0.041 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 31.000 | ||||
| Minimum | 0.999 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.010 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.032 | ||||
| Mean of outliers low | 0.999 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.032 | ||||
| Mean of outliers high | 1.010 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.001 | ||||
| Quartile 3 | 0.001 | ||||
| Maximum | 0.001 | ||||
| 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 | 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) | 0.004 | ||||
| Compounded annual return (geometric extrapolation) | 0.004 | ||||
| Calmar ratio (compounded annual return / max draw down) | 3.607 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.499 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.040 | ||||
| SD | 0.021 | ||||
| Sharpe ratio (Glass type estimate) | -1.888 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.886 | ||||
| df | 684.000 | ||||
| t | -3.052 | ||||
| p | 0.999 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.103 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.671 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.102 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.669 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.377 | ||||
| Upside Potential Ratio | 1.485 | ||||
| Upside part of mean | 0.018 | ||||
| Downside part of mean | -0.058 | ||||
| Upside SD | 0.018 | ||||
| Downside SD | 0.012 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 677.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 685.000 | ||||
| Mean of predictor | 0.691 | ||||
| Mean of criterion | -0.040 | ||||
| SD of predictor | 0.364 | ||||
| SD of criterion | 0.021 | ||||
| Covariance | -0.000 | ||||
| r | -0.031 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.039 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 683.000 | ||||
| t(b) | -0.816 | ||||
| p(b) | 0.793 | ||||
| t(a) | -2.935 | ||||
| p(a) | 0.998 | ||||
| Lowerbound of 95% confidence interval for beta | -0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.065 | ||||
| Upperbound of 95% confidence interval for alpha | -0.013 | ||||
| Treynor index (mean / b) | 21.995 | ||||
| Jensen alpha (a) | -0.039 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.040 | ||||
| SD | 0.021 | ||||
| Sharpe ratio (Glass type estimate) | -1.913 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.910 | ||||
| df | 684.000 | ||||
| t | -3.092 | ||||
| p | 0.999 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.128 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.695 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.127 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.694 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.379 | ||||
| Upside Potential Ratio | 1.464 | ||||
| Upside part of mean | 0.018 | ||||
| Downside part of mean | -0.058 | ||||
| Upside SD | 0.018 | ||||
| Downside SD | 0.012 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 677.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 685.000 | ||||
| Mean of predictor | 0.625 | ||||
| Mean of criterion | -0.040 | ||||
| SD of predictor | 0.363 | ||||
| SD of criterion | 0.021 | ||||
| Covariance | -0.000 | ||||
| r | -0.031 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.039 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 683.000 | ||||
| t(b) | -0.816 | ||||
| p(b) | 0.792 | ||||
| t(a) | -2.988 | ||||
| p(a) | 0.999 | ||||
| Lowerbound of 95% confidence interval for beta | -0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.065 | ||||
| Upperbound of 95% confidence interval for alpha | -0.013 | ||||
| Treynor index (mean / b) | 22.245 | ||||
| Jensen alpha (a) | -0.039 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 685.000 | ||||
| Minimum | 0.987 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.028 | ||||
| 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 | 7.000 | ||||
| Percentage of outliers low | 0.010 | ||||
| Mean of outliers low | 0.995 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.012 | ||||
| Mean of outliers high | 1.006 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.348 | ||||
| VaR(95%) (moments method) | -1.496 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.538 | ||||
| VaR(95%) (regression method) | -0.025 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.013 | ||||
| Median | 0.018 | ||||
| Quartile 3 | 0.024 | ||||
| Maximum | 0.029 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.029 | ||||
| Inter Quartile Range | 0.011 | ||||
| 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) | 0.004 | ||||
| Compounded annual return (geometric extrapolation) | 0.004 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.120 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.120 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.238 | ||||
| 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 | 0.993 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.502 | ||||
| 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 | 0.867 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.500 | ||||
| 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) | -8749392447603733.000 | ||||
| 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) | 130804023503904751657183703203840.000 | ||||
| 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 | ||||