Advanced Statistics: MORE FX
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 | -0.171 | ||||
| SD | 0.241 | ||||
| Sharpe ratio (Glass type estimate) | -0.711 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.695 | ||||
| df | 34.000 | ||||
| t | -1.214 | ||||
| p | 0.884 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.866 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.454 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.855 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.464 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.772 | ||||
| Upside Potential Ratio | 0.319 | ||||
| Upside part of mean | 0.071 | ||||
| Downside part of mean | -0.242 | ||||
| Upside SD | 0.098 | ||||
| Downside SD | 0.221 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.565 | ||||
| Mean of criterion | -0.171 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 0.241 | ||||
| Covariance | 0.006 | ||||
| r | 0.082 | ||||
| b (slope, estimate of beta) | 0.069 | ||||
| a (intercept, estimate of alpha) | -0.210 | ||||
| Mean Square Error | 0.059 | ||||
| DF error | 33.000 | ||||
| t(b) | 0.474 | ||||
| p(b) | 0.319 | ||||
| t(a) | -1.277 | ||||
| p(a) | 0.895 | ||||
| Lowerbound of 95% confidence interval for beta | -0.227 | ||||
| Upperbound of 95% confidence interval for beta | 0.365 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.545 | ||||
| Upperbound of 95% confidence interval for alpha | 0.125 | ||||
| Treynor index (mean / b) | -2.480 | ||||
| Jensen alpha (a) | -0.210 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.205 | ||||
| SD | 0.270 | ||||
| Sharpe ratio (Glass type estimate) | -0.757 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.740 | ||||
| df | 34.000 | ||||
| t | -1.293 | ||||
| p | 0.898 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.913 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.410 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.901 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.421 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.795 | ||||
| Upside Potential Ratio | 0.256 | ||||
| Upside part of mean | 0.066 | ||||
| Downside part of mean | -0.271 | ||||
| Upside SD | 0.091 | ||||
| Downside SD | 0.257 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.514 | ||||
| Mean of criterion | -0.205 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.270 | ||||
| Covariance | 0.007 | ||||
| r | 0.096 | ||||
| b (slope, estimate of beta) | 0.096 | ||||
| a (intercept, estimate of alpha) | -0.254 | ||||
| Mean Square Error | 0.075 | ||||
| DF error | 33.000 | ||||
| t(b) | 0.554 | ||||
| p(b) | 0.291 | ||||
| t(a) | -1.387 | ||||
| p(a) | 0.913 | ||||
| Lowerbound of 95% confidence interval for beta | -0.256 | ||||
| Upperbound of 95% confidence interval for beta | 0.448 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.626 | ||||
| Upperbound of 95% confidence interval for alpha | 0.118 | ||||
| Treynor index (mean / b) | -2.131 | ||||
| Jensen alpha (a) | -0.254 | ||||
| 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 | 0.163 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.066 | ||||
| Expected Shortfall on VaR | 0.140 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.691 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.165 | ||||
| Mean of quarter 1 | 0.935 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.024 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.086 | ||||
| Mean of outliers low | 0.804 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.086 | ||||
| Mean of outliers high | 1.072 | ||||
| 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) | -0.726 | ||||
| VaR(95%) (regression method) | 0.199 | ||||
| Expected Shortfall (regression method) | 0.306 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.489 | ||||
| Quartile 1 | 0.489 | ||||
| Median | 0.489 | ||||
| Quartile 3 | 0.489 | ||||
| Maximum | 0.489 | ||||
| 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) | -0.128 | ||||
| Compounded annual return (geometric extrapolation) | -0.148 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.303 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.912 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.162 | ||||
| SD | 0.285 | ||||
| Sharpe ratio (Glass type estimate) | -0.568 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.567 | ||||
| df | 775.000 | ||||
| t | -0.978 | ||||
| p | 0.836 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.707 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.571 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.707 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.572 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.780 | ||||
| Upside Potential Ratio | 2.336 | ||||
| Upside part of mean | 0.484 | ||||
| Downside part of mean | -0.646 | ||||
| Upside SD | 0.195 | ||||
| Downside SD | 0.207 | ||||
| N nonnegative terms | 55.000 | ||||
| N negative terms | 721.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 776.000 | ||||
| Mean of predictor | 0.597 | ||||
| Mean of criterion | -0.162 | ||||
| SD of predictor | 0.331 | ||||
| SD of criterion | 0.285 | ||||
| Covariance | -0.001 | ||||
| r | -0.014 | ||||
| b (slope, estimate of beta) | -0.012 | ||||
| a (intercept, estimate of alpha) | -0.154 | ||||
| Mean Square Error | 0.081 | ||||
| DF error | 774.000 | ||||
| t(b) | -0.398 | ||||
| p(b) | 0.655 | ||||
| t(a) | -0.927 | ||||
| p(a) | 0.823 | ||||
| Lowerbound of 95% confidence interval for beta | -0.073 | ||||
| Upperbound of 95% confidence interval for beta | 0.048 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.481 | ||||
| Upperbound of 95% confidence interval for alpha | 0.173 | ||||
| Treynor index (mean / b) | 13.133 | ||||
| Jensen alpha (a) | -0.154 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.202 | ||||
| SD | 0.285 | ||||
| Sharpe ratio (Glass type estimate) | -0.709 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.708 | ||||
| df | 775.000 | ||||
| t | -1.219 | ||||
| p | 0.888 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.848 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.431 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.847 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.431 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.922 | ||||
| Upside Potential Ratio | 2.127 | ||||
| Upside part of mean | 0.467 | ||||
| Downside part of mean | -0.669 | ||||
| Upside SD | 0.183 | ||||
| Downside SD | 0.219 | ||||
| N nonnegative terms | 55.000 | ||||
| N negative terms | 721.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 776.000 | ||||
| Mean of predictor | 0.540 | ||||
| Mean of criterion | -0.202 | ||||
| SD of predictor | 0.336 | ||||
| SD of criterion | 0.285 | ||||
| Covariance | -0.001 | ||||
| r | -0.014 | ||||
| b (slope, estimate of beta) | -0.012 | ||||
| a (intercept, estimate of alpha) | -0.196 | ||||
| Mean Square Error | 0.082 | ||||
| DF error | 774.000 | ||||
| t(b) | -0.394 | ||||
| p(b) | 0.653 | ||||
| t(a) | -1.174 | ||||
| p(a) | 0.880 | ||||
| Lowerbound of 95% confidence interval for beta | -0.072 | ||||
| Upperbound of 95% confidence interval for beta | 0.048 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.523 | ||||
| Upperbound of 95% confidence interval for alpha | 0.132 | ||||
| Treynor index (mean / b) | 16.844 | ||||
| Jensen alpha (a) | -0.196 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 776.000 | ||||
| Minimum | 0.837 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.228 | ||||
| Mean of quarter 1 | 0.991 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 60.000 | ||||
| Percentage of outliers low | 0.077 | ||||
| Mean of outliers low | 0.970 | ||||
| Number of outliers high | 55.000 | ||||
| Percentage of outliers high | 0.071 | ||||
| Mean of outliers high | 1.026 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.328 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.045 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.024 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.010 | ||||
| Quartile 1 | 0.149 | ||||
| Median | 0.288 | ||||
| Quartile 3 | 0.427 | ||||
| Maximum | 0.567 | ||||
| Mean of quarter 1 | 0.010 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.567 | ||||
| Inter Quartile Range | 0.278 | ||||
| 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) | -0.126 | ||||
| Compounded annual return (geometric extrapolation) | -0.146 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.258 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.258 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.016 | ||||
| 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 | 1.052 | ||||
| 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 | 0.933 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.486 | ||||
| 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) | -8737958216317000.000 | ||||
| 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) | 2281827266347088511043292339634176.000 | ||||
| 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 | ||||