Advanced Statistics: FXCould1
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 | -0.055 | ||||
| SD | 0.018 | ||||
| Sharpe ratio (Glass type estimate) | -3.090 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.017 | ||||
| df | 32.000 | ||||
| t | -5.125 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.475 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.671 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.411 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.623 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.326 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.024 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.565 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 0.018 | ||||
| Covariance | 0.000 | ||||
| r | 0.075 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | -0.057 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 31.000 | ||||
| t(b) | 0.416 | ||||
| p(b) | 0.340 | ||||
| t(a) | -4.614 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.017 | ||||
| Upperbound of 95% confidence interval for beta | 0.026 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.083 | ||||
| Upperbound of 95% confidence interval for alpha | -0.032 | ||||
| Treynor index (mean / b) | -12.241 | ||||
| Jensen alpha (a) | -0.057 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.055 | ||||
| SD | 0.018 | ||||
| Sharpe ratio (Glass type estimate) | -3.049 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.977 | ||||
| df | 32.000 | ||||
| t | -5.056 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.429 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.635 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.366 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.588 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.309 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.024 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.512 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.282 | ||||
| SD of criterion | 0.018 | ||||
| Covariance | 0.000 | ||||
| r | 0.069 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | -0.057 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 31.000 | ||||
| t(b) | 0.383 | ||||
| p(b) | 0.352 | ||||
| t(a) | -4.582 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.019 | ||||
| Upperbound of 95% confidence interval for beta | 0.028 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.083 | ||||
| Upperbound of 95% confidence interval for alpha | -0.032 | ||||
| Treynor index (mean / b) | -12.529 | ||||
| Jensen alpha (a) | -0.057 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 33.000 | ||||
| Minimum | 0.971 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.997 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.030 | ||||
| Mean of outliers low | 0.971 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.029 | ||||
| Quartile 1 | 0.029 | ||||
| Median | 0.029 | ||||
| Quartile 3 | 0.029 | ||||
| Maximum | 0.029 | ||||
| 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) | -0.011 | ||||
| Compounded annual return (geometric extrapolation) | -0.011 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.367 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.711 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.054 | ||||
| SD | 0.015 | ||||
| Sharpe ratio (Glass type estimate) | -3.537 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.534 | ||||
| df | 741.000 | ||||
| t | -5.953 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.715 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.358 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.712 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.355 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.684 | ||||
| Upside Potential Ratio | 0.344 | ||||
| Upside part of mean | 0.005 | ||||
| Downside part of mean | -0.060 | ||||
| Upside SD | 0.005 | ||||
| Downside SD | 0.015 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 739.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 742.000 | ||||
| Mean of predictor | 0.635 | ||||
| Mean of criterion | -0.054 | ||||
| SD of predictor | 0.379 | ||||
| SD of criterion | 0.015 | ||||
| Covariance | 0.000 | ||||
| r | 0.007 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.055 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 740.000 | ||||
| t(b) | 0.187 | ||||
| p(b) | 0.426 | ||||
| t(a) | -5.937 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.073 | ||||
| Upperbound of 95% confidence interval for alpha | -0.037 | ||||
| Treynor index (mean / b) | -194.896 | ||||
| Jensen alpha (a) | -0.055 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.055 | ||||
| SD | 0.015 | ||||
| Sharpe ratio (Glass type estimate) | -3.525 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.521 | ||||
| df | 741.000 | ||||
| t | -5.932 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.702 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.345 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.700 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.343 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.667 | ||||
| Upside Potential Ratio | 0.340 | ||||
| Upside part of mean | 0.005 | ||||
| Downside part of mean | -0.060 | ||||
| Upside SD | 0.005 | ||||
| Downside SD | 0.015 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 739.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 742.000 | ||||
| Mean of predictor | 0.564 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.376 | ||||
| SD of criterion | 0.015 | ||||
| Covariance | 0.000 | ||||
| r | 0.006 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.055 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 740.000 | ||||
| t(b) | 0.175 | ||||
| p(b) | 0.430 | ||||
| t(a) | -5.919 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.073 | ||||
| Upperbound of 95% confidence interval for alpha | -0.037 | ||||
| Treynor index (mean / b) | -205.827 | ||||
| Jensen alpha (a) | -0.055 | ||||
| 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 | 0.002 | ||||
| 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 | 742.000 | ||||
| Minimum | 0.984 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.008 | ||||
| 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 | 4.000 | ||||
| Percentage of outliers low | 0.005 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.004 | ||||
| Mean of outliers high | 1.005 | ||||
| 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) | -1.487 | ||||
| VaR(95%) (regression method) | -0.356 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.011 | ||||
| Median | 0.018 | ||||
| Quartile 3 | 0.025 | ||||
| Maximum | 0.032 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.032 | ||||
| Inter Quartile Range | 0.014 | ||||
| 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) | -0.010 | ||||
| Compounded annual return (geometric extrapolation) | -0.010 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.323 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.323 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.812 | ||||
| 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 | 1.061 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.529 | ||||
| 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 | 0.919 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.532 | ||||
| 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) | -8749762766054109.000 | ||||
| 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) | -411111383020497177206920755281920.000 | ||||
| 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 | ||||