Advanced Statistics: FDAX Dragon
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 | -0.066 | ||||
| SD | 0.039 | ||||
| Sharpe ratio (Glass type estimate) | -1.689 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.657 | ||||
| df | 39.000 | ||||
| t | -3.085 | ||||
| p | 0.998 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.817 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.543 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.791 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.522 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.537 | ||||
| Upside Potential Ratio | 0.044 | ||||
| Upside part of mean | 0.002 | ||||
| Downside part of mean | -0.068 | ||||
| Upside SD | 0.003 | ||||
| Downside SD | 0.043 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.505 | ||||
| Mean of criterion | -0.066 | ||||
| SD of predictor | 0.277 | ||||
| SD of criterion | 0.039 | ||||
| Covariance | 0.001 | ||||
| r | 0.065 | ||||
| b (slope, estimate of beta) | 0.009 | ||||
| a (intercept, estimate of alpha) | -0.071 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 38.000 | ||||
| t(b) | 0.404 | ||||
| p(b) | 0.344 | ||||
| t(a) | -2.883 | ||||
| p(a) | 0.997 | ||||
| Lowerbound of 95% confidence interval for beta | -0.037 | ||||
| Upperbound of 95% confidence interval for beta | 0.055 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.120 | ||||
| Upperbound of 95% confidence interval for alpha | -0.021 | ||||
| Treynor index (mean / b) | -7.149 | ||||
| Jensen alpha (a) | -0.071 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.067 | ||||
| SD | 0.040 | ||||
| Sharpe ratio (Glass type estimate) | -1.655 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.623 | ||||
| df | 39.000 | ||||
| t | -3.021 | ||||
| p | 0.998 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.780 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.511 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.755 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.491 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.511 | ||||
| Upside Potential Ratio | 0.043 | ||||
| Upside part of mean | 0.002 | ||||
| Downside part of mean | -0.068 | ||||
| Upside SD | 0.003 | ||||
| Downside SD | 0.044 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.459 | ||||
| Mean of criterion | -0.067 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.040 | ||||
| Covariance | 0.001 | ||||
| r | 0.060 | ||||
| b (slope, estimate of beta) | 0.009 | ||||
| a (intercept, estimate of alpha) | -0.071 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 38.000 | ||||
| t(b) | 0.370 | ||||
| p(b) | 0.357 | ||||
| t(a) | -2.834 | ||||
| p(a) | 0.996 | ||||
| Lowerbound of 95% confidence interval for beta | -0.041 | ||||
| Upperbound of 95% confidence interval for beta | 0.059 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.121 | ||||
| Upperbound of 95% confidence interval for alpha | -0.020 | ||||
| Treynor index (mean / b) | -7.334 | ||||
| Jensen alpha (a) | -0.071 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 40.000 | ||||
| Minimum | 0.933 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.008 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.125 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.250 | ||||
| Mean of outliers high | 1.003 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.402 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 1.206 | ||||
| VaR(95%) (regression method) | 0.012 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.095 | ||||
| Quartile 1 | 0.095 | ||||
| Median | 0.095 | ||||
| Quartile 3 | 0.095 | ||||
| Maximum | 0.095 | ||||
| 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) | -0.022 | ||||
| Compounded annual return (geometric extrapolation) | -0.022 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.236 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.767 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.062 | ||||
| SD | 0.098 | ||||
| Sharpe ratio (Glass type estimate) | -0.632 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.631 | ||||
| df | 877.000 | ||||
| t | -1.156 | ||||
| p | 0.876 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.702 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.440 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.702 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.440 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.911 | ||||
| Upside Potential Ratio | 2.047 | ||||
| Upside part of mean | 0.139 | ||||
| Downside part of mean | -0.200 | ||||
| Upside SD | 0.070 | ||||
| Downside SD | 0.068 | ||||
| N nonnegative terms | 130.000 | ||||
| N negative terms | 748.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 878.000 | ||||
| Mean of predictor | 0.556 | ||||
| Mean of criterion | -0.062 | ||||
| SD of predictor | 0.363 | ||||
| SD of criterion | 0.098 | ||||
| Covariance | 0.001 | ||||
| r | 0.027 | ||||
| b (slope, estimate of beta) | 0.007 | ||||
| a (intercept, estimate of alpha) | -0.066 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 876.000 | ||||
| t(b) | 0.813 | ||||
| p(b) | 0.208 | ||||
| t(a) | -1.227 | ||||
| p(a) | 0.890 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.025 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.171 | ||||
| Upperbound of 95% confidence interval for alpha | 0.039 | ||||
| Treynor index (mean / b) | -8.345 | ||||
| Jensen alpha (a) | -0.066 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.066 | ||||
| SD | 0.097 | ||||
| Sharpe ratio (Glass type estimate) | -0.682 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.682 | ||||
| df | 877.000 | ||||
| t | -1.249 | ||||
| p | 0.894 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.753 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.389 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.753 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.389 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.960 | ||||
| Upside Potential Ratio | 1.968 | ||||
| Upside part of mean | 0.136 | ||||
| Downside part of mean | -0.203 | ||||
| Upside SD | 0.068 | ||||
| Downside SD | 0.069 | ||||
| N nonnegative terms | 130.000 | ||||
| N negative terms | 748.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 878.000 | ||||
| Mean of predictor | 0.490 | ||||
| Mean of criterion | -0.066 | ||||
| SD of predictor | 0.361 | ||||
| SD of criterion | 0.097 | ||||
| Covariance | 0.001 | ||||
| r | 0.028 | ||||
| b (slope, estimate of beta) | 0.007 | ||||
| a (intercept, estimate of alpha) | -0.070 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 876.000 | ||||
| t(b) | 0.817 | ||||
| p(b) | 0.207 | ||||
| t(a) | -1.313 | ||||
| p(a) | 0.905 | ||||
| Lowerbound of 95% confidence interval for beta | -0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.025 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.175 | ||||
| Upperbound of 95% confidence interval for alpha | 0.035 | ||||
| Treynor index (mean / b) | -8.920 | ||||
| Jensen alpha (a) | -0.070 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 878.000 | ||||
| Minimum | 0.930 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.072 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 130.000 | ||||
| Percentage of outliers low | 0.148 | ||||
| Mean of outliers low | 0.996 | ||||
| Number of outliers high | 153.000 | ||||
| Percentage of outliers high | 0.174 | ||||
| Mean of outliers high | 1.003 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.344 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| 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 | 5.000 | ||||
| Minimum | 0.026 | ||||
| Quartile 1 | 0.034 | ||||
| Median | 0.065 | ||||
| Quartile 3 | 0.070 | ||||
| Maximum | 0.162 | ||||
| Mean of quarter 1 | 0.030 | ||||
| Mean of quarter 2 | 0.065 | ||||
| Mean of quarter 3 | 0.070 | ||||
| Mean of quarter 4 | 0.162 | ||||
| Inter Quartile Range | 0.037 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.162 | ||||
| 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) | -0.022 | ||||
| Compounded annual return (geometric extrapolation) | -0.022 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.137 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.137 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.763 | ||||
| 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 | 1.098 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.487 | ||||
| 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 | 0.977 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.491 | ||||
| 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) | -8733506473272633.000 | ||||
| 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) | -232996889949495436107716495409152.000 | ||||
| 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 | ||||