Advanced Statistics: Gold Arrow
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 | 0.014 | ||||
| SD | 0.337 | ||||
| Sharpe ratio (Glass type estimate) | 0.041 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.041 | ||||
| df | 83.000 | ||||
| t | 0.109 | ||||
| p | 0.457 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.700 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.782 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.700 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.782 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.059 | ||||
| Upside Potential Ratio | 1.171 | ||||
| Upside part of mean | 0.274 | ||||
| Downside part of mean | -0.260 | ||||
| Upside SD | 0.239 | ||||
| Downside SD | 0.234 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 69.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 84.000 | ||||
| Mean of predictor | 0.172 | ||||
| Mean of criterion | 0.014 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.337 | ||||
| Covariance | -0.010 | ||||
| r | -0.091 | ||||
| b (slope, estimate of beta) | -0.093 | ||||
| a (intercept, estimate of alpha) | 0.030 | ||||
| Mean Square Error | 0.114 | ||||
| DF error | 82.000 | ||||
| t(b) | -0.826 | ||||
| p(b) | 0.795 | ||||
| t(a) | 0.232 | ||||
| p(a) | 0.409 | ||||
| Lowerbound of 95% confidence interval for beta | -0.318 | ||||
| Upperbound of 95% confidence interval for beta | 0.131 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.227 | ||||
| Upperbound of 95% confidence interval for alpha | 0.286 | ||||
| Treynor index (mean / b) | -0.149 | ||||
| Jensen alpha (a) | 0.030 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.045 | ||||
| SD | 0.351 | ||||
| Sharpe ratio (Glass type estimate) | -0.127 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.126 | ||||
| df | 83.000 | ||||
| t | -0.337 | ||||
| p | 0.631 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.868 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.614 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.867 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.615 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.161 | ||||
| Upside Potential Ratio | 0.898 | ||||
| Upside part of mean | 0.249 | ||||
| Downside part of mean | -0.293 | ||||
| Upside SD | 0.213 | ||||
| Downside SD | 0.277 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 69.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 84.000 | ||||
| Mean of predictor | 0.118 | ||||
| Mean of criterion | -0.045 | ||||
| SD of predictor | 0.327 | ||||
| SD of criterion | 0.351 | ||||
| Covariance | -0.010 | ||||
| r | -0.091 | ||||
| b (slope, estimate of beta) | -0.098 | ||||
| a (intercept, estimate of alpha) | -0.033 | ||||
| Mean Square Error | 0.124 | ||||
| DF error | 82.000 | ||||
| t(b) | -0.829 | ||||
| p(b) | 0.795 | ||||
| t(a) | -0.248 | ||||
| p(a) | 0.598 | ||||
| Lowerbound of 95% confidence interval for beta | -0.332 | ||||
| Upperbound of 95% confidence interval for beta | 0.137 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.299 | ||||
| Upperbound of 95% confidence interval for alpha | 0.233 | ||||
| Treynor index (mean / b) | 0.457 | ||||
| Jensen alpha (a) | -0.033 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.157 | ||||
| Expected Shortfall on VaR | 0.191 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.067 | ||||
| Expected Shortfall on VaR | 0.142 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 84.000 | ||||
| Minimum | 0.618 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.361 | ||||
| Mean of quarter 1 | 0.925 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.094 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 14.000 | ||||
| Percentage of outliers low | 0.167 | ||||
| Mean of outliers low | 0.888 | ||||
| Number of outliers high | 16.000 | ||||
| Percentage of outliers high | 0.190 | ||||
| Mean of outliers high | 1.123 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.700 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.505 | ||||
| VaR(95%) (regression method) | 0.066 | ||||
| Expected Shortfall (regression method) | 0.222 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.095 | ||||
| Quartile 1 | 0.146 | ||||
| Median | 0.205 | ||||
| Quartile 3 | 0.440 | ||||
| Maximum | 0.447 | ||||
| Mean of quarter 1 | 0.120 | ||||
| Mean of quarter 2 | 0.205 | ||||
| Mean of quarter 3 | 0.440 | ||||
| Mean of quarter 4 | 0.447 | ||||
| Inter Quartile Range | 0.293 | ||||
| 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) | -0.001 | ||||
| Compounded annual return (geometric extrapolation) | -0.001 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.001 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.001 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.003 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.356 | ||||
| SD | 0.928 | ||||
| Sharpe ratio (Glass type estimate) | 0.384 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.383 | ||||
| df | 1843.000 | ||||
| t | 1.018 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.355 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.122 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.355 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.122 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.660 | ||||
| Upside Potential Ratio | 3.629 | ||||
| Upside part of mean | 1.959 | ||||
| Downside part of mean | -1.603 | ||||
| Upside SD | 0.755 | ||||
| Downside SD | 0.540 | ||||
| N nonnegative terms | 282.000 | ||||
| N negative terms | 1562.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1844.000 | ||||
| Mean of predictor | 0.258 | ||||
| Mean of criterion | 0.356 | ||||
| SD of predictor | 0.572 | ||||
| SD of criterion | 0.928 | ||||
| Covariance | 0.063 | ||||
| r | 0.120 | ||||
| b (slope, estimate of beta) | 0.194 | ||||
| a (intercept, estimate of alpha) | 0.306 | ||||
| Mean Square Error | 0.850 | ||||
| DF error | 1842.000 | ||||
| t(b) | 5.169 | ||||
| p(b) | 0.440 | ||||
| t(a) | 0.880 | ||||
| p(a) | 0.490 | ||||
| Lowerbound of 95% confidence interval for beta | 0.120 | ||||
| Upperbound of 95% confidence interval for beta | 0.268 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.376 | ||||
| Upperbound of 95% confidence interval for alpha | 0.988 | ||||
| Treynor index (mean / b) | 1.834 | ||||
| Jensen alpha (a) | 0.306 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.045 | ||||
| SD | 0.893 | ||||
| Sharpe ratio (Glass type estimate) | -0.050 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.050 | ||||
| df | 1843.000 | ||||
| t | -0.133 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.789 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.689 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.789 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.689 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.069 | ||||
| Upside Potential Ratio | 2.685 | ||||
| Upside part of mean | 1.744 | ||||
| Downside part of mean | -1.788 | ||||
| Upside SD | 0.612 | ||||
| Downside SD | 0.649 | ||||
| N nonnegative terms | 282.000 | ||||
| N negative terms | 1562.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1844.000 | ||||
| Mean of predictor | 0.097 | ||||
| Mean of criterion | -0.045 | ||||
| SD of predictor | 0.565 | ||||
| SD of criterion | 0.893 | ||||
| Covariance | 0.065 | ||||
| r | 0.129 | ||||
| b (slope, estimate of beta) | 0.204 | ||||
| a (intercept, estimate of alpha) | -0.065 | ||||
| Mean Square Error | 0.784 | ||||
| DF error | 1842.000 | ||||
| t(b) | 5.589 | ||||
| p(b) | 0.435 | ||||
| t(a) | -0.193 | ||||
| p(a) | 0.502 | ||||
| Lowerbound of 95% confidence interval for beta | 0.132 | ||||
| Upperbound of 95% confidence interval for beta | 0.275 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.719 | ||||
| Upperbound of 95% confidence interval for alpha | 0.590 | ||||
| Treynor index (mean / b) | -0.219 | ||||
| Jensen alpha (a) | -0.065 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.087 | ||||
| Expected Shortfall on VaR | 0.107 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1844.000 | ||||
| Minimum | 0.571 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.778 | ||||
| Mean of quarter 1 | 0.976 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.030 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 239.000 | ||||
| Percentage of outliers low | 0.130 | ||||
| Mean of outliers low | 0.954 | ||||
| Number of outliers high | 311.000 | ||||
| Percentage of outliers high | 0.169 | ||||
| Mean of outliers high | 1.044 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.410 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.010 | ||||
| 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 | 7.000 | ||||
| Minimum | 0.055 | ||||
| Quartile 1 | 0.093 | ||||
| Median | 0.222 | ||||
| Quartile 3 | 0.403 | ||||
| Maximum | 0.598 | ||||
| Mean of quarter 1 | 0.069 | ||||
| Mean of quarter 2 | 0.163 | ||||
| Mean of quarter 3 | 0.303 | ||||
| Mean of quarter 4 | 0.551 | ||||
| Inter Quartile Range | 0.310 | ||||
| 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) | -0.001 | ||||
| Compounded annual return (geometric extrapolation) | -0.001 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.001 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.001 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.006 | ||||
| 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 | 0.876 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.569 | ||||
| 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 | 0.713 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.572 | ||||
| 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) | -8773650254672640.000 | ||||
| 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) | 297207688171435931124627440402432.000 | ||||
| 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 | ||||