Advanced Statistics: System 30092309
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.231 | ||||
| SD | 3.302 | ||||
| Sharpe ratio (Glass type estimate) | 0.373 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.369 | ||||
| df | 69.000 | ||||
| t | 0.900 | ||||
| p | 0.186 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.442 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.185 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.445 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.183 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.321 | ||||
| Upside Potential Ratio | 3.881 | ||||
| Upside part of mean | 1.438 | ||||
| Downside part of mean | -0.208 | ||||
| Upside SD | 3.276 | ||||
| Downside SD | 0.371 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 60.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.272 | ||||
| Mean of criterion | 1.231 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 3.302 | ||||
| Covariance | 0.008 | ||||
| r | 0.008 | ||||
| b (slope, estimate of beta) | 0.087 | ||||
| a (intercept, estimate of alpha) | 1.207 | ||||
| Mean Square Error | 11.060 | ||||
| DF error | 68.000 | ||||
| t(b) | 0.064 | ||||
| p(b) | 0.475 | ||||
| t(a) | 0.847 | ||||
| p(a) | 0.200 | ||||
| Lowerbound of 95% confidence interval for beta | -2.625 | ||||
| Upperbound of 95% confidence interval for beta | 2.799 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.637 | ||||
| Upperbound of 95% confidence interval for alpha | 4.052 | ||||
| Treynor index (mean / b) | 14.143 | ||||
| Jensen alpha (a) | 1.207 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.023 | ||||
| SD | 1.293 | ||||
| Sharpe ratio (Glass type estimate) | 0.018 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.017 | ||||
| df | 69.000 | ||||
| t | 0.042 | ||||
| p | 0.483 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.794 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.829 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.794 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.829 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.025 | ||||
| Upside Potential Ratio | 0.500 | ||||
| Upside part of mean | 0.454 | ||||
| Downside part of mean | -0.431 | ||||
| Upside SD | 0.907 | ||||
| Downside SD | 0.908 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 60.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.227 | ||||
| Mean of criterion | 0.023 | ||||
| SD of predictor | 0.288 | ||||
| SD of criterion | 1.293 | ||||
| Covariance | 0.012 | ||||
| r | 0.033 | ||||
| b (slope, estimate of beta) | 0.147 | ||||
| a (intercept, estimate of alpha) | -0.011 | ||||
| Mean Square Error | 1.694 | ||||
| DF error | 68.000 | ||||
| t(b) | 0.271 | ||||
| p(b) | 0.393 | ||||
| t(a) | -0.019 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | -0.937 | ||||
| Upperbound of 95% confidence interval for beta | 1.231 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.114 | ||||
| Upperbound of 95% confidence interval for alpha | 1.092 | ||||
| Treynor index (mean / b) | 0.154 | ||||
| Jensen alpha (a) | -0.011 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.458 | ||||
| Expected Shortfall on VaR | 0.532 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.123 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 70.000 | ||||
| Minimum | 0.112 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 8.914 | ||||
| Mean of quarter 1 | 0.945 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.468 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.086 | ||||
| Mean of outliers low | 0.835 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.171 | ||||
| Mean of outliers high | 1.702 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.780 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 2.825 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.888 | ||||
| Quartile 1 | 0.888 | ||||
| Median | 0.888 | ||||
| Quartile 3 | 0.888 | ||||
| Maximum | 0.888 | ||||
| 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) | 0.082 | ||||
| Compounded annual return (geometric extrapolation) | 0.069 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.078 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.130 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 7.642 | ||||
| SD | 6.898 | ||||
| Sharpe ratio (Glass type estimate) | 1.108 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.107 | ||||
| df | 1541.000 | ||||
| t | 2.688 | ||||
| p | 0.457 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.299 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.917 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.299 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.916 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 6.441 | ||||
| Upside Potential Ratio | 8.280 | ||||
| Upside part of mean | 9.823 | ||||
| Downside part of mean | -2.181 | ||||
| Upside SD | 6.809 | ||||
| Downside SD | 1.186 | ||||
| N nonnegative terms | 179.000 | ||||
| N negative terms | 1363.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1542.000 | ||||
| Mean of predictor | 0.365 | ||||
| Mean of criterion | 7.642 | ||||
| SD of predictor | 0.527 | ||||
| SD of criterion | 6.898 | ||||
| Covariance | 0.099 | ||||
| r | 0.027 | ||||
| b (slope, estimate of beta) | 0.356 | ||||
| a (intercept, estimate of alpha) | 7.512 | ||||
| Mean Square Error | 47.577 | ||||
| DF error | 1540.000 | ||||
| t(b) | 1.067 | ||||
| p(b) | 0.486 | ||||
| t(a) | 2.640 | ||||
| p(a) | 0.466 | ||||
| Lowerbound of 95% confidence interval for beta | -0.298 | ||||
| Upperbound of 95% confidence interval for beta | 1.011 | ||||
| Lowerbound of 95% confidence interval for alpha | 1.930 | ||||
| Upperbound of 95% confidence interval for alpha | 13.094 | ||||
| Treynor index (mean / b) | 21.461 | ||||
| Jensen alpha (a) | 7.512 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.022 | ||||
| SD | 3.402 | ||||
| Sharpe ratio (Glass type estimate) | 0.007 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.007 | ||||
| df | 1541.000 | ||||
| t | 0.016 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.801 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.814 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.801 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.814 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.009 | ||||
| Upside Potential Ratio | 1.668 | ||||
| Upside part of mean | 3.937 | ||||
| Downside part of mean | -3.915 | ||||
| Upside SD | 2.448 | ||||
| Downside SD | 2.361 | ||||
| N nonnegative terms | 179.000 | ||||
| N negative terms | 1363.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1542.000 | ||||
| Mean of predictor | 0.228 | ||||
| Mean of criterion | 0.022 | ||||
| SD of predictor | 0.522 | ||||
| SD of criterion | 3.402 | ||||
| Covariance | 0.023 | ||||
| r | 0.013 | ||||
| b (slope, estimate of beta) | 0.083 | ||||
| a (intercept, estimate of alpha) | 0.003 | ||||
| Mean Square Error | 11.582 | ||||
| DF error | 1540.000 | ||||
| t(b) | 0.501 | ||||
| p(b) | 0.494 | ||||
| t(a) | 0.002 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | -0.242 | ||||
| Upperbound of 95% confidence interval for beta | 0.409 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.749 | ||||
| Upperbound of 95% confidence interval for alpha | 2.756 | ||||
| Treynor index (mean / b) | 0.266 | ||||
| Jensen alpha (a) | 0.003 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.292 | ||||
| Expected Shortfall on VaR | 0.350 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.061 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1542.000 | ||||
| Minimum | 0.120 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 7.816 | ||||
| Mean of quarter 1 | 0.967 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.150 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 158.000 | ||||
| Percentage of outliers low | 0.102 | ||||
| Mean of outliers low | 0.920 | ||||
| Number of outliers high | 201.000 | ||||
| Percentage of outliers high | 0.130 | ||||
| Mean of outliers high | 1.288 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.107 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.990 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.948 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.772 | ||||
| Quartile 1 | 0.807 | ||||
| Median | 0.846 | ||||
| Quartile 3 | 0.875 | ||||
| Maximum | 0.888 | ||||
| Mean of quarter 1 | 0.786 | ||||
| Mean of quarter 2 | 0.833 | ||||
| Mean of quarter 3 | 0.860 | ||||
| Mean of quarter 4 | 0.884 | ||||
| Inter Quartile Range | 0.068 | ||||
| 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) | 0.081 | ||||
| Compounded annual return (geometric extrapolation) | 0.068 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.077 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.077 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.196 | ||||
| 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 | 0.843 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.464 | ||||
| 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 | 0.734 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.467 | ||||
| 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) | -8758279429329471.000 | ||||
| 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) | -116732360619909609512271769239552.000 | ||||
| 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 | ||||