Advanced Statistics: HELIUM II
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 | -0.013 | ||||
| SD | 0.955 | ||||
| Sharpe ratio (Glass type estimate) | -0.013 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.013 | ||||
| df | 45.000 | ||||
| t | -0.026 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.014 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.988 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.014 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.988 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.021 | ||||
| Upside Potential Ratio | 1.397 | ||||
| Upside part of mean | 0.829 | ||||
| Downside part of mean | -0.842 | ||||
| Upside SD | 0.734 | ||||
| Downside SD | 0.594 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 46.000 | ||||
| Mean of predictor | 0.406 | ||||
| Mean of criterion | -0.013 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.955 | ||||
| Covariance | -0.032 | ||||
| r | -0.124 | ||||
| b (slope, estimate of beta) | -0.432 | ||||
| a (intercept, estimate of alpha) | 0.163 | ||||
| Mean Square Error | 0.918 | ||||
| DF error | 44.000 | ||||
| t(b) | -0.827 | ||||
| p(b) | 0.794 | ||||
| t(a) | 0.305 | ||||
| p(a) | 0.381 | ||||
| Lowerbound of 95% confidence interval for beta | -1.486 | ||||
| Upperbound of 95% confidence interval for beta | 0.622 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.912 | ||||
| Upperbound of 95% confidence interval for alpha | 1.238 | ||||
| Treynor index (mean / b) | 0.029 | ||||
| Jensen alpha (a) | 0.163 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.492 | ||||
| SD | 1.056 | ||||
| Sharpe ratio (Glass type estimate) | -0.466 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.458 | ||||
| df | 45.000 | ||||
| t | -0.912 | ||||
| p | 0.817 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.469 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.543 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.463 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.548 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.541 | ||||
| Upside Potential Ratio | 0.717 | ||||
| Upside part of mean | 0.652 | ||||
| Downside part of mean | -1.144 | ||||
| Upside SD | 0.533 | ||||
| Downside SD | 0.909 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 46.000 | ||||
| Mean of predictor | 0.366 | ||||
| Mean of criterion | -0.492 | ||||
| SD of predictor | 0.251 | ||||
| SD of criterion | 1.056 | ||||
| Covariance | -0.020 | ||||
| r | -0.077 | ||||
| b (slope, estimate of beta) | -0.324 | ||||
| a (intercept, estimate of alpha) | -0.373 | ||||
| Mean Square Error | 1.133 | ||||
| DF error | 44.000 | ||||
| t(b) | -0.513 | ||||
| p(b) | 0.695 | ||||
| t(a) | -0.631 | ||||
| p(a) | 0.734 | ||||
| Lowerbound of 95% confidence interval for beta | -1.597 | ||||
| Upperbound of 95% confidence interval for beta | 0.949 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.564 | ||||
| Upperbound of 95% confidence interval for alpha | 0.818 | ||||
| Treynor index (mean / b) | 1.516 | ||||
| Jensen alpha (a) | -0.373 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.419 | ||||
| Expected Shortfall on VaR | 0.485 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.211 | ||||
| Expected Shortfall on VaR | 0.421 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 46.000 | ||||
| Minimum | 0.253 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.181 | ||||
| Mean of quarter 1 | 0.742 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.268 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.239 | ||||
| Mean of outliers low | 0.719 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.217 | ||||
| Mean of outliers high | 1.322 | ||||
| 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) | 0.156 | ||||
| VaR(95%) (regression method) | 0.247 | ||||
| Expected Shortfall (regression method) | 0.451 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.266 | ||||
| Quartile 1 | 0.292 | ||||
| Median | 0.319 | ||||
| Quartile 3 | 0.625 | ||||
| Maximum | 0.932 | ||||
| Mean of quarter 1 | 0.266 | ||||
| Mean of quarter 2 | 0.319 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.932 | ||||
| Inter Quartile Range | 0.333 | ||||
| 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) | -0.214 | ||||
| Compounded annual return (geometric extrapolation) | -0.361 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.387 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.387 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.744 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.127 | ||||
| SD | 0.828 | ||||
| Sharpe ratio (Glass type estimate) | -0.153 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.153 | ||||
| df | 1024.000 | ||||
| t | -0.303 | ||||
| p | 0.505 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.144 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.838 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.144 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.838 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.214 | ||||
| Upside Potential Ratio | 4.977 | ||||
| Upside part of mean | 2.948 | ||||
| Downside part of mean | -3.075 | ||||
| Upside SD | 0.578 | ||||
| Downside SD | 0.592 | ||||
| N nonnegative terms | 218.000 | ||||
| N negative terms | 807.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1025.000 | ||||
| Mean of predictor | 0.454 | ||||
| Mean of criterion | -0.127 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.828 | ||||
| Covariance | -0.003 | ||||
| r | -0.013 | ||||
| b (slope, estimate of beta) | -0.033 | ||||
| a (intercept, estimate of alpha) | -0.112 | ||||
| Mean Square Error | 0.686 | ||||
| DF error | 1023.000 | ||||
| t(b) | -0.402 | ||||
| p(b) | 0.508 | ||||
| t(a) | -0.266 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | -0.191 | ||||
| Upperbound of 95% confidence interval for beta | 0.126 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.937 | ||||
| Upperbound of 95% confidence interval for alpha | 0.713 | ||||
| Treynor index (mean / b) | 3.890 | ||||
| Jensen alpha (a) | -0.112 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.482 | ||||
| SD | 0.857 | ||||
| Sharpe ratio (Glass type estimate) | -0.563 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.563 | ||||
| df | 1024.000 | ||||
| t | -1.114 | ||||
| p | 0.517 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.554 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.428 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.554 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.428 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.718 | ||||
| Upside Potential Ratio | 4.166 | ||||
| Upside part of mean | 2.798 | ||||
| Downside part of mean | -3.281 | ||||
| Upside SD | 0.532 | ||||
| Downside SD | 0.672 | ||||
| N nonnegative terms | 218.000 | ||||
| N negative terms | 807.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1025.000 | ||||
| Mean of predictor | 0.405 | ||||
| Mean of criterion | -0.482 | ||||
| SD of predictor | 0.312 | ||||
| SD of criterion | 0.857 | ||||
| Covariance | -0.003 | ||||
| r | -0.012 | ||||
| b (slope, estimate of beta) | -0.033 | ||||
| a (intercept, estimate of alpha) | -0.469 | ||||
| Mean Square Error | 0.734 | ||||
| DF error | 1023.000 | ||||
| t(b) | -0.383 | ||||
| p(b) | 0.508 | ||||
| t(a) | -1.080 | ||||
| p(a) | 0.521 | ||||
| Lowerbound of 95% confidence interval for beta | -0.201 | ||||
| Upperbound of 95% confidence interval for beta | 0.135 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.322 | ||||
| Upperbound of 95% confidence interval for alpha | 0.384 | ||||
| Treynor index (mean / b) | 14.707 | ||||
| Jensen alpha (a) | -0.469 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.085 | ||||
| Expected Shortfall on VaR | 0.105 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.075 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1025.000 | ||||
| Minimum | 0.527 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.397 | ||||
| Mean of quarter 1 | 0.954 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.045 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 221.000 | ||||
| Percentage of outliers low | 0.216 | ||||
| Mean of outliers low | 0.946 | ||||
| Number of outliers high | 218.000 | ||||
| Percentage of outliers high | 0.213 | ||||
| Mean of outliers high | 1.053 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.266 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 0.091 | ||||
| VaR(95%) (regression method) | 0.042 | ||||
| Expected Shortfall (regression method) | 0.075 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.038 | ||||
| Median | 0.089 | ||||
| Quartile 3 | 0.381 | ||||
| Maximum | 0.952 | ||||
| Mean of quarter 1 | 0.025 | ||||
| Mean of quarter 2 | 0.065 | ||||
| Mean of quarter 3 | 0.202 | ||||
| Mean of quarter 4 | 0.756 | ||||
| Inter Quartile Range | 0.343 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.952 | ||||
| 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) | -0.210 | ||||
| Compounded annual return (geometric extrapolation) | -0.355 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.373 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.470 | ||||
| Compounded annual return / Expected Shortfall lognormal | -3.385 | ||||
| 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 | 0.980 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.494 | ||||
| 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 | 0.857 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.492 | ||||
| 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) | -8748875976723757.000 | ||||
| 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) | 104186443099774071765874033819648.000 | ||||
| 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 | ||||