Advanced Statistics: Test System. Now Closed.
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 | 1.949 | ||||
| SD | 5.418 | ||||
| Sharpe ratio (Glass type estimate) | 0.360 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.356 | ||||
| df | 72.000 | ||||
| t | 0.887 | ||||
| p | 0.189 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.438 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.155 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.441 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.153 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4.527 | ||||
| Upside Potential Ratio | 5.217 | ||||
| Upside part of mean | 2.246 | ||||
| Downside part of mean | -0.297 | ||||
| Upside SD | 5.393 | ||||
| Downside SD | 0.431 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 71.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.319 | ||||
| Mean of criterion | 1.949 | ||||
| SD of predictor | 0.358 | ||||
| SD of criterion | 5.418 | ||||
| Covariance | 0.610 | ||||
| r | 0.314 | ||||
| b (slope, estimate of beta) | 4.751 | ||||
| a (intercept, estimate of alpha) | 0.433 | ||||
| Mean Square Error | 26.832 | ||||
| DF error | 71.000 | ||||
| t(b) | 2.788 | ||||
| p(b) | 0.003 | ||||
| t(a) | 0.200 | ||||
| p(a) | 0.421 | ||||
| Lowerbound of 95% confidence interval for beta | 1.353 | ||||
| Upperbound of 95% confidence interval for beta | 8.149 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.892 | ||||
| Upperbound of 95% confidence interval for alpha | 4.759 | ||||
| Treynor index (mean / b) | 0.410 | ||||
| Jensen alpha (a) | 0.433 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 1.407 | ||||
| Sharpe ratio (Glass type estimate) | -0.031 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.031 | ||||
| df | 72.000 | ||||
| t | -0.077 | ||||
| p | 0.531 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.826 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.763 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.826 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.764 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.050 | ||||
| Upside Potential Ratio | 0.553 | ||||
| Upside part of mean | 0.488 | ||||
| Downside part of mean | -0.532 | ||||
| Upside SD | 1.084 | ||||
| Downside SD | 0.882 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 71.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.253 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.352 | ||||
| SD of criterion | 1.407 | ||||
| Covariance | 0.139 | ||||
| r | 0.281 | ||||
| b (slope, estimate of beta) | 1.125 | ||||
| a (intercept, estimate of alpha) | -0.329 | ||||
| Mean Square Error | 1.849 | ||||
| DF error | 71.000 | ||||
| t(b) | 2.469 | ||||
| p(b) | 0.008 | ||||
| t(a) | -0.584 | ||||
| p(a) | 0.720 | ||||
| Lowerbound of 95% confidence interval for beta | 0.216 | ||||
| Upperbound of 95% confidence interval for beta | 2.033 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.452 | ||||
| Upperbound of 95% confidence interval for alpha | 0.794 | ||||
| Treynor index (mean / b) | -0.039 | ||||
| Jensen alpha (a) | -0.329 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.489 | ||||
| Expected Shortfall on VaR | 0.564 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.085 | ||||
| Expected Shortfall on VaR | 0.187 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 73.000 | ||||
| Minimum | 0.142 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 14.300 | ||||
| Mean of quarter 1 | 0.919 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.759 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.041 | ||||
| Mean of outliers low | 0.485 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.027 | ||||
| Mean of outliers high | 7.835 | ||||
| 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) | -0.174 | ||||
| VaR(95%) (regression method) | 0.035 | ||||
| Expected Shortfall (regression method) | 0.414 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.930 | ||||
| Quartile 1 | 0.930 | ||||
| Median | 0.930 | ||||
| Quartile 3 | 0.930 | ||||
| Maximum | 0.930 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 17.601 | ||||
| SD | 13.011 | ||||
| Sharpe ratio (Glass type estimate) | 1.353 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.352 | ||||
| df | 1595.000 | ||||
| t | 3.339 | ||||
| p | 0.447 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.557 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.148 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.557 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.148 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 11.473 | ||||
| Upside Potential Ratio | 13.738 | ||||
| Upside part of mean | 21.075 | ||||
| Downside part of mean | -3.474 | ||||
| Upside SD | 12.962 | ||||
| Downside SD | 1.534 | ||||
| N nonnegative terms | 45.000 | ||||
| N negative terms | 1551.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1596.000 | ||||
| Mean of predictor | 0.433 | ||||
| Mean of criterion | 17.601 | ||||
| SD of predictor | 0.585 | ||||
| SD of criterion | 13.011 | ||||
| Covariance | 2.169 | ||||
| r | 0.285 | ||||
| b (slope, estimate of beta) | 6.343 | ||||
| a (intercept, estimate of alpha) | 14.853 | ||||
| Mean Square Error | 155.633 | ||||
| DF error | 1594.000 | ||||
| t(b) | 11.873 | ||||
| p(b) | 0.357 | ||||
| t(a) | 2.936 | ||||
| p(a) | 0.463 | ||||
| Lowerbound of 95% confidence interval for beta | 5.295 | ||||
| Upperbound of 95% confidence interval for beta | 7.391 | ||||
| Lowerbound of 95% confidence interval for alpha | 4.929 | ||||
| Upperbound of 95% confidence interval for alpha | 24.778 | ||||
| Treynor index (mean / b) | 2.775 | ||||
| Jensen alpha (a) | 14.853 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 4.832 | ||||
| Sharpe ratio (Glass type estimate) | -0.009 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.009 | ||||
| df | 1595.000 | ||||
| t | -0.022 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.803 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.785 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.803 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.785 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.013 | ||||
| Upside Potential Ratio | 1.992 | ||||
| Upside part of mean | 6.681 | ||||
| Downside part of mean | -6.725 | ||||
| Upside SD | 3.477 | ||||
| Downside SD | 3.353 | ||||
| N nonnegative terms | 45.000 | ||||
| N negative terms | 1551.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1596.000 | ||||
| Mean of predictor | 0.263 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.583 | ||||
| SD of criterion | 4.832 | ||||
| Covariance | 0.866 | ||||
| r | 0.307 | ||||
| b (slope, estimate of beta) | 2.545 | ||||
| a (intercept, estimate of alpha) | -0.714 | ||||
| Mean Square Error | 21.157 | ||||
| DF error | 1594.000 | ||||
| t(b) | 12.889 | ||||
| p(b) | 0.346 | ||||
| t(a) | -0.383 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | 2.157 | ||||
| Upperbound of 95% confidence interval for beta | 2.932 | ||||
| Lowerbound of 95% confidence interval for alpha | -4.370 | ||||
| Upperbound of 95% confidence interval for alpha | 2.943 | ||||
| Treynor index (mean / b) | -0.017 | ||||
| Jensen alpha (a) | -0.714 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.388 | ||||
| Expected Shortfall on VaR | 0.457 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.045 | ||||
| Expected Shortfall on VaR | 0.102 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1596.000 | ||||
| Minimum | 0.083 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 14.458 | ||||
| Mean of quarter 1 | 0.948 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.322 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 47.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.555 | ||||
| Number of outliers high | 45.000 | ||||
| Percentage of outliers high | 0.028 | ||||
| Mean of outliers high | 3.853 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.297 | ||||
| VaR(95%) (moments method) | -0.007 | ||||
| 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 | 3.000 | ||||
| Minimum | 0.768 | ||||
| Quartile 1 | 0.833 | ||||
| Median | 0.898 | ||||
| Quartile 3 | 0.922 | ||||
| Maximum | 0.946 | ||||
| Mean of quarter 1 | 0.768 | ||||
| Mean of quarter 2 | 0.898 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.946 | ||||
| Inter Quartile Range | 0.089 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 1.094 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.460 | ||||
| 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 | 0.987 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.459 | ||||
| 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) | -8722526713591609.000 | ||||
| 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) | 235171815007691285030173734338560.000 | ||||
| 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 | ||||