Advanced Statistics: System 64862505
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 | 0.259 | ||||
| SD | 1.203 | ||||
| Sharpe ratio (Glass type estimate) | 0.216 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.212 | ||||
| df | 40.000 | ||||
| t | 0.399 | ||||
| p | 0.346 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.847 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.276 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.850 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.273 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.378 | ||||
| Upside Potential Ratio | 1.475 | ||||
| Upside part of mean | 1.013 | ||||
| Downside part of mean | -0.754 | ||||
| Upside SD | 0.973 | ||||
| Downside SD | 0.687 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.518 | ||||
| Mean of criterion | 0.259 | ||||
| SD of predictor | 0.238 | ||||
| SD of criterion | 1.203 | ||||
| Covariance | 0.013 | ||||
| r | 0.046 | ||||
| b (slope, estimate of beta) | 0.230 | ||||
| a (intercept, estimate of alpha) | 0.140 | ||||
| Mean Square Error | 1.482 | ||||
| DF error | 39.000 | ||||
| t(b) | 0.284 | ||||
| p(b) | 0.389 | ||||
| t(a) | 0.180 | ||||
| p(a) | 0.429 | ||||
| Lowerbound of 95% confidence interval for beta | -1.408 | ||||
| Upperbound of 95% confidence interval for beta | 1.869 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.439 | ||||
| Upperbound of 95% confidence interval for alpha | 1.720 | ||||
| Treynor index (mean / b) | 1.126 | ||||
| Jensen alpha (a) | 0.140 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.415 | ||||
| SD | 6.624 | ||||
| Sharpe ratio (Glass type estimate) | -0.516 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.506 | ||||
| df | 40.000 | ||||
| t | -0.953 | ||||
| p | 0.827 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.579 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.554 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.572 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.560 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.519 | ||||
| Upside Potential Ratio | 0.110 | ||||
| Upside part of mean | 0.724 | ||||
| Downside part of mean | -4.139 | ||||
| Upside SD | 0.668 | ||||
| Downside SD | 6.583 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.480 | ||||
| Mean of criterion | -3.415 | ||||
| SD of predictor | 0.225 | ||||
| SD of criterion | 6.624 | ||||
| Covariance | 0.181 | ||||
| r | 0.121 | ||||
| b (slope, estimate of beta) | 3.567 | ||||
| a (intercept, estimate of alpha) | -5.129 | ||||
| Mean Square Error | 44.338 | ||||
| DF error | 39.000 | ||||
| t(b) | 0.763 | ||||
| p(b) | 0.225 | ||||
| t(a) | -1.208 | ||||
| p(a) | 0.883 | ||||
| Lowerbound of 95% confidence interval for beta | -5.895 | ||||
| Upperbound of 95% confidence interval for beta | 13.029 | ||||
| Lowerbound of 95% confidence interval for alpha | -13.716 | ||||
| Upperbound of 95% confidence interval for alpha | 3.459 | ||||
| Treynor index (mean / b) | -0.957 | ||||
| Jensen alpha (a) | -5.129 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.968 | ||||
| Expected Shortfall on VaR | 0.982 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.202 | ||||
| Expected Shortfall on VaR | 0.426 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 41.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.200 | ||||
| Mean of quarter 1 | 0.778 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.348 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.122 | ||||
| Mean of outliers low | 0.511 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.122 | ||||
| Mean of outliers high | 1.696 | ||||
| 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) | -0.191 | ||||
| VaR(95%) (regression method) | 0.412 | ||||
| Expected Shortfall (regression method) | 0.709 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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) | -0.293 | ||||
| Compounded annual return (geometric extrapolation) | -0.966 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.966 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.983 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.406 | ||||
| SD | 1.235 | ||||
| Sharpe ratio (Glass type estimate) | 0.329 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.329 | ||||
| df | 906.000 | ||||
| t | 0.612 | ||||
| p | 0.270 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.725 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.382 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.725 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.382 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.616 | ||||
| Upside Potential Ratio | 3.207 | ||||
| Upside part of mean | 2.117 | ||||
| Downside part of mean | -1.711 | ||||
| Upside SD | 1.044 | ||||
| Downside SD | 0.660 | ||||
| N nonnegative terms | 115.000 | ||||
| N negative terms | 792.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 907.000 | ||||
| Mean of predictor | 0.561 | ||||
| Mean of criterion | 0.406 | ||||
| SD of predictor | 0.321 | ||||
| SD of criterion | 1.235 | ||||
| Covariance | -0.016 | ||||
| r | -0.040 | ||||
| b (slope, estimate of beta) | -0.153 | ||||
| a (intercept, estimate of alpha) | 0.492 | ||||
| Mean Square Error | 1.526 | ||||
| DF error | 905.000 | ||||
| t(b) | -1.195 | ||||
| p(b) | 0.884 | ||||
| t(a) | 0.737 | ||||
| p(a) | 0.231 | ||||
| Lowerbound of 95% confidence interval for beta | -0.404 | ||||
| Upperbound of 95% confidence interval for beta | 0.098 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.818 | ||||
| Upperbound of 95% confidence interval for alpha | 1.803 | ||||
| Treynor index (mean / b) | -2.660 | ||||
| Jensen alpha (a) | 0.492 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.371 | ||||
| SD | 6.900 | ||||
| Sharpe ratio (Glass type estimate) | -0.489 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.488 | ||||
| df | 906.000 | ||||
| t | -0.909 | ||||
| p | 0.818 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.542 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.565 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.542 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.565 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.491 | ||||
| Upside Potential Ratio | 0.264 | ||||
| Upside part of mean | 1.816 | ||||
| Downside part of mean | -5.187 | ||||
| Upside SD | 0.678 | ||||
| Downside SD | 6.866 | ||||
| N nonnegative terms | 115.000 | ||||
| N negative terms | 792.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 907.000 | ||||
| Mean of predictor | 0.508 | ||||
| Mean of criterion | -3.371 | ||||
| SD of predictor | 0.324 | ||||
| SD of criterion | 6.900 | ||||
| Covariance | 0.052 | ||||
| r | 0.023 | ||||
| b (slope, estimate of beta) | 0.497 | ||||
| a (intercept, estimate of alpha) | -3.624 | ||||
| Mean Square Error | 47.640 | ||||
| DF error | 905.000 | ||||
| t(b) | 0.702 | ||||
| p(b) | 0.242 | ||||
| t(a) | -0.972 | ||||
| p(a) | 0.834 | ||||
| Lowerbound of 95% confidence interval for beta | -0.893 | ||||
| Upperbound of 95% confidence interval for beta | 1.887 | ||||
| Lowerbound of 95% confidence interval for alpha | -10.939 | ||||
| Upperbound of 95% confidence interval for alpha | 3.691 | ||||
| Treynor index (mean / b) | -6.782 | ||||
| Jensen alpha (a) | -3.624 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.510 | ||||
| Expected Shortfall on VaR | 0.585 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 907.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.764 | ||||
| Mean of quarter 1 | 0.974 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.032 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 99.000 | ||||
| Percentage of outliers low | 0.109 | ||||
| Mean of outliers low | 0.942 | ||||
| Number of outliers high | 116.000 | ||||
| Percentage of outliers high | 0.128 | ||||
| Mean of outliers high | 1.063 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.239 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.007 | ||||
| Extreme Value Index (regression method) | 0.310 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.065 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.037 | ||||
| Quartile 1 | 0.047 | ||||
| Median | 0.048 | ||||
| Quartile 3 | 0.094 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.042 | ||||
| Mean of quarter 2 | 0.048 | ||||
| Mean of quarter 3 | 0.094 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.047 | ||||
| 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 | 1.000 | ||||
| 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) | -0.289 | ||||
| Compounded annual return (geometric extrapolation) | -0.964 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.964 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.964 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.647 | ||||
| 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 | 1.047 | ||||
| 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 | 0.923 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.498 | ||||
| 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) | -8742221678294522.000 | ||||
| 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) | 163521992970504633122598533726208.000 | ||||
| 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 | ||||