Advanced Statistics: es/
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 | 0.510 | ||||
| SD | 0.835 | ||||
| Sharpe ratio (Glass type estimate) | 0.611 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.602 | ||||
| df | 52.000 | ||||
| t | 1.285 | ||||
| p | 0.102 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.331 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.548 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.337 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.542 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.616 | ||||
| Upside Potential Ratio | 2.628 | ||||
| Upside part of mean | 0.830 | ||||
| Downside part of mean | -0.320 | ||||
| Upside SD | 0.778 | ||||
| Downside SD | 0.316 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.368 | ||||
| Mean of criterion | 0.510 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.835 | ||||
| Covariance | -0.065 | ||||
| r | -0.297 | ||||
| b (slope, estimate of beta) | -0.945 | ||||
| a (intercept, estimate of alpha) | 0.858 | ||||
| Mean Square Error | 0.648 | ||||
| DF error | 51.000 | ||||
| t(b) | -2.224 | ||||
| p(b) | 0.985 | ||||
| t(a) | 2.074 | ||||
| p(a) | 0.022 | ||||
| Lowerbound of 95% confidence interval for beta | -1.798 | ||||
| Upperbound of 95% confidence interval for beta | -0.092 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.028 | ||||
| Upperbound of 95% confidence interval for alpha | 1.688 | ||||
| Treynor index (mean / b) | -0.540 | ||||
| Jensen alpha (a) | 0.858 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.247 | ||||
| SD | 0.690 | ||||
| Sharpe ratio (Glass type estimate) | 0.359 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.354 | ||||
| df | 52.000 | ||||
| t | 0.754 | ||||
| p | 0.227 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.578 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.292 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.581 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.289 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.615 | ||||
| Upside Potential Ratio | 1.578 | ||||
| Upside part of mean | 0.635 | ||||
| Downside part of mean | -0.387 | ||||
| Upside SD | 0.557 | ||||
| Downside SD | 0.402 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.330 | ||||
| Mean of criterion | 0.247 | ||||
| SD of predictor | 0.247 | ||||
| SD of criterion | 0.690 | ||||
| Covariance | -0.051 | ||||
| r | -0.301 | ||||
| b (slope, estimate of beta) | -0.843 | ||||
| a (intercept, estimate of alpha) | 0.526 | ||||
| Mean Square Error | 0.441 | ||||
| DF error | 51.000 | ||||
| t(b) | -2.257 | ||||
| p(b) | 0.986 | ||||
| t(a) | 1.550 | ||||
| p(a) | 0.064 | ||||
| Lowerbound of 95% confidence interval for beta | -1.592 | ||||
| Upperbound of 95% confidence interval for beta | -0.093 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.155 | ||||
| Upperbound of 95% confidence interval for alpha | 1.207 | ||||
| Treynor index (mean / b) | -0.294 | ||||
| Jensen alpha (a) | 0.526 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.264 | ||||
| Expected Shortfall on VaR | 0.321 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.079 | ||||
| Expected Shortfall on VaR | 0.171 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 53.000 | ||||
| Minimum | 0.544 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.192 | ||||
| Mean of quarter 1 | 0.910 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.285 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.094 | ||||
| Mean of outliers low | 0.748 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.245 | ||||
| Mean of outliers high | 1.285 | ||||
| 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) | -0.730 | ||||
| VaR(95%) (regression method) | 0.167 | ||||
| Expected Shortfall (regression method) | 0.256 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.177 | ||||
| Quartile 1 | 0.285 | ||||
| Median | 0.394 | ||||
| Quartile 3 | 0.460 | ||||
| Maximum | 0.527 | ||||
| Mean of quarter 1 | 0.177 | ||||
| Mean of quarter 2 | 0.394 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.527 | ||||
| Inter Quartile Range | 0.175 | ||||
| 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) | 0.594 | ||||
| Compounded annual return (geometric extrapolation) | 0.338 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.642 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.642 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.054 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.498 | ||||
| SD | 0.718 | ||||
| Sharpe ratio (Glass type estimate) | 0.694 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.693 | ||||
| df | 1162.000 | ||||
| t | 1.462 | ||||
| p | 0.479 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.237 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.624 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.237 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.624 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.119 | ||||
| Upside Potential Ratio | 4.181 | ||||
| Upside part of mean | 1.862 | ||||
| Downside part of mean | -1.364 | ||||
| Upside SD | 0.564 | ||||
| Downside SD | 0.445 | ||||
| N nonnegative terms | 139.000 | ||||
| N negative terms | 1024.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1163.000 | ||||
| Mean of predictor | 0.377 | ||||
| Mean of criterion | 0.498 | ||||
| SD of predictor | 0.313 | ||||
| SD of criterion | 0.718 | ||||
| Covariance | -0.010 | ||||
| r | -0.046 | ||||
| b (slope, estimate of beta) | -0.105 | ||||
| a (intercept, estimate of alpha) | 0.538 | ||||
| Mean Square Error | 0.515 | ||||
| DF error | 1161.000 | ||||
| t(b) | -1.569 | ||||
| p(b) | 0.529 | ||||
| t(a) | 1.575 | ||||
| p(a) | 0.471 | ||||
| Lowerbound of 95% confidence interval for beta | -0.237 | ||||
| Upperbound of 95% confidence interval for beta | 0.026 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.132 | ||||
| Upperbound of 95% confidence interval for alpha | 1.208 | ||||
| Treynor index (mean / b) | -4.722 | ||||
| Jensen alpha (a) | 0.538 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.246 | ||||
| SD | 0.712 | ||||
| Sharpe ratio (Glass type estimate) | 0.346 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.345 | ||||
| df | 1162.000 | ||||
| t | 0.728 | ||||
| p | 0.489 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.585 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.276 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.585 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.276 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.480 | ||||
| Upside Potential Ratio | 3.375 | ||||
| Upside part of mean | 1.729 | ||||
| Downside part of mean | -1.483 | ||||
| Upside SD | 0.494 | ||||
| Downside SD | 0.512 | ||||
| N nonnegative terms | 139.000 | ||||
| N negative terms | 1024.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1163.000 | ||||
| Mean of predictor | 0.328 | ||||
| Mean of criterion | 0.246 | ||||
| SD of predictor | 0.310 | ||||
| SD of criterion | 0.712 | ||||
| Covariance | -0.008 | ||||
| r | -0.035 | ||||
| b (slope, estimate of beta) | -0.081 | ||||
| a (intercept, estimate of alpha) | 0.272 | ||||
| Mean Square Error | 0.506 | ||||
| DF error | 1161.000 | ||||
| t(b) | -1.201 | ||||
| p(b) | 0.522 | ||||
| t(a) | 0.805 | ||||
| p(a) | 0.485 | ||||
| Lowerbound of 95% confidence interval for beta | -0.213 | ||||
| Upperbound of 95% confidence interval for beta | 0.051 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.392 | ||||
| Upperbound of 95% confidence interval for alpha | 0.937 | ||||
| Treynor index (mean / b) | -3.043 | ||||
| Jensen alpha (a) | 0.272 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.069 | ||||
| Expected Shortfall on VaR | 0.086 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1163.000 | ||||
| Minimum | 0.653 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.620 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.028 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 117.000 | ||||
| Percentage of outliers low | 0.101 | ||||
| Mean of outliers low | 0.950 | ||||
| Number of outliers high | 140.000 | ||||
| Percentage of outliers high | 0.120 | ||||
| Mean of outliers high | 1.059 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.203 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.366 | ||||
| VaR(95%) (regression method) | 0.017 | ||||
| Expected Shortfall (regression method) | 0.059 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 17.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.018 | ||||
| Median | 0.071 | ||||
| Quartile 3 | 0.190 | ||||
| Maximum | 0.635 | ||||
| Mean of quarter 1 | 0.010 | ||||
| Mean of quarter 2 | 0.042 | ||||
| Mean of quarter 3 | 0.145 | ||||
| Mean of quarter 4 | 0.565 | ||||
| Inter Quartile Range | 0.173 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.235 | ||||
| Mean of outliers high | 0.565 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -47.421 | ||||
| VaR(95%) (moments method) | 0.401 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -2.366 | ||||
| VaR(95%) (regression method) | 0.677 | ||||
| Expected Shortfall (regression method) | 0.683 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.591 | ||||
| Compounded annual return (geometric extrapolation) | 0.336 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.530 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.596 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.924 | ||||
| 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 | 0.940 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.462 | ||||
| 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 | 0.832 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.461 | ||||
| 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) | -8745191458625828.000 | ||||
| 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) | -3087647931015220507082854928220160.000 | ||||
| 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 | ||||