Advanced Statistics: EMiniProfits.com
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 | -0.130 | ||||
| SD | 0.673 | ||||
| Sharpe ratio (Glass type estimate) | -0.194 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.190 | ||||
| df | 37.000 | ||||
| t | -0.345 | ||||
| p | 0.634 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.295 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.910 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.292 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.912 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.283 | ||||
| Upside Potential Ratio | 0.709 | ||||
| Upside part of mean | 0.327 | ||||
| Downside part of mean | -0.457 | ||||
| Upside SD | 0.479 | ||||
| Downside SD | 0.461 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.489 | ||||
| Mean of criterion | -0.130 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.673 | ||||
| Covariance | -0.012 | ||||
| r | -0.064 | ||||
| b (slope, estimate of beta) | -0.159 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.463 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.384 | ||||
| p(b) | 0.648 | ||||
| t(a) | -0.121 | ||||
| p(a) | 0.548 | ||||
| Lowerbound of 95% confidence interval for beta | -1.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.681 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.931 | ||||
| Upperbound of 95% confidence interval for alpha | 0.826 | ||||
| Treynor index (mean / b) | 0.819 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.385 | ||||
| SD | 0.771 | ||||
| Sharpe ratio (Glass type estimate) | -0.498 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.488 | ||||
| df | 37.000 | ||||
| t | -0.887 | ||||
| p | 0.810 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.602 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.612 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.595 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.619 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.563 | ||||
| Upside Potential Ratio | 0.365 | ||||
| Upside part of mean | 0.249 | ||||
| Downside part of mean | -0.634 | ||||
| Upside SD | 0.354 | ||||
| Downside SD | 0.683 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.445 | ||||
| Mean of criterion | -0.385 | ||||
| SD of predictor | 0.259 | ||||
| SD of criterion | 0.771 | ||||
| Covariance | -0.004 | ||||
| r | -0.019 | ||||
| b (slope, estimate of beta) | -0.057 | ||||
| a (intercept, estimate of alpha) | -0.359 | ||||
| Mean Square Error | 0.611 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.114 | ||||
| p(b) | 0.545 | ||||
| t(a) | -0.731 | ||||
| p(a) | 0.765 | ||||
| Lowerbound of 95% confidence interval for beta | -1.062 | ||||
| Upperbound of 95% confidence interval for beta | 0.948 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.356 | ||||
| Upperbound of 95% confidence interval for alpha | 0.638 | ||||
| Treynor index (mean / b) | 6.785 | ||||
| Jensen alpha (a) | -0.359 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.329 | ||||
| Expected Shortfall on VaR | 0.386 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.128 | ||||
| Expected Shortfall on VaR | 0.274 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 38.000 | ||||
| Minimum | 0.371 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.832 | ||||
| Mean of quarter 1 | 0.869 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.104 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.105 | ||||
| Mean of outliers low | 0.671 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.053 | ||||
| Mean of outliers high | 1.521 | ||||
| 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) | -0.039 | ||||
| VaR(95%) (regression method) | 0.245 | ||||
| Expected Shortfall (regression method) | 0.492 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.847 | ||||
| Quartile 1 | 0.847 | ||||
| Median | 0.847 | ||||
| Quartile 3 | 0.847 | ||||
| Maximum | 0.847 | ||||
| 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) | -0.208 | ||||
| Compounded annual return (geometric extrapolation) | -0.289 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.341 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.747 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.286 | ||||
| SD | 0.427 | ||||
| Sharpe ratio (Glass type estimate) | -0.669 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.669 | ||||
| df | 847.000 | ||||
| t | -1.204 | ||||
| p | 0.886 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.759 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.421 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.759 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.421 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.904 | ||||
| Upside Potential Ratio | 2.194 | ||||
| Upside part of mean | 0.693 | ||||
| Downside part of mean | -0.979 | ||||
| Upside SD | 0.287 | ||||
| Downside SD | 0.316 | ||||
| N nonnegative terms | 58.000 | ||||
| N negative terms | 790.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 848.000 | ||||
| Mean of predictor | 0.510 | ||||
| Mean of criterion | -0.286 | ||||
| SD of predictor | 0.306 | ||||
| SD of criterion | 0.427 | ||||
| Covariance | -0.006 | ||||
| r | -0.043 | ||||
| b (slope, estimate of beta) | -0.060 | ||||
| a (intercept, estimate of alpha) | -0.255 | ||||
| Mean Square Error | 0.182 | ||||
| DF error | 846.000 | ||||
| t(b) | -1.247 | ||||
| p(b) | 0.894 | ||||
| t(a) | -1.071 | ||||
| p(a) | 0.858 | ||||
| Lowerbound of 95% confidence interval for beta | -0.154 | ||||
| Upperbound of 95% confidence interval for beta | 0.034 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.723 | ||||
| Upperbound of 95% confidence interval for alpha | 0.213 | ||||
| Treynor index (mean / b) | 4.787 | ||||
| Jensen alpha (a) | -0.255 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.377 | ||||
| SD | 0.429 | ||||
| Sharpe ratio (Glass type estimate) | -0.879 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.878 | ||||
| df | 847.000 | ||||
| t | -1.581 | ||||
| p | 0.943 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.969 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.211 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.968 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.212 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.115 | ||||
| Upside Potential Ratio | 1.939 | ||||
| Upside part of mean | 0.656 | ||||
| Downside part of mean | -1.033 | ||||
| Upside SD | 0.264 | ||||
| Downside SD | 0.338 | ||||
| N nonnegative terms | 58.000 | ||||
| N negative terms | 790.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 848.000 | ||||
| Mean of predictor | 0.462 | ||||
| Mean of criterion | -0.377 | ||||
| SD of predictor | 0.307 | ||||
| SD of criterion | 0.429 | ||||
| Covariance | -0.005 | ||||
| r | -0.042 | ||||
| b (slope, estimate of beta) | -0.058 | ||||
| a (intercept, estimate of alpha) | -0.350 | ||||
| Mean Square Error | 0.184 | ||||
| DF error | 846.000 | ||||
| t(b) | -1.213 | ||||
| p(b) | 0.887 | ||||
| t(a) | -1.463 | ||||
| p(a) | 0.928 | ||||
| Lowerbound of 95% confidence interval for beta | -0.152 | ||||
| Upperbound of 95% confidence interval for beta | 0.036 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.820 | ||||
| Upperbound of 95% confidence interval for alpha | 0.120 | ||||
| Treynor index (mean / b) | 6.482 | ||||
| Jensen alpha (a) | -0.350 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.044 | ||||
| Expected Shortfall on VaR | 0.055 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 848.000 | ||||
| Minimum | 0.812 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.279 | ||||
| Mean of quarter 1 | 0.986 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 49.000 | ||||
| Percentage of outliers low | 0.058 | ||||
| Mean of outliers low | 0.938 | ||||
| Number of outliers high | 58.000 | ||||
| Percentage of outliers high | 0.068 | ||||
| Mean of outliers high | 1.039 | ||||
| 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) | -0.294 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.035 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.029 | ||||
| Quartile 1 | 0.038 | ||||
| Median | 0.069 | ||||
| Quartile 3 | 0.135 | ||||
| Maximum | 0.858 | ||||
| Mean of quarter 1 | 0.031 | ||||
| Mean of quarter 2 | 0.051 | ||||
| Mean of quarter 3 | 0.088 | ||||
| Mean of quarter 4 | 0.504 | ||||
| Inter Quartile Range | 0.097 | ||||
| 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 | 0.167 | ||||
| Mean of outliers high | 0.858 | ||||
| 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) | -0.204 | ||||
| Compounded annual return (geometric extrapolation) | -0.283 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.330 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.562 | ||||
| Compounded annual return / Expected Shortfall lognormal | -5.196 | ||||
| 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 | 0.900 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.458 | ||||
| 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 | 0.794 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.460 | ||||
| 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) | -8749835456508065.000 | ||||
| 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) | -481673253700708854243569185062912.000 | ||||
| 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 | ||||