Advanced Statistics: Artex
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 | 1002.986 | ||||
| SD | 1716.473 | ||||
| Sharpe ratio (Glass type estimate) | 0.584 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.577 | ||||
| df | 63.000 | ||||
| t | 1.349 | ||||
| p | 0.091 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.273 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.437 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.277 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.432 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1038.056 | ||||
| Upside Potential Ratio | 1039.565 | ||||
| Upside part of mean | 1004.444 | ||||
| Downside part of mean | -1.458 | ||||
| Upside SD | 1727.447 | ||||
| Downside SD | 0.966 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.328 | ||||
| Mean of criterion | 1002.986 | ||||
| SD of predictor | 0.300 | ||||
| SD of criterion | 1716.473 | ||||
| Covariance | 37.758 | ||||
| r | 0.073 | ||||
| b (slope, estimate of beta) | 420.107 | ||||
| a (intercept, estimate of alpha) | 865.371 | ||||
| Mean Square Error | 2977681.672 | ||||
| DF error | 62.000 | ||||
| t(b) | 0.579 | ||||
| p(b) | 0.282 | ||||
| t(a) | 1.104 | ||||
| p(a) | 0.137 | ||||
| Lowerbound of 95% confidence interval for beta | -1029.506 | ||||
| Upperbound of 95% confidence interval for beta | 1869.720 | ||||
| Lowerbound of 95% confidence interval for alpha | -701.936 | ||||
| Upperbound of 95% confidence interval for alpha | 2432.677 | ||||
| Treynor index (mean / b) | 2.387 | ||||
| Jensen alpha (a) | 865.371 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.501 | ||||
| SD | 7.405 | ||||
| Sharpe ratio (Glass type estimate) | -0.203 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.200 | ||||
| df | 63.000 | ||||
| t | -0.468 | ||||
| p | 0.679 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.051 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.648 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.050 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.649 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.272 | ||||
| Upside Potential Ratio | 0.682 | ||||
| Upside part of mean | 3.766 | ||||
| Downside part of mean | -5.267 | ||||
| Upside SD | 4.866 | ||||
| Downside SD | 5.522 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.280 | ||||
| Mean of criterion | -1.501 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 7.405 | ||||
| Covariance | 0.270 | ||||
| r | 0.123 | ||||
| b (slope, estimate of beta) | 3.099 | ||||
| a (intercept, estimate of alpha) | -2.367 | ||||
| Mean Square Error | 54.872 | ||||
| DF error | 62.000 | ||||
| t(b) | 0.980 | ||||
| p(b) | 0.165 | ||||
| t(a) | -0.712 | ||||
| p(a) | 0.760 | ||||
| Lowerbound of 95% confidence interval for beta | -3.223 | ||||
| Upperbound of 95% confidence interval for beta | 9.421 | ||||
| Lowerbound of 95% confidence interval for alpha | -9.019 | ||||
| Upperbound of 95% confidence interval for alpha | 4.284 | ||||
| Treynor index (mean / b) | -0.484 | ||||
| Jensen alpha (a) | -2.367 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.974 | ||||
| Expected Shortfall on VaR | 0.987 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.343 | ||||
| Expected Shortfall on VaR | 0.677 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 64.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.927 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.044 | ||||
| Maximum | 3571.500 | ||||
| Mean of quarter 1 | 0.528 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 335.813 | ||||
| Inter Quartile Range | 0.118 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.203 | ||||
| Mean of outliers low | 0.463 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.094 | ||||
| Mean of outliers high | 893.656 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.387 | ||||
| VaR(95%) (moments method) | 0.334 | ||||
| Expected Shortfall (moments method) | 0.352 | ||||
| Extreme Value Index (regression method) | -2.067 | ||||
| VaR(95%) (regression method) | 0.524 | ||||
| Expected Shortfall (regression method) | 0.535 | ||||
| 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) | -0.187 | ||||
| Compounded annual return (geometric extrapolation) | -0.767 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.767 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.777 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1355.657 | ||||
| SD | 1355.472 | ||||
| Sharpe ratio (Glass type estimate) | 1.000 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.000 | ||||
| df | 1407.000 | ||||
| t | 2.319 | ||||
| p | 0.461 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.154 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.846 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.153 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.846 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 627.561 | ||||
| Upside Potential Ratio | 632.329 | ||||
| Upside part of mean | 1365.957 | ||||
| Downside part of mean | -10.300 | ||||
| Upside SD | 1357.574 | ||||
| Downside SD | 2.160 | ||||
| N nonnegative terms | 346.000 | ||||
| N negative terms | 1062.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1408.000 | ||||
| Mean of predictor | 0.460 | ||||
| Mean of criterion | 1355.657 | ||||
| SD of predictor | 0.563 | ||||
| SD of criterion | 1355.472 | ||||
| Covariance | 61.657 | ||||
| r | 0.081 | ||||
| b (slope, estimate of beta) | 194.505 | ||||
| a (intercept, estimate of alpha) | 1266.097 | ||||
| Mean Square Error | 1826609.171 | ||||
| DF error | 1406.000 | ||||
| t(b) | 3.039 | ||||
| p(b) | 0.460 | ||||
| t(a) | 2.169 | ||||
| p(a) | 0.471 | ||||
| Lowerbound of 95% confidence interval for beta | 68.968 | ||||
| Upperbound of 95% confidence interval for beta | 320.043 | ||||
| Lowerbound of 95% confidence interval for alpha | 120.985 | ||||
| Upperbound of 95% confidence interval for alpha | 2411.210 | ||||
| Treynor index (mean / b) | 6.970 | ||||
| Jensen alpha (a) | 1266.097 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.490 | ||||
| SD | 13.351 | ||||
| Sharpe ratio (Glass type estimate) | -0.112 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.112 | ||||
| df | 1407.000 | ||||
| t | -0.259 | ||||
| p | 0.504 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.957 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.734 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.957 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.734 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.153 | ||||
| Upside Potential Ratio | 2.319 | ||||
| Upside part of mean | 22.571 | ||||
| Downside part of mean | -24.061 | ||||
| Upside SD | 9.131 | ||||
| Downside SD | 9.734 | ||||
| N nonnegative terms | 346.000 | ||||
| N negative terms | 1062.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1408.000 | ||||
| Mean of predictor | 0.304 | ||||
| Mean of criterion | -1.490 | ||||
| SD of predictor | 0.558 | ||||
| SD of criterion | 13.351 | ||||
| Covariance | 0.400 | ||||
| r | 0.054 | ||||
| b (slope, estimate of beta) | 1.285 | ||||
| a (intercept, estimate of alpha) | -1.881 | ||||
| Mean Square Error | 177.862 | ||||
| DF error | 1406.000 | ||||
| t(b) | 2.016 | ||||
| p(b) | 0.473 | ||||
| t(a) | -0.327 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | 0.035 | ||||
| Upperbound of 95% confidence interval for beta | 2.535 | ||||
| Lowerbound of 95% confidence interval for alpha | -13.172 | ||||
| Upperbound of 95% confidence interval for alpha | 9.411 | ||||
| Treynor index (mean / b) | -1.159 | ||||
| Jensen alpha (a) | -1.881 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.744 | ||||
| Expected Shortfall on VaR | 0.811 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.115 | ||||
| Expected Shortfall on VaR | 0.249 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1408.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2640.286 | ||||
| Mean of quarter 1 | 0.843 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 21.854 | ||||
| Inter Quartile Range | 0.004 | ||||
| Number outliers low | 326.000 | ||||
| Percentage of outliers low | 0.232 | ||||
| Mean of outliers low | 0.831 | ||||
| Number of outliers high | 315.000 | ||||
| Percentage of outliers high | 0.224 | ||||
| Mean of outliers high | 24.304 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.780 | ||||
| VaR(95%) (moments method) | 0.042 | ||||
| Expected Shortfall (moments method) | 0.228 | ||||
| Extreme Value Index (regression method) | -0.093 | ||||
| VaR(95%) (regression method) | 0.119 | ||||
| Expected Shortfall (regression method) | 0.179 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.084 | ||||
| Quartile 1 | 0.244 | ||||
| Median | 0.310 | ||||
| Quartile 3 | 0.570 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.164 | ||||
| Mean of quarter 2 | 0.269 | ||||
| Mean of quarter 3 | 0.442 | ||||
| Mean of quarter 4 | 0.804 | ||||
| Inter Quartile Range | 0.325 | ||||
| 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) | -0.186 | ||||
| Compounded annual return (geometric extrapolation) | -0.764 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.764 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.951 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.942 | ||||
| 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 | 1.721 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.546 | ||||
| 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 | 1.568 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.544 | ||||
| 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) | -8662275942422590.000 | ||||
| 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) | -168290475886278420675851137843200.000 | ||||
| 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 | ||||