Advanced Statistics: MAJIK DAILY
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 | 1.310 | ||||
| SD | 2.796 | ||||
| Sharpe ratio (Glass type estimate) | 0.468 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.464 | ||||
| df | 75.000 | ||||
| t | 1.179 | ||||
| p | 0.121 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.316 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.249 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.319 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.246 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.751 | ||||
| Upside Potential Ratio | 3.487 | ||||
| Upside part of mean | 1.660 | ||||
| Downside part of mean | -0.350 | ||||
| Upside SD | 2.763 | ||||
| Downside SD | 0.476 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 63.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 76.000 | ||||
| Mean of predictor | 0.280 | ||||
| Mean of criterion | 1.310 | ||||
| SD of predictor | 0.280 | ||||
| SD of criterion | 2.796 | ||||
| Covariance | 0.274 | ||||
| r | 0.350 | ||||
| b (slope, estimate of beta) | 3.497 | ||||
| a (intercept, estimate of alpha) | 0.331 | ||||
| Mean Square Error | 6.953 | ||||
| DF error | 74.000 | ||||
| t(b) | 3.215 | ||||
| p(b) | 0.001 | ||||
| t(a) | 0.303 | ||||
| p(a) | 0.381 | ||||
| Lowerbound of 95% confidence interval for beta | 1.330 | ||||
| Upperbound of 95% confidence interval for beta | 5.665 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.844 | ||||
| Upperbound of 95% confidence interval for alpha | 2.505 | ||||
| Treynor index (mean / b) | 0.374 | ||||
| Jensen alpha (a) | 0.331 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.087 | ||||
| SD | 1.380 | ||||
| Sharpe ratio (Glass type estimate) | 0.063 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.063 | ||||
| df | 75.000 | ||||
| t | 0.159 | ||||
| p | 0.437 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.716 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.842 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.716 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.842 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.090 | ||||
| Upside Potential Ratio | 0.749 | ||||
| Upside part of mean | 0.725 | ||||
| Downside part of mean | -0.638 | ||||
| Upside SD | 0.971 | ||||
| Downside SD | 0.968 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 63.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 76.000 | ||||
| Mean of predictor | 0.239 | ||||
| Mean of criterion | 0.087 | ||||
| SD of predictor | 0.272 | ||||
| SD of criterion | 1.380 | ||||
| Covariance | 0.107 | ||||
| r | 0.286 | ||||
| b (slope, estimate of beta) | 1.454 | ||||
| a (intercept, estimate of alpha) | -0.260 | ||||
| Mean Square Error | 1.773 | ||||
| DF error | 74.000 | ||||
| t(b) | 2.569 | ||||
| p(b) | 0.006 | ||||
| t(a) | -0.477 | ||||
| p(a) | 0.683 | ||||
| Lowerbound of 95% confidence interval for beta | 0.326 | ||||
| Upperbound of 95% confidence interval for beta | 2.581 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.349 | ||||
| Upperbound of 95% confidence interval for alpha | 0.828 | ||||
| Treynor index (mean / b) | 0.060 | ||||
| Jensen alpha (a) | -0.260 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.477 | ||||
| Expected Shortfall on VaR | 0.553 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.090 | ||||
| Expected Shortfall on VaR | 0.201 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 76.000 | ||||
| Minimum | 0.182 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 7.442 | ||||
| Mean of quarter 1 | 0.895 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.556 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.105 | ||||
| Mean of outliers low | 0.751 | ||||
| Number of outliers high | 16.000 | ||||
| Percentage of outliers high | 0.211 | ||||
| Mean of outliers high | 1.660 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.724 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -1.356 | ||||
| VaR(95%) (regression method) | 0.100 | ||||
| Expected Shortfall (regression method) | 0.146 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.866 | ||||
| Quartile 1 | 0.866 | ||||
| Median | 0.866 | ||||
| Quartile 3 | 0.866 | ||||
| Maximum | 0.866 | ||||
| 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) | 0.205 | ||||
| Compounded annual return (geometric extrapolation) | 0.140 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.162 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.254 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 10.866 | ||||
| SD | 10.705 | ||||
| Sharpe ratio (Glass type estimate) | 1.015 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.015 | ||||
| df | 1668.000 | ||||
| t | 2.562 | ||||
| p | 0.469 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.238 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.792 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.237 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.792 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 8.919 | ||||
| Upside Potential Ratio | 10.949 | ||||
| Upside part of mean | 13.339 | ||||
| Downside part of mean | -2.474 | ||||
| Upside SD | 10.654 | ||||
| Downside SD | 1.218 | ||||
| N nonnegative terms | 214.000 | ||||
| N negative terms | 1455.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1669.000 | ||||
| Mean of predictor | 0.429 | ||||
| Mean of criterion | 10.866 | ||||
| SD of predictor | 0.600 | ||||
| SD of criterion | 10.705 | ||||
| Covariance | 1.577 | ||||
| r | 0.246 | ||||
| b (slope, estimate of beta) | 4.385 | ||||
| a (intercept, estimate of alpha) | 8.983 | ||||
| Mean Square Error | 107.749 | ||||
| DF error | 1667.000 | ||||
| t(b) | 10.348 | ||||
| p(b) | 0.345 | ||||
| t(a) | 2.182 | ||||
| p(a) | 0.466 | ||||
| Lowerbound of 95% confidence interval for beta | 3.554 | ||||
| Upperbound of 95% confidence interval for beta | 5.217 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.908 | ||||
| Upperbound of 95% confidence interval for alpha | 17.057 | ||||
| Treynor index (mean / b) | 2.478 | ||||
| Jensen alpha (a) | 8.983 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.087 | ||||
| SD | 3.759 | ||||
| Sharpe ratio (Glass type estimate) | 0.023 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.023 | ||||
| df | 1668.000 | ||||
| t | 0.058 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.753 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.800 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.754 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.800 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.034 | ||||
| Upside Potential Ratio | 1.763 | ||||
| Upside part of mean | 4.536 | ||||
| Downside part of mean | -4.449 | ||||
| Upside SD | 2.739 | ||||
| Downside SD | 2.573 | ||||
| N nonnegative terms | 214.000 | ||||
| N negative terms | 1455.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1669.000 | ||||
| Mean of predictor | 0.253 | ||||
| Mean of criterion | 0.087 | ||||
| SD of predictor | 0.593 | ||||
| SD of criterion | 3.759 | ||||
| Covariance | 0.566 | ||||
| r | 0.254 | ||||
| b (slope, estimate of beta) | 1.609 | ||||
| a (intercept, estimate of alpha) | -0.320 | ||||
| Mean Square Error | 13.229 | ||||
| DF error | 1667.000 | ||||
| t(b) | 10.716 | ||||
| p(b) | 0.340 | ||||
| t(a) | -0.222 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | 1.315 | ||||
| Upperbound of 95% confidence interval for beta | 1.904 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.148 | ||||
| Upperbound of 95% confidence interval for alpha | 2.507 | ||||
| Treynor index (mean / b) | 0.054 | ||||
| Jensen alpha (a) | -0.320 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.317 | ||||
| Expected Shortfall on VaR | 0.378 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.069 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1669.000 | ||||
| Minimum | 0.125 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 20.944 | ||||
| Mean of quarter 1 | 0.963 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.204 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 199.000 | ||||
| Percentage of outliers low | 0.119 | ||||
| Mean of outliers low | 0.922 | ||||
| Number of outliers high | 223.000 | ||||
| Percentage of outliers high | 0.134 | ||||
| Mean of outliers high | 1.381 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.953 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.735 | ||||
| VaR(95%) (regression method) | 0.008 | ||||
| Expected Shortfall (regression method) | 0.058 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.952 | ||||
| Quartile 1 | 0.952 | ||||
| Median | 0.952 | ||||
| Quartile 3 | 0.952 | ||||
| Maximum | 0.952 | ||||
| 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) | 0.204 | ||||
| Compounded annual return (geometric extrapolation) | 0.140 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.147 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.369 | ||||
| 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 | 0.970 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.448 | ||||
| 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 | 0.869 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.449 | ||||
| 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) | -8737029736817364.000 | ||||
| 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) | -201417010888080301864410593361920.000 | ||||
| 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 | ||||