Advanced Statistics: TIME POWER
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.996 | ||||
| SD | 1.115 | ||||
| Sharpe ratio (Glass type estimate) | -0.893 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.875 | ||||
| df | 38.000 | ||||
| t | -1.610 | ||||
| p | 0.942 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.993 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.218 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.980 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.230 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.062 | ||||
| Upside Potential Ratio | 0.751 | ||||
| Upside part of mean | 0.704 | ||||
| Downside part of mean | -1.699 | ||||
| Upside SD | 0.645 | ||||
| Downside SD | 0.937 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.511 | ||||
| Mean of criterion | -0.996 | ||||
| SD of predictor | 0.289 | ||||
| SD of criterion | 1.115 | ||||
| Covariance | -0.050 | ||||
| r | -0.155 | ||||
| b (slope, estimate of beta) | -0.597 | ||||
| a (intercept, estimate of alpha) | -0.690 | ||||
| Mean Square Error | 1.246 | ||||
| DF error | 37.000 | ||||
| t(b) | -0.953 | ||||
| p(b) | 0.827 | ||||
| t(a) | -0.990 | ||||
| p(a) | 0.836 | ||||
| Lowerbound of 95% confidence interval for beta | -1.867 | ||||
| Upperbound of 95% confidence interval for beta | 0.672 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.103 | ||||
| Upperbound of 95% confidence interval for alpha | 0.722 | ||||
| Treynor index (mean / b) | 1.667 | ||||
| Jensen alpha (a) | -0.690 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.586 | ||||
| SD | 4.274 | ||||
| Sharpe ratio (Glass type estimate) | -0.839 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.822 | ||||
| df | 38.000 | ||||
| t | -1.513 | ||||
| p | 0.931 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.937 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.270 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.925 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.280 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.831 | ||||
| Upside Potential Ratio | 0.130 | ||||
| Upside part of mean | 0.559 | ||||
| Downside part of mean | -4.146 | ||||
| Upside SD | 0.486 | ||||
| Downside SD | 4.316 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.461 | ||||
| Mean of criterion | -3.586 | ||||
| SD of predictor | 0.281 | ||||
| SD of criterion | 4.274 | ||||
| Covariance | -0.048 | ||||
| r | -0.040 | ||||
| b (slope, estimate of beta) | -0.613 | ||||
| a (intercept, estimate of alpha) | -3.304 | ||||
| Mean Square Error | 18.728 | ||||
| DF error | 37.000 | ||||
| t(b) | -0.245 | ||||
| p(b) | 0.596 | ||||
| t(a) | -1.241 | ||||
| p(a) | 0.889 | ||||
| Lowerbound of 95% confidence interval for beta | -5.683 | ||||
| Upperbound of 95% confidence interval for beta | 4.458 | ||||
| Lowerbound of 95% confidence interval for alpha | -8.700 | ||||
| Upperbound of 95% confidence interval for alpha | 2.092 | ||||
| Treynor index (mean / b) | 5.855 | ||||
| Jensen alpha (a) | -3.304 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.903 | ||||
| Expected Shortfall on VaR | 0.937 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.428 | ||||
| Expected Shortfall on VaR | 0.763 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.771 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.927 | ||||
| Mean of quarter 1 | 0.531 | ||||
| Mean of quarter 2 | 0.928 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.232 | ||||
| Inter Quartile Range | 0.229 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.077 | ||||
| Mean of outliers low | 0.260 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.077 | ||||
| Mean of outliers high | 1.621 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.088 | ||||
| VaR(95%) (moments method) | 0.477 | ||||
| Expected Shortfall (moments method) | 0.611 | ||||
| Extreme Value Index (regression method) | 0.020 | ||||
| VaR(95%) (regression method) | 0.601 | ||||
| Expected Shortfall (regression method) | 0.836 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.220 | ||||
| Quartile 1 | 0.415 | ||||
| Median | 0.610 | ||||
| Quartile 3 | 0.805 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.220 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.390 | ||||
| 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) | -0.308 | ||||
| Compounded annual return (geometric extrapolation) | -0.971 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.971 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.971 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.037 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2485.459 | ||||
| SD | 3471.208 | ||||
| Sharpe ratio (Glass type estimate) | 0.716 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.715 | ||||
| df | 857.000 | ||||
| t | 1.296 | ||||
| p | 0.098 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.368 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.799 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.368 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.799 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1450.459 | ||||
| Upside Potential Ratio | 1454.858 | ||||
| Upside part of mean | 2492.998 | ||||
| Downside part of mean | -7.539 | ||||
| Upside SD | 3472.580 | ||||
| Downside SD | 1.714 | ||||
| N nonnegative terms | 217.000 | ||||
| N negative terms | 641.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 858.000 | ||||
| Mean of predictor | 0.504 | ||||
| Mean of criterion | 2485.459 | ||||
| SD of predictor | 0.312 | ||||
| SD of criterion | 3471.208 | ||||
| Covariance | -321.767 | ||||
| r | -0.297 | ||||
| b (slope, estimate of beta) | -3308.727 | ||||
| a (intercept, estimate of alpha) | 4153.879 | ||||
| Mean Square Error | 10997475.859 | ||||
| DF error | 856.000 | ||||
| t(b) | -9.108 | ||||
| p(b) | 1.000 | ||||
| t(a) | 2.255 | ||||
| p(a) | 0.012 | ||||
| Lowerbound of 95% confidence interval for beta | -4021.709 | ||||
| Upperbound of 95% confidence interval for beta | -2595.745 | ||||
| Lowerbound of 95% confidence interval for alpha | 539.157 | ||||
| Upperbound of 95% confidence interval for alpha | 7768.601 | ||||
| Treynor index (mean / b) | -0.751 | ||||
| Jensen alpha (a) | 4153.879 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.560 | ||||
| SD | 12.239 | ||||
| Sharpe ratio (Glass type estimate) | -0.291 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.291 | ||||
| df | 857.000 | ||||
| t | -0.526 | ||||
| p | 0.701 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.374 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.792 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.374 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.793 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.386 | ||||
| Upside Potential Ratio | 1.597 | ||||
| Upside part of mean | 14.728 | ||||
| Downside part of mean | -18.287 | ||||
| Upside SD | 8.039 | ||||
| Downside SD | 9.221 | ||||
| N nonnegative terms | 217.000 | ||||
| N negative terms | 641.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 858.000 | ||||
| Mean of predictor | 0.455 | ||||
| Mean of criterion | -3.560 | ||||
| SD of predictor | 0.314 | ||||
| SD of criterion | 12.239 | ||||
| Covariance | -0.864 | ||||
| r | -0.224 | ||||
| b (slope, estimate of beta) | -8.742 | ||||
| a (intercept, estimate of alpha) | 0.416 | ||||
| Mean Square Error | 142.404 | ||||
| DF error | 856.000 | ||||
| t(b) | -6.740 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.063 | ||||
| p(a) | 0.475 | ||||
| Lowerbound of 95% confidence interval for beta | -11.288 | ||||
| Upperbound of 95% confidence interval for beta | -6.197 | ||||
| Lowerbound of 95% confidence interval for alpha | -12.579 | ||||
| Upperbound of 95% confidence interval for alpha | 13.410 | ||||
| Treynor index (mean / b) | 0.407 | ||||
| Jensen alpha (a) | 0.416 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.716 | ||||
| Expected Shortfall on VaR | 0.785 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.083 | ||||
| Expected Shortfall on VaR | 0.183 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 858.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 6151.000 | ||||
| Mean of quarter 1 | 0.886 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 38.973 | ||||
| Inter Quartile Range | 0.009 | ||||
| Number outliers low | 175.000 | ||||
| Percentage of outliers low | 0.204 | ||||
| Mean of outliers low | 0.863 | ||||
| Number of outliers high | 168.000 | ||||
| Percentage of outliers high | 0.196 | ||||
| Mean of outliers high | 49.594 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.799 | ||||
| VaR(95%) (moments method) | 0.064 | ||||
| Expected Shortfall (moments method) | 0.367 | ||||
| Extreme Value Index (regression method) | 0.083 | ||||
| VaR(95%) (regression method) | 0.088 | ||||
| Expected Shortfall (regression method) | 0.145 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.059 | ||||
| Quartile 3 | 0.171 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.014 | ||||
| Mean of quarter 3 | 0.112 | ||||
| Mean of quarter 4 | 0.658 | ||||
| Inter Quartile Range | 0.160 | ||||
| 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 | 0.125 | ||||
| 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) | -0.305 | ||||
| Compounded annual return (geometric extrapolation) | -0.970 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.970 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.474 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.236 | ||||
| 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 | 0.830 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.468 | ||||
| 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 | 0.721 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.466 | ||||
| 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) | -8759624078437973.000 | ||||
| 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) | -95654179720622821391600982163456.000 | ||||
| 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 | ||||