Advanced Statistics: Triple ETF Market Timer
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 | 1.091 | ||||
| SD | 0.853 | ||||
| Sharpe ratio (Glass type estimate) | 1.278 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.261 | ||||
| df | 54.000 | ||||
| t | 2.737 | ||||
| p | 0.004 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.326 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.220 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.315 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.207 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.896 | ||||
| Upside Potential Ratio | 4.097 | ||||
| Upside part of mean | 1.544 | ||||
| Downside part of mean | -0.453 | ||||
| Upside SD | 0.820 | ||||
| Downside SD | 0.377 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 18.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 55.000 | ||||
| Mean of predictor | 0.336 | ||||
| Mean of criterion | 1.091 | ||||
| SD of predictor | 0.222 | ||||
| SD of criterion | 0.853 | ||||
| Covariance | 0.163 | ||||
| r | 0.858 | ||||
| b (slope, estimate of beta) | 3.292 | ||||
| a (intercept, estimate of alpha) | -0.015 | ||||
| Mean Square Error | 0.196 | ||||
| DF error | 53.000 | ||||
| t(b) | 12.139 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.067 | ||||
| p(a) | 0.527 | ||||
| Lowerbound of 95% confidence interval for beta | 2.748 | ||||
| Upperbound of 95% confidence interval for beta | 3.835 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.469 | ||||
| Upperbound of 95% confidence interval for alpha | 0.438 | ||||
| Treynor index (mean / b) | 0.331 | ||||
| Jensen alpha (a) | -0.015 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.740 | ||||
| SD | 0.804 | ||||
| Sharpe ratio (Glass type estimate) | 0.921 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.908 | ||||
| df | 54.000 | ||||
| t | 1.972 | ||||
| p | 0.027 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.015 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.849 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.023 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.839 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.410 | ||||
| Upside Potential Ratio | 2.476 | ||||
| Upside part of mean | 1.300 | ||||
| Downside part of mean | -0.560 | ||||
| Upside SD | 0.636 | ||||
| Downside SD | 0.525 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 18.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 55.000 | ||||
| Mean of predictor | 0.308 | ||||
| Mean of criterion | 0.740 | ||||
| SD of predictor | 0.212 | ||||
| SD of criterion | 0.804 | ||||
| Covariance | 0.142 | ||||
| r | 0.833 | ||||
| b (slope, estimate of beta) | 3.152 | ||||
| a (intercept, estimate of alpha) | -0.230 | ||||
| Mean Square Error | 0.202 | ||||
| DF error | 53.000 | ||||
| t(b) | 10.961 | ||||
| p(b) | -0.000 | ||||
| t(a) | -1.010 | ||||
| p(a) | 0.842 | ||||
| Lowerbound of 95% confidence interval for beta | 2.575 | ||||
| Upperbound of 95% confidence interval for beta | 3.728 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.687 | ||||
| Upperbound of 95% confidence interval for alpha | 0.227 | ||||
| Treynor index (mean / b) | 0.235 | ||||
| Jensen alpha (a) | -0.230 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.274 | ||||
| Expected Shortfall on VaR | 0.339 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.062 | ||||
| Expected Shortfall on VaR | 0.147 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 55.000 | ||||
| Minimum | 0.386 | ||||
| Quartile 1 | 0.984 | ||||
| Median | 1.065 | ||||
| Quartile 3 | 1.166 | ||||
| Maximum | 2.134 | ||||
| Mean of quarter 1 | 0.859 | ||||
| Mean of quarter 2 | 1.025 | ||||
| Mean of quarter 3 | 1.103 | ||||
| Mean of quarter 4 | 1.392 | ||||
| Inter Quartile Range | 0.182 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.036 | ||||
| Mean of outliers low | 0.544 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.055 | ||||
| Mean of outliers high | 1.751 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.839 | ||||
| VaR(95%) (moments method) | 0.113 | ||||
| Expected Shortfall (moments method) | 0.786 | ||||
| Extreme Value Index (regression method) | 0.768 | ||||
| VaR(95%) (regression method) | 0.152 | ||||
| Expected Shortfall (regression method) | 0.773 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.058 | ||||
| Median | 0.121 | ||||
| Quartile 3 | 0.237 | ||||
| Maximum | 0.614 | ||||
| Mean of quarter 1 | 0.034 | ||||
| Mean of quarter 2 | 0.102 | ||||
| Mean of quarter 3 | 0.139 | ||||
| Mean of quarter 4 | 0.415 | ||||
| Inter Quartile Range | 0.180 | ||||
| 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 | 0.100 | ||||
| Mean of outliers high | 0.614 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.401 | ||||
| VaR(95%) (moments method) | 0.491 | ||||
| Expected Shortfall (moments method) | 0.513 | ||||
| Extreme Value Index (regression method) | 0.319 | ||||
| VaR(95%) (regression method) | 0.660 | ||||
| Expected Shortfall (regression method) | 1.101 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 7.728 | ||||
| Compounded annual return (geometric extrapolation) | 1.191 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.940 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.869 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.517 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.052 | ||||
| SD | 0.709 | ||||
| Sharpe ratio (Glass type estimate) | 1.485 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.484 | ||||
| df | 1215.000 | ||||
| t | 3.199 | ||||
| p | 0.442 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.573 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.396 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.572 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.396 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.231 | ||||
| Upside Potential Ratio | 8.049 | ||||
| Upside part of mean | 3.796 | ||||
| Downside part of mean | -2.744 | ||||
| Upside SD | 0.532 | ||||
| Downside SD | 0.472 | ||||
| N nonnegative terms | 691.000 | ||||
| N negative terms | 525.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1216.000 | ||||
| Mean of predictor | 0.343 | ||||
| Mean of criterion | 1.052 | ||||
| SD of predictor | 0.211 | ||||
| SD of criterion | 0.709 | ||||
| Covariance | 0.119 | ||||
| r | 0.800 | ||||
| b (slope, estimate of beta) | 2.692 | ||||
| a (intercept, estimate of alpha) | 0.129 | ||||
| Mean Square Error | 0.181 | ||||
| DF error | 1214.000 | ||||
| t(b) | 46.512 | ||||
| p(b) | 0.100 | ||||
| t(a) | 0.651 | ||||
| p(a) | 0.491 | ||||
| Lowerbound of 95% confidence interval for beta | 2.578 | ||||
| Upperbound of 95% confidence interval for beta | 2.805 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.260 | ||||
| Upperbound of 95% confidence interval for alpha | 0.518 | ||||
| Treynor index (mean / b) | 0.391 | ||||
| Jensen alpha (a) | 0.129 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.798 | ||||
| SD | 0.714 | ||||
| Sharpe ratio (Glass type estimate) | 1.117 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.116 | ||||
| df | 1215.000 | ||||
| t | 2.406 | ||||
| p | 0.456 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.206 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.028 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.205 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.027 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.559 | ||||
| Upside Potential Ratio | 7.161 | ||||
| Upside part of mean | 3.665 | ||||
| Downside part of mean | -2.867 | ||||
| Upside SD | 0.500 | ||||
| Downside SD | 0.512 | ||||
| N nonnegative terms | 691.000 | ||||
| N negative terms | 525.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1216.000 | ||||
| Mean of predictor | 0.320 | ||||
| Mean of criterion | 0.798 | ||||
| SD of predictor | 0.211 | ||||
| SD of criterion | 0.714 | ||||
| Covariance | 0.120 | ||||
| r | 0.799 | ||||
| b (slope, estimate of beta) | 2.709 | ||||
| a (intercept, estimate of alpha) | -0.070 | ||||
| Mean Square Error | 0.185 | ||||
| DF error | 1214.000 | ||||
| t(b) | 46.267 | ||||
| p(b) | 0.101 | ||||
| t(a) | -0.351 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | 2.594 | ||||
| Upperbound of 95% confidence interval for beta | 2.824 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.464 | ||||
| Upperbound of 95% confidence interval for alpha | 0.323 | ||||
| Treynor index (mean / b) | 0.294 | ||||
| Jensen alpha (a) | -0.070 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.067 | ||||
| Expected Shortfall on VaR | 0.084 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1216.000 | ||||
| Minimum | 0.645 | ||||
| Quartile 1 | 0.993 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.015 | ||||
| Maximum | 1.368 | ||||
| Mean of quarter 1 | 0.960 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.051 | ||||
| Inter Quartile Range | 0.022 | ||||
| Number outliers low | 93.000 | ||||
| Percentage of outliers low | 0.076 | ||||
| Mean of outliers low | 0.911 | ||||
| Number of outliers high | 116.000 | ||||
| Percentage of outliers high | 0.095 | ||||
| Mean of outliers high | 1.087 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.617 | ||||
| VaR(95%) (moments method) | 0.033 | ||||
| Expected Shortfall (moments method) | 0.099 | ||||
| Extreme Value Index (regression method) | 0.264 | ||||
| VaR(95%) (regression method) | 0.035 | ||||
| Expected Shortfall (regression method) | 0.063 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 85.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.024 | ||||
| Quartile 3 | 0.093 | ||||
| Maximum | 0.703 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.018 | ||||
| Mean of quarter 3 | 0.048 | ||||
| Mean of quarter 4 | 0.230 | ||||
| Inter Quartile Range | 0.083 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.082 | ||||
| Mean of outliers high | 0.396 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.271 | ||||
| VaR(95%) (moments method) | 0.231 | ||||
| Expected Shortfall (moments method) | 0.378 | ||||
| Extreme Value Index (regression method) | 0.368 | ||||
| VaR(95%) (regression method) | 0.256 | ||||
| Expected Shortfall (regression method) | 0.467 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 10.502 | ||||
| Compounded annual return (geometric extrapolation) | 1.320 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.877 | ||||
| Compounded annual return / average of 25% largest draw downs | 5.744 | ||||
| Compounded annual return / Expected Shortfall lognormal | 15.704 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2.693 | ||||
| SD | 1.514 | ||||
| Sharpe ratio (Glass type estimate) | 1.779 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.769 | ||||
| df | 130.000 | ||||
| t | 1.258 | ||||
| p | 0.445 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.004 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.556 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.011 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.549 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.710 | ||||
| Upside Potential Ratio | 10.199 | ||||
| Upside part of mean | 10.134 | ||||
| Downside part of mean | -7.441 | ||||
| Upside SD | 1.146 | ||||
| Downside SD | 0.994 | ||||
| N nonnegative terms | 74.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.060 | ||||
| Mean of criterion | 2.693 | ||||
| SD of predictor | 0.402 | ||||
| SD of criterion | 1.514 | ||||
| Covariance | 0.563 | ||||
| r | 0.927 | ||||
| b (slope, estimate of beta) | 3.492 | ||||
| a (intercept, estimate of alpha) | -1.008 | ||||
| Mean Square Error | 0.326 | ||||
| DF error | 129.000 | ||||
| t(b) | 28.010 | ||||
| p(b) | 0.012 | ||||
| t(a) | -1.232 | ||||
| p(a) | 0.569 | ||||
| Lowerbound of 95% confidence interval for beta | 3.245 | ||||
| Upperbound of 95% confidence interval for beta | 3.739 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.627 | ||||
| Upperbound of 95% confidence interval for alpha | 0.611 | ||||
| Treynor index (mean / b) | 0.771 | ||||
| Jensen alpha (a) | -1.008 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.536 | ||||
| SD | 1.533 | ||||
| Sharpe ratio (Glass type estimate) | 1.002 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.996 | ||||
| df | 130.000 | ||||
| t | 0.709 | ||||
| p | 0.469 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.774 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.775 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.778 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.771 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.379 | ||||
| Upside Potential Ratio | 8.572 | ||||
| Upside part of mean | 9.549 | ||||
| Downside part of mean | -8.013 | ||||
| Upside SD | 1.049 | ||||
| Downside SD | 1.114 | ||||
| N nonnegative terms | 74.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.978 | ||||
| Mean of criterion | 1.536 | ||||
| SD of predictor | 0.401 | ||||
| SD of criterion | 1.533 | ||||
| Covariance | 0.568 | ||||
| r | 0.924 | ||||
| b (slope, estimate of beta) | 3.533 | ||||
| a (intercept, estimate of alpha) | -1.919 | ||||
| Mean Square Error | 0.345 | ||||
| DF error | 129.000 | ||||
| t(b) | 27.488 | ||||
| p(b) | 0.012 | ||||
| t(a) | -2.283 | ||||
| p(a) | 0.625 | ||||
| Lowerbound of 95% confidence interval for beta | 3.279 | ||||
| Upperbound of 95% confidence interval for beta | 3.787 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.581 | ||||
| Upperbound of 95% confidence interval for alpha | -0.256 | ||||
| Treynor index (mean / b) | 0.435 | ||||
| Jensen alpha (a) | -1.919 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.139 | ||||
| Expected Shortfall on VaR | 0.172 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.059 | ||||
| Expected Shortfall on VaR | 0.122 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.645 | ||||
| Quartile 1 | 0.972 | ||||
| Median | 1.013 | ||||
| Quartile 3 | 1.059 | ||||
| Maximum | 1.368 | ||||
| Mean of quarter 1 | 0.898 | ||||
| Mean of quarter 2 | 0.992 | ||||
| Mean of quarter 3 | 1.034 | ||||
| Mean of quarter 4 | 1.119 | ||||
| Inter Quartile Range | 0.087 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.741 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.038 | ||||
| Mean of outliers high | 1.253 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.187 | ||||
| VaR(95%) (moments method) | 0.080 | ||||
| Expected Shortfall (moments method) | 0.103 | ||||
| Extreme Value Index (regression method) | -0.157 | ||||
| VaR(95%) (regression method) | 0.109 | ||||
| Expected Shortfall (regression method) | 0.148 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.023 | ||||
| Median | 0.032 | ||||
| Quartile 3 | 0.141 | ||||
| Maximum | 0.703 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.025 | ||||
| Mean of quarter 3 | 0.098 | ||||
| Mean of quarter 4 | 0.462 | ||||
| Inter Quartile Range | 0.118 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.167 | ||||
| Mean of outliers high | 0.616 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -43.472 | ||||
| VaR(95%) (moments method) | 0.373 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -2.087 | ||||
| VaR(95%) (regression method) | 0.953 | ||||
| Expected Shortfall (regression method) | 0.976 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 2.407 | ||||
| Compounded annual return (geometric extrapolation) | 3.854 | ||||
| Calmar ratio (compounded annual return / max draw down) | 5.480 | ||||
| Compounded annual return / average of 25% largest draw downs | 8.336 | ||||
| Compounded annual return / Expected Shortfall lognormal | 22.396 | ||||