Advanced Statistics: Compound ETF
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 | -0.745 | ||||
| SD | 0.634 | ||||
| Sharpe ratio (Glass type estimate) | -1.174 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.148 | ||||
| df | 34.000 | ||||
| t | -2.005 | ||||
| p | 0.974 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.347 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.015 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.327 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.032 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.726 | ||||
| Upside Potential Ratio | 0.868 | ||||
| Upside part of mean | 0.375 | ||||
| Downside part of mean | -1.120 | ||||
| Upside SD | 0.501 | ||||
| Downside SD | 0.432 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.542 | ||||
| Mean of criterion | -0.745 | ||||
| SD of predictor | 0.231 | ||||
| SD of criterion | 0.634 | ||||
| Covariance | -0.032 | ||||
| r | -0.220 | ||||
| b (slope, estimate of beta) | -0.607 | ||||
| a (intercept, estimate of alpha) | -0.416 | ||||
| Mean Square Error | 0.395 | ||||
| DF error | 33.000 | ||||
| t(b) | -1.298 | ||||
| p(b) | 0.898 | ||||
| t(a) | -0.931 | ||||
| p(a) | 0.821 | ||||
| Lowerbound of 95% confidence interval for beta | -1.558 | ||||
| Upperbound of 95% confidence interval for beta | 0.344 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.325 | ||||
| Upperbound of 95% confidence interval for alpha | 0.493 | ||||
| Treynor index (mean / b) | 1.228 | ||||
| Jensen alpha (a) | -0.416 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.932 | ||||
| SD | 0.550 | ||||
| Sharpe ratio (Glass type estimate) | -1.694 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.657 | ||||
| df | 34.000 | ||||
| t | -2.894 | ||||
| p | 0.997 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.899 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.467 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.870 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.443 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.941 | ||||
| Upside Potential Ratio | 0.604 | ||||
| Upside part of mean | 0.290 | ||||
| Downside part of mean | -1.223 | ||||
| Upside SD | 0.368 | ||||
| Downside SD | 0.480 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.505 | ||||
| Mean of criterion | -0.932 | ||||
| SD of predictor | 0.220 | ||||
| SD of criterion | 0.550 | ||||
| Covariance | -0.042 | ||||
| r | -0.347 | ||||
| b (slope, estimate of beta) | -0.869 | ||||
| a (intercept, estimate of alpha) | -0.494 | ||||
| Mean Square Error | 0.274 | ||||
| DF error | 33.000 | ||||
| t(b) | -2.124 | ||||
| p(b) | 0.979 | ||||
| t(a) | -1.335 | ||||
| p(a) | 0.905 | ||||
| Lowerbound of 95% confidence interval for beta | -1.701 | ||||
| Upperbound of 95% confidence interval for beta | -0.036 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.246 | ||||
| Upperbound of 95% confidence interval for alpha | 0.259 | ||||
| Treynor index (mean / b) | 1.073 | ||||
| Jensen alpha (a) | -0.494 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.287 | ||||
| Expected Shortfall on VaR | 0.332 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.250 | ||||
| Expected Shortfall on VaR | 0.312 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.746 | ||||
| Quartile 1 | 0.863 | ||||
| Median | 0.943 | ||||
| Quartile 3 | 0.971 | ||||
| Maximum | 1.839 | ||||
| Mean of quarter 1 | 0.793 | ||||
| Mean of quarter 2 | 0.896 | ||||
| Mean of quarter 3 | 0.957 | ||||
| Mean of quarter 4 | 1.121 | ||||
| Inter Quartile Range | 0.107 | ||||
| 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 | 0.057 | ||||
| Mean of outliers high | 1.510 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.748 | ||||
| VaR(95%) (moments method) | 0.224 | ||||
| Expected Shortfall (moments method) | 0.228 | ||||
| Extreme Value Index (regression method) | -1.969 | ||||
| VaR(95%) (regression method) | 0.235 | ||||
| Expected Shortfall (regression method) | 0.238 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.960 | ||||
| Quartile 1 | 0.960 | ||||
| Median | 0.960 | ||||
| Quartile 3 | 0.960 | ||||
| Maximum | 0.960 | ||||
| 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) | -0.317 | ||||
| Compounded annual return (geometric extrapolation) | -0.589 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.613 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.772 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.699 | ||||
| SD | 0.778 | ||||
| Sharpe ratio (Glass type estimate) | -0.898 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.897 | ||||
| df | 766.000 | ||||
| t | -1.537 | ||||
| p | 0.938 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.044 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.249 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.044 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.249 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.967 | ||||
| Upside Potential Ratio | 7.101 | ||||
| Upside part of mean | 2.521 | ||||
| Downside part of mean | -3.220 | ||||
| Upside SD | 0.693 | ||||
| Downside SD | 0.355 | ||||
| N nonnegative terms | 285.000 | ||||
| N negative terms | 482.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 767.000 | ||||
| Mean of predictor | 0.573 | ||||
| Mean of criterion | -0.699 | ||||
| SD of predictor | 0.331 | ||||
| SD of criterion | 0.778 | ||||
| Covariance | -0.132 | ||||
| r | -0.511 | ||||
| b (slope, estimate of beta) | -1.201 | ||||
| a (intercept, estimate of alpha) | -0.010 | ||||
| Mean Square Error | 0.448 | ||||
| DF error | 765.000 | ||||
| t(b) | -16.447 | ||||
| p(b) | 1.000 | ||||
| t(a) | -0.025 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | -1.344 | ||||
| Upperbound of 95% confidence interval for beta | -1.058 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.782 | ||||
| Upperbound of 95% confidence interval for alpha | 0.762 | ||||
| Treynor index (mean / b) | 0.582 | ||||
| Jensen alpha (a) | -0.010 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.932 | ||||
| SD | 0.646 | ||||
| Sharpe ratio (Glass type estimate) | -1.443 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.442 | ||||
| df | 766.000 | ||||
| t | -2.469 | ||||
| p | 0.993 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.591 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.295 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.590 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.294 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.550 | ||||
| Upside Potential Ratio | 6.433 | ||||
| Upside part of mean | 2.352 | ||||
| Downside part of mean | -3.285 | ||||
| Upside SD | 0.535 | ||||
| Downside SD | 0.366 | ||||
| N nonnegative terms | 285.000 | ||||
| N negative terms | 482.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 767.000 | ||||
| Mean of predictor | 0.517 | ||||
| Mean of criterion | -0.932 | ||||
| SD of predictor | 0.335 | ||||
| SD of criterion | 0.646 | ||||
| Covariance | -0.134 | ||||
| r | -0.617 | ||||
| b (slope, estimate of beta) | -1.188 | ||||
| a (intercept, estimate of alpha) | -0.318 | ||||
| Mean Square Error | 0.259 | ||||
| DF error | 765.000 | ||||
| t(b) | -21.670 | ||||
| p(b) | 1.000 | ||||
| t(a) | -1.065 | ||||
| p(a) | 0.856 | ||||
| Lowerbound of 95% confidence interval for beta | -1.296 | ||||
| Upperbound of 95% confidence interval for beta | -1.080 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.905 | ||||
| Upperbound of 95% confidence interval for alpha | 0.268 | ||||
| Treynor index (mean / b) | 0.785 | ||||
| Jensen alpha (a) | -0.318 | ||||
| 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 | 0.082 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.057 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 767.000 | ||||
| Minimum | 0.865 | ||||
| Quartile 1 | 0.981 | ||||
| Median | 0.996 | ||||
| Quartile 3 | 1.008 | ||||
| Maximum | 2.001 | ||||
| Mean of quarter 1 | 0.963 | ||||
| Mean of quarter 2 | 0.989 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.037 | ||||
| Inter Quartile Range | 0.027 | ||||
| Number outliers low | 26.000 | ||||
| Percentage of outliers low | 0.034 | ||||
| Mean of outliers low | 0.923 | ||||
| Number of outliers high | 34.000 | ||||
| Percentage of outliers high | 0.044 | ||||
| Mean of outliers high | 1.112 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.227 | ||||
| VaR(95%) (moments method) | 0.040 | ||||
| Expected Shortfall (moments method) | 0.060 | ||||
| Extreme Value Index (regression method) | 0.041 | ||||
| VaR(95%) (regression method) | 0.035 | ||||
| Expected Shortfall (regression method) | 0.046 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.008 | ||||
| Quartile 1 | 0.055 | ||||
| Median | 0.059 | ||||
| Quartile 3 | 0.067 | ||||
| Maximum | 0.967 | ||||
| Mean of quarter 1 | 0.031 | ||||
| Mean of quarter 2 | 0.059 | ||||
| Mean of quarter 3 | 0.067 | ||||
| Mean of quarter 4 | 0.967 | ||||
| Inter Quartile Range | 0.013 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.200 | ||||
| Mean of outliers low | 0.008 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| Mean of outliers high | 0.967 | ||||
| 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) | -0.316 | ||||
| Compounded annual return (geometric extrapolation) | -0.589 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.609 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.609 | ||||
| Compounded annual return / Expected Shortfall lognormal | -7.161 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.217 | ||||
| SD | 1.519 | ||||
| Sharpe ratio (Glass type estimate) | 0.802 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.797 | ||||
| df | 130.000 | ||||
| t | 0.567 | ||||
| p | 0.475 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.973 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.574 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.977 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.570 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.227 | ||||
| Upside Potential Ratio | 12.697 | ||||
| Upside part of mean | 4.790 | ||||
| Downside part of mean | -3.573 | ||||
| Upside SD | 1.467 | ||||
| Downside SD | 0.377 | ||||
| N nonnegative terms | 53.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.029 | ||||
| Mean of criterion | 1.217 | ||||
| SD of predictor | 0.459 | ||||
| SD of criterion | 1.519 | ||||
| Covariance | -0.168 | ||||
| r | -0.241 | ||||
| b (slope, estimate of beta) | -0.798 | ||||
| a (intercept, estimate of alpha) | 2.038 | ||||
| Mean Square Error | 2.189 | ||||
| DF error | 129.000 | ||||
| t(b) | -2.824 | ||||
| p(b) | 0.652 | ||||
| t(a) | 0.965 | ||||
| p(a) | 0.446 | ||||
| Lowerbound of 95% confidence interval for beta | -1.357 | ||||
| Upperbound of 95% confidence interval for beta | -0.239 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.141 | ||||
| Upperbound of 95% confidence interval for alpha | 6.218 | ||||
| Treynor index (mean / b) | -1.525 | ||||
| Jensen alpha (a) | 2.038 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.458 | ||||
| SD | 1.122 | ||||
| Sharpe ratio (Glass type estimate) | 0.409 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.406 | ||||
| df | 130.000 | ||||
| t | 0.289 | ||||
| p | 0.487 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.364 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.180 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.366 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.178 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.183 | ||||
| Upside Potential Ratio | 10.594 | ||||
| Upside part of mean | 4.104 | ||||
| Downside part of mean | -3.646 | ||||
| Upside SD | 1.049 | ||||
| Downside SD | 0.387 | ||||
| N nonnegative terms | 53.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.923 | ||||
| Mean of criterion | 0.458 | ||||
| SD of predictor | 0.457 | ||||
| SD of criterion | 1.122 | ||||
| Covariance | -0.182 | ||||
| r | -0.355 | ||||
| b (slope, estimate of beta) | -0.873 | ||||
| a (intercept, estimate of alpha) | 1.264 | ||||
| Mean Square Error | 1.108 | ||||
| DF error | 129.000 | ||||
| t(b) | -4.317 | ||||
| p(b) | 0.721 | ||||
| t(a) | 0.842 | ||||
| p(a) | 0.453 | ||||
| Lowerbound of 95% confidence interval for beta | -1.273 | ||||
| Upperbound of 95% confidence interval for beta | -0.473 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.705 | ||||
| Upperbound of 95% confidence interval for alpha | 4.233 | ||||
| Treynor index (mean / b) | -0.525 | ||||
| Jensen alpha (a) | 1.264 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.106 | ||||
| Expected Shortfall on VaR | 0.131 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.060 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.914 | ||||
| Quartile 1 | 0.980 | ||||
| Median | 0.995 | ||||
| Quartile 3 | 1.012 | ||||
| Maximum | 2.001 | ||||
| Mean of quarter 1 | 0.959 | ||||
| Mean of quarter 2 | 0.987 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.070 | ||||
| Inter Quartile Range | 0.032 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.918 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.242 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.200 | ||||
| VaR(95%) (moments method) | 0.041 | ||||
| Expected Shortfall (moments method) | 0.051 | ||||
| Extreme Value Index (regression method) | -0.361 | ||||
| VaR(95%) (regression method) | 0.037 | ||||
| Expected Shortfall (regression method) | 0.043 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.011 | ||||
| Median | 0.092 | ||||
| Quartile 3 | 0.242 | ||||
| Maximum | 0.454 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.171 | ||||
| Mean of quarter 4 | 0.454 | ||||
| Inter Quartile Range | 0.231 | ||||
| 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) | 0.571 | ||||
| Compounded annual return (geometric extrapolation) | 0.653 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.437 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.437 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.966 | ||||