Advanced Statistics: QLD and PSQ
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 | 1.103 | ||||
| SD | 0.622 | ||||
| Sharpe ratio (Glass type estimate) | 1.773 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.749 | ||||
| df | 55.000 | ||||
| t | 3.830 | ||||
| p | 0.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.800 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.731 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.784 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.713 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 5.463 | ||||
| Upside Potential Ratio | 7.063 | ||||
| Upside part of mean | 1.426 | ||||
| Downside part of mean | -0.323 | ||||
| Upside SD | 0.664 | ||||
| Downside SD | 0.202 | ||||
| N nonnegative terms | 38.000 | ||||
| N negative terms | 18.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 56.000 | ||||
| Mean of predictor | 0.439 | ||||
| Mean of criterion | 1.103 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.622 | ||||
| Covariance | 0.131 | ||||
| r | 0.861 | ||||
| b (slope, estimate of beta) | 2.189 | ||||
| a (intercept, estimate of alpha) | 0.143 | ||||
| Mean Square Error | 0.102 | ||||
| DF error | 54.000 | ||||
| t(b) | 12.436 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.857 | ||||
| p(a) | 0.198 | ||||
| Lowerbound of 95% confidence interval for beta | 1.836 | ||||
| Upperbound of 95% confidence interval for beta | 2.542 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.192 | ||||
| Upperbound of 95% confidence interval for alpha | 0.477 | ||||
| Treynor index (mean / b) | 0.504 | ||||
| Jensen alpha (a) | 0.143 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.901 | ||||
| SD | 0.548 | ||||
| Sharpe ratio (Glass type estimate) | 1.644 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.621 | ||||
| df | 55.000 | ||||
| t | 3.551 | ||||
| p | 0.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.679 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.595 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.665 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.578 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4.089 | ||||
| Upside Potential Ratio | 5.654 | ||||
| Upside part of mean | 1.246 | ||||
| Downside part of mean | -0.345 | ||||
| Upside SD | 0.561 | ||||
| Downside SD | 0.220 | ||||
| N nonnegative terms | 38.000 | ||||
| N negative terms | 18.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 56.000 | ||||
| Mean of predictor | 0.402 | ||||
| Mean of criterion | 0.901 | ||||
| SD of predictor | 0.233 | ||||
| SD of criterion | 0.548 | ||||
| Covariance | 0.111 | ||||
| r | 0.865 | ||||
| b (slope, estimate of beta) | 2.033 | ||||
| a (intercept, estimate of alpha) | 0.083 | ||||
| Mean Square Error | 0.077 | ||||
| DF error | 54.000 | ||||
| t(b) | 12.688 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.576 | ||||
| p(a) | 0.284 | ||||
| Lowerbound of 95% confidence interval for beta | 1.712 | ||||
| Upperbound of 95% confidence interval for beta | 2.355 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.205 | ||||
| Upperbound of 95% confidence interval for alpha | 0.371 | ||||
| Treynor index (mean / b) | 0.443 | ||||
| Jensen alpha (a) | 0.083 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.169 | ||||
| Expected Shortfall on VaR | 0.221 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.099 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 56.000 | ||||
| Minimum | 0.755 | ||||
| Quartile 1 | 0.964 | ||||
| Median | 1.057 | ||||
| Quartile 3 | 1.175 | ||||
| Maximum | 1.603 | ||||
| Mean of quarter 1 | 0.902 | ||||
| Mean of quarter 2 | 1.014 | ||||
| Mean of quarter 3 | 1.123 | ||||
| Mean of quarter 4 | 1.342 | ||||
| Inter Quartile Range | 0.211 | ||||
| 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 | 0.036 | ||||
| Mean of outliers high | 1.550 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.124 | ||||
| VaR(95%) (moments method) | 0.090 | ||||
| Expected Shortfall (moments method) | 0.117 | ||||
| Extreme Value Index (regression method) | 0.216 | ||||
| VaR(95%) (regression method) | 0.107 | ||||
| Expected Shortfall (regression method) | 0.170 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.022 | ||||
| Quartile 1 | 0.082 | ||||
| Median | 0.105 | ||||
| Quartile 3 | 0.168 | ||||
| Maximum | 0.362 | ||||
| Mean of quarter 1 | 0.045 | ||||
| Mean of quarter 2 | 0.096 | ||||
| Mean of quarter 3 | 0.129 | ||||
| Mean of quarter 4 | 0.257 | ||||
| Inter Quartile Range | 0.086 | ||||
| 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 | 0.362 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.614 | ||||
| VaR(95%) (moments method) | 0.303 | ||||
| Expected Shortfall (moments method) | 0.313 | ||||
| Extreme Value Index (regression method) | 0.164 | ||||
| VaR(95%) (regression method) | 0.386 | ||||
| Expected Shortfall (regression method) | 0.557 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 17.416 | ||||
| Compounded annual return (geometric extrapolation) | 1.573 | ||||
| Calmar ratio (compounded annual return / max draw down) | 4.344 | ||||
| Compounded annual return / average of 25% largest draw downs | 6.125 | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.120 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.109 | ||||
| SD | 0.677 | ||||
| Sharpe ratio (Glass type estimate) | 1.640 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.639 | ||||
| df | 1229.000 | ||||
| t | 3.553 | ||||
| p | 0.436 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.733 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.547 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.732 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.546 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.546 | ||||
| Upside Potential Ratio | 9.615 | ||||
| Upside part of mean | 4.190 | ||||
| Downside part of mean | -3.081 | ||||
| Upside SD | 0.522 | ||||
| Downside SD | 0.436 | ||||
| N nonnegative terms | 668.000 | ||||
| N negative terms | 562.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1230.000 | ||||
| Mean of predictor | 0.456 | ||||
| Mean of criterion | 1.109 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.677 | ||||
| Covariance | 0.145 | ||||
| r | 0.655 | ||||
| b (slope, estimate of beta) | 1.349 | ||||
| a (intercept, estimate of alpha) | 0.494 | ||||
| Mean Square Error | 0.262 | ||||
| DF error | 1228.000 | ||||
| t(b) | 30.349 | ||||
| p(b) | 0.173 | ||||
| t(a) | 2.086 | ||||
| p(a) | 0.470 | ||||
| Lowerbound of 95% confidence interval for beta | 1.262 | ||||
| Upperbound of 95% confidence interval for beta | 1.436 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.029 | ||||
| Upperbound of 95% confidence interval for alpha | 0.959 | ||||
| Treynor index (mean / b) | 0.823 | ||||
| Jensen alpha (a) | 0.494 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.881 | ||||
| SD | 0.674 | ||||
| Sharpe ratio (Glass type estimate) | 1.307 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.306 | ||||
| df | 1229.000 | ||||
| t | 2.831 | ||||
| p | 0.449 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.400 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.212 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.400 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.212 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.913 | ||||
| Upside Potential Ratio | 8.824 | ||||
| Upside part of mean | 4.063 | ||||
| Downside part of mean | -3.182 | ||||
| Upside SD | 0.495 | ||||
| Downside SD | 0.460 | ||||
| N nonnegative terms | 668.000 | ||||
| N negative terms | 562.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1230.000 | ||||
| Mean of predictor | 0.402 | ||||
| Mean of criterion | 0.881 | ||||
| SD of predictor | 0.330 | ||||
| SD of criterion | 0.674 | ||||
| Covariance | 0.146 | ||||
| r | 0.656 | ||||
| b (slope, estimate of beta) | 1.340 | ||||
| a (intercept, estimate of alpha) | 0.343 | ||||
| Mean Square Error | 0.259 | ||||
| DF error | 1228.000 | ||||
| t(b) | 30.422 | ||||
| p(b) | 0.172 | ||||
| t(a) | 1.454 | ||||
| p(a) | 0.479 | ||||
| Lowerbound of 95% confidence interval for beta | 1.253 | ||||
| Upperbound of 95% confidence interval for beta | 1.426 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.120 | ||||
| Upperbound of 95% confidence interval for alpha | 0.805 | ||||
| Treynor index (mean / b) | 0.657 | ||||
| Jensen alpha (a) | 0.343 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.063 | ||||
| Expected Shortfall on VaR | 0.079 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1230.000 | ||||
| Minimum | 0.768 | ||||
| Quartile 1 | 0.987 | ||||
| Median | 1.003 | ||||
| Quartile 3 | 1.022 | ||||
| Maximum | 1.358 | ||||
| Mean of quarter 1 | 0.958 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.011 | ||||
| Mean of quarter 4 | 1.053 | ||||
| Inter Quartile Range | 0.035 | ||||
| Number outliers low | 46.000 | ||||
| Percentage of outliers low | 0.037 | ||||
| Mean of outliers low | 0.896 | ||||
| Number of outliers high | 53.000 | ||||
| Percentage of outliers high | 0.043 | ||||
| Mean of outliers high | 1.111 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.263 | ||||
| VaR(95%) (moments method) | 0.038 | ||||
| Expected Shortfall (moments method) | 0.065 | ||||
| Extreme Value Index (regression method) | 0.052 | ||||
| VaR(95%) (regression method) | 0.040 | ||||
| Expected Shortfall (regression method) | 0.058 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 82.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.016 | ||||
| Median | 0.051 | ||||
| Quartile 3 | 0.142 | ||||
| Maximum | 0.597 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.033 | ||||
| Mean of quarter 3 | 0.083 | ||||
| Mean of quarter 4 | 0.232 | ||||
| Inter Quartile Range | 0.126 | ||||
| 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 | 0.024 | ||||
| Mean of outliers high | 0.474 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.131 | ||||
| VaR(95%) (moments method) | 0.253 | ||||
| Expected Shortfall (moments method) | 0.342 | ||||
| Extreme Value Index (regression method) | 0.337 | ||||
| VaR(95%) (regression method) | 0.214 | ||||
| Expected Shortfall (regression method) | 0.302 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 16.132 | ||||
| Compounded annual return (geometric extrapolation) | 1.521 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.549 | ||||
| Compounded annual return / average of 25% largest draw downs | 6.546 | ||||
| Compounded annual return / Expected Shortfall lognormal | 19.225 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2.007 | ||||
| SD | 1.100 | ||||
| Sharpe ratio (Glass type estimate) | 1.825 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.814 | ||||
| df | 130.000 | ||||
| t | 1.290 | ||||
| p | 0.444 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.959 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.602 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.966 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.595 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.964 | ||||
| Upside Potential Ratio | 11.121 | ||||
| Upside part of mean | 7.529 | ||||
| Downside part of mean | -5.522 | ||||
| Upside SD | 0.870 | ||||
| Downside SD | 0.677 | ||||
| N nonnegative terms | 69.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.030 | ||||
| Mean of criterion | 2.007 | ||||
| SD of predictor | 0.423 | ||||
| SD of criterion | 1.100 | ||||
| Covariance | 0.398 | ||||
| r | 0.855 | ||||
| b (slope, estimate of beta) | 2.223 | ||||
| a (intercept, estimate of alpha) | -0.282 | ||||
| Mean Square Error | 0.327 | ||||
| DF error | 129.000 | ||||
| t(b) | 18.759 | ||||
| p(b) | 0.032 | ||||
| t(a) | -0.344 | ||||
| p(a) | 0.519 | ||||
| Lowerbound of 95% confidence interval for beta | 1.988 | ||||
| Upperbound of 95% confidence interval for beta | 2.457 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.900 | ||||
| Upperbound of 95% confidence interval for alpha | 1.336 | ||||
| Treynor index (mean / b) | 0.903 | ||||
| Jensen alpha (a) | -0.282 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.416 | ||||
| SD | 1.083 | ||||
| Sharpe ratio (Glass type estimate) | 1.308 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.300 | ||||
| df | 130.000 | ||||
| t | 0.925 | ||||
| p | 0.460 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.471 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.082 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.476 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.076 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.956 | ||||
| Upside Potential Ratio | 9.929 | ||||
| Upside part of mean | 7.188 | ||||
| Downside part of mean | -5.772 | ||||
| Upside SD | 0.804 | ||||
| Downside SD | 0.724 | ||||
| N nonnegative terms | 69.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.939 | ||||
| Mean of criterion | 1.416 | ||||
| SD of predictor | 0.421 | ||||
| SD of criterion | 1.083 | ||||
| Covariance | 0.388 | ||||
| r | 0.851 | ||||
| b (slope, estimate of beta) | 2.187 | ||||
| a (intercept, estimate of alpha) | -0.638 | ||||
| Mean Square Error | 0.326 | ||||
| DF error | 129.000 | ||||
| t(b) | 18.401 | ||||
| p(b) | 0.034 | ||||
| t(a) | -0.783 | ||||
| p(a) | 0.544 | ||||
| Lowerbound of 95% confidence interval for beta | 1.952 | ||||
| Upperbound of 95% confidence interval for beta | 2.422 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.251 | ||||
| Upperbound of 95% confidence interval for alpha | 0.974 | ||||
| Treynor index (mean / b) | 0.647 | ||||
| Jensen alpha (a) | -0.638 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.099 | ||||
| Expected Shortfall on VaR | 0.124 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.047 | ||||
| Expected Shortfall on VaR | 0.091 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.768 | ||||
| Quartile 1 | 0.970 | ||||
| Median | 1.005 | ||||
| Quartile 3 | 1.047 | ||||
| Maximum | 1.358 | ||||
| Mean of quarter 1 | 0.929 | ||||
| Mean of quarter 2 | 0.988 | ||||
| Mean of quarter 3 | 1.027 | ||||
| Mean of quarter 4 | 1.088 | ||||
| Inter Quartile Range | 0.077 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.768 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.008 | ||||
| Mean of outliers high | 1.358 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.087 | ||||
| VaR(95%) (moments method) | 0.067 | ||||
| Expected Shortfall (moments method) | 0.087 | ||||
| Extreme Value Index (regression method) | 0.074 | ||||
| VaR(95%) (regression method) | 0.067 | ||||
| Expected Shortfall (regression method) | 0.094 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.010 | ||||
| Quartile 1 | 0.040 | ||||
| Median | 0.100 | ||||
| Quartile 3 | 0.181 | ||||
| Maximum | 0.597 | ||||
| Mean of quarter 1 | 0.021 | ||||
| Mean of quarter 2 | 0.071 | ||||
| Mean of quarter 3 | 0.154 | ||||
| Mean of quarter 4 | 0.459 | ||||
| Inter Quartile Range | 0.141 | ||||
| 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 | 0.111 | ||||
| Mean of outliers high | 0.597 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.711 | ||||
| VaR(95%) (moments method) | 0.396 | ||||
| Expected Shortfall (moments method) | 0.398 | ||||
| Extreme Value Index (regression method) | -0.032 | ||||
| VaR(95%) (regression method) | 0.677 | ||||
| Expected Shortfall (regression method) | 0.938 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 2.150 | ||||
| Compounded annual return (geometric extrapolation) | 3.306 | ||||
| Calmar ratio (compounded annual return / max draw down) | 5.541 | ||||
| Compounded annual return / average of 25% largest draw downs | 7.203 | ||||
| Compounded annual return / Expected Shortfall lognormal | 26.681 | ||||