Advanced Statistics: rydex qqqq
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 | -0.042 | ||||
| SD | 0.072 | ||||
| Sharpe ratio (Glass type estimate) | -0.582 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.577 | ||||
| df | 87.000 | ||||
| t | -1.576 | ||||
| p | 0.941 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.309 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.149 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.306 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.152 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.952 | ||||
| Upside Potential Ratio | 0.510 | ||||
| Upside part of mean | 0.022 | ||||
| Downside part of mean | -0.064 | ||||
| Upside SD | 0.057 | ||||
| Downside SD | 0.044 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 86.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 88.000 | ||||
| Mean of predictor | 0.194 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.285 | ||||
| SD of criterion | 0.072 | ||||
| Covariance | -0.003 | ||||
| r | -0.159 | ||||
| b (slope, estimate of beta) | -0.040 | ||||
| a (intercept, estimate of alpha) | -0.034 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 86.000 | ||||
| t(b) | -1.495 | ||||
| p(b) | 0.931 | ||||
| t(a) | -1.266 | ||||
| p(a) | 0.896 | ||||
| Lowerbound of 95% confidence interval for beta | -0.093 | ||||
| Upperbound of 95% confidence interval for beta | 0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.087 | ||||
| Upperbound of 95% confidence interval for alpha | 0.019 | ||||
| Treynor index (mean / b) | 1.041 | ||||
| Jensen alpha (a) | -0.034 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.069 | ||||
| Sharpe ratio (Glass type estimate) | -0.637 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.631 | ||||
| df | 87.000 | ||||
| t | -1.724 | ||||
| p | 0.956 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.365 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.095 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.361 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.099 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.970 | ||||
| Upside Potential Ratio | 0.458 | ||||
| Upside part of mean | 0.021 | ||||
| Downside part of mean | -0.065 | ||||
| Upside SD | 0.053 | ||||
| Downside SD | 0.045 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 86.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 88.000 | ||||
| Mean of predictor | 0.154 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.280 | ||||
| SD of criterion | 0.069 | ||||
| Covariance | -0.003 | ||||
| r | -0.166 | ||||
| b (slope, estimate of beta) | -0.041 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 86.000 | ||||
| t(b) | -1.560 | ||||
| p(b) | 0.939 | ||||
| t(a) | -1.471 | ||||
| p(a) | 0.927 | ||||
| Lowerbound of 95% confidence interval for beta | -0.093 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.089 | ||||
| Upperbound of 95% confidence interval for alpha | 0.013 | ||||
| Treynor index (mean / b) | 1.074 | ||||
| Jensen alpha (a) | -0.038 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.044 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 88.000 | ||||
| Minimum | 0.919 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.159 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.045 | ||||
| Mean of outliers low | 0.962 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.034 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -13351.718 | ||||
| VaR(95%) (moments method) | -inf | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -4.238 | ||||
| VaR(95%) (regression method) | -0.827 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.147 | ||||
| Quartile 1 | 0.147 | ||||
| Median | 0.147 | ||||
| Quartile 3 | 0.147 | ||||
| Maximum | 0.147 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.040 | ||||
| SD | 0.085 | ||||
| Sharpe ratio (Glass type estimate) | -0.476 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.476 | ||||
| df | 1939.000 | ||||
| t | -1.295 | ||||
| p | 0.519 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.196 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.244 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.196 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.245 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.646 | ||||
| Upside Potential Ratio | 1.424 | ||||
| Upside part of mean | 0.089 | ||||
| Downside part of mean | -0.129 | ||||
| Upside SD | 0.057 | ||||
| Downside SD | 0.063 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 1908.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1940.000 | ||||
| Mean of predictor | 0.309 | ||||
| Mean of criterion | -0.040 | ||||
| SD of predictor | 0.519 | ||||
| SD of criterion | 0.085 | ||||
| Covariance | -0.003 | ||||
| r | -0.066 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 1938.000 | ||||
| t(b) | -2.894 | ||||
| p(b) | 0.533 | ||||
| t(a) | -1.190 | ||||
| p(a) | 0.514 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | -0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.098 | ||||
| Upperbound of 95% confidence interval for alpha | 0.024 | ||||
| Treynor index (mean / b) | 3.764 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.085 | ||||
| Sharpe ratio (Glass type estimate) | -0.516 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.516 | ||||
| df | 1939.000 | ||||
| t | -1.404 | ||||
| p | 0.520 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.236 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.204 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.236 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.205 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.684 | ||||
| Upside Potential Ratio | 1.357 | ||||
| Upside part of mean | 0.087 | ||||
| Downside part of mean | -0.131 | ||||
| Upside SD | 0.056 | ||||
| Downside SD | 0.064 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 1908.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1940.000 | ||||
| Mean of predictor | 0.177 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.513 | ||||
| SD of criterion | 0.085 | ||||
| Covariance | -0.003 | ||||
| r | -0.067 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | -0.042 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 1938.000 | ||||
| t(b) | -2.957 | ||||
| p(b) | 0.534 | ||||
| t(a) | -1.344 | ||||
| p(a) | 0.515 | ||||
| Lowerbound of 95% confidence interval for beta | -0.019 | ||||
| Upperbound of 95% confidence interval for beta | -0.004 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.103 | ||||
| Upperbound of 95% confidence interval for alpha | 0.019 | ||||
| Treynor index (mean / b) | 3.952 | ||||
| Jensen alpha (a) | -0.042 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1940.000 | ||||
| Minimum | 0.910 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.088 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 57.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 62.000 | ||||
| Percentage of outliers high | 0.032 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -14.289 | ||||
| VaR(95%) (moments method) | -126646.246 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.119 | ||||
| VaR(95%) (regression method) | -0.026 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.013 | ||||
| Median | 0.019 | ||||
| Quartile 3 | 0.117 | ||||
| Maximum | 0.215 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.019 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.215 | ||||
| Inter Quartile Range | 0.104 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 1.022 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.434 | ||||
| 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 | 0.927 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.434 | ||||
| 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) | -8723778679104766.000 | ||||
| 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) | 176697715979465570133519267528704.000 | ||||
| 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 | ||||