Advanced Statistics: ETN/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 | -0.071 | ||||
| SD | 0.032 | ||||
| Sharpe ratio (Glass type estimate) | -2.226 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.175 | ||||
| df | 33.000 | ||||
| t | -3.747 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.494 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.931 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.452 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.898 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.893 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.071 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.038 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.562 | ||||
| Mean of criterion | -0.071 | ||||
| SD of predictor | 0.340 | ||||
| SD of criterion | 0.032 | ||||
| Covariance | 0.002 | ||||
| r | 0.184 | ||||
| b (slope, estimate of beta) | 0.017 | ||||
| a (intercept, estimate of alpha) | -0.081 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 32.000 | ||||
| t(b) | 1.056 | ||||
| p(b) | 0.149 | ||||
| t(a) | -3.839 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.051 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.124 | ||||
| Upperbound of 95% confidence interval for alpha | -0.038 | ||||
| Treynor index (mean / b) | -4.120 | ||||
| Jensen alpha (a) | -0.081 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.072 | ||||
| SD | 0.033 | ||||
| Sharpe ratio (Glass type estimate) | -2.196 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.146 | ||||
| df | 33.000 | ||||
| t | -3.697 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.461 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.904 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.420 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.872 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.875 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.072 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.038 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.500 | ||||
| Mean of criterion | -0.072 | ||||
| SD of predictor | 0.307 | ||||
| SD of criterion | 0.033 | ||||
| Covariance | 0.002 | ||||
| r | 0.189 | ||||
| b (slope, estimate of beta) | 0.020 | ||||
| a (intercept, estimate of alpha) | -0.082 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 32.000 | ||||
| t(b) | 1.089 | ||||
| p(b) | 0.142 | ||||
| t(a) | -3.815 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.058 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.126 | ||||
| Upperbound of 95% confidence interval for alpha | -0.038 | ||||
| Treynor index (mean / b) | -3.564 | ||||
| Jensen alpha (a) | -0.082 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.025 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.958 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.991 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers low | 0.059 | ||||
| Mean of outliers low | 0.961 | ||||
| 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) | -3.444 | ||||
| VaR(95%) (regression method) | 0.070 | ||||
| Expected Shortfall (regression method) | 0.080 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.076 | ||||
| Quartile 1 | 0.076 | ||||
| Median | 0.076 | ||||
| Quartile 3 | 0.076 | ||||
| Maximum | 0.076 | ||||
| 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) | -0.027 | ||||
| Compounded annual return (geometric extrapolation) | -0.027 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.362 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.091 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.064 | ||||
| SD | 0.121 | ||||
| Sharpe ratio (Glass type estimate) | -0.531 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.531 | ||||
| df | 758.000 | ||||
| t | -0.904 | ||||
| p | 0.817 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.683 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.621 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.683 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.621 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.825 | ||||
| Upside Potential Ratio | 1.351 | ||||
| Upside part of mean | 0.105 | ||||
| Downside part of mean | -0.169 | ||||
| Upside SD | 0.092 | ||||
| Downside SD | 0.078 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 749.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 759.000 | ||||
| Mean of predictor | 0.610 | ||||
| Mean of criterion | -0.064 | ||||
| SD of predictor | 0.369 | ||||
| SD of criterion | 0.121 | ||||
| Covariance | 0.001 | ||||
| r | 0.016 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.067 | ||||
| Mean Square Error | 0.015 | ||||
| DF error | 757.000 | ||||
| t(b) | 0.453 | ||||
| p(b) | 0.325 | ||||
| t(a) | -0.945 | ||||
| p(a) | 0.828 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.029 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.207 | ||||
| Upperbound of 95% confidence interval for alpha | 0.073 | ||||
| Treynor index (mean / b) | -11.902 | ||||
| Jensen alpha (a) | -0.067 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.071 | ||||
| SD | 0.118 | ||||
| Sharpe ratio (Glass type estimate) | -0.602 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.602 | ||||
| df | 758.000 | ||||
| t | -1.025 | ||||
| p | 0.847 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.754 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.550 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.754 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.550 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.889 | ||||
| Upside Potential Ratio | 1.262 | ||||
| Upside part of mean | 0.101 | ||||
| Downside part of mean | -0.172 | ||||
| Upside SD | 0.087 | ||||
| Downside SD | 0.080 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 749.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 759.000 | ||||
| Mean of predictor | 0.544 | ||||
| Mean of criterion | -0.071 | ||||
| SD of predictor | 0.361 | ||||
| SD of criterion | 0.118 | ||||
| Covariance | 0.001 | ||||
| r | 0.018 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.074 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 757.000 | ||||
| t(b) | 0.498 | ||||
| p(b) | 0.309 | ||||
| t(a) | -1.066 | ||||
| p(a) | 0.857 | ||||
| Lowerbound of 95% confidence interval for beta | -0.017 | ||||
| Upperbound of 95% confidence interval for beta | 0.029 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.211 | ||||
| Upperbound of 95% confidence interval for alpha | 0.063 | ||||
| Treynor index (mean / b) | -12.033 | ||||
| Jensen alpha (a) | -0.074 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 759.000 | ||||
| Minimum | 0.918 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.145 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.014 | ||||
| Mean of outliers low | 0.967 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.013 | ||||
| Mean of outliers high | 1.031 | ||||
| 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) | -0.301 | ||||
| VaR(95%) (regression method) | -0.049 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.096 | ||||
| Quartile 1 | 0.124 | ||||
| Median | 0.152 | ||||
| Quartile 3 | 0.180 | ||||
| Maximum | 0.208 | ||||
| Mean of quarter 1 | 0.096 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.208 | ||||
| Inter Quartile Range | 0.056 | ||||
| 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) | -0.026 | ||||
| Compounded annual return (geometric extrapolation) | -0.027 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.129 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.129 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.762 | ||||
| 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 | 1.027 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.452 | ||||
| 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 | 0.923 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.454 | ||||
| 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) | -8730837399299410.000 | ||||
| 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) | 5995799349422663839153696020627456.000 | ||||
| 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 | ||||