Advanced Statistics: ETF Steady
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 | 0.063 | ||||
| SD | 0.321 | ||||
| Sharpe ratio (Glass type estimate) | 0.196 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.193 | ||||
| df | 50.000 | ||||
| t | 0.405 | ||||
| p | 0.344 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.756 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.147 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.758 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.145 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.326 | ||||
| Upside Potential Ratio | 1.930 | ||||
| Upside part of mean | 0.373 | ||||
| Downside part of mean | -0.310 | ||||
| Upside SD | 0.253 | ||||
| Downside SD | 0.194 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 51.000 | ||||
| Mean of predictor | 0.422 | ||||
| Mean of criterion | 0.063 | ||||
| SD of predictor | 0.396 | ||||
| SD of criterion | 0.321 | ||||
| Covariance | 0.005 | ||||
| r | 0.036 | ||||
| b (slope, estimate of beta) | 0.029 | ||||
| a (intercept, estimate of alpha) | 0.051 | ||||
| Mean Square Error | 0.105 | ||||
| DF error | 49.000 | ||||
| t(b) | 0.252 | ||||
| p(b) | 0.401 | ||||
| t(a) | 0.308 | ||||
| p(a) | 0.380 | ||||
| Lowerbound of 95% confidence interval for beta | -0.204 | ||||
| Upperbound of 95% confidence interval for beta | 0.262 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.280 | ||||
| Upperbound of 95% confidence interval for alpha | 0.382 | ||||
| Treynor index (mean / b) | 2.155 | ||||
| Jensen alpha (a) | 0.051 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.014 | ||||
| SD | 0.315 | ||||
| Sharpe ratio (Glass type estimate) | 0.044 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.043 | ||||
| df | 50.000 | ||||
| t | 0.090 | ||||
| p | 0.464 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.907 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.994 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.908 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.994 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.066 | ||||
| Upside Potential Ratio | 1.635 | ||||
| Upside part of mean | 0.344 | ||||
| Downside part of mean | -0.330 | ||||
| Upside SD | 0.230 | ||||
| Downside SD | 0.210 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 51.000 | ||||
| Mean of predictor | 0.352 | ||||
| Mean of criterion | 0.014 | ||||
| SD of predictor | 0.342 | ||||
| SD of criterion | 0.315 | ||||
| Covariance | 0.006 | ||||
| r | 0.056 | ||||
| b (slope, estimate of beta) | 0.052 | ||||
| a (intercept, estimate of alpha) | -0.004 | ||||
| Mean Square Error | 0.101 | ||||
| DF error | 49.000 | ||||
| t(b) | 0.395 | ||||
| p(b) | 0.347 | ||||
| t(a) | -0.028 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | -0.213 | ||||
| Upperbound of 95% confidence interval for beta | 0.316 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.328 | ||||
| Upperbound of 95% confidence interval for alpha | 0.319 | ||||
| Treynor index (mean / b) | 0.266 | ||||
| Jensen alpha (a) | -0.004 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.138 | ||||
| Expected Shortfall on VaR | 0.170 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.076 | ||||
| Expected Shortfall on VaR | 0.145 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 51.000 | ||||
| Minimum | 0.786 | ||||
| Quartile 1 | 0.985 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.006 | ||||
| Maximum | 1.289 | ||||
| Mean of quarter 1 | 0.911 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.126 | ||||
| Inter Quartile Range | 0.022 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.157 | ||||
| Mean of outliers low | 0.876 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.196 | ||||
| Mean of outliers high | 1.157 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.737 | ||||
| VaR(95%) (moments method) | 0.057 | ||||
| Expected Shortfall (moments method) | 0.066 | ||||
| Extreme Value Index (regression method) | -0.221 | ||||
| VaR(95%) (regression method) | 0.116 | ||||
| Expected Shortfall (regression method) | 0.158 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.035 | ||||
| Quartile 1 | 0.081 | ||||
| Median | 0.188 | ||||
| Quartile 3 | 0.283 | ||||
| Maximum | 0.293 | ||||
| Mean of quarter 1 | 0.035 | ||||
| Mean of quarter 2 | 0.097 | ||||
| Mean of quarter 3 | 0.279 | ||||
| Mean of quarter 4 | 0.293 | ||||
| Inter Quartile Range | 0.201 | ||||
| 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) | 0.066 | ||||
| Compounded annual return (geometric extrapolation) | 0.060 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.203 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.203 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.351 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.032 | ||||
| SD | 0.195 | ||||
| Sharpe ratio (Glass type estimate) | 0.164 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.164 | ||||
| df | 1127.000 | ||||
| t | 0.341 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.780 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.109 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.780 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.109 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.240 | ||||
| Upside Potential Ratio | 5.879 | ||||
| Upside part of mean | 0.785 | ||||
| Downside part of mean | -0.753 | ||||
| Upside SD | 0.142 | ||||
| Downside SD | 0.134 | ||||
| N nonnegative terms | 248.000 | ||||
| N negative terms | 880.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1128.000 | ||||
| Mean of predictor | 0.405 | ||||
| Mean of criterion | 0.032 | ||||
| SD of predictor | 0.294 | ||||
| SD of criterion | 0.195 | ||||
| Covariance | 0.003 | ||||
| r | 0.052 | ||||
| b (slope, estimate of beta) | 0.034 | ||||
| a (intercept, estimate of alpha) | 0.018 | ||||
| Mean Square Error | 0.038 | ||||
| DF error | 1126.000 | ||||
| t(b) | 1.746 | ||||
| p(b) | 0.474 | ||||
| t(a) | 0.192 | ||||
| p(a) | 0.497 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.073 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.167 | ||||
| Upperbound of 95% confidence interval for alpha | 0.203 | ||||
| Treynor index (mean / b) | 0.931 | ||||
| Jensen alpha (a) | 0.018 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.013 | ||||
| SD | 0.195 | ||||
| Sharpe ratio (Glass type estimate) | 0.067 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.067 | ||||
| df | 1127.000 | ||||
| t | 0.139 | ||||
| p | 0.497 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.878 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.011 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.878 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.011 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.096 | ||||
| Upside Potential Ratio | 5.704 | ||||
| Upside part of mean | 0.775 | ||||
| Downside part of mean | -0.762 | ||||
| Upside SD | 0.140 | ||||
| Downside SD | 0.136 | ||||
| N nonnegative terms | 248.000 | ||||
| N negative terms | 880.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1128.000 | ||||
| Mean of predictor | 0.362 | ||||
| Mean of criterion | 0.013 | ||||
| SD of predictor | 0.292 | ||||
| SD of criterion | 0.195 | ||||
| Covariance | 0.003 | ||||
| r | 0.053 | ||||
| b (slope, estimate of beta) | 0.036 | ||||
| a (intercept, estimate of alpha) | 0.000 | ||||
| Mean Square Error | 0.038 | ||||
| DF error | 1126.000 | ||||
| t(b) | 1.787 | ||||
| p(b) | 0.473 | ||||
| t(a) | 0.002 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.075 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.185 | ||||
| Upperbound of 95% confidence interval for alpha | 0.185 | ||||
| Treynor index (mean / b) | 0.367 | ||||
| Jensen alpha (a) | 0.000 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.025 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1128.000 | ||||
| Minimum | 0.932 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.067 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.012 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 235.000 | ||||
| Percentage of outliers low | 0.208 | ||||
| Mean of outliers low | 0.987 | ||||
| Number of outliers high | 252.000 | ||||
| Percentage of outliers high | 0.223 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.491 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | -0.136 | ||||
| VaR(95%) (regression method) | 0.012 | ||||
| Expected Shortfall (regression method) | 0.018 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 17.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.013 | ||||
| Median | 0.021 | ||||
| Quartile 3 | 0.096 | ||||
| Maximum | 0.327 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.019 | ||||
| Mean of quarter 3 | 0.053 | ||||
| Mean of quarter 4 | 0.227 | ||||
| Inter Quartile Range | 0.082 | ||||
| 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 | 0.118 | ||||
| Mean of outliers high | 0.323 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.004 | ||||
| VaR(95%) (moments method) | 0.208 | ||||
| Expected Shortfall (moments method) | 0.280 | ||||
| Extreme Value Index (regression method) | -1.352 | ||||
| VaR(95%) (regression method) | 0.229 | ||||
| Expected Shortfall (regression method) | 0.237 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.065 | ||||
| Compounded annual return (geometric extrapolation) | 0.059 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.179 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.259 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.396 | ||||
| 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 | 0.959 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.455 | ||||
| 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 | 0.855 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.457 | ||||
| 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) | -8741125073088402.000 | ||||
| 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) | 137591068276789010063703098261504.000 | ||||
| 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 | ||||