Advanced Statistics: CrowderOptions.com - ETF Extremes
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 | 0.313 | ||||
| SD | 1.068 | ||||
| Sharpe ratio (Glass type estimate) | 0.293 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.289 | ||||
| df | 54.000 | ||||
| t | 0.627 | ||||
| p | 0.267 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.626 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.209 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.628 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.206 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.338 | ||||
| Upside Potential Ratio | 2.156 | ||||
| Upside part of mean | 0.504 | ||||
| Downside part of mean | -0.191 | ||||
| Upside SD | 1.036 | ||||
| Downside SD | 0.234 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 53.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 55.000 | ||||
| Mean of predictor | 0.422 | ||||
| Mean of criterion | 0.313 | ||||
| SD of predictor | 0.264 | ||||
| SD of criterion | 1.068 | ||||
| Covariance | -0.076 | ||||
| r | -0.270 | ||||
| b (slope, estimate of beta) | -1.092 | ||||
| a (intercept, estimate of alpha) | 0.774 | ||||
| Mean Square Error | 1.077 | ||||
| DF error | 53.000 | ||||
| t(b) | -2.044 | ||||
| p(b) | 0.977 | ||||
| t(a) | 1.447 | ||||
| p(a) | 0.077 | ||||
| Lowerbound of 95% confidence interval for beta | -2.164 | ||||
| Upperbound of 95% confidence interval for beta | -0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.299 | ||||
| Upperbound of 95% confidence interval for alpha | 1.846 | ||||
| Treynor index (mean / b) | -0.286 | ||||
| Jensen alpha (a) | 0.774 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.046 | ||||
| SD | 0.628 | ||||
| Sharpe ratio (Glass type estimate) | 0.073 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.072 | ||||
| df | 54.000 | ||||
| t | 0.156 | ||||
| p | 0.438 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.843 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.988 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.844 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.987 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.153 | ||||
| Upside Potential Ratio | 0.919 | ||||
| Upside part of mean | 0.274 | ||||
| Downside part of mean | -0.228 | ||||
| Upside SD | 0.546 | ||||
| Downside SD | 0.298 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 53.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 55.000 | ||||
| Mean of predictor | 0.380 | ||||
| Mean of criterion | 0.046 | ||||
| SD of predictor | 0.261 | ||||
| SD of criterion | 0.628 | ||||
| Covariance | -0.042 | ||||
| r | -0.255 | ||||
| b (slope, estimate of beta) | -0.613 | ||||
| a (intercept, estimate of alpha) | 0.279 | ||||
| Mean Square Error | 0.375 | ||||
| DF error | 53.000 | ||||
| t(b) | -1.921 | ||||
| p(b) | 0.970 | ||||
| t(a) | 0.897 | ||||
| p(a) | 0.187 | ||||
| Lowerbound of 95% confidence interval for beta | -1.253 | ||||
| Upperbound of 95% confidence interval for beta | 0.027 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.345 | ||||
| Upperbound of 95% confidence interval for alpha | 0.902 | ||||
| Treynor index (mean / b) | -0.074 | ||||
| Jensen alpha (a) | 0.279 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.255 | ||||
| Expected Shortfall on VaR | 0.308 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.054 | ||||
| Expected Shortfall on VaR | 0.118 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 55.000 | ||||
| Minimum | 0.563 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 3.220 | ||||
| Mean of quarter 1 | 0.951 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.165 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.073 | ||||
| Mean of outliers low | 0.830 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.036 | ||||
| Mean of outliers high | 2.158 | ||||
| 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) | 3.086 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.573 | ||||
| Quartile 1 | 0.573 | ||||
| Median | 0.573 | ||||
| Quartile 3 | 0.573 | ||||
| Maximum | 0.573 | ||||
| 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) | 0.111 | ||||
| Compounded annual return (geometric extrapolation) | 0.094 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.164 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.305 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.684 | ||||
| SD | 1.447 | ||||
| Sharpe ratio (Glass type estimate) | 0.473 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.473 | ||||
| df | 1202.000 | ||||
| t | 1.013 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.442 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.388 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.442 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.387 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.417 | ||||
| Upside Potential Ratio | 3.226 | ||||
| Upside part of mean | 1.559 | ||||
| Downside part of mean | -0.874 | ||||
| Upside SD | 1.364 | ||||
| Downside SD | 0.483 | ||||
| N nonnegative terms | 38.000 | ||||
| N negative terms | 1165.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1203.000 | ||||
| Mean of predictor | 0.441 | ||||
| Mean of criterion | 0.684 | ||||
| SD of predictor | 0.349 | ||||
| SD of criterion | 1.447 | ||||
| Covariance | -0.063 | ||||
| r | -0.126 | ||||
| b (slope, estimate of beta) | -0.522 | ||||
| a (intercept, estimate of alpha) | 0.914 | ||||
| Mean Square Error | 2.064 | ||||
| DF error | 1201.000 | ||||
| t(b) | -4.391 | ||||
| p(b) | 0.580 | ||||
| t(a) | 1.360 | ||||
| p(a) | 0.475 | ||||
| Lowerbound of 95% confidence interval for beta | -0.755 | ||||
| Upperbound of 95% confidence interval for beta | -0.289 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.405 | ||||
| Upperbound of 95% confidence interval for alpha | 2.234 | ||||
| Treynor index (mean / b) | -1.312 | ||||
| Jensen alpha (a) | 0.914 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.045 | ||||
| SD | 1.074 | ||||
| Sharpe ratio (Glass type estimate) | 0.042 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.042 | ||||
| df | 1202.000 | ||||
| t | 0.091 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.872 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.957 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.872 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.957 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.062 | ||||
| Upside Potential Ratio | 1.528 | ||||
| Upside part of mean | 1.121 | ||||
| Downside part of mean | -1.075 | ||||
| Upside SD | 0.784 | ||||
| Downside SD | 0.733 | ||||
| N nonnegative terms | 38.000 | ||||
| N negative terms | 1165.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1203.000 | ||||
| Mean of predictor | 0.376 | ||||
| Mean of criterion | 0.045 | ||||
| SD of predictor | 0.363 | ||||
| SD of criterion | 1.074 | ||||
| Covariance | -0.055 | ||||
| r | -0.142 | ||||
| b (slope, estimate of beta) | -0.420 | ||||
| a (intercept, estimate of alpha) | 0.203 | ||||
| Mean Square Error | 1.131 | ||||
| DF error | 1201.000 | ||||
| t(b) | -4.971 | ||||
| p(b) | 0.590 | ||||
| t(a) | 0.409 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | -0.585 | ||||
| Upperbound of 95% confidence interval for beta | -0.254 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.772 | ||||
| Upperbound of 95% confidence interval for alpha | 1.179 | ||||
| Treynor index (mean / b) | -0.108 | ||||
| Jensen alpha (a) | 0.203 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.103 | ||||
| Expected Shortfall on VaR | 0.128 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1203.000 | ||||
| Minimum | 0.311 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 3.473 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.024 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 48.000 | ||||
| Percentage of outliers low | 0.040 | ||||
| Mean of outliers low | 0.920 | ||||
| Number of outliers high | 38.000 | ||||
| Percentage of outliers high | 0.032 | ||||
| Mean of outliers high | 1.189 | ||||
| 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) | 0.409 | ||||
| VaR(95%) (regression method) | -0.005 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.012 | ||||
| Quartile 1 | 0.057 | ||||
| Median | 0.206 | ||||
| Quartile 3 | 0.547 | ||||
| Maximum | 0.771 | ||||
| Mean of quarter 1 | 0.019 | ||||
| Mean of quarter 2 | 0.112 | ||||
| Mean of quarter 3 | 0.377 | ||||
| Mean of quarter 4 | 0.730 | ||||
| Inter Quartile Range | 0.490 | ||||
| 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) | 0.111 | ||||
| Compounded annual return (geometric extrapolation) | 0.094 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.121 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.128 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.734 | ||||
| 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 | 1.058 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.390 | ||||
| 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 | 0.980 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.391 | ||||
| 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) | -8695567564163856.000 | ||||
| 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) | 404355717932538911458190163968000.000 | ||||
| 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 | ||||