Advanced Statistics: Schulenberg 2X-Hedged IWM (^IWM2)
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 | 0.143 | ||||
| SD | 0.256 | ||||
| Sharpe ratio (Glass type estimate) | 0.560 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.553 | ||||
| df | 61.000 | ||||
| t | 1.273 | ||||
| p | 0.104 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.310 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.426 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.315 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.421 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.021 | ||||
| Upside Potential Ratio | 2.407 | ||||
| Upside part of mean | 0.338 | ||||
| Downside part of mean | -0.194 | ||||
| Upside SD | 0.215 | ||||
| Downside SD | 0.140 | ||||
| N nonnegative terms | 21.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 62.000 | ||||
| Mean of predictor | 0.311 | ||||
| Mean of criterion | 0.143 | ||||
| SD of predictor | 0.236 | ||||
| SD of criterion | 0.256 | ||||
| Covariance | -0.000 | ||||
| r | -0.001 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | 0.144 | ||||
| Mean Square Error | 0.067 | ||||
| DF error | 60.000 | ||||
| t(b) | -0.012 | ||||
| p(b) | 0.505 | ||||
| t(a) | 1.183 | ||||
| p(a) | 0.121 | ||||
| Lowerbound of 95% confidence interval for beta | -0.282 | ||||
| Upperbound of 95% confidence interval for beta | 0.279 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | 0.387 | ||||
| Treynor index (mean / b) | -88.515 | ||||
| Jensen alpha (a) | 0.144 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.111 | ||||
| SD | 0.249 | ||||
| Sharpe ratio (Glass type estimate) | 0.448 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.442 | ||||
| df | 61.000 | ||||
| t | 1.018 | ||||
| p | 0.156 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.420 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.312 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.424 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.308 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.734 | ||||
| Upside Potential Ratio | 2.083 | ||||
| Upside part of mean | 0.316 | ||||
| Downside part of mean | -0.205 | ||||
| Upside SD | 0.197 | ||||
| Downside SD | 0.152 | ||||
| N nonnegative terms | 21.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 62.000 | ||||
| Mean of predictor | 0.281 | ||||
| Mean of criterion | 0.111 | ||||
| SD of predictor | 0.221 | ||||
| SD of criterion | 0.249 | ||||
| Covariance | 0.001 | ||||
| r | 0.018 | ||||
| b (slope, estimate of beta) | 0.020 | ||||
| a (intercept, estimate of alpha) | 0.106 | ||||
| Mean Square Error | 0.063 | ||||
| DF error | 60.000 | ||||
| t(b) | 0.139 | ||||
| p(b) | 0.445 | ||||
| t(a) | 0.898 | ||||
| p(a) | 0.186 | ||||
| Lowerbound of 95% confidence interval for beta | -0.270 | ||||
| Upperbound of 95% confidence interval for beta | 0.311 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.130 | ||||
| Upperbound of 95% confidence interval for alpha | 0.341 | ||||
| Treynor index (mean / b) | 5.501 | ||||
| Jensen alpha (a) | 0.106 | ||||
| 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 | 0.129 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.044 | ||||
| Expected Shortfall on VaR | 0.090 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 62.000 | ||||
| Minimum | 0.790 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.045 | ||||
| Maximum | 1.290 | ||||
| Mean of quarter 1 | 0.947 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.008 | ||||
| Mean of quarter 4 | 1.107 | ||||
| Inter Quartile Range | 0.045 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.081 | ||||
| Mean of outliers low | 0.881 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.065 | ||||
| Mean of outliers high | 1.198 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -10.290 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 0.213 | ||||
| VaR(95%) (regression method) | 0.052 | ||||
| Expected Shortfall (regression method) | 0.102 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.012 | ||||
| Median | 0.049 | ||||
| Quartile 3 | 0.121 | ||||
| Maximum | 0.270 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.020 | ||||
| Mean of quarter 3 | 0.093 | ||||
| Mean of quarter 4 | 0.194 | ||||
| Inter Quartile Range | 0.109 | ||||
| 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) | -3.346 | ||||
| VaR(95%) (moments method) | 0.219 | ||||
| Expected Shortfall (moments method) | 0.219 | ||||
| Extreme Value Index (regression method) | -0.430 | ||||
| VaR(95%) (regression method) | 0.293 | ||||
| Expected Shortfall (regression method) | 0.339 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.238 | ||||
| Compounded annual return (geometric extrapolation) | 0.168 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.622 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.868 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.300 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.149 | ||||
| SD | 0.279 | ||||
| Sharpe ratio (Glass type estimate) | 0.534 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.534 | ||||
| df | 1364.000 | ||||
| t | 1.220 | ||||
| p | 0.483 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.325 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.393 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.325 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.393 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.785 | ||||
| Upside Potential Ratio | 6.388 | ||||
| Upside part of mean | 1.212 | ||||
| Downside part of mean | -1.063 | ||||
| Upside SD | 0.204 | ||||
| Downside SD | 0.190 | ||||
| N nonnegative terms | 419.000 | ||||
| N negative terms | 946.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1365.000 | ||||
| Mean of predictor | 0.319 | ||||
| Mean of criterion | 0.149 | ||||
| SD of predictor | 0.288 | ||||
| SD of criterion | 0.279 | ||||
| Covariance | 0.010 | ||||
| r | 0.124 | ||||
| b (slope, estimate of beta) | 0.120 | ||||
| a (intercept, estimate of alpha) | 0.111 | ||||
| Mean Square Error | 0.076 | ||||
| DF error | 1363.000 | ||||
| t(b) | 4.601 | ||||
| p(b) | 0.421 | ||||
| t(a) | 0.912 | ||||
| p(a) | 0.484 | ||||
| Lowerbound of 95% confidence interval for beta | 0.069 | ||||
| Upperbound of 95% confidence interval for beta | 0.170 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.127 | ||||
| Upperbound of 95% confidence interval for alpha | 0.349 | ||||
| Treynor index (mean / b) | 1.246 | ||||
| Jensen alpha (a) | 0.111 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.110 | ||||
| SD | 0.279 | ||||
| Sharpe ratio (Glass type estimate) | 0.394 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.394 | ||||
| df | 1364.000 | ||||
| t | 0.900 | ||||
| p | 0.488 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.464 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.253 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.465 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.253 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.561 | ||||
| Upside Potential Ratio | 6.080 | ||||
| Upside part of mean | 1.192 | ||||
| Downside part of mean | -1.082 | ||||
| Upside SD | 0.198 | ||||
| Downside SD | 0.196 | ||||
| N nonnegative terms | 419.000 | ||||
| N negative terms | 946.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1365.000 | ||||
| Mean of predictor | 0.277 | ||||
| Mean of criterion | 0.110 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 0.279 | ||||
| Covariance | 0.010 | ||||
| r | 0.126 | ||||
| b (slope, estimate of beta) | 0.122 | ||||
| a (intercept, estimate of alpha) | 0.076 | ||||
| Mean Square Error | 0.077 | ||||
| DF error | 1363.000 | ||||
| t(b) | 4.677 | ||||
| p(b) | 0.420 | ||||
| t(a) | 0.627 | ||||
| p(a) | 0.489 | ||||
| Lowerbound of 95% confidence interval for beta | 0.071 | ||||
| Upperbound of 95% confidence interval for beta | 0.173 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.162 | ||||
| Upperbound of 95% confidence interval for alpha | 0.314 | ||||
| Treynor index (mean / b) | 0.901 | ||||
| Jensen alpha (a) | 0.076 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1365.000 | ||||
| Minimum | 0.855 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.149 | ||||
| Mean of quarter 1 | 0.984 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.018 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 249.000 | ||||
| Percentage of outliers low | 0.182 | ||||
| Mean of outliers low | 0.979 | ||||
| Number of outliers high | 232.000 | ||||
| Percentage of outliers high | 0.170 | ||||
| Mean of outliers high | 1.024 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.694 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.003 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.025 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 31.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.026 | ||||
| Quartile 3 | 0.085 | ||||
| Maximum | 0.378 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.016 | ||||
| Mean of quarter 3 | 0.060 | ||||
| Mean of quarter 4 | 0.197 | ||||
| Inter Quartile Range | 0.081 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.097 | ||||
| Mean of outliers high | 0.310 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.137 | ||||
| VaR(95%) (moments method) | 0.192 | ||||
| Expected Shortfall (moments method) | 0.248 | ||||
| Extreme Value Index (regression method) | 0.624 | ||||
| VaR(95%) (regression method) | 0.206 | ||||
| Expected Shortfall (regression method) | 0.521 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.236 | ||||
| Compounded annual return (geometric extrapolation) | 0.167 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.440 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.847 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.828 | ||||
| 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 | 0.818 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.458 | ||||
| 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 | 0.711 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.463 | ||||
| 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) | -8760256519669110.000 | ||||
| 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) | -116519319665411032968684323733504.000 | ||||
| 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 | ||||