Advanced Statistics: ETF OPTION TIMER
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 | -0.031 | ||||
| SD | 0.062 | ||||
| Sharpe ratio (Glass type estimate) | -0.497 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.493 | ||||
| df | 89.000 | ||||
| t | -1.361 | ||||
| p | 0.912 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.215 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.224 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.212 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.227 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.758 | ||||
| Upside Potential Ratio | 0.725 | ||||
| Upside part of mean | 0.030 | ||||
| Downside part of mean | -0.060 | ||||
| Upside SD | 0.047 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 85.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 90.000 | ||||
| Mean of predictor | 0.141 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.171 | ||||
| SD of criterion | 0.062 | ||||
| Covariance | -0.000 | ||||
| r | -0.032 | ||||
| b (slope, estimate of beta) | -0.012 | ||||
| a (intercept, estimate of alpha) | -0.029 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 88.000 | ||||
| t(b) | -0.299 | ||||
| p(b) | 0.617 | ||||
| t(a) | -1.247 | ||||
| p(a) | 0.892 | ||||
| Lowerbound of 95% confidence interval for beta | -0.089 | ||||
| Upperbound of 95% confidence interval for beta | 0.065 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.076 | ||||
| Upperbound of 95% confidence interval for alpha | 0.017 | ||||
| Treynor index (mean / b) | 2.660 | ||||
| Jensen alpha (a) | -0.029 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.033 | ||||
| SD | 0.061 | ||||
| Sharpe ratio (Glass type estimate) | -0.532 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.527 | ||||
| df | 89.000 | ||||
| t | -1.456 | ||||
| p | 0.926 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.250 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.190 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.247 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.193 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.776 | ||||
| Upside Potential Ratio | 0.673 | ||||
| Upside part of mean | 0.028 | ||||
| Downside part of mean | -0.061 | ||||
| Upside SD | 0.045 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 85.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 90.000 | ||||
| Mean of predictor | 0.126 | ||||
| Mean of criterion | -0.033 | ||||
| SD of predictor | 0.168 | ||||
| SD of criterion | 0.061 | ||||
| Covariance | -0.000 | ||||
| r | -0.029 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | -0.031 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 88.000 | ||||
| t(b) | -0.274 | ||||
| p(b) | 0.608 | ||||
| t(a) | -1.358 | ||||
| p(a) | 0.911 | ||||
| Lowerbound of 95% confidence interval for beta | -0.088 | ||||
| Upperbound of 95% confidence interval for beta | 0.067 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.077 | ||||
| Upperbound of 95% confidence interval for alpha | 0.015 | ||||
| Treynor index (mean / b) | 3.061 | ||||
| Jensen alpha (a) | -0.031 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 90.000 | ||||
| Minimum | 0.914 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.104 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.033 | ||||
| Mean of outliers low | 0.953 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.056 | ||||
| Mean of outliers high | 1.048 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -162.822 | ||||
| VaR(95%) (moments method) | -9069236017623567238658364062671007978736013638734184448.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -1.729 | ||||
| VaR(95%) (regression method) | -0.129 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.027 | ||||
| Median | 0.054 | ||||
| Quartile 3 | 0.070 | ||||
| Maximum | 0.086 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.054 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.086 | ||||
| Inter Quartile Range | 0.042 | ||||
| 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) | 0.012 | ||||
| Compounded annual return (geometric extrapolation) | 0.011 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.133 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.133 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.296 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.031 | ||||
| SD | 0.053 | ||||
| Sharpe ratio (Glass type estimate) | -0.594 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.593 | ||||
| df | 1976.000 | ||||
| t | -1.630 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.307 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.120 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.307 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.120 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.832 | ||||
| Upside Potential Ratio | 2.309 | ||||
| Upside part of mean | 0.087 | ||||
| Downside part of mean | -0.118 | ||||
| Upside SD | 0.037 | ||||
| Downside SD | 0.038 | ||||
| N nonnegative terms | 93.000 | ||||
| N negative terms | 1884.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1977.000 | ||||
| Mean of predictor | 0.172 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.200 | ||||
| SD of criterion | 0.053 | ||||
| Covariance | 0.000 | ||||
| r | 0.035 | ||||
| b (slope, estimate of beta) | 0.009 | ||||
| a (intercept, estimate of alpha) | -0.033 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 1975.000 | ||||
| t(b) | 1.561 | ||||
| p(b) | 0.478 | ||||
| t(a) | -1.711 | ||||
| p(a) | 0.524 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.071 | ||||
| Upperbound of 95% confidence interval for alpha | 0.005 | ||||
| Treynor index (mean / b) | -3.387 | ||||
| Jensen alpha (a) | -0.033 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.033 | ||||
| SD | 0.053 | ||||
| Sharpe ratio (Glass type estimate) | -0.619 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.619 | ||||
| df | 1976.000 | ||||
| t | -1.702 | ||||
| p | 0.519 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.333 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.094 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.333 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.095 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.858 | ||||
| Upside Potential Ratio | 2.262 | ||||
| Upside part of mean | 0.086 | ||||
| Downside part of mean | -0.119 | ||||
| Upside SD | 0.037 | ||||
| Downside SD | 0.038 | ||||
| N nonnegative terms | 93.000 | ||||
| N negative terms | 1884.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1977.000 | ||||
| Mean of predictor | 0.152 | ||||
| Mean of criterion | -0.033 | ||||
| SD of predictor | 0.203 | ||||
| SD of criterion | 0.053 | ||||
| Covariance | 0.000 | ||||
| r | 0.035 | ||||
| b (slope, estimate of beta) | 0.009 | ||||
| a (intercept, estimate of alpha) | -0.034 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 1975.000 | ||||
| t(b) | 1.540 | ||||
| p(b) | 0.478 | ||||
| t(a) | -1.771 | ||||
| p(a) | 0.525 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.072 | ||||
| Upperbound of 95% confidence interval for alpha | 0.004 | ||||
| Treynor index (mean / b) | -3.630 | ||||
| Jensen alpha (a) | -0.034 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1977.000 | ||||
| Minimum | 0.963 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.037 | ||||
| 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 | 63.000 | ||||
| Percentage of outliers low | 0.032 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 93.000 | ||||
| Percentage of outliers high | 0.047 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.154 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.018 | ||||
| VaR(95%) (regression method) | -0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.004 | ||||
| Quartile 3 | 0.083 | ||||
| Maximum | 0.132 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.046 | ||||
| Mean of quarter 4 | 0.111 | ||||
| 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 | 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) | -0.276 | ||||
| VaR(95%) (moments method) | 0.118 | ||||
| Expected Shortfall (moments method) | 0.133 | ||||
| Extreme Value Index (regression method) | 1.495 | ||||
| VaR(95%) (regression method) | 0.156 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.012 | ||||
| Compounded annual return (geometric extrapolation) | 0.011 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.086 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.102 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.656 | ||||
| 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 | 0.750 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.410 | ||||
| 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 | 0.665 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.413 | ||||
| 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) | -8756208263848482.000 | ||||
| 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) | -706467909418865669126482057756672.000 | ||||
| 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 | ||||