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 | 0.061 | ||||
| Sharpe ratio (Glass type estimate) | -0.507 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.503 | ||||
| df | 91.000 | ||||
| t | -1.404 | ||||
| p | 0.918 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.218 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.206 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.215 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.209 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.773 | ||||
| Upside Potential Ratio | 0.716 | ||||
| Upside part of mean | 0.029 | ||||
| Downside part of mean | -0.060 | ||||
| Upside SD | 0.047 | ||||
| Downside SD | 0.040 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 87.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 92.000 | ||||
| Mean of predictor | 0.195 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.212 | ||||
| SD of criterion | 0.061 | ||||
| Covariance | -0.000 | ||||
| r | -0.030 | ||||
| b (slope, estimate of beta) | -0.009 | ||||
| a (intercept, estimate of alpha) | -0.029 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 90.000 | ||||
| t(b) | -0.283 | ||||
| p(b) | 0.611 | ||||
| t(a) | -1.278 | ||||
| p(a) | 0.898 | ||||
| Lowerbound of 95% confidence interval for beta | -0.069 | ||||
| Upperbound of 95% confidence interval for beta | 0.052 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.075 | ||||
| Upperbound of 95% confidence interval for alpha | 0.016 | ||||
| Treynor index (mean / b) | 3.612 | ||||
| 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) | -0.542 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.537 | ||||
| df | 91.000 | ||||
| t | -1.500 | ||||
| p | 0.931 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.252 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.172 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.249 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.175 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.789 | ||||
| Upside Potential Ratio | 0.665 | ||||
| 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 | 87.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 92.000 | ||||
| Mean of predictor | 0.172 | ||||
| Mean of criterion | -0.033 | ||||
| SD of predictor | 0.199 | ||||
| SD of criterion | 0.061 | ||||
| Covariance | -0.000 | ||||
| r | -0.028 | ||||
| b (slope, estimate of beta) | -0.009 | ||||
| a (intercept, estimate of alpha) | -0.031 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 90.000 | ||||
| t(b) | -0.266 | ||||
| p(b) | 0.604 | ||||
| t(a) | -1.383 | ||||
| p(a) | 0.915 | ||||
| Lowerbound of 95% confidence interval for beta | -0.072 | ||||
| Upperbound of 95% confidence interval for beta | 0.055 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.077 | ||||
| Upperbound of 95% confidence interval for alpha | 0.014 | ||||
| Treynor index (mean / b) | 3.860 | ||||
| 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 | 0.038 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.032 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 92.000 | ||||
| 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 | 0.054 | ||||
| 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) | -324908661349590042471397210029000581393078202906231963648.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -1.729 | ||||
| VaR(95%) (regression method) | -0.139 | ||||
| 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) | 0.130 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.130 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.292 | ||||
| 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 | 0.052 | ||||
| Sharpe ratio (Glass type estimate) | -0.607 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.607 | ||||
| df | 2027.000 | ||||
| t | -1.689 | ||||
| p | 0.954 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.312 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.098 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.312 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.098 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.851 | ||||
| Upside Potential Ratio | 2.279 | ||||
| Upside part of mean | 0.085 | ||||
| Downside part of mean | -0.117 | ||||
| Upside SD | 0.037 | ||||
| Downside SD | 0.037 | ||||
| N nonnegative terms | 93.000 | ||||
| N negative terms | 1935.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2028.000 | ||||
| Mean of predictor | 0.217 | ||||
| Mean of criterion | -0.032 | ||||
| SD of predictor | 0.211 | ||||
| SD of criterion | 0.052 | ||||
| Covariance | 0.000 | ||||
| r | 0.033 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.033 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 2026.000 | ||||
| t(b) | 1.475 | ||||
| p(b) | 0.070 | ||||
| t(a) | -1.780 | ||||
| p(a) | 0.962 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.019 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.070 | ||||
| Upperbound of 95% confidence interval for alpha | 0.003 | ||||
| Treynor index (mean / b) | -3.912 | ||||
| Jensen alpha (a) | -0.033 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.033 | ||||
| SD | 0.052 | ||||
| Sharpe ratio (Glass type estimate) | -0.633 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.633 | ||||
| df | 2027.000 | ||||
| t | -1.761 | ||||
| p | 0.961 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.338 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.072 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.337 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.072 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.876 | ||||
| Upside Potential Ratio | 2.233 | ||||
| Upside part of mean | 0.084 | ||||
| Downside part of mean | -0.117 | ||||
| Upside SD | 0.036 | ||||
| Downside SD | 0.038 | ||||
| N nonnegative terms | 93.000 | ||||
| N negative terms | 1935.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2028.000 | ||||
| Mean of predictor | 0.194 | ||||
| Mean of criterion | -0.033 | ||||
| SD of predictor | 0.213 | ||||
| SD of criterion | 0.052 | ||||
| Covariance | 0.000 | ||||
| r | 0.032 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.035 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 2026.000 | ||||
| t(b) | 1.458 | ||||
| p(b) | 0.072 | ||||
| t(a) | -1.840 | ||||
| p(a) | 0.967 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.019 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.071 | ||||
| Upperbound of 95% confidence interval for alpha | 0.002 | ||||
| Treynor index (mean / b) | -4.171 | ||||
| Jensen alpha (a) | -0.035 | ||||
| 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 | 2028.000 | ||||
| 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 | 0.031 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 93.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| 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) | 0.011 | ||||
| Compounded annual return (geometric extrapolation) | 0.011 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.084 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.099 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.634 | ||||
| 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 | 1.233 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.467 | ||||
| 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 | 1.121 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.471 | ||||
| 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) | -8705409475145369.000 | ||||
| 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) | -612408269329015397017607766802432.000 | ||||
| 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 | ||||