Advanced Statistics: Scarecrow Symphonic ETF
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 | 0.007 | ||||
| SD | 0.151 | ||||
| Sharpe ratio (Glass type estimate) | 0.048 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.047 | ||||
| df | 54.000 | ||||
| t | 0.102 | ||||
| p | 0.459 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.868 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.963 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.868 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.963 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.070 | ||||
| Upside Potential Ratio | 1.201 | ||||
| Upside part of mean | 0.124 | ||||
| Downside part of mean | -0.117 | ||||
| Upside SD | 0.109 | ||||
| Downside SD | 0.104 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 55.000 | ||||
| Mean of predictor | 0.409 | ||||
| Mean of criterion | 0.007 | ||||
| SD of predictor | 0.323 | ||||
| SD of criterion | 0.151 | ||||
| Covariance | 0.010 | ||||
| r | 0.195 | ||||
| b (slope, estimate of beta) | 0.091 | ||||
| a (intercept, estimate of alpha) | -0.030 | ||||
| Mean Square Error | 0.022 | ||||
| DF error | 53.000 | ||||
| t(b) | 1.445 | ||||
| p(b) | 0.077 | ||||
| t(a) | -0.404 | ||||
| p(a) | 0.656 | ||||
| Lowerbound of 95% confidence interval for beta | -0.035 | ||||
| Upperbound of 95% confidence interval for beta | 0.218 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.180 | ||||
| Upperbound of 95% confidence interval for alpha | 0.120 | ||||
| Treynor index (mean / b) | 0.079 | ||||
| Jensen alpha (a) | -0.030 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.004 | ||||
| SD | 0.153 | ||||
| Sharpe ratio (Glass type estimate) | -0.027 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.027 | ||||
| df | 54.000 | ||||
| t | -0.058 | ||||
| p | 0.523 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.943 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.888 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.942 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.889 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.037 | ||||
| Upside Potential Ratio | 1.056 | ||||
| Upside part of mean | 0.118 | ||||
| Downside part of mean | -0.123 | ||||
| Upside SD | 0.102 | ||||
| Downside SD | 0.112 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 45.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 55.000 | ||||
| Mean of predictor | 0.355 | ||||
| Mean of criterion | -0.004 | ||||
| SD of predictor | 0.302 | ||||
| SD of criterion | 0.153 | ||||
| Covariance | 0.010 | ||||
| r | 0.222 | ||||
| b (slope, estimate of beta) | 0.113 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 53.000 | ||||
| t(b) | 1.660 | ||||
| p(b) | 0.051 | ||||
| t(a) | -0.594 | ||||
| p(a) | 0.722 | ||||
| Lowerbound of 95% confidence interval for beta | -0.023 | ||||
| Upperbound of 95% confidence interval for beta | 0.249 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.194 | ||||
| Upperbound of 95% confidence interval for alpha | 0.105 | ||||
| Treynor index (mean / b) | -0.037 | ||||
| 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%) | 0.071 | ||||
| Expected Shortfall on VaR | 0.087 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.063 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 55.000 | ||||
| Minimum | 0.819 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.155 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.044 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.127 | ||||
| Mean of outliers low | 0.947 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.236 | ||||
| Mean of outliers high | 1.047 | ||||
| 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) | 1.008 | ||||
| VaR(95%) (regression method) | 0.030 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.018 | ||||
| Quartile 1 | 0.038 | ||||
| Median | 0.073 | ||||
| Quartile 3 | 0.127 | ||||
| Maximum | 0.205 | ||||
| Mean of quarter 1 | 0.018 | ||||
| Mean of quarter 2 | 0.044 | ||||
| Mean of quarter 3 | 0.101 | ||||
| Mean of quarter 4 | 0.205 | ||||
| Inter Quartile Range | 0.089 | ||||
| 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) | 0.044 | ||||
| Compounded annual return (geometric extrapolation) | 0.041 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.198 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.198 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.465 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.017 | ||||
| SD | 0.207 | ||||
| Sharpe ratio (Glass type estimate) | 0.083 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.082 | ||||
| df | 1211.000 | ||||
| t | 0.177 | ||||
| p | 0.497 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.829 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.994 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.829 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.994 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.115 | ||||
| Upside Potential Ratio | 3.781 | ||||
| Upside part of mean | 0.562 | ||||
| Downside part of mean | -0.545 | ||||
| Upside SD | 0.144 | ||||
| Downside SD | 0.149 | ||||
| N nonnegative terms | 199.000 | ||||
| N negative terms | 1013.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1212.000 | ||||
| Mean of predictor | 0.433 | ||||
| Mean of criterion | 0.017 | ||||
| SD of predictor | 0.346 | ||||
| SD of criterion | 0.207 | ||||
| Covariance | 0.017 | ||||
| r | 0.231 | ||||
| b (slope, estimate of beta) | 0.139 | ||||
| a (intercept, estimate of alpha) | -0.043 | ||||
| Mean Square Error | 0.041 | ||||
| DF error | 1210.000 | ||||
| t(b) | 8.277 | ||||
| p(b) | 0.384 | ||||
| t(a) | -0.458 | ||||
| p(a) | 0.507 | ||||
| Lowerbound of 95% confidence interval for beta | 0.106 | ||||
| Upperbound of 95% confidence interval for beta | 0.171 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.227 | ||||
| Upperbound of 95% confidence interval for alpha | 0.141 | ||||
| Treynor index (mean / b) | 0.123 | ||||
| Jensen alpha (a) | -0.043 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.005 | ||||
| SD | 0.209 | ||||
| Sharpe ratio (Glass type estimate) | -0.022 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.022 | ||||
| df | 1211.000 | ||||
| t | -0.047 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.933 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.890 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.933 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.890 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.029 | ||||
| Upside Potential Ratio | 3.559 | ||||
| Upside part of mean | 0.552 | ||||
| Downside part of mean | -0.557 | ||||
| Upside SD | 0.139 | ||||
| Downside SD | 0.155 | ||||
| N nonnegative terms | 199.000 | ||||
| N negative terms | 1013.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1212.000 | ||||
| Mean of predictor | 0.374 | ||||
| Mean of criterion | -0.005 | ||||
| SD of predictor | 0.341 | ||||
| SD of criterion | 0.209 | ||||
| Covariance | 0.017 | ||||
| r | 0.232 | ||||
| b (slope, estimate of beta) | 0.142 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.041 | ||||
| DF error | 1210.000 | ||||
| t(b) | 8.304 | ||||
| p(b) | 0.384 | ||||
| t(a) | -0.609 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | 0.108 | ||||
| Upperbound of 95% confidence interval for beta | 0.175 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.243 | ||||
| Upperbound of 95% confidence interval for alpha | 0.128 | ||||
| Treynor index (mean / b) | -0.032 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1212.000 | ||||
| Minimum | 0.843 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.130 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 165.000 | ||||
| Percentage of outliers low | 0.136 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 207.000 | ||||
| Percentage of outliers high | 0.171 | ||||
| Mean of outliers high | 1.013 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.560 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.011 | ||||
| Extreme Value Index (regression method) | 0.345 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.021 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 13.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.015 | ||||
| Median | 0.029 | ||||
| Quartile 3 | 0.067 | ||||
| Maximum | 0.206 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.028 | ||||
| Mean of quarter 3 | 0.052 | ||||
| Mean of quarter 4 | 0.163 | ||||
| Inter Quartile Range | 0.052 | ||||
| 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 | 0.154 | ||||
| Mean of outliers high | 0.192 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.801 | ||||
| VaR(95%) (moments method) | 0.143 | ||||
| Expected Shortfall (moments method) | 0.144 | ||||
| Extreme Value Index (regression method) | -1.445 | ||||
| VaR(95%) (regression method) | 0.218 | ||||
| Expected Shortfall (regression method) | 0.226 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.043 | ||||
| Compounded annual return (geometric extrapolation) | 0.040 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.196 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.247 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.534 | ||||
| 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 | 1.114 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.518 | ||||
| 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 | 0.977 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.522 | ||||
| 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) | -8741070128503161.000 | ||||
| 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) | -395383506344373898548501180055552.000 | ||||
| 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 | ||||