Advanced Statistics: ActionPro 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 | -0.149 | ||||
| SD | 0.100 | ||||
| Sharpe ratio (Glass type estimate) | -1.489 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.455 | ||||
| df | 33.000 | ||||
| t | -2.507 | ||||
| p | 0.991 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.697 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.261 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.671 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.239 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.385 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.149 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.108 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.593 | ||||
| Mean of criterion | -0.149 | ||||
| SD of predictor | 0.306 | ||||
| SD of criterion | 0.100 | ||||
| Covariance | 0.003 | ||||
| r | 0.091 | ||||
| b (slope, estimate of beta) | 0.030 | ||||
| a (intercept, estimate of alpha) | -0.167 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.514 | ||||
| p(b) | 0.305 | ||||
| t(a) | -2.408 | ||||
| p(a) | 0.989 | ||||
| Lowerbound of 95% confidence interval for beta | -0.088 | ||||
| Upperbound of 95% confidence interval for beta | 0.147 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.308 | ||||
| Upperbound of 95% confidence interval for alpha | -0.026 | ||||
| Treynor index (mean / b) | -5.028 | ||||
| Jensen alpha (a) | -0.167 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.155 | ||||
| SD | 0.107 | ||||
| Sharpe ratio (Glass type estimate) | -1.452 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.419 | ||||
| df | 33.000 | ||||
| t | -2.444 | ||||
| p | 0.990 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.658 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.227 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.633 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.205 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.356 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.155 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.114 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.536 | ||||
| Mean of criterion | -0.155 | ||||
| SD of predictor | 0.290 | ||||
| SD of criterion | 0.107 | ||||
| Covariance | 0.002 | ||||
| r | 0.078 | ||||
| b (slope, estimate of beta) | 0.029 | ||||
| a (intercept, estimate of alpha) | -0.171 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.441 | ||||
| p(b) | 0.331 | ||||
| t(a) | -2.333 | ||||
| p(a) | 0.987 | ||||
| Lowerbound of 95% confidence interval for beta | -0.104 | ||||
| Upperbound of 95% confidence interval for beta | 0.161 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.319 | ||||
| Upperbound of 95% confidence interval for alpha | -0.022 | ||||
| Treynor index (mean / b) | -5.419 | ||||
| Jensen alpha (a) | -0.171 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.062 | ||||
| Expected Shortfall on VaR | 0.074 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.043 | ||||
| Expected Shortfall on VaR | 0.085 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.861 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.967 | ||||
| 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 | 6.000 | ||||
| Percentage of outliers low | 0.176 | ||||
| Mean of outliers low | 0.950 | ||||
| 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) | 1.618 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.940 | ||||
| VaR(95%) (regression method) | 0.042 | ||||
| Expected Shortfall (regression method) | 1.012 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.270 | ||||
| Quartile 1 | 0.270 | ||||
| Median | 0.270 | ||||
| Quartile 3 | 0.270 | ||||
| Maximum | 0.270 | ||||
| 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) | -0.095 | ||||
| Compounded annual return (geometric extrapolation) | -0.105 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.389 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.429 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.152 | ||||
| SD | 0.067 | ||||
| Sharpe ratio (Glass type estimate) | -2.273 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.271 | ||||
| df | 748.000 | ||||
| t | -3.843 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.437 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.107 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.436 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.106 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.609 | ||||
| Upside Potential Ratio | 1.099 | ||||
| Upside part of mean | 0.064 | ||||
| Downside part of mean | -0.216 | ||||
| Upside SD | 0.034 | ||||
| Downside SD | 0.058 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 732.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 749.000 | ||||
| Mean of predictor | 0.635 | ||||
| Mean of criterion | -0.152 | ||||
| SD of predictor | 0.367 | ||||
| SD of criterion | 0.067 | ||||
| Covariance | -0.000 | ||||
| r | -0.007 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.151 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 747.000 | ||||
| t(b) | -0.186 | ||||
| p(b) | 0.574 | ||||
| t(a) | -3.799 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.229 | ||||
| Upperbound of 95% confidence interval for alpha | -0.073 | ||||
| Treynor index (mean / b) | 122.476 | ||||
| Jensen alpha (a) | -0.151 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.154 | ||||
| SD | 0.067 | ||||
| Sharpe ratio (Glass type estimate) | -2.291 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.289 | ||||
| df | 748.000 | ||||
| t | -3.873 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.455 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.125 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.454 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.124 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.613 | ||||
| Upside Potential Ratio | 1.075 | ||||
| Upside part of mean | 0.063 | ||||
| Downside part of mean | -0.218 | ||||
| Upside SD | 0.034 | ||||
| Downside SD | 0.059 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 732.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 749.000 | ||||
| Mean of predictor | 0.564 | ||||
| Mean of criterion | -0.154 | ||||
| SD of predictor | 0.383 | ||||
| SD of criterion | 0.067 | ||||
| Covariance | -0.000 | ||||
| r | -0.008 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.153 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 747.000 | ||||
| t(b) | -0.206 | ||||
| p(b) | 0.582 | ||||
| t(a) | -3.836 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.232 | ||||
| Upperbound of 95% confidence interval for alpha | -0.075 | ||||
| Treynor index (mean / b) | 116.352 | ||||
| Jensen alpha (a) | -0.153 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 749.000 | ||||
| Minimum | 0.955 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.031 | ||||
| Mean of quarter 1 | 0.997 | ||||
| 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 | 47.000 | ||||
| Percentage of outliers low | 0.063 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 19.000 | ||||
| Percentage of outliers high | 0.025 | ||||
| Mean of outliers high | 1.010 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.595 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | -0.246 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.008 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.029 | ||||
| Quartile 1 | 0.090 | ||||
| Median | 0.151 | ||||
| Quartile 3 | 0.211 | ||||
| Maximum | 0.272 | ||||
| Mean of quarter 1 | 0.029 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.272 | ||||
| Inter Quartile Range | 0.121 | ||||
| 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) | -0.095 | ||||
| Compounded annual return (geometric extrapolation) | -0.104 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.383 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.383 | ||||
| Compounded annual return / Expected Shortfall lognormal | -11.436 | ||||
| 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 | 1.042 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.468 | ||||
| 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 | 0.931 | ||||
| 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) | -8734484451583079.000 | ||||
| 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) | -74894199205925098457177702531072.000 | ||||
| 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 | ||||