Advanced Statistics: TimerSignals - EEM
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 | -0.004 | ||||
| SD | 0.059 | ||||
| Sharpe ratio (Glass type estimate) | -0.063 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.062 | ||||
| df | 46.000 | ||||
| t | -0.124 | ||||
| p | 0.549 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.053 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.928 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.052 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.929 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.098 | ||||
| Upside Potential Ratio | 1.747 | ||||
| Upside part of mean | 0.066 | ||||
| Downside part of mean | -0.069 | ||||
| Upside SD | 0.044 | ||||
| Downside SD | 0.038 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 47.000 | ||||
| Mean of predictor | 0.418 | ||||
| Mean of criterion | -0.004 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 0.059 | ||||
| Covariance | -0.001 | ||||
| r | -0.037 | ||||
| b (slope, estimate of beta) | -0.007 | ||||
| a (intercept, estimate of alpha) | -0.001 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 45.000 | ||||
| t(b) | -0.250 | ||||
| p(b) | 0.598 | ||||
| t(a) | -0.018 | ||||
| p(a) | 0.507 | ||||
| Lowerbound of 95% confidence interval for beta | -0.067 | ||||
| Upperbound of 95% confidence interval for beta | 0.052 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.066 | ||||
| Upperbound of 95% confidence interval for alpha | 0.065 | ||||
| Treynor index (mean / b) | 0.495 | ||||
| Jensen alpha (a) | -0.001 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.005 | ||||
| SD | 0.058 | ||||
| Sharpe ratio (Glass type estimate) | -0.091 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.090 | ||||
| df | 46.000 | ||||
| t | -0.181 | ||||
| p | 0.571 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.081 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.900 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.080 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.901 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.140 | ||||
| Upside Potential Ratio | 1.692 | ||||
| Upside part of mean | 0.064 | ||||
| Downside part of mean | -0.070 | ||||
| Upside SD | 0.043 | ||||
| Downside SD | 0.038 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 47.000 | ||||
| Mean of predictor | 0.372 | ||||
| Mean of criterion | -0.005 | ||||
| SD of predictor | 0.272 | ||||
| SD of criterion | 0.058 | ||||
| Covariance | -0.000 | ||||
| r | -0.027 | ||||
| b (slope, estimate of beta) | -0.006 | ||||
| a (intercept, estimate of alpha) | -0.003 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 45.000 | ||||
| t(b) | -0.180 | ||||
| p(b) | 0.571 | ||||
| t(a) | -0.099 | ||||
| p(a) | 0.539 | ||||
| Lowerbound of 95% confidence interval for beta | -0.070 | ||||
| Upperbound of 95% confidence interval for beta | 0.059 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.068 | ||||
| Upperbound of 95% confidence interval for alpha | 0.061 | ||||
| Treynor index (mean / b) | 0.927 | ||||
| Jensen alpha (a) | -0.003 | ||||
| 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 | 0.035 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 47.000 | ||||
| Minimum | 0.954 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.047 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.025 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.149 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.234 | ||||
| Mean of outliers high | 1.027 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -34.017 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.295 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.033 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.012 | ||||
| Quartile 1 | 0.013 | ||||
| Median | 0.015 | ||||
| Quartile 3 | 0.058 | ||||
| Maximum | 0.101 | ||||
| Mean of quarter 1 | 0.012 | ||||
| Mean of quarter 2 | 0.015 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.101 | ||||
| Inter Quartile Range | 0.045 | ||||
| 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) | 0.042 | ||||
| Compounded annual return (geometric extrapolation) | 0.039 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.391 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.391 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.143 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.003 | ||||
| SD | 0.078 | ||||
| Sharpe ratio (Glass type estimate) | -0.035 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.035 | ||||
| df | 1037.000 | ||||
| t | -0.069 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.020 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.950 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.019 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.950 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.050 | ||||
| Upside Potential Ratio | 4.637 | ||||
| Upside part of mean | 0.251 | ||||
| Downside part of mean | -0.253 | ||||
| Upside SD | 0.056 | ||||
| Downside SD | 0.054 | ||||
| N nonnegative terms | 158.000 | ||||
| N negative terms | 880.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1038.000 | ||||
| Mean of predictor | 0.430 | ||||
| Mean of criterion | -0.003 | ||||
| SD of predictor | 0.343 | ||||
| SD of criterion | 0.078 | ||||
| Covariance | 0.001 | ||||
| r | 0.031 | ||||
| b (slope, estimate of beta) | 0.007 | ||||
| a (intercept, estimate of alpha) | -0.006 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1036.000 | ||||
| t(b) | 1.012 | ||||
| p(b) | 0.484 | ||||
| t(a) | -0.147 | ||||
| p(a) | 0.502 | ||||
| Lowerbound of 95% confidence interval for beta | -0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.083 | ||||
| Upperbound of 95% confidence interval for alpha | 0.071 | ||||
| Treynor index (mean / b) | -0.379 | ||||
| Jensen alpha (a) | -0.006 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.006 | ||||
| SD | 0.078 | ||||
| Sharpe ratio (Glass type estimate) | -0.074 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.074 | ||||
| df | 1037.000 | ||||
| t | -0.147 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.058 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.911 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.058 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.911 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.106 | ||||
| Upside Potential Ratio | 4.566 | ||||
| Upside part of mean | 0.249 | ||||
| Downside part of mean | -0.255 | ||||
| Upside SD | 0.056 | ||||
| Downside SD | 0.055 | ||||
| N nonnegative terms | 158.000 | ||||
| N negative terms | 880.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1038.000 | ||||
| Mean of predictor | 0.373 | ||||
| Mean of criterion | -0.006 | ||||
| SD of predictor | 0.336 | ||||
| SD of criterion | 0.078 | ||||
| Covariance | 0.001 | ||||
| r | 0.033 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.009 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1036.000 | ||||
| t(b) | 1.065 | ||||
| p(b) | 0.483 | ||||
| t(a) | -0.219 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | -0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.022 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.086 | ||||
| Upperbound of 95% confidence interval for alpha | 0.069 | ||||
| Treynor index (mean / b) | -0.751 | ||||
| Jensen alpha (a) | -0.009 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1038.000 | ||||
| Minimum | 0.971 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.027 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 139.000 | ||||
| Percentage of outliers low | 0.134 | ||||
| Mean of outliers low | 0.994 | ||||
| Number of outliers high | 170.000 | ||||
| Percentage of outliers high | 0.164 | ||||
| Mean of outliers high | 1.006 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.353 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | -0.438 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.008 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 16.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.019 | ||||
| Quartile 3 | 0.027 | ||||
| Maximum | 0.138 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.023 | ||||
| Mean of quarter 4 | 0.063 | ||||
| Inter Quartile Range | 0.021 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.062 | ||||
| Mean of outliers high | 0.138 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.451 | ||||
| VaR(95%) (moments method) | 0.069 | ||||
| Expected Shortfall (moments method) | 0.142 | ||||
| Extreme Value Index (regression method) | 1.800 | ||||
| VaR(95%) (regression method) | 0.098 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.041 | ||||
| Compounded annual return (geometric extrapolation) | 0.039 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.283 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.616 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.932 | ||||
| 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 | 0.887 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.506 | ||||
| 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 | 0.757 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.511 | ||||
| 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) | -8762850168107729.000 | ||||
| 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) | 757179637524354887929305688440832.000 | ||||
| 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 | ||||