Advanced Statistics: Dow Eagle
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 | -0.035 | ||||
| SD | 0.131 | ||||
| Sharpe ratio (Glass type estimate) | -0.265 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.262 | ||||
| df | 79.000 | ||||
| t | -0.684 | ||||
| p | 0.752 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.024 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.496 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.023 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.498 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.348 | ||||
| Upside Potential Ratio | 0.669 | ||||
| Upside part of mean | 0.067 | ||||
| Downside part of mean | -0.102 | ||||
| Upside SD | 0.085 | ||||
| Downside SD | 0.100 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 74.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.126 | ||||
| Mean of criterion | -0.035 | ||||
| SD of predictor | 0.246 | ||||
| SD of criterion | 0.131 | ||||
| Covariance | -0.002 | ||||
| r | -0.076 | ||||
| b (slope, estimate of beta) | -0.040 | ||||
| a (intercept, estimate of alpha) | -0.030 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 78.000 | ||||
| t(b) | -0.672 | ||||
| p(b) | 0.748 | ||||
| t(a) | -0.576 | ||||
| p(a) | 0.717 | ||||
| Lowerbound of 95% confidence interval for beta | -0.160 | ||||
| Upperbound of 95% confidence interval for beta | 0.079 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.133 | ||||
| Upperbound of 95% confidence interval for alpha | 0.073 | ||||
| Treynor index (mean / b) | 0.860 | ||||
| Jensen alpha (a) | -0.030 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.138 | ||||
| Sharpe ratio (Glass type estimate) | -0.318 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.315 | ||||
| df | 79.000 | ||||
| t | -0.821 | ||||
| p | 0.793 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.078 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.444 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.076 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.446 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.391 | ||||
| Upside Potential Ratio | 0.567 | ||||
| Upside part of mean | 0.063 | ||||
| Downside part of mean | -0.107 | ||||
| Upside SD | 0.080 | ||||
| Downside SD | 0.112 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 74.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.095 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.247 | ||||
| SD of criterion | 0.138 | ||||
| Covariance | -0.002 | ||||
| r | -0.068 | ||||
| b (slope, estimate of beta) | -0.038 | ||||
| a (intercept, estimate of alpha) | -0.040 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 78.000 | ||||
| t(b) | -0.601 | ||||
| p(b) | 0.725 | ||||
| t(a) | -0.746 | ||||
| p(a) | 0.771 | ||||
| Lowerbound of 95% confidence interval for beta | -0.163 | ||||
| Upperbound of 95% confidence interval for beta | 0.088 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.147 | ||||
| Upperbound of 95% confidence interval for alpha | 0.067 | ||||
| Treynor index (mean / b) | 1.156 | ||||
| Jensen alpha (a) | -0.040 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.067 | ||||
| Expected Shortfall on VaR | 0.082 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.060 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 80.000 | ||||
| Minimum | 0.767 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.137 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.023 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.075 | ||||
| Mean of outliers low | 0.932 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.075 | ||||
| Mean of outliers high | 1.078 | ||||
| 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) | 0.688 | ||||
| VaR(95%) (regression method) | 0.012 | ||||
| Expected Shortfall (regression method) | 0.095 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.050 | ||||
| Quartile 1 | 0.060 | ||||
| Median | 0.069 | ||||
| Quartile 3 | 0.151 | ||||
| Maximum | 0.233 | ||||
| Mean of quarter 1 | 0.050 | ||||
| Mean of quarter 2 | 0.069 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.233 | ||||
| Inter Quartile Range | 0.091 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.001 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.001 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.003 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.025 | ||||
| SD | 0.190 | ||||
| Sharpe ratio (Glass type estimate) | -0.134 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.134 | ||||
| df | 1767.000 | ||||
| t | -0.347 | ||||
| p | 0.505 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.888 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.621 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.888 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.621 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.181 | ||||
| Upside Potential Ratio | 2.175 | ||||
| Upside part of mean | 0.305 | ||||
| Downside part of mean | -0.330 | ||||
| Upside SD | 0.128 | ||||
| Downside SD | 0.140 | ||||
| N nonnegative terms | 69.000 | ||||
| N negative terms | 1699.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1768.000 | ||||
| Mean of predictor | 0.302 | ||||
| Mean of criterion | -0.025 | ||||
| SD of predictor | 0.555 | ||||
| SD of criterion | 0.190 | ||||
| Covariance | 0.009 | ||||
| r | 0.081 | ||||
| b (slope, estimate of beta) | 0.028 | ||||
| a (intercept, estimate of alpha) | -0.034 | ||||
| Mean Square Error | 0.036 | ||||
| DF error | 1766.000 | ||||
| t(b) | 3.410 | ||||
| p(b) | 0.460 | ||||
| t(a) | -0.463 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | 0.012 | ||||
| Upperbound of 95% confidence interval for beta | 0.044 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.177 | ||||
| Upperbound of 95% confidence interval for alpha | 0.109 | ||||
| Treynor index (mean / b) | -0.918 | ||||
| Jensen alpha (a) | -0.034 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.193 | ||||
| Sharpe ratio (Glass type estimate) | -0.227 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.226 | ||||
| df | 1767.000 | ||||
| t | -0.588 | ||||
| p | 0.509 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.981 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.528 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.981 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.528 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.295 | ||||
| Upside Potential Ratio | 2.000 | ||||
| Upside part of mean | 0.297 | ||||
| Downside part of mean | -0.340 | ||||
| Upside SD | 0.124 | ||||
| Downside SD | 0.148 | ||||
| N nonnegative terms | 69.000 | ||||
| N negative terms | 1699.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1768.000 | ||||
| Mean of predictor | 0.153 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.543 | ||||
| SD of criterion | 0.193 | ||||
| Covariance | 0.008 | ||||
| r | 0.076 | ||||
| b (slope, estimate of beta) | 0.027 | ||||
| a (intercept, estimate of alpha) | -0.048 | ||||
| Mean Square Error | 0.037 | ||||
| DF error | 1766.000 | ||||
| t(b) | 3.195 | ||||
| p(b) | 0.462 | ||||
| t(a) | -0.645 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | 0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.044 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.194 | ||||
| Upperbound of 95% confidence interval for alpha | 0.098 | ||||
| Treynor index (mean / b) | -1.622 | ||||
| Jensen alpha (a) | -0.048 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1768.000 | ||||
| Minimum | 0.804 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.098 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 70.000 | ||||
| Percentage of outliers low | 0.040 | ||||
| Mean of outliers low | 0.972 | ||||
| Number of outliers high | 69.000 | ||||
| Percentage of outliers high | 0.039 | ||||
| Mean of outliers high | 1.030 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.655 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.007 | ||||
| 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 | 7.000 | ||||
| Minimum | 0.055 | ||||
| Quartile 1 | 0.058 | ||||
| Median | 0.097 | ||||
| Quartile 3 | 0.105 | ||||
| Maximum | 0.235 | ||||
| Mean of quarter 1 | 0.057 | ||||
| Mean of quarter 2 | 0.077 | ||||
| Mean of quarter 3 | 0.098 | ||||
| Mean of quarter 4 | 0.173 | ||||
| Inter Quartile Range | 0.047 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.235 | ||||
| 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) | 0.001 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.001 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.009 | ||||
| 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 | 1.817 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.775 | ||||
| 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 | 1.524 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.757 | ||||
| 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) | -8731996397866635.000 | ||||
| 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) | 346614886657959344029583852699648.000 | ||||
| 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 | ||||