Advanced Statistics: Gold Survivor eMini Russell
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 | -0.053 | ||||
| SD | 0.094 | ||||
| Sharpe ratio (Glass type estimate) | -0.564 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.559 | ||||
| df | 90.000 | ||||
| t | -1.552 | ||||
| p | 0.938 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.278 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.154 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.275 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.158 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.661 | ||||
| Upside Potential Ratio | 0.447 | ||||
| Upside part of mean | 0.036 | ||||
| Downside part of mean | -0.089 | ||||
| Upside SD | 0.051 | ||||
| Downside SD | 0.080 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 85.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 91.000 | ||||
| Mean of predictor | 0.195 | ||||
| Mean of criterion | -0.053 | ||||
| SD of predictor | 0.252 | ||||
| SD of criterion | 0.094 | ||||
| Covariance | 0.003 | ||||
| r | 0.107 | ||||
| b (slope, estimate of beta) | 0.040 | ||||
| a (intercept, estimate of alpha) | -0.061 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 89.000 | ||||
| t(b) | 1.016 | ||||
| p(b) | 0.156 | ||||
| t(a) | -1.737 | ||||
| p(a) | 0.957 | ||||
| Lowerbound of 95% confidence interval for beta | -0.038 | ||||
| Upperbound of 95% confidence interval for beta | 0.118 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.130 | ||||
| Upperbound of 95% confidence interval for alpha | 0.009 | ||||
| Treynor index (mean / b) | -1.324 | ||||
| Jensen alpha (a) | -0.061 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.099 | ||||
| Sharpe ratio (Glass type estimate) | -0.581 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.576 | ||||
| df | 90.000 | ||||
| t | -1.599 | ||||
| p | 0.943 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.296 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.138 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.293 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.141 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.657 | ||||
| Upside Potential Ratio | 0.393 | ||||
| Upside part of mean | 0.034 | ||||
| Downside part of mean | -0.092 | ||||
| Upside SD | 0.048 | ||||
| Downside SD | 0.088 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 85.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 91.000 | ||||
| Mean of predictor | 0.162 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.249 | ||||
| SD of criterion | 0.099 | ||||
| Covariance | 0.003 | ||||
| r | 0.116 | ||||
| b (slope, estimate of beta) | 0.046 | ||||
| a (intercept, estimate of alpha) | -0.065 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 89.000 | ||||
| t(b) | 1.100 | ||||
| p(b) | 0.137 | ||||
| t(a) | -1.778 | ||||
| p(a) | 0.961 | ||||
| Lowerbound of 95% confidence interval for beta | -0.037 | ||||
| Upperbound of 95% confidence interval for beta | 0.130 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.138 | ||||
| Upperbound of 95% confidence interval for alpha | 0.008 | ||||
| Treynor index (mean / b) | -1.247 | ||||
| Jensen alpha (a) | -0.065 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.051 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.052 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 91.000 | ||||
| Minimum | 0.806 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.119 | ||||
| Mean of quarter 1 | 0.984 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.110 | ||||
| Mean of outliers low | 0.963 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.121 | ||||
| Mean of outliers high | 1.027 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.564 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | 0.839 | ||||
| VaR(95%) (regression method) | 0.013 | ||||
| Expected Shortfall (regression method) | 0.172 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.194 | ||||
| Quartile 1 | 0.194 | ||||
| Median | 0.194 | ||||
| Quartile 3 | 0.194 | ||||
| Maximum | 0.194 | ||||
| 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) | -0.013 | ||||
| Compounded annual return (geometric extrapolation) | -0.013 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.069 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.218 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 0.198 | ||||
| Sharpe ratio (Glass type estimate) | -0.192 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.192 | ||||
| df | 1997.000 | ||||
| t | -0.531 | ||||
| p | 0.508 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.902 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.517 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.902 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.518 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.282 | ||||
| Upside Potential Ratio | 1.446 | ||||
| Upside part of mean | 0.195 | ||||
| Downside part of mean | -0.233 | ||||
| Upside SD | 0.145 | ||||
| Downside SD | 0.135 | ||||
| N nonnegative terms | 75.000 | ||||
| N negative terms | 1923.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1998.000 | ||||
| Mean of predictor | 0.299 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.528 | ||||
| SD of criterion | 0.198 | ||||
| Covariance | 0.020 | ||||
| r | 0.193 | ||||
| b (slope, estimate of beta) | 0.072 | ||||
| a (intercept, estimate of alpha) | -0.060 | ||||
| Mean Square Error | 0.038 | ||||
| DF error | 1996.000 | ||||
| t(b) | 8.782 | ||||
| p(b) | 0.404 | ||||
| t(a) | -0.848 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | 0.056 | ||||
| Upperbound of 95% confidence interval for beta | 0.088 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.198 | ||||
| Upperbound of 95% confidence interval for alpha | 0.078 | ||||
| Treynor index (mean / b) | -0.526 | ||||
| Jensen alpha (a) | -0.060 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.198 | ||||
| Sharpe ratio (Glass type estimate) | -0.291 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.291 | ||||
| df | 1997.000 | ||||
| t | -0.803 | ||||
| p | 0.511 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.001 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.419 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.001 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.419 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.393 | ||||
| Upside Potential Ratio | 1.270 | ||||
| Upside part of mean | 0.186 | ||||
| Downside part of mean | -0.243 | ||||
| Upside SD | 0.133 | ||||
| Downside SD | 0.146 | ||||
| N nonnegative terms | 75.000 | ||||
| N negative terms | 1923.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1998.000 | ||||
| Mean of predictor | 0.159 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.529 | ||||
| SD of criterion | 0.198 | ||||
| Covariance | 0.020 | ||||
| r | 0.195 | ||||
| b (slope, estimate of beta) | 0.073 | ||||
| a (intercept, estimate of alpha) | -0.069 | ||||
| Mean Square Error | 0.038 | ||||
| DF error | 1996.000 | ||||
| t(b) | 8.870 | ||||
| p(b) | 0.403 | ||||
| t(a) | -0.984 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | 0.057 | ||||
| Upperbound of 95% confidence interval for beta | 0.089 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.207 | ||||
| Upperbound of 95% confidence interval for alpha | 0.069 | ||||
| Treynor index (mean / b) | -0.790 | ||||
| Jensen alpha (a) | -0.069 | ||||
| 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 | 0.025 | ||||
| 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 | 1998.000 | ||||
| Minimum | 0.798 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.259 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 137.000 | ||||
| Percentage of outliers low | 0.069 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 104.000 | ||||
| Percentage of outliers high | 0.052 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.291 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.200 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.032 | ||||
| Quartile 1 | 0.061 | ||||
| Median | 0.084 | ||||
| Quartile 3 | 0.149 | ||||
| Maximum | 0.207 | ||||
| Mean of quarter 1 | 0.045 | ||||
| Mean of quarter 2 | 0.069 | ||||
| Mean of quarter 3 | 0.099 | ||||
| Mean of quarter 4 | 0.186 | ||||
| Inter Quartile Range | 0.088 | ||||
| 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) | -0.013 | ||||
| Compounded annual return (geometric extrapolation) | -0.013 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.065 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.072 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.535 | ||||
| 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 | 0.850 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.477 | ||||
| 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 | 0.734 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.484 | ||||
| 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) | -8761047084220863.000 | ||||
| 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) | -441513298577283796008178735382528.000 | ||||
| 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 | ||||