Advanced Statistics: Gold Survivor Energy Portfolio
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 | 0.079 | ||||
| SD | 0.109 | ||||
| Sharpe ratio (Glass type estimate) | 0.720 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.714 | ||||
| df | 86.000 | ||||
| t | 1.940 | ||||
| p | 0.028 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.017 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.454 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.022 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.450 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.738 | ||||
| Upside Potential Ratio | 3.485 | ||||
| Upside part of mean | 0.158 | ||||
| Downside part of mean | -0.079 | ||||
| Upside SD | 0.101 | ||||
| Downside SD | 0.045 | ||||
| N nonnegative terms | 30.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 87.000 | ||||
| Mean of predictor | 0.142 | ||||
| Mean of criterion | 0.079 | ||||
| SD of predictor | 0.262 | ||||
| SD of criterion | 0.109 | ||||
| Covariance | -0.004 | ||||
| r | -0.151 | ||||
| b (slope, estimate of beta) | -0.063 | ||||
| a (intercept, estimate of alpha) | 0.088 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 85.000 | ||||
| t(b) | -1.413 | ||||
| p(b) | 0.919 | ||||
| t(a) | 2.147 | ||||
| p(a) | 0.017 | ||||
| Lowerbound of 95% confidence interval for beta | -0.152 | ||||
| Upperbound of 95% confidence interval for beta | 0.026 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.006 | ||||
| Upperbound of 95% confidence interval for alpha | 0.169 | ||||
| Treynor index (mean / b) | -1.246 | ||||
| Jensen alpha (a) | 0.088 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.073 | ||||
| SD | 0.106 | ||||
| Sharpe ratio (Glass type estimate) | 0.685 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.679 | ||||
| df | 86.000 | ||||
| t | 1.844 | ||||
| p | 0.034 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.052 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.418 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.056 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.414 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.577 | ||||
| Upside Potential Ratio | 3.314 | ||||
| Upside part of mean | 0.153 | ||||
| Downside part of mean | -0.080 | ||||
| Upside SD | 0.097 | ||||
| Downside SD | 0.046 | ||||
| N nonnegative terms | 30.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 87.000 | ||||
| Mean of predictor | 0.107 | ||||
| Mean of criterion | 0.073 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.106 | ||||
| Covariance | -0.004 | ||||
| r | -0.156 | ||||
| b (slope, estimate of beta) | -0.062 | ||||
| a (intercept, estimate of alpha) | 0.079 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 85.000 | ||||
| t(b) | -1.456 | ||||
| p(b) | 0.926 | ||||
| t(a) | 2.012 | ||||
| p(a) | 0.024 | ||||
| Lowerbound of 95% confidence interval for beta | -0.147 | ||||
| Upperbound of 95% confidence interval for beta | 0.023 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.001 | ||||
| Upperbound of 95% confidence interval for alpha | 0.158 | ||||
| Treynor index (mean / b) | -1.169 | ||||
| Jensen alpha (a) | 0.079 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.043 | ||||
| Expected Shortfall on VaR | 0.055 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 87.000 | ||||
| Minimum | 0.951 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.019 | ||||
| Maximum | 1.123 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.005 | ||||
| Mean of quarter 4 | 1.053 | ||||
| Inter Quartile Range | 0.019 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.080 | ||||
| Mean of outliers low | 0.963 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.126 | ||||
| Mean of outliers high | 1.077 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -21.728 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | -0.455 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.022 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.013 | ||||
| Quartile 1 | 0.017 | ||||
| Median | 0.022 | ||||
| Quartile 3 | 0.054 | ||||
| Maximum | 0.106 | ||||
| Mean of quarter 1 | 0.014 | ||||
| Mean of quarter 2 | 0.017 | ||||
| Mean of quarter 3 | 0.037 | ||||
| Mean of quarter 4 | 0.089 | ||||
| Inter Quartile Range | 0.037 | ||||
| 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) | 0.183 | ||||
| Compounded annual return (geometric extrapolation) | 0.124 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.172 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.397 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.232 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.143 | ||||
| SD | 0.383 | ||||
| Sharpe ratio (Glass type estimate) | 0.374 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.374 | ||||
| df | 1909.000 | ||||
| t | 1.009 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.352 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.100 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.352 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.100 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.595 | ||||
| Upside Potential Ratio | 3.862 | ||||
| Upside part of mean | 0.927 | ||||
| Downside part of mean | -0.784 | ||||
| Upside SD | 0.298 | ||||
| Downside SD | 0.240 | ||||
| N nonnegative terms | 489.000 | ||||
| N negative terms | 1421.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1910.000 | ||||
| Mean of predictor | 0.257 | ||||
| Mean of criterion | 0.143 | ||||
| SD of predictor | 0.567 | ||||
| SD of criterion | 0.383 | ||||
| Covariance | -0.034 | ||||
| r | -0.158 | ||||
| b (slope, estimate of beta) | -0.107 | ||||
| a (intercept, estimate of alpha) | 0.170 | ||||
| Mean Square Error | 0.143 | ||||
| DF error | 1908.000 | ||||
| t(b) | -6.979 | ||||
| p(b) | 0.579 | ||||
| t(a) | 1.217 | ||||
| p(a) | 0.486 | ||||
| Lowerbound of 95% confidence interval for beta | -0.136 | ||||
| Upperbound of 95% confidence interval for beta | -0.077 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.104 | ||||
| Upperbound of 95% confidence interval for alpha | 0.445 | ||||
| Treynor index (mean / b) | -1.342 | ||||
| Jensen alpha (a) | 0.170 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.072 | ||||
| SD | 0.376 | ||||
| Sharpe ratio (Glass type estimate) | 0.191 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.191 | ||||
| df | 1909.000 | ||||
| t | 0.517 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.535 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.917 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.535 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.917 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.270 | ||||
| Upside Potential Ratio | 3.331 | ||||
| Upside part of mean | 0.889 | ||||
| Downside part of mean | -0.817 | ||||
| Upside SD | 0.265 | ||||
| Downside SD | 0.267 | ||||
| N nonnegative terms | 489.000 | ||||
| N negative terms | 1421.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1910.000 | ||||
| Mean of predictor | 0.099 | ||||
| Mean of criterion | 0.072 | ||||
| SD of predictor | 0.562 | ||||
| SD of criterion | 0.376 | ||||
| Covariance | -0.034 | ||||
| r | -0.162 | ||||
| b (slope, estimate of beta) | -0.109 | ||||
| a (intercept, estimate of alpha) | 0.083 | ||||
| Mean Square Error | 0.138 | ||||
| DF error | 1908.000 | ||||
| t(b) | -7.175 | ||||
| p(b) | 0.581 | ||||
| t(a) | 0.601 | ||||
| p(a) | 0.493 | ||||
| Lowerbound of 95% confidence interval for beta | -0.138 | ||||
| Upperbound of 95% confidence interval for beta | -0.079 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.187 | ||||
| Upperbound of 95% confidence interval for alpha | 0.352 | ||||
| Treynor index (mean / b) | -0.663 | ||||
| Jensen alpha (a) | 0.083 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1910.000 | ||||
| Minimum | 0.661 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.502 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.014 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 440.000 | ||||
| Percentage of outliers low | 0.230 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 449.000 | ||||
| Percentage of outliers high | 0.235 | ||||
| Mean of outliers high | 1.015 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.884 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.061 | ||||
| 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 | 26.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.013 | ||||
| Median | 0.052 | ||||
| Quartile 3 | 0.121 | ||||
| Maximum | 0.339 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.028 | ||||
| Mean of quarter 3 | 0.086 | ||||
| Mean of quarter 4 | 0.193 | ||||
| Inter Quartile Range | 0.107 | ||||
| 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 | 0.038 | ||||
| Mean of outliers high | 0.339 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.143 | ||||
| VaR(95%) (moments method) | 0.216 | ||||
| Expected Shortfall (moments method) | 0.297 | ||||
| Extreme Value Index (regression method) | 0.547 | ||||
| VaR(95%) (regression method) | 0.233 | ||||
| Expected Shortfall (regression method) | 0.461 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.182 | ||||
| Compounded annual return (geometric extrapolation) | 0.123 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.362 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.638 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.644 | ||||
| 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 | 0.936 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.545 | ||||
| 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 | 0.780 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.567 | ||||
| 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) | -8767940857059642.000 | ||||
| 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) | 160803647584525474575779631202304.000 | ||||
| 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 | ||||