Advanced Statistics: Legacy Metals
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 | -0.043 | ||||
| SD | 0.003 | ||||
| Sharpe ratio (Glass type estimate) | -16.273 | ||||
| Sharpe ratio (Hedges UMVUE) | -15.888 | ||||
| df | 32.000 | ||||
| t | -26.985 | ||||
| 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) | -19.956 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -11.820 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.392 | ||||
| Upside Potential Ratio | 0.019 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.585 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.289 | ||||
| SD of criterion | 0.003 | ||||
| Covariance | -0.000 | ||||
| r | -0.098 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.042 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 31.000 | ||||
| t(b) | -0.550 | ||||
| p(b) | 0.707 | ||||
| t(a) | -22.687 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | -0.038 | ||||
| Treynor index (mean / b) | 47.932 | ||||
| Jensen alpha (a) | -0.042 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.042 | ||||
| SD | 0.003 | ||||
| Sharpe ratio (Glass type estimate) | -16.278 | ||||
| Sharpe ratio (Hedges UMVUE) | -15.893 | ||||
| df | 32.000 | ||||
| t | -26.994 | ||||
| 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) | -19.962 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -11.824 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.392 | ||||
| Upside Potential Ratio | 0.019 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.533 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.269 | ||||
| SD of criterion | 0.003 | ||||
| Covariance | -0.000 | ||||
| r | -0.096 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.042 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 31.000 | ||||
| t(b) | -0.536 | ||||
| p(b) | 0.702 | ||||
| t(a) | -22.820 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | -0.038 | ||||
| Treynor index (mean / b) | 45.800 | ||||
| Jensen alpha (a) | -0.042 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 33.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.004 | ||||
| Mean of quarter 1 | 1.000 | ||||
| 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 | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.030 | ||||
| Mean of outliers high | 1.004 | ||||
| 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) | 0.002 | ||||
| Compounded annual return (geometric extrapolation) | 0.002 | ||||
| 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 | 0.310 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.042 | ||||
| SD | 0.044 | ||||
| Sharpe ratio (Glass type estimate) | -0.937 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.936 | ||||
| df | 735.000 | ||||
| t | -1.571 | ||||
| p | 0.942 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.107 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.233 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.107 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.234 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.606 | ||||
| Upside Potential Ratio | 1.357 | ||||
| Upside part of mean | 0.035 | ||||
| Downside part of mean | -0.077 | ||||
| Upside SD | 0.036 | ||||
| Downside SD | 0.026 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 732.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 736.000 | ||||
| Mean of predictor | 0.631 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.349 | ||||
| SD of criterion | 0.044 | ||||
| Covariance | -0.000 | ||||
| r | -0.014 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.040 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 734.000 | ||||
| t(b) | -0.373 | ||||
| p(b) | 0.645 | ||||
| t(a) | -1.519 | ||||
| p(a) | 0.935 | ||||
| Lowerbound of 95% confidence interval for beta | -0.011 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.093 | ||||
| Upperbound of 95% confidence interval for alpha | 0.012 | ||||
| Treynor index (mean / b) | 23.790 | ||||
| Jensen alpha (a) | -0.040 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.042 | ||||
| SD | 0.044 | ||||
| Sharpe ratio (Glass type estimate) | -0.969 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.968 | ||||
| df | 735.000 | ||||
| t | -1.624 | ||||
| p | 0.948 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.139 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.202 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.138 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.202 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.623 | ||||
| Upside Potential Ratio | 1.316 | ||||
| Upside part of mean | 0.034 | ||||
| Downside part of mean | -0.077 | ||||
| Upside SD | 0.035 | ||||
| Downside SD | 0.026 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 732.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 736.000 | ||||
| Mean of predictor | 0.569 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.352 | ||||
| SD of criterion | 0.044 | ||||
| Covariance | -0.000 | ||||
| r | -0.014 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.042 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 734.000 | ||||
| t(b) | -0.368 | ||||
| p(b) | 0.643 | ||||
| t(a) | -1.579 | ||||
| p(a) | 0.943 | ||||
| Lowerbound of 95% confidence interval for beta | -0.011 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.093 | ||||
| Upperbound of 95% confidence interval for alpha | 0.010 | ||||
| Treynor index (mean / b) | 25.130 | ||||
| Jensen alpha (a) | -0.042 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 736.000 | ||||
| Minimum | 0.968 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.053 | ||||
| Mean of quarter 1 | 0.999 | ||||
| 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 | 7.000 | ||||
| Percentage of outliers low | 0.010 | ||||
| Mean of outliers low | 0.987 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.005 | ||||
| Mean of outliers high | 1.025 | ||||
| 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) | 0.187 | ||||
| VaR(95%) (regression method) | -0.008 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.017 | ||||
| Quartile 1 | 0.031 | ||||
| Median | 0.045 | ||||
| Quartile 3 | 0.059 | ||||
| Maximum | 0.073 | ||||
| Mean of quarter 1 | 0.017 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.073 | ||||
| Inter Quartile Range | 0.028 | ||||
| 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) | 0.002 | ||||
| Compounded annual return (geometric extrapolation) | 0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.021 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.021 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.269 | ||||
| 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 | 1.061 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.529 | ||||
| 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 | 0.919 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.532 | ||||
| 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) | -8749762286515094.000 | ||||
| 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) | -293648149263739479883528720613376.000 | ||||
| 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 | ||||