Advanced Statistics: Seleukos Bonds and Metals Futures
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.054 | ||||
| SD | 0.141 | ||||
| Sharpe ratio (Glass type estimate) | 0.380 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.377 | ||||
| df | 80.000 | ||||
| t | 0.988 | ||||
| p | 0.163 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.377 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.136 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.380 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.134 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.675 | ||||
| Upside Potential Ratio | 2.106 | ||||
| Upside part of mean | 0.167 | ||||
| Downside part of mean | -0.114 | ||||
| Upside SD | 0.116 | ||||
| Downside SD | 0.079 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 53.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 81.000 | ||||
| Mean of predictor | 0.154 | ||||
| Mean of criterion | 0.054 | ||||
| SD of predictor | 0.238 | ||||
| SD of criterion | 0.141 | ||||
| Covariance | -0.003 | ||||
| r | -0.090 | ||||
| b (slope, estimate of beta) | -0.053 | ||||
| a (intercept, estimate of alpha) | 0.062 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 79.000 | ||||
| t(b) | -0.803 | ||||
| p(b) | 0.788 | ||||
| t(a) | 1.117 | ||||
| p(a) | 0.134 | ||||
| Lowerbound of 95% confidence interval for beta | -0.185 | ||||
| Upperbound of 95% confidence interval for beta | 0.079 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.048 | ||||
| Upperbound of 95% confidence interval for alpha | 0.172 | ||||
| Treynor index (mean / b) | -1.008 | ||||
| Jensen alpha (a) | 0.062 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.044 | ||||
| SD | 0.139 | ||||
| Sharpe ratio (Glass type estimate) | 0.316 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.313 | ||||
| df | 80.000 | ||||
| t | 0.820 | ||||
| p | 0.207 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.441 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.071 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.443 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.069 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.524 | ||||
| Upside Potential Ratio | 1.919 | ||||
| Upside part of mean | 0.160 | ||||
| Downside part of mean | -0.117 | ||||
| Upside SD | 0.110 | ||||
| Downside SD | 0.084 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 53.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 81.000 | ||||
| Mean of predictor | 0.124 | ||||
| Mean of criterion | 0.044 | ||||
| SD of predictor | 0.241 | ||||
| SD of criterion | 0.139 | ||||
| Covariance | -0.003 | ||||
| r | -0.075 | ||||
| b (slope, estimate of beta) | -0.043 | ||||
| a (intercept, estimate of alpha) | 0.049 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 79.000 | ||||
| t(b) | -0.670 | ||||
| p(b) | 0.748 | ||||
| t(a) | 0.908 | ||||
| p(a) | 0.183 | ||||
| Lowerbound of 95% confidence interval for beta | -0.172 | ||||
| Upperbound of 95% confidence interval for beta | 0.085 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.059 | ||||
| Upperbound of 95% confidence interval for alpha | 0.157 | ||||
| Treynor index (mean / b) | -1.011 | ||||
| Jensen alpha (a) | 0.049 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.060 | ||||
| Expected Shortfall on VaR | 0.076 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.052 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 81.000 | ||||
| Minimum | 0.857 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.015 | ||||
| Maximum | 1.162 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.058 | ||||
| Inter Quartile Range | 0.018 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.074 | ||||
| Mean of outliers low | 0.933 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.111 | ||||
| Mean of outliers high | 1.093 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.628 | ||||
| VaR(95%) (moments method) | 0.016 | ||||
| Expected Shortfall (moments method) | 0.052 | ||||
| Extreme Value Index (regression method) | 0.510 | ||||
| VaR(95%) (regression method) | 0.033 | ||||
| Expected Shortfall (regression method) | 0.088 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.043 | ||||
| Quartile 1 | 0.049 | ||||
| Median | 0.067 | ||||
| Quartile 3 | 0.097 | ||||
| Maximum | 0.143 | ||||
| Mean of quarter 1 | 0.045 | ||||
| Mean of quarter 2 | 0.055 | ||||
| Mean of quarter 3 | 0.080 | ||||
| Mean of quarter 4 | 0.123 | ||||
| Inter Quartile Range | 0.048 | ||||
| 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) | 0.120 | ||||
| Compounded annual return (geometric extrapolation) | 0.092 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.640 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.745 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.211 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.092 | ||||
| SD | 0.311 | ||||
| Sharpe ratio (Glass type estimate) | 0.296 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.296 | ||||
| df | 1776.000 | ||||
| t | 0.771 | ||||
| p | 0.491 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.457 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.049 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.457 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.048 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.442 | ||||
| Upside Potential Ratio | 4.039 | ||||
| Upside part of mean | 0.843 | ||||
| Downside part of mean | -0.751 | ||||
| Upside SD | 0.231 | ||||
| Downside SD | 0.209 | ||||
| N nonnegative terms | 547.000 | ||||
| N negative terms | 1230.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1777.000 | ||||
| Mean of predictor | 0.256 | ||||
| Mean of criterion | 0.092 | ||||
| SD of predictor | 0.551 | ||||
| SD of criterion | 0.311 | ||||
| Covariance | -0.005 | ||||
| r | -0.027 | ||||
| b (slope, estimate of beta) | -0.015 | ||||
| a (intercept, estimate of alpha) | 0.096 | ||||
| Mean Square Error | 0.097 | ||||
| DF error | 1775.000 | ||||
| t(b) | -1.123 | ||||
| p(b) | 0.517 | ||||
| t(a) | 0.803 | ||||
| p(a) | 0.488 | ||||
| Lowerbound of 95% confidence interval for beta | -0.041 | ||||
| Upperbound of 95% confidence interval for beta | 0.011 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.139 | ||||
| Upperbound of 95% confidence interval for alpha | 0.331 | ||||
| Treynor index (mean / b) | -6.117 | ||||
| Jensen alpha (a) | 0.096 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.043 | ||||
| SD | 0.314 | ||||
| Sharpe ratio (Glass type estimate) | 0.138 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.138 | ||||
| df | 1776.000 | ||||
| t | 0.359 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.615 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.891 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.615 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.891 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.189 | ||||
| Upside Potential Ratio | 3.569 | ||||
| Upside part of mean | 0.819 | ||||
| Downside part of mean | -0.775 | ||||
| Upside SD | 0.214 | ||||
| Downside SD | 0.229 | ||||
| N nonnegative terms | 547.000 | ||||
| N negative terms | 1230.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1777.000 | ||||
| Mean of predictor | 0.106 | ||||
| Mean of criterion | 0.043 | ||||
| SD of predictor | 0.549 | ||||
| SD of criterion | 0.314 | ||||
| Covariance | -0.003 | ||||
| r | -0.018 | ||||
| b (slope, estimate of beta) | -0.010 | ||||
| a (intercept, estimate of alpha) | 0.044 | ||||
| Mean Square Error | 0.099 | ||||
| DF error | 1775.000 | ||||
| t(b) | -0.745 | ||||
| p(b) | 0.511 | ||||
| t(a) | 0.368 | ||||
| p(a) | 0.494 | ||||
| Lowerbound of 95% confidence interval for beta | -0.037 | ||||
| Upperbound of 95% confidence interval for beta | 0.017 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.192 | ||||
| Upperbound of 95% confidence interval for alpha | 0.281 | ||||
| Treynor index (mean / b) | -4.289 | ||||
| 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%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1777.000 | ||||
| Minimum | 0.733 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.291 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 240.000 | ||||
| Percentage of outliers low | 0.135 | ||||
| Mean of outliers low | 0.982 | ||||
| Number of outliers high | 288.000 | ||||
| Percentage of outliers high | 0.162 | ||||
| Mean of outliers high | 1.019 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.044 | ||||
| VaR(95%) (moments method) | 0.008 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.667 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.026 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 23.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.017 | ||||
| Quartile 3 | 0.061 | ||||
| Maximum | 0.380 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.046 | ||||
| Mean of quarter 4 | 0.165 | ||||
| Inter Quartile Range | 0.051 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.087 | ||||
| Mean of outliers high | 0.289 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.113 | ||||
| VaR(95%) (moments method) | 0.156 | ||||
| Expected Shortfall (moments method) | 0.206 | ||||
| Extreme Value Index (regression method) | 0.376 | ||||
| VaR(95%) (regression method) | 0.245 | ||||
| Expected Shortfall (regression method) | 0.481 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.119 | ||||
| Compounded annual return (geometric extrapolation) | 0.091 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.240 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.553 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.338 | ||||
| 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 | 0.734 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.524 | ||||
| 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 | 0.589 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.548 | ||||
| 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) | -8780256841813375.000 | ||||
| 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) | 129925723771229449854340072210432.000 | ||||
| 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 | ||||