Advanced Statistics: Commodity Capturer
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 | -0.200 | ||||
| SD | 0.244 | ||||
| Sharpe ratio (Glass type estimate) | -0.821 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.808 | ||||
| df | 48.000 | ||||
| t | -1.659 | ||||
| p | 0.948 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.800 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.167 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.791 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.175 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.910 | ||||
| Upside Potential Ratio | 0.701 | ||||
| Upside part of mean | 0.154 | ||||
| Downside part of mean | -0.354 | ||||
| Upside SD | 0.115 | ||||
| Downside SD | 0.220 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 49.000 | ||||
| Mean of predictor | 0.452 | ||||
| Mean of criterion | -0.200 | ||||
| SD of predictor | 0.238 | ||||
| SD of criterion | 0.244 | ||||
| Covariance | 0.014 | ||||
| r | 0.233 | ||||
| b (slope, estimate of beta) | 0.239 | ||||
| a (intercept, estimate of alpha) | -0.308 | ||||
| Mean Square Error | 0.057 | ||||
| DF error | 47.000 | ||||
| t(b) | 1.645 | ||||
| p(b) | 0.053 | ||||
| t(a) | -2.274 | ||||
| p(a) | 0.986 | ||||
| Lowerbound of 95% confidence interval for beta | -0.053 | ||||
| Upperbound of 95% confidence interval for beta | 0.532 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.581 | ||||
| Upperbound of 95% confidence interval for alpha | -0.036 | ||||
| Treynor index (mean / b) | -0.836 | ||||
| Jensen alpha (a) | -0.308 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.233 | ||||
| SD | 0.259 | ||||
| Sharpe ratio (Glass type estimate) | -0.898 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.884 | ||||
| df | 48.000 | ||||
| t | -1.815 | ||||
| p | 0.962 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.880 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.093 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.870 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.102 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.963 | ||||
| Upside Potential Ratio | 0.610 | ||||
| Upside part of mean | 0.147 | ||||
| Downside part of mean | -0.380 | ||||
| Upside SD | 0.109 | ||||
| Downside SD | 0.242 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 49.000 | ||||
| Mean of predictor | 0.416 | ||||
| Mean of criterion | -0.233 | ||||
| SD of predictor | 0.230 | ||||
| SD of criterion | 0.259 | ||||
| Covariance | 0.015 | ||||
| r | 0.246 | ||||
| b (slope, estimate of beta) | 0.278 | ||||
| a (intercept, estimate of alpha) | -0.348 | ||||
| Mean Square Error | 0.064 | ||||
| DF error | 47.000 | ||||
| t(b) | 1.743 | ||||
| p(b) | 0.044 | ||||
| t(a) | -2.453 | ||||
| p(a) | 0.991 | ||||
| Lowerbound of 95% confidence interval for beta | -0.043 | ||||
| Upperbound of 95% confidence interval for beta | 0.599 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.634 | ||||
| Upperbound of 95% confidence interval for alpha | -0.063 | ||||
| Treynor index (mean / b) | -0.837 | ||||
| Jensen alpha (a) | -0.348 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.133 | ||||
| Expected Shortfall on VaR | 0.159 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.088 | ||||
| Expected Shortfall on VaR | 0.168 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 49.000 | ||||
| Minimum | 0.759 | ||||
| Quartile 1 | 0.981 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.119 | ||||
| Mean of quarter 1 | 0.900 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.056 | ||||
| Inter Quartile Range | 0.019 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.204 | ||||
| Mean of outliers low | 0.878 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.163 | ||||
| Mean of outliers high | 1.080 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.219 | ||||
| VaR(95%) (moments method) | 0.066 | ||||
| Expected Shortfall (moments method) | 0.086 | ||||
| Extreme Value Index (regression method) | -0.061 | ||||
| VaR(95%) (regression method) | 0.118 | ||||
| Expected Shortfall (regression method) | 0.171 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.126 | ||||
| Quartile 1 | 0.256 | ||||
| Median | 0.386 | ||||
| Quartile 3 | 0.515 | ||||
| Maximum | 0.645 | ||||
| Mean of quarter 1 | 0.126 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.645 | ||||
| Inter Quartile Range | 0.260 | ||||
| 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) | -0.132 | ||||
| Compounded annual return (geometric extrapolation) | -0.172 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.267 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.267 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.081 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.204 | ||||
| SD | 0.230 | ||||
| Sharpe ratio (Glass type estimate) | -0.885 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.885 | ||||
| df | 1082.000 | ||||
| t | -1.800 | ||||
| p | 0.527 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.850 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.080 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.849 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.080 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.174 | ||||
| Upside Potential Ratio | 4.634 | ||||
| Upside part of mean | 0.804 | ||||
| Downside part of mean | -1.008 | ||||
| Upside SD | 0.152 | ||||
| Downside SD | 0.174 | ||||
| N nonnegative terms | 250.000 | ||||
| N negative terms | 833.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1083.000 | ||||
| Mean of predictor | 0.485 | ||||
| Mean of criterion | -0.204 | ||||
| SD of predictor | 0.326 | ||||
| SD of criterion | 0.230 | ||||
| Covariance | 0.018 | ||||
| r | 0.240 | ||||
| b (slope, estimate of beta) | 0.170 | ||||
| a (intercept, estimate of alpha) | -0.286 | ||||
| Mean Square Error | 0.050 | ||||
| DF error | 1081.000 | ||||
| t(b) | 8.138 | ||||
| p(b) | 0.349 | ||||
| t(a) | -2.592 | ||||
| p(a) | 0.550 | ||||
| Lowerbound of 95% confidence interval for beta | 0.129 | ||||
| Upperbound of 95% confidence interval for beta | 0.211 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.503 | ||||
| Upperbound of 95% confidence interval for alpha | -0.070 | ||||
| Treynor index (mean / b) | -1.199 | ||||
| Jensen alpha (a) | -0.286 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.231 | ||||
| SD | 0.231 | ||||
| Sharpe ratio (Glass type estimate) | -0.997 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.996 | ||||
| df | 1082.000 | ||||
| t | -2.026 | ||||
| p | 0.531 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.961 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.031 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.961 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.031 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.295 | ||||
| Upside Potential Ratio | 4.454 | ||||
| Upside part of mean | 0.793 | ||||
| Downside part of mean | -1.023 | ||||
| Upside SD | 0.148 | ||||
| Downside SD | 0.178 | ||||
| N nonnegative terms | 250.000 | ||||
| N negative terms | 833.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1083.000 | ||||
| Mean of predictor | 0.431 | ||||
| Mean of criterion | -0.231 | ||||
| SD of predictor | 0.330 | ||||
| SD of criterion | 0.231 | ||||
| Covariance | 0.018 | ||||
| r | 0.236 | ||||
| b (slope, estimate of beta) | 0.165 | ||||
| a (intercept, estimate of alpha) | -0.302 | ||||
| Mean Square Error | 0.051 | ||||
| DF error | 1081.000 | ||||
| t(b) | 7.988 | ||||
| p(b) | 0.351 | ||||
| t(a) | -2.720 | ||||
| p(a) | 0.552 | ||||
| Lowerbound of 95% confidence interval for beta | 0.125 | ||||
| Upperbound of 95% confidence interval for beta | 0.206 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.520 | ||||
| Upperbound of 95% confidence interval for alpha | -0.084 | ||||
| Treynor index (mean / b) | -1.393 | ||||
| Jensen alpha (a) | -0.302 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1083.000 | ||||
| Minimum | 0.896 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.111 | ||||
| Mean of quarter 1 | 0.985 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.012 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 270.000 | ||||
| Percentage of outliers low | 0.249 | ||||
| Mean of outliers low | 0.985 | ||||
| Number of outliers high | 252.000 | ||||
| Percentage of outliers high | 0.233 | ||||
| Mean of outliers high | 1.013 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.281 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| 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 | 16.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.011 | ||||
| Median | 0.024 | ||||
| Quartile 3 | 0.033 | ||||
| Maximum | 0.663 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.014 | ||||
| Mean of quarter 3 | 0.028 | ||||
| Mean of quarter 4 | 0.229 | ||||
| Inter Quartile Range | 0.022 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.188 | ||||
| Mean of outliers high | 0.294 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.224 | ||||
| VaR(95%) (moments method) | 0.127 | ||||
| Expected Shortfall (moments method) | 0.231 | ||||
| Extreme Value Index (regression method) | 1.243 | ||||
| VaR(95%) (regression method) | 0.372 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.130 | ||||
| Compounded annual return (geometric extrapolation) | -0.170 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.257 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.743 | ||||
| Compounded annual return / Expected Shortfall lognormal | -5.692 | ||||
| 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 | 1.216 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.348 | ||||
| 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 | 1.153 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.345 | ||||
| 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) | -8617052636460073.000 | ||||
| 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) | -168000925395451646381827156869120.000 | ||||
| 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 | ||||