Advanced Statistics: Commodity Trader, Counter-Trend
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 | -0.014 | ||||
| SD | 0.100 | ||||
| Sharpe ratio (Glass type estimate) | -0.137 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.135 | ||||
| df | 46.000 | ||||
| t | -0.271 | ||||
| p | 0.606 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.127 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.854 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.126 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.856 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.217 | ||||
| Upside Potential Ratio | 0.981 | ||||
| Upside part of mean | 0.062 | ||||
| Downside part of mean | -0.076 | ||||
| Upside SD | 0.076 | ||||
| Downside SD | 0.063 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 47.000 | ||||
| Mean of predictor | 0.393 | ||||
| Mean of criterion | -0.014 | ||||
| SD of predictor | 0.277 | ||||
| SD of criterion | 0.100 | ||||
| Covariance | 0.000 | ||||
| r | 0.002 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.014 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 45.000 | ||||
| t(b) | 0.015 | ||||
| p(b) | 0.494 | ||||
| t(a) | -0.254 | ||||
| p(a) | 0.600 | ||||
| Lowerbound of 95% confidence interval for beta | -0.108 | ||||
| Upperbound of 95% confidence interval for beta | 0.109 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.125 | ||||
| Upperbound of 95% confidence interval for alpha | 0.097 | ||||
| Treynor index (mean / b) | -16.543 | ||||
| Jensen alpha (a) | -0.014 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 0.099 | ||||
| Sharpe ratio (Glass type estimate) | -0.187 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.184 | ||||
| df | 46.000 | ||||
| t | -0.369 | ||||
| p | 0.643 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.177 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.805 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.175 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.808 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.277 | ||||
| Upside Potential Ratio | 0.884 | ||||
| Upside part of mean | 0.059 | ||||
| Downside part of mean | -0.078 | ||||
| Upside SD | 0.072 | ||||
| Downside SD | 0.067 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 47.000 | ||||
| Mean of predictor | 0.351 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.099 | ||||
| Covariance | 0.000 | ||||
| r | 0.009 | ||||
| b (slope, estimate of beta) | 0.003 | ||||
| a (intercept, estimate of alpha) | -0.020 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 45.000 | ||||
| t(b) | 0.059 | ||||
| p(b) | 0.477 | ||||
| t(a) | -0.362 | ||||
| p(a) | 0.640 | ||||
| Lowerbound of 95% confidence interval for beta | -0.110 | ||||
| Upperbound of 95% confidence interval for beta | 0.116 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.129 | ||||
| Upperbound of 95% confidence interval for alpha | 0.090 | ||||
| Treynor index (mean / b) | -5.558 | ||||
| Jensen alpha (a) | -0.020 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.047 | ||||
| Expected Shortfall on VaR | 0.059 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 47.000 | ||||
| Minimum | 0.883 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.137 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.170 | ||||
| Mean of outliers low | 0.983 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.149 | ||||
| Mean of outliers high | 1.037 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -8.019 | ||||
| VaR(95%) (moments method) | -0.006 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.347 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.117 | ||||
| Quartile 1 | 0.117 | ||||
| Median | 0.117 | ||||
| Quartile 3 | 0.117 | ||||
| Maximum | 0.117 | ||||
| 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) | 0.027 | ||||
| Compounded annual return (geometric extrapolation) | 0.026 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.221 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.441 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.017 | ||||
| SD | 0.064 | ||||
| Sharpe ratio (Glass type estimate) | -0.265 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.265 | ||||
| df | 1042.000 | ||||
| t | -0.529 | ||||
| p | 0.508 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.247 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.717 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.247 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.718 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.401 | ||||
| Upside Potential Ratio | 3.269 | ||||
| Upside part of mean | 0.138 | ||||
| Downside part of mean | -0.154 | ||||
| Upside SD | 0.048 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 977.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1043.000 | ||||
| Mean of predictor | 0.416 | ||||
| Mean of criterion | -0.017 | ||||
| SD of predictor | 0.303 | ||||
| SD of criterion | 0.064 | ||||
| Covariance | -0.000 | ||||
| r | -0.016 | ||||
| b (slope, estimate of beta) | -0.003 | ||||
| a (intercept, estimate of alpha) | -0.015 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 1041.000 | ||||
| t(b) | -0.527 | ||||
| p(b) | 0.510 | ||||
| t(a) | -0.482 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | -0.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.009 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.078 | ||||
| Upperbound of 95% confidence interval for alpha | 0.047 | ||||
| Treynor index (mean / b) | 4.920 | ||||
| Jensen alpha (a) | -0.015 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.019 | ||||
| SD | 0.064 | ||||
| Sharpe ratio (Glass type estimate) | -0.297 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.297 | ||||
| df | 1042.000 | ||||
| t | -0.593 | ||||
| p | 0.509 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.280 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.685 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.280 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.685 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.444 | ||||
| Upside Potential Ratio | 3.208 | ||||
| Upside part of mean | 0.136 | ||||
| Downside part of mean | -0.155 | ||||
| Upside SD | 0.047 | ||||
| Downside SD | 0.043 | ||||
| N nonnegative terms | 66.000 | ||||
| N negative terms | 977.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1043.000 | ||||
| Mean of predictor | 0.370 | ||||
| Mean of criterion | -0.019 | ||||
| SD of predictor | 0.304 | ||||
| SD of criterion | 0.064 | ||||
| Covariance | -0.000 | ||||
| r | -0.014 | ||||
| b (slope, estimate of beta) | -0.003 | ||||
| a (intercept, estimate of alpha) | -0.018 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 1041.000 | ||||
| t(b) | -0.457 | ||||
| p(b) | 0.509 | ||||
| t(a) | -0.557 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | -0.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.081 | ||||
| Upperbound of 95% confidence interval for alpha | 0.045 | ||||
| Treynor index (mean / b) | 6.381 | ||||
| Jensen alpha (a) | -0.018 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1043.000 | ||||
| Minimum | 0.965 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.045 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 202.000 | ||||
| Percentage of outliers low | 0.194 | ||||
| Mean of outliers low | 0.998 | ||||
| Number of outliers high | 196.000 | ||||
| Percentage of outliers high | 0.188 | ||||
| Mean of outliers high | 1.003 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.162 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.152 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.005 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.016 | ||||
| Quartile 3 | 0.030 | ||||
| Maximum | 0.171 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | 0.022 | ||||
| Mean of quarter 4 | 0.105 | ||||
| Inter Quartile Range | 0.027 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.171 | ||||
| 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) | 0.026 | ||||
| Compounded annual return (geometric extrapolation) | 0.025 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.149 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.243 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.126 | ||||
| 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 | 0.999 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.495 | ||||
| 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 | 0.874 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.499 | ||||
| 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) | -8748221123093912.000 | ||||
| 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) | -360939348827151476354591964004352.000 | ||||
| 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 | ||||