Advanced Statistics: Parcours Commodities
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 | 0.117 | ||||
| SD | 0.110 | ||||
| Sharpe ratio (Glass type estimate) | 1.063 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.053 | ||||
| df | 79.000 | ||||
| t | 2.745 | ||||
| p | 0.004 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.283 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.837 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.276 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.830 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.533 | ||||
| Upside Potential Ratio | 4.281 | ||||
| Upside part of mean | 0.198 | ||||
| Downside part of mean | -0.081 | ||||
| Upside SD | 0.105 | ||||
| Downside SD | 0.046 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.234 | ||||
| Mean of criterion | 0.117 | ||||
| SD of predictor | 0.211 | ||||
| SD of criterion | 0.110 | ||||
| Covariance | -0.001 | ||||
| r | -0.060 | ||||
| b (slope, estimate of beta) | -0.031 | ||||
| a (intercept, estimate of alpha) | 0.124 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 78.000 | ||||
| t(b) | -0.534 | ||||
| p(b) | 0.703 | ||||
| t(a) | 2.765 | ||||
| p(a) | 0.004 | ||||
| Lowerbound of 95% confidence interval for beta | -0.149 | ||||
| Upperbound of 95% confidence interval for beta | 0.086 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.035 | ||||
| Upperbound of 95% confidence interval for alpha | 0.214 | ||||
| Treynor index (mean / b) | -3.722 | ||||
| Jensen alpha (a) | 0.124 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.110 | ||||
| SD | 0.107 | ||||
| Sharpe ratio (Glass type estimate) | 1.029 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.019 | ||||
| df | 79.000 | ||||
| t | 2.656 | ||||
| p | 0.005 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.250 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.801 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.243 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.794 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.356 | ||||
| Upside Potential Ratio | 4.097 | ||||
| Upside part of mean | 0.192 | ||||
| Downside part of mean | -0.082 | ||||
| Upside SD | 0.101 | ||||
| Downside SD | 0.047 | ||||
| N nonnegative terms | 37.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.211 | ||||
| Mean of criterion | 0.110 | ||||
| SD of predictor | 0.200 | ||||
| SD of criterion | 0.107 | ||||
| Covariance | -0.001 | ||||
| r | -0.053 | ||||
| b (slope, estimate of beta) | -0.028 | ||||
| a (intercept, estimate of alpha) | 0.116 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 78.000 | ||||
| t(b) | -0.467 | ||||
| p(b) | 0.679 | ||||
| t(a) | 2.664 | ||||
| p(a) | 0.005 | ||||
| Lowerbound of 95% confidence interval for beta | -0.149 | ||||
| Upperbound of 95% confidence interval for beta | 0.092 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.029 | ||||
| Upperbound of 95% confidence interval for alpha | 0.203 | ||||
| Treynor index (mean / b) | -3.898 | ||||
| Jensen alpha (a) | 0.116 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.041 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 80.000 | ||||
| Minimum | 0.958 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.032 | ||||
| Maximum | 1.109 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.015 | ||||
| Mean of quarter 4 | 1.058 | ||||
| Inter Quartile Range | 0.034 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.050 | ||||
| Mean of outliers high | 1.097 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.288 | ||||
| VaR(95%) (moments method) | 0.009 | ||||
| Expected Shortfall (moments method) | 0.011 | ||||
| Extreme Value Index (regression method) | -0.939 | ||||
| VaR(95%) (regression method) | 0.022 | ||||
| Expected Shortfall (regression method) | 0.025 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.038 | ||||
| Quartile 3 | 0.051 | ||||
| Maximum | 0.090 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.022 | ||||
| Mean of quarter 3 | 0.044 | ||||
| Mean of quarter 4 | 0.079 | ||||
| Inter Quartile Range | 0.042 | ||||
| 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) | 0.270 | ||||
| Compounded annual return (geometric extrapolation) | 0.167 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.852 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.123 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.140 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.115 | ||||
| SD | 0.110 | ||||
| Sharpe ratio (Glass type estimate) | 1.039 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.039 | ||||
| df | 1765.000 | ||||
| t | 2.698 | ||||
| p | 0.459 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.283 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.795 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.283 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.794 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.707 | ||||
| Upside Potential Ratio | 7.518 | ||||
| Upside part of mean | 0.505 | ||||
| Downside part of mean | -0.390 | ||||
| Upside SD | 0.088 | ||||
| Downside SD | 0.067 | ||||
| N nonnegative terms | 586.000 | ||||
| N negative terms | 1180.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1766.000 | ||||
| Mean of predictor | 0.256 | ||||
| Mean of criterion | 0.115 | ||||
| SD of predictor | 0.221 | ||||
| SD of criterion | 0.110 | ||||
| Covariance | -0.000 | ||||
| r | -0.005 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | 0.115 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 1764.000 | ||||
| t(b) | -0.196 | ||||
| p(b) | 0.502 | ||||
| t(a) | 2.704 | ||||
| p(a) | 0.468 | ||||
| Lowerbound of 95% confidence interval for beta | -0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.032 | ||||
| Upperbound of 95% confidence interval for alpha | 0.199 | ||||
| Treynor index (mean / b) | -49.213 | ||||
| Jensen alpha (a) | 0.115 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.109 | ||||
| SD | 0.110 | ||||
| Sharpe ratio (Glass type estimate) | 0.988 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.988 | ||||
| df | 1765.000 | ||||
| t | 2.566 | ||||
| p | 0.461 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.232 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.744 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.232 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.743 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.593 | ||||
| Upside Potential Ratio | 7.351 | ||||
| Upside part of mean | 0.501 | ||||
| Downside part of mean | -0.393 | ||||
| Upside SD | 0.086 | ||||
| Downside SD | 0.068 | ||||
| N nonnegative terms | 586.000 | ||||
| N negative terms | 1180.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1766.000 | ||||
| Mean of predictor | 0.231 | ||||
| Mean of criterion | 0.109 | ||||
| SD of predictor | 0.222 | ||||
| SD of criterion | 0.110 | ||||
| Covariance | -0.000 | ||||
| r | -0.005 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | 0.109 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 1764.000 | ||||
| t(b) | -0.195 | ||||
| p(b) | 0.502 | ||||
| t(a) | 2.572 | ||||
| p(a) | 0.469 | ||||
| Lowerbound of 95% confidence interval for beta | -0.025 | ||||
| Upperbound of 95% confidence interval for beta | 0.021 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.026 | ||||
| Upperbound of 95% confidence interval for alpha | 0.192 | ||||
| Treynor index (mean / b) | -47.297 | ||||
| Jensen alpha (a) | 0.109 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1766.000 | ||||
| Minimum | 0.923 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.092 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 144.000 | ||||
| Percentage of outliers low | 0.082 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 185.000 | ||||
| Percentage of outliers high | 0.105 | ||||
| Mean of outliers high | 1.013 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.494 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.010 | ||||
| Extreme Value Index (regression method) | 0.259 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.008 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 59.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.012 | ||||
| Quartile 3 | 0.030 | ||||
| Maximum | 0.121 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.007 | ||||
| Mean of quarter 3 | 0.019 | ||||
| Mean of quarter 4 | 0.060 | ||||
| Inter Quartile Range | 0.026 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.068 | ||||
| Mean of outliers high | 0.100 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.086 | ||||
| VaR(95%) (moments method) | 0.062 | ||||
| Expected Shortfall (moments method) | 0.085 | ||||
| Extreme Value Index (regression method) | 0.344 | ||||
| VaR(95%) (regression method) | 0.061 | ||||
| Expected Shortfall (regression method) | 0.098 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.267 | ||||
| Compounded annual return (geometric extrapolation) | 0.165 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.358 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.769 | ||||
| Compounded annual return / Expected Shortfall lognormal | 12.217 | ||||
| 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 | 1.035 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.470 | ||||
| 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 | 0.923 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.473 | ||||
| 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) | -8736076346019522.000 | ||||
| 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) | 245178619924754057507278164066304.000 | ||||
| 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 | ||||