Advanced Statistics: Diversified Metal Miners
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 | -0.024 | ||||
| SD | 0.415 | ||||
| Sharpe ratio (Glass type estimate) | -0.058 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.057 | ||||
| df | 59.000 | ||||
| t | -0.129 | ||||
| p | 0.551 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.934 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.819 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.934 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.820 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.101 | ||||
| Upside Potential Ratio | 1.972 | ||||
| Upside part of mean | 0.471 | ||||
| Downside part of mean | -0.494 | ||||
| Upside SD | 0.335 | ||||
| Downside SD | 0.239 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.340 | ||||
| Mean of criterion | -0.024 | ||||
| SD of predictor | 0.258 | ||||
| SD of criterion | 0.415 | ||||
| Covariance | 0.038 | ||||
| r | 0.354 | ||||
| b (slope, estimate of beta) | 0.570 | ||||
| a (intercept, estimate of alpha) | -0.218 | ||||
| Mean Square Error | 0.153 | ||||
| DF error | 58.000 | ||||
| t(b) | 2.882 | ||||
| p(b) | 0.003 | ||||
| t(a) | -1.162 | ||||
| p(a) | 0.875 | ||||
| Lowerbound of 95% confidence interval for beta | 0.174 | ||||
| Upperbound of 95% confidence interval for beta | 0.966 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.593 | ||||
| Upperbound of 95% confidence interval for alpha | 0.157 | ||||
| Treynor index (mean / b) | -0.042 | ||||
| Jensen alpha (a) | -0.218 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.100 | ||||
| SD | 0.387 | ||||
| Sharpe ratio (Glass type estimate) | -0.260 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.257 | ||||
| df | 59.000 | ||||
| t | -0.581 | ||||
| p | 0.718 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.137 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.619 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.134 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.621 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.392 | ||||
| Upside Potential Ratio | 1.652 | ||||
| Upside part of mean | 0.423 | ||||
| Downside part of mean | -0.524 | ||||
| Upside SD | 0.286 | ||||
| Downside SD | 0.256 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.305 | ||||
| Mean of criterion | -0.100 | ||||
| SD of predictor | 0.238 | ||||
| SD of criterion | 0.387 | ||||
| Covariance | 0.030 | ||||
| r | 0.323 | ||||
| b (slope, estimate of beta) | 0.524 | ||||
| a (intercept, estimate of alpha) | -0.260 | ||||
| Mean Square Error | 0.136 | ||||
| DF error | 58.000 | ||||
| t(b) | 2.599 | ||||
| p(b) | 0.006 | ||||
| t(a) | -1.479 | ||||
| p(a) | 0.928 | ||||
| Lowerbound of 95% confidence interval for beta | 0.120 | ||||
| Upperbound of 95% confidence interval for beta | 0.927 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.613 | ||||
| Upperbound of 95% confidence interval for alpha | 0.092 | ||||
| Treynor index (mean / b) | -0.192 | ||||
| Jensen alpha (a) | -0.260 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.175 | ||||
| Expected Shortfall on VaR | 0.212 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.103 | ||||
| Expected Shortfall on VaR | 0.174 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 60.000 | ||||
| Minimum | 0.794 | ||||
| Quartile 1 | 0.931 | ||||
| Median | 0.993 | ||||
| Quartile 3 | 1.044 | ||||
| Maximum | 1.460 | ||||
| Mean of quarter 1 | 0.879 | ||||
| Mean of quarter 2 | 0.965 | ||||
| Mean of quarter 3 | 1.017 | ||||
| Mean of quarter 4 | 1.146 | ||||
| Inter Quartile Range | 0.113 | ||||
| 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 | 0.050 | ||||
| Mean of outliers high | 1.385 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.485 | ||||
| VaR(95%) (moments method) | 0.130 | ||||
| Expected Shortfall (moments method) | 0.147 | ||||
| Extreme Value Index (regression method) | -0.267 | ||||
| VaR(95%) (regression method) | 0.128 | ||||
| Expected Shortfall (regression method) | 0.151 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.028 | ||||
| Quartile 1 | 0.186 | ||||
| Median | 0.344 | ||||
| Quartile 3 | 0.501 | ||||
| Maximum | 0.659 | ||||
| Mean of quarter 1 | 0.028 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.659 | ||||
| Inter Quartile Range | 0.315 | ||||
| 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) | -0.049 | ||||
| Compounded annual return (geometric extrapolation) | -0.055 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.083 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.083 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.260 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.066 | ||||
| SD | 0.340 | ||||
| Sharpe ratio (Glass type estimate) | -0.194 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.194 | ||||
| df | 1314.000 | ||||
| t | -0.435 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.069 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.681 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.069 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.681 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.293 | ||||
| Upside Potential Ratio | 7.527 | ||||
| Upside part of mean | 1.701 | ||||
| Downside part of mean | -1.767 | ||||
| Upside SD | 0.255 | ||||
| Downside SD | 0.226 | ||||
| N nonnegative terms | 629.000 | ||||
| N negative terms | 686.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1315.000 | ||||
| Mean of predictor | 0.366 | ||||
| Mean of criterion | -0.066 | ||||
| SD of predictor | 0.310 | ||||
| SD of criterion | 0.340 | ||||
| Covariance | 0.024 | ||||
| r | 0.229 | ||||
| b (slope, estimate of beta) | 0.252 | ||||
| a (intercept, estimate of alpha) | -0.158 | ||||
| Mean Square Error | 0.110 | ||||
| DF error | 1313.000 | ||||
| t(b) | 8.525 | ||||
| p(b) | 0.355 | ||||
| t(a) | -1.067 | ||||
| p(a) | 0.519 | ||||
| Lowerbound of 95% confidence interval for beta | 0.194 | ||||
| Upperbound of 95% confidence interval for beta | 0.310 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.449 | ||||
| Upperbound of 95% confidence interval for alpha | 0.133 | ||||
| Treynor index (mean / b) | -0.263 | ||||
| Jensen alpha (a) | -0.158 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.123 | ||||
| SD | 0.337 | ||||
| Sharpe ratio (Glass type estimate) | -0.366 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.365 | ||||
| df | 1314.000 | ||||
| t | -0.819 | ||||
| p | 0.511 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.241 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.509 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.240 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.510 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.532 | ||||
| Upside Potential Ratio | 7.203 | ||||
| Upside part of mean | 1.670 | ||||
| Downside part of mean | -1.793 | ||||
| Upside SD | 0.245 | ||||
| Downside SD | 0.232 | ||||
| N nonnegative terms | 629.000 | ||||
| N negative terms | 686.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1315.000 | ||||
| Mean of predictor | 0.319 | ||||
| Mean of criterion | -0.123 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.337 | ||||
| Covariance | 0.024 | ||||
| r | 0.226 | ||||
| b (slope, estimate of beta) | 0.248 | ||||
| a (intercept, estimate of alpha) | -0.202 | ||||
| Mean Square Error | 0.108 | ||||
| DF error | 1313.000 | ||||
| t(b) | 8.414 | ||||
| p(b) | 0.357 | ||||
| t(a) | -1.375 | ||||
| p(a) | 0.524 | ||||
| Lowerbound of 95% confidence interval for beta | 0.190 | ||||
| Upperbound of 95% confidence interval for beta | 0.305 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.491 | ||||
| Upperbound of 95% confidence interval for alpha | 0.086 | ||||
| Treynor index (mean / b) | -0.498 | ||||
| Jensen alpha (a) | -0.202 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| 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 | 1315.000 | ||||
| Minimum | 0.887 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.008 | ||||
| Maximum | 1.219 | ||||
| Mean of quarter 1 | 0.978 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.023 | ||||
| Inter Quartile Range | 0.017 | ||||
| Number outliers low | 42.000 | ||||
| Percentage of outliers low | 0.032 | ||||
| Mean of outliers low | 0.944 | ||||
| Number of outliers high | 52.000 | ||||
| Percentage of outliers high | 0.040 | ||||
| Mean of outliers high | 1.061 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.252 | ||||
| VaR(95%) (moments method) | 0.022 | ||||
| Expected Shortfall (moments method) | 0.036 | ||||
| Extreme Value Index (regression method) | 0.197 | ||||
| VaR(95%) (regression method) | 0.020 | ||||
| Expected Shortfall (regression method) | 0.030 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.080 | ||||
| Quartile 1 | 0.088 | ||||
| Median | 0.098 | ||||
| Quartile 3 | 0.248 | ||||
| Maximum | 0.675 | ||||
| Mean of quarter 1 | 0.080 | ||||
| Mean of quarter 2 | 0.091 | ||||
| Mean of quarter 3 | 0.106 | ||||
| Mean of quarter 4 | 0.675 | ||||
| Inter Quartile Range | 0.160 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 0.675 | ||||
| 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) | -0.065 | ||||
| Compounded annual return (geometric extrapolation) | -0.076 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.113 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.113 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.795 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.650 | ||||
| SD | 0.423 | ||||
| Sharpe ratio (Glass type estimate) | 1.537 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.528 | ||||
| df | 130.000 | ||||
| t | 1.087 | ||||
| p | 0.453 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.244 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.312 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.250 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.306 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.624 | ||||
| Upside Potential Ratio | 10.248 | ||||
| Upside part of mean | 2.537 | ||||
| Downside part of mean | -1.888 | ||||
| Upside SD | 0.343 | ||||
| Downside SD | 0.248 | ||||
| N nonnegative terms | 64.000 | ||||
| N negative terms | 67.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.085 | ||||
| Mean of criterion | 0.650 | ||||
| SD of predictor | 0.456 | ||||
| SD of criterion | 0.423 | ||||
| Covariance | 0.018 | ||||
| r | 0.095 | ||||
| b (slope, estimate of beta) | 0.088 | ||||
| a (intercept, estimate of alpha) | 0.555 | ||||
| Mean Square Error | 0.178 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.078 | ||||
| p(b) | 0.440 | ||||
| t(a) | 0.918 | ||||
| p(a) | 0.449 | ||||
| Lowerbound of 95% confidence interval for beta | -0.073 | ||||
| Upperbound of 95% confidence interval for beta | 0.249 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.640 | ||||
| Upperbound of 95% confidence interval for alpha | 1.749 | ||||
| Treynor index (mean / b) | 7.408 | ||||
| Jensen alpha (a) | 0.555 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.561 | ||||
| SD | 0.419 | ||||
| Sharpe ratio (Glass type estimate) | 1.340 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.332 | ||||
| df | 130.000 | ||||
| t | 0.947 | ||||
| p | 0.459 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.439 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.114 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.445 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.108 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.193 | ||||
| Upside Potential Ratio | 9.690 | ||||
| Upside part of mean | 2.481 | ||||
| Downside part of mean | -1.919 | ||||
| Upside SD | 0.332 | ||||
| Downside SD | 0.256 | ||||
| N nonnegative terms | 64.000 | ||||
| N negative terms | 67.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.980 | ||||
| Mean of criterion | 0.561 | ||||
| SD of predictor | 0.455 | ||||
| SD of criterion | 0.419 | ||||
| Covariance | 0.018 | ||||
| r | 0.096 | ||||
| b (slope, estimate of beta) | 0.089 | ||||
| a (intercept, estimate of alpha) | 0.474 | ||||
| Mean Square Error | 0.175 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.099 | ||||
| p(b) | 0.439 | ||||
| t(a) | 0.794 | ||||
| p(a) | 0.456 | ||||
| Lowerbound of 95% confidence interval for beta | -0.071 | ||||
| Upperbound of 95% confidence interval for beta | 0.248 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.707 | ||||
| Upperbound of 95% confidence interval for alpha | 1.656 | ||||
| Treynor index (mean / b) | 6.328 | ||||
| Jensen alpha (a) | 0.474 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.040 | ||||
| Expected Shortfall on VaR | 0.050 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.887 | ||||
| Quartile 1 | 0.990 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.011 | ||||
| Maximum | 1.105 | ||||
| Mean of quarter 1 | 0.976 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.005 | ||||
| Mean of quarter 4 | 1.033 | ||||
| Inter Quartile Range | 0.021 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.920 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.081 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.005 | ||||
| VaR(95%) (moments method) | 0.022 | ||||
| Expected Shortfall (moments method) | 0.030 | ||||
| Extreme Value Index (regression method) | 0.130 | ||||
| VaR(95%) (regression method) | 0.025 | ||||
| Expected Shortfall (regression method) | 0.037 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 14.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.016 | ||||
| Quartile 3 | 0.040 | ||||
| Maximum | 0.185 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.012 | ||||
| Mean of quarter 3 | 0.025 | ||||
| Mean of quarter 4 | 0.110 | ||||
| Inter Quartile Range | 0.035 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.173 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.098 | ||||
| VaR(95%) (moments method) | 0.104 | ||||
| Expected Shortfall (moments method) | 0.141 | ||||
| Extreme Value Index (regression method) | -0.540 | ||||
| VaR(95%) (regression method) | 0.134 | ||||
| Expected Shortfall (regression method) | 0.157 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.707 | ||||
| Compounded annual return (geometric extrapolation) | 0.832 | ||||
| Calmar ratio (compounded annual return / max draw down) | 4.493 | ||||
| Compounded annual return / average of 25% largest draw downs | 7.595 | ||||
| Compounded annual return / Expected Shortfall lognormal | 16.665 | ||||