Advanced Statistics: Gold & Silver 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 | -0.040 | ||||
| SD | 0.336 | ||||
| Sharpe ratio (Glass type estimate) | -0.120 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.118 | ||||
| df | 58.000 | ||||
| t | -0.265 | ||||
| p | 0.604 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.003 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.765 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.002 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.766 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.211 | ||||
| Upside Potential Ratio | 2.151 | ||||
| Upside part of mean | 0.408 | ||||
| Downside part of mean | -0.448 | ||||
| Upside SD | 0.273 | ||||
| Downside SD | 0.190 | ||||
| N nonnegative terms | 25.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 59.000 | ||||
| Mean of predictor | 0.329 | ||||
| Mean of criterion | -0.040 | ||||
| SD of predictor | 0.330 | ||||
| SD of criterion | 0.336 | ||||
| Covariance | 0.050 | ||||
| r | 0.451 | ||||
| b (slope, estimate of beta) | 0.459 | ||||
| a (intercept, estimate of alpha) | -0.191 | ||||
| Mean Square Error | 0.091 | ||||
| DF error | 57.000 | ||||
| t(b) | 3.818 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.346 | ||||
| p(a) | 0.908 | ||||
| Lowerbound of 95% confidence interval for beta | 0.218 | ||||
| Upperbound of 95% confidence interval for beta | 0.699 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.475 | ||||
| Upperbound of 95% confidence interval for alpha | 0.093 | ||||
| Treynor index (mean / b) | -0.087 | ||||
| Jensen alpha (a) | -0.191 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.091 | ||||
| SD | 0.315 | ||||
| Sharpe ratio (Glass type estimate) | -0.288 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.285 | ||||
| df | 58.000 | ||||
| t | -0.639 | ||||
| p | 0.737 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.173 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.598 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.170 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.601 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.457 | ||||
| Upside Potential Ratio | 1.889 | ||||
| Upside part of mean | 0.375 | ||||
| Downside part of mean | -0.466 | ||||
| Upside SD | 0.242 | ||||
| Downside SD | 0.199 | ||||
| N nonnegative terms | 25.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 59.000 | ||||
| Mean of predictor | 0.279 | ||||
| Mean of criterion | -0.091 | ||||
| SD of predictor | 0.289 | ||||
| SD of criterion | 0.315 | ||||
| Covariance | 0.036 | ||||
| r | 0.395 | ||||
| b (slope, estimate of beta) | 0.430 | ||||
| a (intercept, estimate of alpha) | -0.211 | ||||
| Mean Square Error | 0.085 | ||||
| DF error | 57.000 | ||||
| t(b) | 3.245 | ||||
| p(b) | 0.001 | ||||
| t(a) | -1.543 | ||||
| p(a) | 0.936 | ||||
| Lowerbound of 95% confidence interval for beta | 0.165 | ||||
| Upperbound of 95% confidence interval for beta | 0.695 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.484 | ||||
| Upperbound of 95% confidence interval for alpha | 0.063 | ||||
| Treynor index (mean / b) | -0.211 | ||||
| Jensen alpha (a) | -0.211 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.145 | ||||
| Expected Shortfall on VaR | 0.177 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.093 | ||||
| Expected Shortfall on VaR | 0.136 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 59.000 | ||||
| Minimum | 0.869 | ||||
| Quartile 1 | 0.938 | ||||
| Median | 0.971 | ||||
| Quartile 3 | 1.039 | ||||
| Maximum | 1.359 | ||||
| Mean of quarter 1 | 0.911 | ||||
| Mean of quarter 2 | 0.954 | ||||
| Mean of quarter 3 | 1.013 | ||||
| Mean of quarter 4 | 1.124 | ||||
| Inter Quartile Range | 0.100 | ||||
| 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 | 0.051 | ||||
| Mean of outliers high | 1.309 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.089 | ||||
| VaR(95%) (moments method) | 0.096 | ||||
| Expected Shortfall (moments method) | 0.115 | ||||
| Extreme Value Index (regression method) | -0.612 | ||||
| VaR(95%) (regression method) | 0.091 | ||||
| Expected Shortfall (regression method) | 0.097 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.076 | ||||
| Quartile 1 | 0.212 | ||||
| Median | 0.349 | ||||
| Quartile 3 | 0.486 | ||||
| Maximum | 0.622 | ||||
| Mean of quarter 1 | 0.076 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.622 | ||||
| Inter Quartile Range | 0.273 | ||||
| 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) | -0.042 | ||||
| Compounded annual return (geometric extrapolation) | -0.046 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.073 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.073 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.258 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.057 | ||||
| SD | 0.303 | ||||
| Sharpe ratio (Glass type estimate) | -0.187 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.186 | ||||
| df | 1291.000 | ||||
| t | -0.414 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.069 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.696 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.069 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.696 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.263 | ||||
| Upside Potential Ratio | 7.161 | ||||
| Upside part of mean | 1.543 | ||||
| Downside part of mean | -1.600 | ||||
| Upside SD | 0.213 | ||||
| Downside SD | 0.215 | ||||
| N nonnegative terms | 629.000 | ||||
| N negative terms | 663.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1292.000 | ||||
| Mean of predictor | 0.352 | ||||
| Mean of criterion | -0.057 | ||||
| SD of predictor | 0.309 | ||||
| SD of criterion | 0.303 | ||||
| Covariance | 0.012 | ||||
| r | 0.131 | ||||
| b (slope, estimate of beta) | 0.129 | ||||
| a (intercept, estimate of alpha) | -0.102 | ||||
| Mean Square Error | 0.091 | ||||
| DF error | 1290.000 | ||||
| t(b) | 4.749 | ||||
| p(b) | 0.434 | ||||
| t(a) | -0.750 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | 0.076 | ||||
| Upperbound of 95% confidence interval for beta | 0.182 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.368 | ||||
| Upperbound of 95% confidence interval for alpha | 0.165 | ||||
| Treynor index (mean / b) | -0.439 | ||||
| Jensen alpha (a) | -0.102 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.103 | ||||
| SD | 0.304 | ||||
| Sharpe ratio (Glass type estimate) | -0.338 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.338 | ||||
| df | 1291.000 | ||||
| t | -0.750 | ||||
| p | 0.513 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.220 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.545 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.220 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.545 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.463 | ||||
| Upside Potential Ratio | 6.851 | ||||
| Upside part of mean | 1.521 | ||||
| Downside part of mean | -1.624 | ||||
| Upside SD | 0.208 | ||||
| Downside SD | 0.222 | ||||
| N nonnegative terms | 629.000 | ||||
| N negative terms | 663.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1292.000 | ||||
| Mean of predictor | 0.304 | ||||
| Mean of criterion | -0.103 | ||||
| SD of predictor | 0.307 | ||||
| SD of criterion | 0.304 | ||||
| Covariance | 0.012 | ||||
| r | 0.129 | ||||
| b (slope, estimate of beta) | 0.127 | ||||
| a (intercept, estimate of alpha) | -0.141 | ||||
| Mean Square Error | 0.091 | ||||
| DF error | 1290.000 | ||||
| t(b) | 4.655 | ||||
| p(b) | 0.436 | ||||
| t(a) | -1.039 | ||||
| p(a) | 0.514 | ||||
| Lowerbound of 95% confidence interval for beta | 0.074 | ||||
| Upperbound of 95% confidence interval for beta | 0.181 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.408 | ||||
| Upperbound of 95% confidence interval for alpha | 0.126 | ||||
| Treynor index (mean / b) | -0.808 | ||||
| Jensen alpha (a) | -0.141 | ||||
| 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 | 0.038 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1292.000 | ||||
| Minimum | 0.851 | ||||
| Quartile 1 | 0.992 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.008 | ||||
| Maximum | 1.150 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.020 | ||||
| Inter Quartile Range | 0.016 | ||||
| Number outliers low | 44.000 | ||||
| Percentage of outliers low | 0.034 | ||||
| Mean of outliers low | 0.949 | ||||
| Number of outliers high | 48.000 | ||||
| Percentage of outliers high | 0.037 | ||||
| Mean of outliers high | 1.051 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.307 | ||||
| VaR(95%) (moments method) | 0.021 | ||||
| Expected Shortfall (moments method) | 0.035 | ||||
| Extreme Value Index (regression method) | 0.145 | ||||
| VaR(95%) (regression method) | 0.019 | ||||
| Expected Shortfall (regression method) | 0.028 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.014 | ||||
| Quartile 1 | 0.029 | ||||
| Median | 0.049 | ||||
| Quartile 3 | 0.081 | ||||
| Maximum | 0.648 | ||||
| Mean of quarter 1 | 0.018 | ||||
| Mean of quarter 2 | 0.048 | ||||
| Mean of quarter 3 | 0.050 | ||||
| Mean of quarter 4 | 0.369 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.167 | ||||
| Mean of outliers high | 0.648 | ||||
| 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) | -0.051 | ||||
| Compounded annual return (geometric extrapolation) | -0.057 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.088 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.154 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.486 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.755 | ||||
| SD | 0.401 | ||||
| Sharpe ratio (Glass type estimate) | 1.882 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.871 | ||||
| df | 130.000 | ||||
| t | 1.331 | ||||
| p | 0.442 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.903 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.660 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.910 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.652 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.058 | ||||
| Upside Potential Ratio | 10.246 | ||||
| Upside part of mean | 2.529 | ||||
| Downside part of mean | -1.774 | ||||
| Upside SD | 0.318 | ||||
| Downside SD | 0.247 | ||||
| N nonnegative terms | 69.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.166 | ||||
| Mean of criterion | 0.755 | ||||
| SD of predictor | 0.515 | ||||
| SD of criterion | 0.401 | ||||
| Covariance | 0.010 | ||||
| r | 0.050 | ||||
| b (slope, estimate of beta) | 0.039 | ||||
| a (intercept, estimate of alpha) | 0.709 | ||||
| Mean Square Error | 0.162 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.570 | ||||
| p(b) | 0.468 | ||||
| t(a) | 1.235 | ||||
| p(a) | 0.431 | ||||
| Lowerbound of 95% confidence interval for beta | -0.097 | ||||
| Upperbound of 95% confidence interval for beta | 0.175 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.427 | ||||
| Upperbound of 95% confidence interval for alpha | 1.845 | ||||
| Treynor index (mean / b) | 19.321 | ||||
| Jensen alpha (a) | 0.709 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.674 | ||||
| SD | 0.399 | ||||
| Sharpe ratio (Glass type estimate) | 1.689 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.680 | ||||
| df | 130.000 | ||||
| t | 1.195 | ||||
| p | 0.448 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.093 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.466 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.100 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.459 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.652 | ||||
| Upside Potential Ratio | 9.753 | ||||
| Upside part of mean | 2.480 | ||||
| Downside part of mean | -1.805 | ||||
| Upside SD | 0.309 | ||||
| Downside SD | 0.254 | ||||
| N nonnegative terms | 69.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.033 | ||||
| Mean of criterion | 0.674 | ||||
| SD of predictor | 0.515 | ||||
| SD of criterion | 0.399 | ||||
| Covariance | 0.011 | ||||
| r | 0.055 | ||||
| b (slope, estimate of beta) | 0.043 | ||||
| a (intercept, estimate of alpha) | 0.630 | ||||
| Mean Square Error | 0.160 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.627 | ||||
| p(b) | 0.465 | ||||
| t(a) | 1.105 | ||||
| p(a) | 0.438 | ||||
| Lowerbound of 95% confidence interval for beta | -0.092 | ||||
| Upperbound of 95% confidence interval for beta | 0.178 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.498 | ||||
| Upperbound of 95% confidence interval for alpha | 1.759 | ||||
| Treynor index (mean / b) | 15.781 | ||||
| Jensen alpha (a) | 0.630 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.899 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.012 | ||||
| Maximum | 1.106 | ||||
| Mean of quarter 1 | 0.976 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.033 | ||||
| Inter Quartile Range | 0.021 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.937 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.069 | ||||
| Mean of outliers high | 1.060 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.233 | ||||
| VaR(95%) (moments method) | 0.023 | ||||
| Expected Shortfall (moments method) | 0.037 | ||||
| Extreme Value Index (regression method) | 0.365 | ||||
| VaR(95%) (regression method) | 0.023 | ||||
| Expected Shortfall (regression method) | 0.042 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.030 | ||||
| Quartile 3 | 0.069 | ||||
| Maximum | 0.167 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.016 | ||||
| Mean of quarter 3 | 0.036 | ||||
| Mean of quarter 4 | 0.165 | ||||
| Inter Quartile Range | 0.064 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.167 | ||||
| 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) | 0.864 | ||||
| Compounded annual return (geometric extrapolation) | 1.051 | ||||
| Calmar ratio (compounded annual return / max draw down) | 6.308 | ||||
| Compounded annual return / average of 25% largest draw downs | 6.373 | ||||
| Compounded annual return / Expected Shortfall lognormal | 22.315 | ||||