Advanced Statistics: Diversified Rare Earths Basket
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 | -0.120 | ||||
| SD | 0.968 | ||||
| Sharpe ratio (Glass type estimate) | -0.124 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.121 | ||||
| df | 35.000 | ||||
| t | -0.214 | ||||
| p | 0.584 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.255 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.009 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.253 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.011 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.284 | ||||
| Upside Potential Ratio | 2.165 | ||||
| Upside part of mean | 0.912 | ||||
| Downside part of mean | -1.031 | ||||
| Upside SD | 0.857 | ||||
| Downside SD | 0.421 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 25.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.466 | ||||
| Mean of criterion | -0.120 | ||||
| SD of predictor | 0.432 | ||||
| SD of criterion | 0.968 | ||||
| Covariance | 0.095 | ||||
| r | 0.228 | ||||
| b (slope, estimate of beta) | 0.511 | ||||
| a (intercept, estimate of alpha) | -0.358 | ||||
| Mean Square Error | 0.915 | ||||
| DF error | 34.000 | ||||
| t(b) | 1.365 | ||||
| p(b) | 0.091 | ||||
| t(a) | -0.618 | ||||
| p(a) | 0.730 | ||||
| Lowerbound of 95% confidence interval for beta | -0.250 | ||||
| Upperbound of 95% confidence interval for beta | 1.272 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.535 | ||||
| Upperbound of 95% confidence interval for alpha | 0.819 | ||||
| Treynor index (mean / b) | -0.234 | ||||
| Jensen alpha (a) | -0.358 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.433 | ||||
| SD | 0.739 | ||||
| Sharpe ratio (Glass type estimate) | -0.586 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.573 | ||||
| df | 35.000 | ||||
| t | -1.015 | ||||
| p | 0.841 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.722 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.558 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.713 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.566 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.919 | ||||
| Upside Potential Ratio | 1.481 | ||||
| Upside part of mean | 0.697 | ||||
| Downside part of mean | -1.130 | ||||
| Upside SD | 0.569 | ||||
| Downside SD | 0.471 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 25.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.393 | ||||
| Mean of criterion | -0.433 | ||||
| SD of predictor | 0.332 | ||||
| SD of criterion | 0.739 | ||||
| Covariance | 0.069 | ||||
| r | 0.280 | ||||
| b (slope, estimate of beta) | 0.624 | ||||
| a (intercept, estimate of alpha) | -0.678 | ||||
| Mean Square Error | 0.517 | ||||
| DF error | 34.000 | ||||
| t(b) | 1.703 | ||||
| p(b) | 0.049 | ||||
| t(a) | -1.543 | ||||
| p(a) | 0.934 | ||||
| Lowerbound of 95% confidence interval for beta | -0.121 | ||||
| Upperbound of 95% confidence interval for beta | 1.368 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.571 | ||||
| Upperbound of 95% confidence interval for alpha | 0.215 | ||||
| Treynor index (mean / b) | -0.693 | ||||
| Jensen alpha (a) | -0.678 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.321 | ||||
| Expected Shortfall on VaR | 0.377 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.226 | ||||
| Expected Shortfall on VaR | 0.312 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.710 | ||||
| Quartile 1 | 0.866 | ||||
| Median | 0.925 | ||||
| Quartile 3 | 1.047 | ||||
| Maximum | 2.394 | ||||
| Mean of quarter 1 | 0.798 | ||||
| Mean of quarter 2 | 0.891 | ||||
| Mean of quarter 3 | 0.983 | ||||
| Mean of quarter 4 | 1.302 | ||||
| Inter Quartile Range | 0.181 | ||||
| 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 | 0.056 | ||||
| Mean of outliers high | 1.872 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.173 | ||||
| VaR(95%) (moments method) | 0.220 | ||||
| Expected Shortfall (moments method) | 0.259 | ||||
| Extreme Value Index (regression method) | -0.671 | ||||
| VaR(95%) (regression method) | 0.202 | ||||
| Expected Shortfall (regression method) | 0.215 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.794 | ||||
| Quartile 1 | 0.794 | ||||
| Median | 0.794 | ||||
| Quartile 3 | 0.794 | ||||
| Maximum | 0.794 | ||||
| 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) | -0.229 | ||||
| Compounded annual return (geometric extrapolation) | -0.322 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.406 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.855 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.175 | ||||
| SD | 0.809 | ||||
| Sharpe ratio (Glass type estimate) | -0.216 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.216 | ||||
| df | 791.000 | ||||
| t | -0.376 | ||||
| p | 0.646 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.343 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.911 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.343 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.912 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.364 | ||||
| Upside Potential Ratio | 6.556 | ||||
| Upside part of mean | 3.147 | ||||
| Downside part of mean | -3.322 | ||||
| Upside SD | 0.650 | ||||
| Downside SD | 0.480 | ||||
| N nonnegative terms | 338.000 | ||||
| N negative terms | 454.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 792.000 | ||||
| Mean of predictor | 0.458 | ||||
| Mean of criterion | -0.175 | ||||
| SD of predictor | 0.333 | ||||
| SD of criterion | 0.809 | ||||
| Covariance | 0.049 | ||||
| r | 0.181 | ||||
| b (slope, estimate of beta) | 0.439 | ||||
| a (intercept, estimate of alpha) | -0.376 | ||||
| Mean Square Error | 0.634 | ||||
| DF error | 790.000 | ||||
| t(b) | 5.161 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.817 | ||||
| p(a) | 0.793 | ||||
| Lowerbound of 95% confidence interval for beta | 0.272 | ||||
| Upperbound of 95% confidence interval for beta | 0.606 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.278 | ||||
| Upperbound of 95% confidence interval for alpha | 0.526 | ||||
| Treynor index (mean / b) | -0.398 | ||||
| Jensen alpha (a) | -0.376 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.488 | ||||
| SD | 0.796 | ||||
| Sharpe ratio (Glass type estimate) | -0.613 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.613 | ||||
| df | 791.000 | ||||
| t | -1.066 | ||||
| p | 0.857 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.741 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.515 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.740 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.515 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.851 | ||||
| Upside Potential Ratio | 5.193 | ||||
| Upside part of mean | 2.978 | ||||
| Downside part of mean | -3.466 | ||||
| Upside SD | 0.551 | ||||
| Downside SD | 0.573 | ||||
| N nonnegative terms | 338.000 | ||||
| N negative terms | 454.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 792.000 | ||||
| Mean of predictor | 0.402 | ||||
| Mean of criterion | -0.488 | ||||
| SD of predictor | 0.332 | ||||
| SD of criterion | 0.796 | ||||
| Covariance | 0.038 | ||||
| r | 0.145 | ||||
| b (slope, estimate of beta) | 0.347 | ||||
| a (intercept, estimate of alpha) | -0.627 | ||||
| Mean Square Error | 0.620 | ||||
| DF error | 790.000 | ||||
| t(b) | 4.118 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.381 | ||||
| p(a) | 0.916 | ||||
| Lowerbound of 95% confidence interval for beta | 0.181 | ||||
| Upperbound of 95% confidence interval for beta | 0.512 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.519 | ||||
| Upperbound of 95% confidence interval for alpha | 0.264 | ||||
| Treynor index (mean / b) | -1.407 | ||||
| Jensen alpha (a) | -0.627 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.079 | ||||
| Expected Shortfall on VaR | 0.098 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.064 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 792.000 | ||||
| Minimum | 0.485 | ||||
| Quartile 1 | 0.983 | ||||
| Median | 0.996 | ||||
| Quartile 3 | 1.011 | ||||
| Maximum | 1.769 | ||||
| Mean of quarter 1 | 0.960 | ||||
| Mean of quarter 2 | 0.990 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.044 | ||||
| Inter Quartile Range | 0.029 | ||||
| Number outliers low | 21.000 | ||||
| Percentage of outliers low | 0.027 | ||||
| Mean of outliers low | 0.879 | ||||
| Number of outliers high | 35.000 | ||||
| Percentage of outliers high | 0.044 | ||||
| Mean of outliers high | 1.128 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.412 | ||||
| VaR(95%) (moments method) | 0.042 | ||||
| Expected Shortfall (moments method) | 0.078 | ||||
| Extreme Value Index (regression method) | 0.370 | ||||
| VaR(95%) (regression method) | 0.034 | ||||
| Expected Shortfall (regression method) | 0.057 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.017 | ||||
| Quartile 3 | 0.415 | ||||
| Maximum | 0.812 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.017 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.812 | ||||
| Inter Quartile Range | 0.406 | ||||
| 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) | -0.244 | ||||
| Compounded annual return (geometric extrapolation) | -0.358 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.441 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.441 | ||||
| Compounded annual return / Expected Shortfall lognormal | -3.660 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.050 | ||||
| SD | 1.515 | ||||
| Sharpe ratio (Glass type estimate) | 0.693 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.689 | ||||
| df | 130.000 | ||||
| t | 0.490 | ||||
| p | 0.479 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.081 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.465 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.084 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.462 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.253 | ||||
| Upside Potential Ratio | 6.768 | ||||
| Upside part of mean | 5.672 | ||||
| Downside part of mean | -4.622 | ||||
| Upside SD | 1.257 | ||||
| Downside SD | 0.838 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 75.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.741 | ||||
| Mean of criterion | 1.050 | ||||
| SD of predictor | 0.720 | ||||
| SD of criterion | 1.515 | ||||
| Covariance | 0.231 | ||||
| r | 0.212 | ||||
| b (slope, estimate of beta) | 0.446 | ||||
| a (intercept, estimate of alpha) | 0.273 | ||||
| Mean Square Error | 2.210 | ||||
| DF error | 129.000 | ||||
| t(b) | 2.465 | ||||
| p(b) | 0.366 | ||||
| t(a) | 0.129 | ||||
| p(a) | 0.493 | ||||
| Lowerbound of 95% confidence interval for beta | 0.088 | ||||
| Upperbound of 95% confidence interval for beta | 0.805 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.933 | ||||
| Upperbound of 95% confidence interval for alpha | 4.480 | ||||
| Treynor index (mean / b) | 2.353 | ||||
| Jensen alpha (a) | 0.273 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.036 | ||||
| SD | 1.499 | ||||
| Sharpe ratio (Glass type estimate) | -0.024 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.024 | ||||
| df | 130.000 | ||||
| t | -0.017 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.796 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.748 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.796 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.748 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.033 | ||||
| Upside Potential Ratio | 4.581 | ||||
| Upside part of mean | 5.093 | ||||
| Downside part of mean | -5.130 | ||||
| Upside SD | 0.998 | ||||
| Downside SD | 1.112 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 75.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.479 | ||||
| Mean of criterion | -0.036 | ||||
| SD of predictor | 0.722 | ||||
| SD of criterion | 1.499 | ||||
| Covariance | 0.177 | ||||
| r | 0.164 | ||||
| b (slope, estimate of beta) | 0.340 | ||||
| a (intercept, estimate of alpha) | -0.540 | ||||
| Mean Square Error | 2.205 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.886 | ||||
| p(b) | 0.396 | ||||
| t(a) | -0.255 | ||||
| p(a) | 0.514 | ||||
| Lowerbound of 95% confidence interval for beta | -0.017 | ||||
| Upperbound of 95% confidence interval for beta | 0.697 | ||||
| Lowerbound of 95% confidence interval for alpha | -4.728 | ||||
| Upperbound of 95% confidence interval for alpha | 3.649 | ||||
| Treynor index (mean / b) | -0.107 | ||||
| Jensen alpha (a) | -0.540 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.141 | ||||
| Expected Shortfall on VaR | 0.174 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.043 | ||||
| Expected Shortfall on VaR | 0.094 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.485 | ||||
| Quartile 1 | 0.977 | ||||
| Median | 0.997 | ||||
| Quartile 3 | 1.020 | ||||
| Maximum | 1.769 | ||||
| Mean of quarter 1 | 0.944 | ||||
| Mean of quarter 2 | 0.987 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.080 | ||||
| Inter Quartile Range | 0.043 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.659 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.264 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.631 | ||||
| VaR(95%) (moments method) | 0.060 | ||||
| Expected Shortfall (moments method) | 0.159 | ||||
| Extreme Value Index (regression method) | 0.930 | ||||
| VaR(95%) (regression method) | 0.039 | ||||
| Expected Shortfall (regression method) | 0.321 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.031 | ||||
| Quartile 1 | 0.113 | ||||
| Median | 0.265 | ||||
| Quartile 3 | 0.432 | ||||
| Maximum | 0.554 | ||||
| Mean of quarter 1 | 0.031 | ||||
| Mean of quarter 2 | 0.140 | ||||
| Mean of quarter 3 | 0.391 | ||||
| Mean of quarter 4 | 0.554 | ||||
| Inter Quartile Range | 0.319 | ||||
| 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) | 0.008 | ||||
| Compounded annual return (geometric extrapolation) | 0.008 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.014 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.014 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.044 | ||||