Advanced Statistics: Global Investing Report-Sector Leaders
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 | 0.240 | ||||
| SD | 0.459 | ||||
| Sharpe ratio (Glass type estimate) | 0.523 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.519 | ||||
| df | 94.000 | ||||
| t | 1.472 | ||||
| p | 0.072 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.179 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.222 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.182 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.219 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.983 | ||||
| Upside Potential Ratio | 2.783 | ||||
| Upside part of mean | 0.680 | ||||
| Downside part of mean | -0.440 | ||||
| Upside SD | 0.392 | ||||
| Downside SD | 0.244 | ||||
| N nonnegative terms | 49.000 | ||||
| N negative terms | 46.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 95.000 | ||||
| Mean of predictor | 0.182 | ||||
| Mean of criterion | 0.240 | ||||
| SD of predictor | 0.192 | ||||
| SD of criterion | 0.459 | ||||
| Covariance | 0.037 | ||||
| r | 0.425 | ||||
| b (slope, estimate of beta) | 1.017 | ||||
| a (intercept, estimate of alpha) | 0.055 | ||||
| Mean Square Error | 0.175 | ||||
| DF error | 93.000 | ||||
| t(b) | 4.523 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.357 | ||||
| p(a) | 0.361 | ||||
| Lowerbound of 95% confidence interval for beta | 0.570 | ||||
| Upperbound of 95% confidence interval for beta | 1.463 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.251 | ||||
| Upperbound of 95% confidence interval for alpha | 0.361 | ||||
| Treynor index (mean / b) | 0.236 | ||||
| Jensen alpha (a) | 0.055 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.142 | ||||
| SD | 0.434 | ||||
| Sharpe ratio (Glass type estimate) | 0.327 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.325 | ||||
| df | 94.000 | ||||
| t | 0.921 | ||||
| p | 0.180 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.372 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.025 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.373 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.023 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.522 | ||||
| Upside Potential Ratio | 2.255 | ||||
| Upside part of mean | 0.615 | ||||
| Downside part of mean | -0.473 | ||||
| Upside SD | 0.338 | ||||
| Downside SD | 0.273 | ||||
| N nonnegative terms | 49.000 | ||||
| N negative terms | 46.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 95.000 | ||||
| Mean of predictor | 0.163 | ||||
| Mean of criterion | 0.142 | ||||
| SD of predictor | 0.183 | ||||
| SD of criterion | 0.434 | ||||
| Covariance | 0.032 | ||||
| r | 0.404 | ||||
| b (slope, estimate of beta) | 0.959 | ||||
| a (intercept, estimate of alpha) | -0.014 | ||||
| Mean Square Error | 0.160 | ||||
| DF error | 93.000 | ||||
| t(b) | 4.264 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.098 | ||||
| p(a) | 0.539 | ||||
| Lowerbound of 95% confidence interval for beta | 0.512 | ||||
| Upperbound of 95% confidence interval for beta | 1.405 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.306 | ||||
| Upperbound of 95% confidence interval for alpha | 0.277 | ||||
| Treynor index (mean / b) | 0.148 | ||||
| Jensen alpha (a) | -0.014 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.177 | ||||
| Expected Shortfall on VaR | 0.218 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.083 | ||||
| Expected Shortfall on VaR | 0.158 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 95.000 | ||||
| Minimum | 0.651 | ||||
| Quartile 1 | 0.943 | ||||
| Median | 1.006 | ||||
| Quartile 3 | 1.091 | ||||
| Maximum | 1.498 | ||||
| Mean of quarter 1 | 0.882 | ||||
| Mean of quarter 2 | 0.980 | ||||
| Mean of quarter 3 | 1.047 | ||||
| Mean of quarter 4 | 1.186 | ||||
| Inter Quartile Range | 0.149 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.011 | ||||
| Mean of outliers low | 0.651 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.042 | ||||
| Mean of outliers high | 1.448 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.112 | ||||
| VaR(95%) (moments method) | 0.121 | ||||
| Expected Shortfall (moments method) | 0.170 | ||||
| Extreme Value Index (regression method) | 0.376 | ||||
| VaR(95%) (regression method) | 0.120 | ||||
| Expected Shortfall (regression method) | 0.201 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.058 | ||||
| Median | 0.095 | ||||
| Quartile 3 | 0.202 | ||||
| Maximum | 0.669 | ||||
| Mean of quarter 1 | 0.037 | ||||
| Mean of quarter 2 | 0.075 | ||||
| Mean of quarter 3 | 0.160 | ||||
| Mean of quarter 4 | 0.366 | ||||
| Inter Quartile Range | 0.144 | ||||
| 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 | 0.091 | ||||
| Mean of outliers high | 0.669 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.549 | ||||
| VaR(95%) (moments method) | 0.445 | ||||
| Expected Shortfall (moments method) | 1.003 | ||||
| Extreme Value Index (regression method) | 5.641 | ||||
| VaR(95%) (regression method) | 1.646 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.425 | ||||
| Compounded annual return (geometric extrapolation) | 0.205 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.306 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.560 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.939 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.222 | ||||
| SD | 0.366 | ||||
| Sharpe ratio (Glass type estimate) | 0.606 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.606 | ||||
| df | 2088.000 | ||||
| t | 1.712 | ||||
| p | 0.044 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.088 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.301 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.088 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.300 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.892 | ||||
| Upside Potential Ratio | 7.915 | ||||
| Upside part of mean | 1.971 | ||||
| Downside part of mean | -1.748 | ||||
| Upside SD | 0.269 | ||||
| Downside SD | 0.249 | ||||
| N nonnegative terms | 1090.000 | ||||
| N negative terms | 999.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2089.000 | ||||
| Mean of predictor | 0.202 | ||||
| Mean of criterion | 0.222 | ||||
| SD of predictor | 0.209 | ||||
| SD of criterion | 0.366 | ||||
| Covariance | 0.029 | ||||
| r | 0.381 | ||||
| b (slope, estimate of beta) | 0.666 | ||||
| a (intercept, estimate of alpha) | 0.087 | ||||
| Mean Square Error | 0.115 | ||||
| DF error | 2087.000 | ||||
| t(b) | 18.828 | ||||
| p(b) | -0.000 | ||||
| t(a) | 0.726 | ||||
| p(a) | 0.234 | ||||
| Lowerbound of 95% confidence interval for beta | 0.597 | ||||
| Upperbound of 95% confidence interval for beta | 0.736 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.148 | ||||
| Upperbound of 95% confidence interval for alpha | 0.323 | ||||
| Treynor index (mean / b) | 0.333 | ||||
| Jensen alpha (a) | 0.087 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.155 | ||||
| SD | 0.366 | ||||
| Sharpe ratio (Glass type estimate) | 0.423 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.423 | ||||
| df | 2088.000 | ||||
| t | 1.195 | ||||
| p | 0.116 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.271 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.118 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.271 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.117 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.602 | ||||
| Upside Potential Ratio | 7.517 | ||||
| Upside part of mean | 1.936 | ||||
| Downside part of mean | -1.781 | ||||
| Upside SD | 0.260 | ||||
| Downside SD | 0.257 | ||||
| N nonnegative terms | 1090.000 | ||||
| N negative terms | 999.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2089.000 | ||||
| Mean of predictor | 0.180 | ||||
| Mean of criterion | 0.155 | ||||
| SD of predictor | 0.211 | ||||
| SD of criterion | 0.366 | ||||
| Covariance | 0.029 | ||||
| r | 0.380 | ||||
| b (slope, estimate of beta) | 0.659 | ||||
| a (intercept, estimate of alpha) | 0.036 | ||||
| Mean Square Error | 0.115 | ||||
| DF error | 2087.000 | ||||
| t(b) | 18.770 | ||||
| p(b) | -0.000 | ||||
| t(a) | 0.302 | ||||
| p(a) | 0.381 | ||||
| Lowerbound of 95% confidence interval for beta | 0.591 | ||||
| Upperbound of 95% confidence interval for beta | 0.728 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.199 | ||||
| Upperbound of 95% confidence interval for alpha | 0.272 | ||||
| Treynor index (mean / b) | 0.235 | ||||
| Jensen alpha (a) | 0.036 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.045 | ||||
| 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 | 2089.000 | ||||
| Minimum | 0.850 | ||||
| Quartile 1 | 0.992 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.010 | ||||
| Maximum | 1.155 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.005 | ||||
| Mean of quarter 4 | 1.026 | ||||
| Inter Quartile Range | 0.018 | ||||
| Number outliers low | 82.000 | ||||
| Percentage of outliers low | 0.039 | ||||
| Mean of outliers low | 0.941 | ||||
| Number of outliers high | 81.000 | ||||
| Percentage of outliers high | 0.039 | ||||
| Mean of outliers high | 1.064 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.336 | ||||
| VaR(95%) (moments method) | 0.023 | ||||
| Expected Shortfall (moments method) | 0.041 | ||||
| Extreme Value Index (regression method) | 0.234 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.034 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.035 | ||||
| Quartile 3 | 0.108 | ||||
| Maximum | 0.682 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.024 | ||||
| Mean of quarter 3 | 0.081 | ||||
| Mean of quarter 4 | 0.248 | ||||
| Inter Quartile Range | 0.094 | ||||
| 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 | 0.103 | ||||
| Mean of outliers high | 0.405 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.419 | ||||
| VaR(95%) (moments method) | 0.275 | ||||
| Expected Shortfall (moments method) | 0.528 | ||||
| Extreme Value Index (regression method) | 0.973 | ||||
| VaR(95%) (regression method) | 0.260 | ||||
| Expected Shortfall (regression method) | 7.065 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.488 | ||||
| Compounded annual return (geometric extrapolation) | 0.220 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.323 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.888 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.894 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.176 | ||||
| SD | 0.765 | ||||
| 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 | 2.393 | ||||
| Upside Potential Ratio | 10.263 | ||||
| Upside part of mean | 5.041 | ||||
| Downside part of mean | -3.866 | ||||
| Upside SD | 0.587 | ||||
| Downside SD | 0.491 | ||||
| N nonnegative terms | 70.000 | ||||
| N negative terms | 61.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.029 | ||||
| Mean of criterion | 1.176 | ||||
| SD of predictor | 0.509 | ||||
| SD of criterion | 0.765 | ||||
| Covariance | 0.176 | ||||
| r | 0.453 | ||||
| b (slope, estimate of beta) | 0.681 | ||||
| a (intercept, estimate of alpha) | 0.475 | ||||
| Mean Square Error | 0.469 | ||||
| DF error | 129.000 | ||||
| t(b) | 5.775 | ||||
| p(b) | 0.222 | ||||
| t(a) | 0.486 | ||||
| p(a) | 0.473 | ||||
| Lowerbound of 95% confidence interval for beta | 0.448 | ||||
| Upperbound of 95% confidence interval for beta | 0.915 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.456 | ||||
| Upperbound of 95% confidence interval for alpha | 2.405 | ||||
| Treynor index (mean / b) | 1.726 | ||||
| Jensen alpha (a) | 0.475 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.885 | ||||
| SD | 0.762 | ||||
| Sharpe ratio (Glass type estimate) | 1.162 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.155 | ||||
| df | 130.000 | ||||
| t | 0.822 | ||||
| p | 0.464 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.615 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.935 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.620 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.931 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.724 | ||||
| Upside Potential Ratio | 9.499 | ||||
| Upside part of mean | 4.878 | ||||
| Downside part of mean | -3.993 | ||||
| Upside SD | 0.561 | ||||
| Downside SD | 0.514 | ||||
| N nonnegative terms | 70.000 | ||||
| N negative terms | 61.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.901 | ||||
| Mean of criterion | 0.885 | ||||
| SD of predictor | 0.502 | ||||
| SD of criterion | 0.762 | ||||
| Covariance | 0.168 | ||||
| r | 0.439 | ||||
| b (slope, estimate of beta) | 0.666 | ||||
| a (intercept, estimate of alpha) | 0.285 | ||||
| Mean Square Error | 0.472 | ||||
| DF error | 129.000 | ||||
| t(b) | 5.554 | ||||
| p(b) | 0.230 | ||||
| t(a) | 0.291 | ||||
| p(a) | 0.484 | ||||
| Lowerbound of 95% confidence interval for beta | 0.429 | ||||
| Upperbound of 95% confidence interval for beta | 0.904 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.649 | ||||
| Upperbound of 95% confidence interval for alpha | 2.219 | ||||
| Treynor index (mean / b) | 1.328 | ||||
| Jensen alpha (a) | 0.285 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.071 | ||||
| Expected Shortfall on VaR | 0.089 | ||||
| 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 | 131.000 | ||||
| Minimum | 0.855 | ||||
| Quartile 1 | 0.977 | ||||
| Median | 1.005 | ||||
| Quartile 3 | 1.027 | ||||
| Maximum | 1.155 | ||||
| Mean of quarter 1 | 0.948 | ||||
| Mean of quarter 2 | 0.994 | ||||
| Mean of quarter 3 | 1.014 | ||||
| Mean of quarter 4 | 1.063 | ||||
| Inter Quartile Range | 0.051 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.882 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.123 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.165 | ||||
| VaR(95%) (moments method) | 0.053 | ||||
| Expected Shortfall (moments method) | 0.078 | ||||
| Extreme Value Index (regression method) | 0.097 | ||||
| VaR(95%) (regression method) | 0.060 | ||||
| Expected Shortfall (regression method) | 0.088 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 13.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.018 | ||||
| Median | 0.056 | ||||
| Quartile 3 | 0.145 | ||||
| Maximum | 0.273 | ||||
| Mean of quarter 1 | 0.010 | ||||
| Mean of quarter 2 | 0.040 | ||||
| Mean of quarter 3 | 0.118 | ||||
| Mean of quarter 4 | 0.243 | ||||
| Inter Quartile Range | 0.128 | ||||
| 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) | -5.351 | ||||
| VaR(95%) (moments method) | 0.232 | ||||
| Expected Shortfall (moments method) | 0.232 | ||||
| Extreme Value Index (regression method) | -2.227 | ||||
| VaR(95%) (regression method) | 0.313 | ||||
| Expected Shortfall (regression method) | 0.316 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.183 | ||||
| Compounded annual return (geometric extrapolation) | 1.533 | ||||
| Calmar ratio (compounded annual return / max draw down) | 5.608 | ||||
| Compounded annual return / average of 25% largest draw downs | 6.308 | ||||
| Compounded annual return / Expected Shortfall lognormal | 17.163 | ||||