Advanced Statistics: Top Brasil Performance
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 | -0.047 | ||||
| SD | 0.462 | ||||
| Sharpe ratio (Glass type estimate) | -0.101 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.099 | ||||
| df | 34.000 | ||||
| t | -0.173 | ||||
| p | 0.568 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.248 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.048 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.247 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.049 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.118 | ||||
| Upside Potential Ratio | 1.177 | ||||
| Upside part of mean | 0.465 | ||||
| Downside part of mean | -0.512 | ||||
| Upside SD | 0.227 | ||||
| Downside SD | 0.395 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 15.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.070 | ||||
| Mean of criterion | -0.047 | ||||
| SD of predictor | 0.281 | ||||
| SD of criterion | 0.462 | ||||
| Covariance | 0.100 | ||||
| r | 0.768 | ||||
| b (slope, estimate of beta) | 1.264 | ||||
| a (intercept, estimate of alpha) | -0.135 | ||||
| Mean Square Error | 0.090 | ||||
| DF error | 33.000 | ||||
| t(b) | 6.888 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.767 | ||||
| p(a) | 0.776 | ||||
| Lowerbound of 95% confidence interval for beta | 0.891 | ||||
| Upperbound of 95% confidence interval for beta | 1.637 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.494 | ||||
| Upperbound of 95% confidence interval for alpha | 0.223 | ||||
| Treynor index (mean / b) | -0.037 | ||||
| Jensen alpha (a) | -0.135 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.196 | ||||
| SD | 0.615 | ||||
| Sharpe ratio (Glass type estimate) | -0.319 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.312 | ||||
| df | 34.000 | ||||
| t | -0.544 | ||||
| p | 0.705 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.467 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.834 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.462 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.838 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.343 | ||||
| Upside Potential Ratio | 0.770 | ||||
| Upside part of mean | 0.440 | ||||
| Downside part of mean | -0.636 | ||||
| Upside SD | 0.211 | ||||
| Downside SD | 0.571 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 15.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.030 | ||||
| Mean of criterion | -0.196 | ||||
| SD of predictor | 0.289 | ||||
| SD of criterion | 0.615 | ||||
| Covariance | 0.136 | ||||
| r | 0.765 | ||||
| b (slope, estimate of beta) | 1.627 | ||||
| a (intercept, estimate of alpha) | -0.245 | ||||
| Mean Square Error | 0.162 | ||||
| DF error | 33.000 | ||||
| t(b) | 6.813 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.039 | ||||
| p(a) | 0.847 | ||||
| Lowerbound of 95% confidence interval for beta | 1.141 | ||||
| Upperbound of 95% confidence interval for beta | 2.112 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.725 | ||||
| Upperbound of 95% confidence interval for alpha | 0.235 | ||||
| Treynor index (mean / b) | -0.121 | ||||
| Jensen alpha (a) | -0.245 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.265 | ||||
| Expected Shortfall on VaR | 0.317 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.086 | ||||
| Expected Shortfall on VaR | 0.191 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.399 | ||||
| Quartile 1 | 0.954 | ||||
| Median | 1.021 | ||||
| Quartile 3 | 1.066 | ||||
| Maximum | 1.226 | ||||
| Mean of quarter 1 | 0.850 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.042 | ||||
| Mean of quarter 4 | 1.116 | ||||
| Inter Quartile Range | 0.111 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.399 | ||||
| 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) | 0.462 | ||||
| VaR(95%) (moments method) | 0.143 | ||||
| Expected Shortfall (moments method) | 0.308 | ||||
| Extreme Value Index (regression method) | 0.962 | ||||
| VaR(95%) (regression method) | 0.124 | ||||
| Expected Shortfall (regression method) | 2.663 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.635 | ||||
| Quartile 1 | 0.635 | ||||
| Median | 0.635 | ||||
| Quartile 3 | 0.635 | ||||
| Maximum | 0.635 | ||||
| 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) | -0.123 | ||||
| Compounded annual return (geometric extrapolation) | -0.141 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.222 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.446 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.070 | ||||
| SD | 0.567 | ||||
| Sharpe ratio (Glass type estimate) | -0.123 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.123 | ||||
| df | 1014.000 | ||||
| t | -0.212 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.264 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.018 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.264 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.018 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.173 | ||||
| Upside Potential Ratio | 6.002 | ||||
| Upside part of mean | 2.421 | ||||
| Downside part of mean | -2.491 | ||||
| Upside SD | 0.398 | ||||
| Downside SD | 0.403 | ||||
| N nonnegative terms | 424.000 | ||||
| N negative terms | 591.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1015.000 | ||||
| Mean of predictor | 0.120 | ||||
| Mean of criterion | -0.070 | ||||
| SD of predictor | 0.317 | ||||
| SD of criterion | 0.567 | ||||
| Covariance | 0.058 | ||||
| r | 0.322 | ||||
| b (slope, estimate of beta) | 0.575 | ||||
| a (intercept, estimate of alpha) | -0.139 | ||||
| Mean Square Error | 0.288 | ||||
| DF error | 1013.000 | ||||
| t(b) | 10.824 | ||||
| p(b) | 0.299 | ||||
| t(a) | -0.444 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | 0.471 | ||||
| Upperbound of 95% confidence interval for beta | 0.679 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.753 | ||||
| Upperbound of 95% confidence interval for alpha | 0.475 | ||||
| Treynor index (mean / b) | -0.121 | ||||
| Jensen alpha (a) | -0.139 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.232 | ||||
| SD | 0.572 | ||||
| Sharpe ratio (Glass type estimate) | -0.405 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.405 | ||||
| df | 1014.000 | ||||
| t | -0.696 | ||||
| p | 0.511 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.546 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.736 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.546 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.736 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.534 | ||||
| Upside Potential Ratio | 5.408 | ||||
| Upside part of mean | 2.349 | ||||
| Downside part of mean | -2.581 | ||||
| Upside SD | 0.372 | ||||
| Downside SD | 0.434 | ||||
| N nonnegative terms | 424.000 | ||||
| N negative terms | 591.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1015.000 | ||||
| Mean of predictor | 0.070 | ||||
| Mean of criterion | -0.232 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 0.572 | ||||
| Covariance | 0.059 | ||||
| r | 0.323 | ||||
| b (slope, estimate of beta) | 0.582 | ||||
| a (intercept, estimate of alpha) | -0.273 | ||||
| Mean Square Error | 0.293 | ||||
| DF error | 1013.000 | ||||
| t(b) | 10.875 | ||||
| p(b) | 0.298 | ||||
| t(a) | -0.864 | ||||
| p(a) | 0.517 | ||||
| Lowerbound of 95% confidence interval for beta | 0.477 | ||||
| Upperbound of 95% confidence interval for beta | 0.688 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.891 | ||||
| Upperbound of 95% confidence interval for alpha | 0.346 | ||||
| Treynor index (mean / b) | -0.398 | ||||
| Jensen alpha (a) | -0.273 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.050 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1015.000 | ||||
| Minimum | 0.785 | ||||
| Quartile 1 | 0.994 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.006 | ||||
| Maximum | 1.268 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.026 | ||||
| Inter Quartile Range | 0.013 | ||||
| Number outliers low | 73.000 | ||||
| Percentage of outliers low | 0.072 | ||||
| Mean of outliers low | 0.940 | ||||
| Number of outliers high | 74.000 | ||||
| Percentage of outliers high | 0.073 | ||||
| Mean of outliers high | 1.059 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.608 | ||||
| VaR(95%) (moments method) | 0.025 | ||||
| Expected Shortfall (moments method) | 0.070 | ||||
| Extreme Value Index (regression method) | 0.375 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.040 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.662 | ||||
| Quartile 1 | 0.662 | ||||
| Median | 0.662 | ||||
| Quartile 3 | 0.662 | ||||
| Maximum | 0.662 | ||||
| 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) | -0.144 | ||||
| Compounded annual return (geometric extrapolation) | -0.171 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.259 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.753 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.209 | ||||
| SD | 0.891 | ||||
| Sharpe ratio (Glass type estimate) | 0.234 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.233 | ||||
| df | 171.000 | ||||
| t | 0.166 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.538 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.006 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.538 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.005 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.362 | ||||
| Upside Potential Ratio | 5.454 | ||||
| Upside part of mean | 3.151 | ||||
| Downside part of mean | -2.942 | ||||
| Upside SD | 0.675 | ||||
| Downside SD | 0.578 | ||||
| N nonnegative terms | 72.000 | ||||
| N negative terms | 100.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.619 | ||||
| Mean of criterion | 0.209 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.891 | ||||
| Covariance | -0.009 | ||||
| r | -0.037 | ||||
| b (slope, estimate of beta) | -0.121 | ||||
| a (intercept, estimate of alpha) | 0.284 | ||||
| Mean Square Error | 0.797 | ||||
| DF error | 170.000 | ||||
| t(b) | -0.480 | ||||
| p(b) | 0.518 | ||||
| t(a) | 0.223 | ||||
| p(a) | 0.491 | ||||
| Lowerbound of 95% confidence interval for beta | -0.621 | ||||
| Upperbound of 95% confidence interval for beta | 0.378 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.228 | ||||
| Upperbound of 95% confidence interval for alpha | 2.796 | ||||
| Treynor index (mean / b) | -1.719 | ||||
| Jensen alpha (a) | 0.284 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.182 | ||||
| SD | 0.887 | ||||
| Sharpe ratio (Glass type estimate) | -0.205 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.204 | ||||
| df | 171.000 | ||||
| t | -0.145 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.976 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.567 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.976 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.568 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.284 | ||||
| Upside Potential Ratio | 4.615 | ||||
| Upside part of mean | 2.951 | ||||
| Downside part of mean | -3.132 | ||||
| Upside SD | 0.611 | ||||
| Downside SD | 0.639 | ||||
| N nonnegative terms | 72.000 | ||||
| N negative terms | 100.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.582 | ||||
| Mean of criterion | -0.182 | ||||
| SD of predictor | 0.269 | ||||
| SD of criterion | 0.887 | ||||
| Covariance | -0.011 | ||||
| r | -0.048 | ||||
| b (slope, estimate of beta) | -0.159 | ||||
| a (intercept, estimate of alpha) | -0.089 | ||||
| Mean Square Error | 0.790 | ||||
| DF error | 170.000 | ||||
| t(b) | -0.628 | ||||
| p(b) | 0.524 | ||||
| t(a) | -0.071 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | -0.657 | ||||
| Upperbound of 95% confidence interval for beta | 0.340 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.587 | ||||
| Upperbound of 95% confidence interval for alpha | 2.409 | ||||
| Treynor index (mean / b) | 1.145 | ||||
| Jensen alpha (a) | -0.089 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.076 | ||||
| Expected Shortfall on VaR | 0.094 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 172.000 | ||||
| Minimum | 0.785 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.004 | ||||
| Maximum | 1.268 | ||||
| Mean of quarter 1 | 0.968 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.035 | ||||
| Inter Quartile Range | 0.009 | ||||
| Number outliers low | 16.000 | ||||
| Percentage of outliers low | 0.093 | ||||
| Mean of outliers low | 0.930 | ||||
| Number of outliers high | 14.000 | ||||
| Percentage of outliers high | 0.081 | ||||
| Mean of outliers high | 1.091 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.999 | ||||
| VaR(95%) (moments method) | 0.027 | ||||
| Expected Shortfall (moments method) | 23.432 | ||||
| Extreme Value Index (regression method) | 0.376 | ||||
| VaR(95%) (regression method) | 0.019 | ||||
| Expected Shortfall (regression method) | 0.038 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.123 | ||||
| Quartile 1 | 0.157 | ||||
| Median | 0.190 | ||||
| Quartile 3 | 0.224 | ||||
| Maximum | 0.258 | ||||
| Mean of quarter 1 | 0.123 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.258 | ||||
| Inter Quartile Range | 0.068 | ||||
| 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) | -0.133 | ||||
| Compounded annual return (geometric extrapolation) | -0.129 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.498 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.498 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.363 | ||||
