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 | -0.106 | ||||
| SD | 0.304 | ||||
| Sharpe ratio (Glass type estimate) | -0.347 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.343 | ||||
| df | 62.000 | ||||
| t | -0.796 | ||||
| p | 0.785 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.204 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.512 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.201 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.514 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.403 | ||||
| Upside Potential Ratio | 1.043 | ||||
| Upside part of mean | 0.273 | ||||
| Downside part of mean | -0.379 | ||||
| Upside SD | 0.153 | ||||
| Downside SD | 0.262 | ||||
| N nonnegative terms | 34.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.322 | ||||
| Mean of criterion | -0.106 | ||||
| SD of predictor | 0.281 | ||||
| SD of criterion | 0.304 | ||||
| Covariance | 0.023 | ||||
| r | 0.270 | ||||
| b (slope, estimate of beta) | 0.292 | ||||
| a (intercept, estimate of alpha) | -0.200 | ||||
| Mean Square Error | 0.087 | ||||
| DF error | 61.000 | ||||
| t(b) | 2.186 | ||||
| p(b) | 0.016 | ||||
| t(a) | -1.470 | ||||
| p(a) | 0.927 | ||||
| Lowerbound of 95% confidence interval for beta | 0.025 | ||||
| Upperbound of 95% confidence interval for beta | 0.559 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.471 | ||||
| Upperbound of 95% confidence interval for alpha | 0.072 | ||||
| Treynor index (mean / b) | -0.362 | ||||
| Jensen alpha (a) | -0.200 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.159 | ||||
| SD | 0.345 | ||||
| Sharpe ratio (Glass type estimate) | -0.462 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.456 | ||||
| df | 62.000 | ||||
| t | -1.059 | ||||
| p | 0.853 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.320 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.399 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.316 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.403 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.508 | ||||
| Upside Potential Ratio | 0.833 | ||||
| Upside part of mean | 0.261 | ||||
| Downside part of mean | -0.421 | ||||
| Upside SD | 0.144 | ||||
| Downside SD | 0.314 | ||||
| N nonnegative terms | 34.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.281 | ||||
| Mean of criterion | -0.159 | ||||
| SD of predictor | 0.269 | ||||
| SD of criterion | 0.345 | ||||
| Covariance | 0.028 | ||||
| r | 0.299 | ||||
| b (slope, estimate of beta) | 0.383 | ||||
| a (intercept, estimate of alpha) | -0.267 | ||||
| Mean Square Error | 0.110 | ||||
| DF error | 61.000 | ||||
| t(b) | 2.444 | ||||
| p(b) | 0.009 | ||||
| t(a) | -1.764 | ||||
| p(a) | 0.959 | ||||
| Lowerbound of 95% confidence interval for beta | 0.070 | ||||
| Upperbound of 95% confidence interval for beta | 0.696 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.570 | ||||
| Upperbound of 95% confidence interval for alpha | 0.036 | ||||
| Treynor index (mean / b) | -0.416 | ||||
| Jensen alpha (a) | -0.267 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.162 | ||||
| Expected Shortfall on VaR | 0.196 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.068 | ||||
| Expected Shortfall on VaR | 0.144 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 63.000 | ||||
| Minimum | 0.601 | ||||
| Quartile 1 | 0.970 | ||||
| Median | 1.006 | ||||
| Quartile 3 | 1.030 | ||||
| Maximum | 1.174 | ||||
| Mean of quarter 1 | 0.893 | ||||
| Mean of quarter 2 | 0.990 | ||||
| Mean of quarter 3 | 1.018 | ||||
| Mean of quarter 4 | 1.080 | ||||
| Inter Quartile Range | 0.061 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.048 | ||||
| Mean of outliers low | 0.712 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.032 | ||||
| Mean of outliers high | 1.168 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.261 | ||||
| VaR(95%) (moments method) | 0.095 | ||||
| Expected Shortfall (moments method) | 0.160 | ||||
| Extreme Value Index (regression method) | 0.712 | ||||
| VaR(95%) (regression method) | 0.093 | ||||
| Expected Shortfall (regression method) | 0.311 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.480 | ||||
| Quartile 1 | 0.483 | ||||
| Median | 0.485 | ||||
| Quartile 3 | 0.487 | ||||
| Maximum | 0.489 | ||||
| Mean of quarter 1 | 0.480 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.489 | ||||
| Inter Quartile Range | 0.004 | ||||
| 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) | -0.087 | ||||
| Compounded annual return (geometric extrapolation) | -0.109 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.223 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.223 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.556 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.258 | ||||
| SD | 0.970 | ||||
| Sharpe ratio (Glass type estimate) | 0.266 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.266 | ||||
| df | 1396.000 | ||||
| t | 0.614 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.583 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.115 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.583 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.115 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.463 | ||||
| Upside Potential Ratio | 5.167 | ||||
| Upside part of mean | 2.878 | ||||
| Downside part of mean | -2.620 | ||||
| Upside SD | 0.794 | ||||
| Downside SD | 0.557 | ||||
| N nonnegative terms | 683.000 | ||||
| N negative terms | 714.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1397.000 | ||||
| Mean of predictor | 0.435 | ||||
| Mean of criterion | 0.258 | ||||
| SD of predictor | 0.488 | ||||
| SD of criterion | 0.970 | ||||
| Covariance | 0.259 | ||||
| r | 0.547 | ||||
| b (slope, estimate of beta) | 1.086 | ||||
| a (intercept, estimate of alpha) | -0.215 | ||||
| Mean Square Error | 0.660 | ||||
| DF error | 1395.000 | ||||
| t(b) | 24.376 | ||||
| p(b) | 0.170 | ||||
| t(a) | -0.610 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | 0.999 | ||||
| Upperbound of 95% confidence interval for beta | 1.174 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.906 | ||||
| Upperbound of 95% confidence interval for alpha | 0.476 | ||||
| Treynor index (mean / b) | 0.238 | ||||
| Jensen alpha (a) | -0.215 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.164 | ||||
| SD | 0.914 | ||||
| Sharpe ratio (Glass type estimate) | -0.179 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.179 | ||||
| df | 1396.000 | ||||
| t | -0.414 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.028 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.670 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.028 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.670 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.245 | ||||
| Upside Potential Ratio | 3.963 | ||||
| Upside part of mean | 2.652 | ||||
| Downside part of mean | -2.816 | ||||
| Upside SD | 0.621 | ||||
| Downside SD | 0.669 | ||||
| N nonnegative terms | 683.000 | ||||
| N negative terms | 714.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1397.000 | ||||
| Mean of predictor | 0.317 | ||||
| Mean of criterion | -0.164 | ||||
| SD of predictor | 0.486 | ||||
| SD of criterion | 0.914 | ||||
| Covariance | 0.245 | ||||
| r | 0.551 | ||||
| b (slope, estimate of beta) | 1.035 | ||||
| a (intercept, estimate of alpha) | -0.492 | ||||
| Mean Square Error | 0.582 | ||||
| DF error | 1395.000 | ||||
| t(b) | 24.659 | ||||
| p(b) | 0.168 | ||||
| t(a) | -1.488 | ||||
| p(a) | 0.525 | ||||
| Lowerbound of 95% confidence interval for beta | 0.953 | ||||
| Upperbound of 95% confidence interval for beta | 1.118 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.140 | ||||
| Upperbound of 95% confidence interval for alpha | 0.157 | ||||
| Treynor index (mean / b) | -0.158 | ||||
| Jensen alpha (a) | -0.492 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.089 | ||||
| Expected Shortfall on VaR | 0.110 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.051 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1397.000 | ||||
| Minimum | 0.454 | ||||
| Quartile 1 | 0.993 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.006 | ||||
| Maximum | 2.115 | ||||
| Mean of quarter 1 | 0.963 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.042 | ||||
| Inter Quartile Range | 0.013 | ||||
| Number outliers low | 116.000 | ||||
| Percentage of outliers low | 0.083 | ||||
| Mean of outliers low | 0.915 | ||||
| Number of outliers high | 115.000 | ||||
| Percentage of outliers high | 0.082 | ||||
| Mean of outliers high | 1.100 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.912 | ||||
| VaR(95%) (moments method) | 0.034 | ||||
| Expected Shortfall (moments method) | 0.411 | ||||
| Extreme Value Index (regression method) | 0.650 | ||||
| VaR(95%) (regression method) | 0.027 | ||||
| Expected Shortfall (regression method) | 0.084 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.427 | ||||
| Quartile 1 | 0.486 | ||||
| Median | 0.544 | ||||
| Quartile 3 | 0.603 | ||||
| Maximum | 0.662 | ||||
| Mean of quarter 1 | 0.427 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.662 | ||||
| Inter Quartile Range | 0.117 | ||||
| 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) | -0.088 | ||||
| Compounded annual return (geometric extrapolation) | -0.113 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.170 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.170 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.023 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.651 | ||||
| SD | 0.513 | ||||
| Sharpe ratio (Glass type estimate) | -1.270 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.262 | ||||
| df | 130.000 | ||||
| t | -0.898 | ||||
| p | 0.539 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.043 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.509 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.038 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.514 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.315 | ||||
| Upside Potential Ratio | 2.382 | ||||
| Upside part of mean | 1.179 | ||||
| Downside part of mean | -1.830 | ||||
| Upside SD | 0.132 | ||||
| Downside SD | 0.495 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 63.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.076 | ||||
| Mean of criterion | -0.651 | ||||
| SD of predictor | 0.436 | ||||
| SD of criterion | 0.513 | ||||
| Covariance | -0.002 | ||||
| r | -0.008 | ||||
| b (slope, estimate of beta) | -0.010 | ||||
| a (intercept, estimate of alpha) | -0.640 | ||||
| Mean Square Error | 0.265 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.095 | ||||
| p(b) | 0.505 | ||||
| t(a) | -0.870 | ||||
| p(a) | 0.549 | ||||
| Lowerbound of 95% confidence interval for beta | -0.214 | ||||
| Upperbound of 95% confidence interval for beta | 0.195 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.097 | ||||
| Upperbound of 95% confidence interval for alpha | 0.816 | ||||
| Treynor index (mean / b) | 66.230 | ||||
| Jensen alpha (a) | -0.640 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.816 | ||||
| SD | 0.610 | ||||
| Sharpe ratio (Glass type estimate) | -1.338 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.330 | ||||
| df | 130.000 | ||||
| t | -0.946 | ||||
| p | 0.541 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.112 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.441 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.107 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.446 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.370 | ||||
| Upside Potential Ratio | 1.966 | ||||
| Upside part of mean | 1.170 | ||||
| Downside part of mean | -1.986 | ||||
| Upside SD | 0.131 | ||||
| Downside SD | 0.595 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 63.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.979 | ||||
| Mean of criterion | -0.816 | ||||
| SD of predictor | 0.436 | ||||
| SD of criterion | 0.610 | ||||
| Covariance | -0.004 | ||||
| r | -0.015 | ||||
| b (slope, estimate of beta) | -0.021 | ||||
| a (intercept, estimate of alpha) | -0.795 | ||||
| Mean Square Error | 0.375 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.173 | ||||
| p(b) | 0.510 | ||||
| t(a) | -0.910 | ||||
| p(a) | 0.551 | ||||
| Lowerbound of 95% confidence interval for beta | -0.265 | ||||
| Upperbound of 95% confidence interval for beta | 0.222 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.524 | ||||
| Upperbound of 95% confidence interval for alpha | 0.934 | ||||
| Treynor index (mean / b) | 38.253 | ||||
| Jensen alpha (a) | -0.795 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.063 | ||||
| Expected Shortfall on VaR | 0.078 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.664 | ||||
| Quartile 1 | 0.993 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.007 | ||||
| Maximum | 1.031 | ||||
| Mean of quarter 1 | 0.975 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.014 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.868 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.008 | ||||
| Mean of outliers high | 1.031 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.629 | ||||
| VaR(95%) (moments method) | 0.022 | ||||
| Expected Shortfall (moments method) | 0.064 | ||||
| Extreme Value Index (regression method) | 0.543 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.032 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.018 | ||||
| Quartile 3 | 0.035 | ||||
| Maximum | 0.378 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.030 | ||||
| Mean of quarter 4 | 0.209 | ||||
| Inter Quartile Range | 0.029 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.378 | ||||
| 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) | -0.640 | ||||
| Compounded annual return (geometric extrapolation) | -0.538 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.423 | ||||
| Compounded annual return / average of 25% largest draw downs | -2.577 | ||||
| Compounded annual return / Expected Shortfall lognormal | -6.935 | ||||