Advanced Statistics: mbtrader
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 | 0.162 | ||||
| SD | 0.374 | ||||
| Sharpe ratio (Glass type estimate) | 0.433 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.428 | ||||
| df | 67.000 | ||||
| t | 1.030 | ||||
| p | 0.153 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.396 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.258 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.399 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.254 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.623 | ||||
| Upside Potential Ratio | 1.930 | ||||
| Upside part of mean | 0.502 | ||||
| Downside part of mean | -0.340 | ||||
| Upside SD | 0.269 | ||||
| Downside SD | 0.260 | ||||
| N nonnegative terms | 41.000 | ||||
| N negative terms | 27.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.235 | ||||
| Mean of criterion | 0.162 | ||||
| SD of predictor | 0.309 | ||||
| SD of criterion | 0.374 | ||||
| Covariance | 0.052 | ||||
| r | 0.446 | ||||
| b (slope, estimate of beta) | 0.540 | ||||
| a (intercept, estimate of alpha) | 0.035 | ||||
| Mean Square Error | 0.114 | ||||
| DF error | 66.000 | ||||
| t(b) | 4.043 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.240 | ||||
| p(a) | 0.405 | ||||
| Lowerbound of 95% confidence interval for beta | 0.273 | ||||
| Upperbound of 95% confidence interval for beta | 0.806 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.255 | ||||
| Upperbound of 95% confidence interval for alpha | 0.325 | ||||
| Treynor index (mean / b) | 0.300 | ||||
| Jensen alpha (a) | 0.035 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.086 | ||||
| SD | 0.405 | ||||
| Sharpe ratio (Glass type estimate) | 0.211 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.209 | ||||
| df | 67.000 | ||||
| t | 0.503 | ||||
| p | 0.308 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.613 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.035 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.615 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.033 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.265 | ||||
| Upside Potential Ratio | 1.453 | ||||
| Upside part of mean | 0.469 | ||||
| Downside part of mean | -0.384 | ||||
| Upside SD | 0.240 | ||||
| Downside SD | 0.323 | ||||
| N nonnegative terms | 41.000 | ||||
| N negative terms | 27.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.188 | ||||
| Mean of criterion | 0.086 | ||||
| SD of predictor | 0.300 | ||||
| SD of criterion | 0.405 | ||||
| Covariance | 0.050 | ||||
| r | 0.413 | ||||
| b (slope, estimate of beta) | 0.557 | ||||
| a (intercept, estimate of alpha) | -0.019 | ||||
| Mean Square Error | 0.138 | ||||
| DF error | 66.000 | ||||
| t(b) | 3.680 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.120 | ||||
| p(a) | 0.547 | ||||
| Lowerbound of 95% confidence interval for beta | 0.255 | ||||
| Upperbound of 95% confidence interval for beta | 0.859 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.336 | ||||
| Upperbound of 95% confidence interval for alpha | 0.298 | ||||
| Treynor index (mean / b) | 0.154 | ||||
| Jensen alpha (a) | -0.019 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.169 | ||||
| Expected Shortfall on VaR | 0.208 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.054 | ||||
| Expected Shortfall on VaR | 0.122 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 68.000 | ||||
| Minimum | 0.532 | ||||
| Quartile 1 | 0.980 | ||||
| Median | 1.023 | ||||
| Quartile 3 | 1.069 | ||||
| Maximum | 1.437 | ||||
| Mean of quarter 1 | 0.896 | ||||
| Mean of quarter 2 | 1.003 | ||||
| Mean of quarter 3 | 1.043 | ||||
| Mean of quarter 4 | 1.126 | ||||
| Inter Quartile Range | 0.089 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.656 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.029 | ||||
| Mean of outliers high | 1.327 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.425 | ||||
| VaR(95%) (moments method) | 0.084 | ||||
| Expected Shortfall (moments method) | 0.179 | ||||
| Extreme Value Index (regression method) | 0.359 | ||||
| VaR(95%) (regression method) | 0.124 | ||||
| Expected Shortfall (regression method) | 0.253 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.047 | ||||
| Quartile 1 | 0.115 | ||||
| Median | 0.174 | ||||
| Quartile 3 | 0.317 | ||||
| Maximum | 0.468 | ||||
| Mean of quarter 1 | 0.079 | ||||
| Mean of quarter 2 | 0.127 | ||||
| Mean of quarter 3 | 0.220 | ||||
| Mean of quarter 4 | 0.409 | ||||
| Inter Quartile Range | 0.203 | ||||
| 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) | 0.191 | ||||
| Compounded annual return (geometric extrapolation) | 0.138 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.295 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.338 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.666 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.260 | ||||
| SD | 0.571 | ||||
| Sharpe ratio (Glass type estimate) | 0.456 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.456 | ||||
| df | 1498.000 | ||||
| t | 1.090 | ||||
| p | 0.486 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.364 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.275 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.364 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.275 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.683 | ||||
| Upside Potential Ratio | 7.078 | ||||
| Upside part of mean | 2.700 | ||||
| Downside part of mean | -2.440 | ||||
| Upside SD | 0.425 | ||||
| Downside SD | 0.381 | ||||
| N nonnegative terms | 777.000 | ||||
| N negative terms | 722.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1499.000 | ||||
| Mean of predictor | 0.468 | ||||
| Mean of criterion | 0.260 | ||||
| SD of predictor | 0.650 | ||||
| SD of criterion | 0.571 | ||||
| Covariance | 0.242 | ||||
| r | 0.651 | ||||
| b (slope, estimate of beta) | 0.573 | ||||
| a (intercept, estimate of alpha) | -0.008 | ||||
| Mean Square Error | 0.188 | ||||
| DF error | 1497.000 | ||||
| t(b) | 33.217 | ||||
| p(b) | 0.117 | ||||
| t(a) | -0.042 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | 0.539 | ||||
| Upperbound of 95% confidence interval for beta | 0.606 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.364 | ||||
| Upperbound of 95% confidence interval for alpha | 0.348 | ||||
| Treynor index (mean / b) | 0.455 | ||||
| Jensen alpha (a) | -0.008 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.098 | ||||
| SD | 0.572 | ||||
| Sharpe ratio (Glass type estimate) | 0.171 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.171 | ||||
| df | 1498.000 | ||||
| t | 0.408 | ||||
| p | 0.495 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.649 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.990 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.649 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.990 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.234 | ||||
| Upside Potential Ratio | 6.284 | ||||
| Upside part of mean | 2.619 | ||||
| Downside part of mean | -2.521 | ||||
| Upside SD | 0.392 | ||||
| Downside SD | 0.417 | ||||
| N nonnegative terms | 777.000 | ||||
| N negative terms | 722.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1499.000 | ||||
| Mean of predictor | 0.275 | ||||
| Mean of criterion | 0.098 | ||||
| SD of predictor | 0.612 | ||||
| SD of criterion | 0.572 | ||||
| Covariance | 0.217 | ||||
| r | 0.618 | ||||
| b (slope, estimate of beta) | 0.578 | ||||
| a (intercept, estimate of alpha) | -0.061 | ||||
| Mean Square Error | 0.203 | ||||
| DF error | 1497.000 | ||||
| t(b) | 30.422 | ||||
| p(b) | 0.133 | ||||
| t(a) | -0.325 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | 0.541 | ||||
| Upperbound of 95% confidence interval for beta | 0.615 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.430 | ||||
| Upperbound of 95% confidence interval for alpha | 0.308 | ||||
| Treynor index (mean / b) | 0.169 | ||||
| Jensen alpha (a) | -0.061 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.056 | ||||
| Expected Shortfall on VaR | 0.070 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.044 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1499.000 | ||||
| Minimum | 0.618 | ||||
| Quartile 1 | 0.990 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.013 | ||||
| Maximum | 1.464 | ||||
| Mean of quarter 1 | 0.967 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.036 | ||||
| Inter Quartile Range | 0.023 | ||||
| Number outliers low | 71.000 | ||||
| Percentage of outliers low | 0.047 | ||||
| Mean of outliers low | 0.919 | ||||
| Number of outliers high | 59.000 | ||||
| Percentage of outliers high | 0.039 | ||||
| Mean of outliers high | 1.095 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.458 | ||||
| VaR(95%) (moments method) | 0.032 | ||||
| Expected Shortfall (moments method) | 0.068 | ||||
| Extreme Value Index (regression method) | 0.350 | ||||
| VaR(95%) (regression method) | 0.028 | ||||
| Expected Shortfall (regression method) | 0.050 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 41.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.024 | ||||
| Quartile 3 | 0.060 | ||||
| Maximum | 0.510 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.015 | ||||
| Mean of quarter 3 | 0.036 | ||||
| Mean of quarter 4 | 0.218 | ||||
| Inter Quartile Range | 0.050 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.146 | ||||
| Mean of outliers high | 0.289 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.138 | ||||
| VaR(95%) (moments method) | 0.169 | ||||
| Expected Shortfall (moments method) | 0.223 | ||||
| Extreme Value Index (regression method) | 0.460 | ||||
| VaR(95%) (regression method) | 0.228 | ||||
| Expected Shortfall (regression method) | 0.496 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.218 | ||||
| Compounded annual return (geometric extrapolation) | 0.152 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.299 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.698 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.177 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.363 | ||||
| SD | 0.790 | ||||
| Sharpe ratio (Glass type estimate) | -0.460 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.457 | ||||
| df | 130.000 | ||||
| t | -0.325 | ||||
| p | 0.514 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.231 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.313 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.230 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.315 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.535 | ||||
| Upside Potential Ratio | 4.414 | ||||
| Upside part of mean | 2.999 | ||||
| Downside part of mean | -3.363 | ||||
| Upside SD | 0.398 | ||||
| Downside SD | 0.680 | ||||
| N nonnegative terms | 75.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.955 | ||||
| Mean of criterion | -0.363 | ||||
| SD of predictor | 0.624 | ||||
| SD of criterion | 0.790 | ||||
| Covariance | 0.054 | ||||
| r | 0.109 | ||||
| b (slope, estimate of beta) | 0.138 | ||||
| a (intercept, estimate of alpha) | -0.634 | ||||
| Mean Square Error | 0.622 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.247 | ||||
| p(b) | 0.431 | ||||
| t(a) | -0.558 | ||||
| p(a) | 0.531 | ||||
| Lowerbound of 95% confidence interval for beta | -0.081 | ||||
| Upperbound of 95% confidence interval for beta | 0.358 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.881 | ||||
| Upperbound of 95% confidence interval for alpha | 1.614 | ||||
| Treynor index (mean / b) | -2.628 | ||||
| Jensen alpha (a) | -0.634 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.728 | ||||
| SD | 0.896 | ||||
| Sharpe ratio (Glass type estimate) | -0.813 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.808 | ||||
| df | 130.000 | ||||
| t | -0.575 | ||||
| p | 0.525 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.585 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.962 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.581 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.966 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.901 | ||||
| Upside Potential Ratio | 3.617 | ||||
| Upside part of mean | 2.924 | ||||
| Downside part of mean | -3.652 | ||||
| Upside SD | 0.381 | ||||
| Downside SD | 0.809 | ||||
| N nonnegative terms | 75.000 | ||||
| N negative terms | 56.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.754 | ||||
| Mean of criterion | -0.728 | ||||
| SD of predictor | 0.629 | ||||
| SD of criterion | 0.896 | ||||
| Covariance | 0.045 | ||||
| r | 0.080 | ||||
| b (slope, estimate of beta) | 0.114 | ||||
| a (intercept, estimate of alpha) | -0.928 | ||||
| Mean Square Error | 0.804 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.911 | ||||
| p(b) | 0.449 | ||||
| t(a) | -0.721 | ||||
| p(a) | 0.540 | ||||
| Lowerbound of 95% confidence interval for beta | -0.134 | ||||
| Upperbound of 95% confidence interval for beta | 0.361 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.474 | ||||
| Upperbound of 95% confidence interval for alpha | 1.618 | ||||
| Treynor index (mean / b) | -6.394 | ||||
| Jensen alpha (a) | -0.928 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.090 | ||||
| Expected Shortfall on VaR | 0.110 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.059 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.618 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.003 | ||||
| Quartile 3 | 1.013 | ||||
| Maximum | 1.164 | ||||
| Mean of quarter 1 | 0.952 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.038 | ||||
| Inter Quartile Range | 0.022 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.069 | ||||
| Mean of outliers low | 0.881 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.053 | ||||
| Mean of outliers high | 1.083 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.560 | ||||
| VaR(95%) (moments method) | 0.038 | ||||
| Expected Shortfall (moments method) | 0.101 | ||||
| Extreme Value Index (regression method) | 0.762 | ||||
| VaR(95%) (regression method) | 0.046 | ||||
| Expected Shortfall (regression method) | 0.212 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.030 | ||||
| Median | 0.098 | ||||
| Quartile 3 | 0.138 | ||||
| Maximum | 0.510 | ||||
| Mean of quarter 1 | 0.011 | ||||
| Mean of quarter 2 | 0.060 | ||||
| Mean of quarter 3 | 0.135 | ||||
| Mean of quarter 4 | 0.325 | ||||
| Inter Quartile Range | 0.108 | ||||
| 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 | 0.510 | ||||
| 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) | -0.579 | ||||
| Compounded annual return (geometric extrapolation) | -0.495 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.972 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.527 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.496 | ||||