Advanced Statistics: Maxie
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 | 0.002 | ||||
| SD | 0.159 | ||||
| Sharpe ratio (Glass type estimate) | 0.015 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.015 | ||||
| df | 58.000 | ||||
| t | 0.033 | ||||
| p | 0.487 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.869 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.899 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.869 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.899 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.020 | ||||
| Upside Potential Ratio | 1.644 | ||||
| Upside part of mean | 0.194 | ||||
| Downside part of mean | -0.191 | ||||
| Upside SD | 0.105 | ||||
| Downside SD | 0.118 | ||||
| N nonnegative terms | 30.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 59.000 | ||||
| Mean of predictor | 0.404 | ||||
| Mean of criterion | 0.002 | ||||
| SD of predictor | 0.231 | ||||
| SD of criterion | 0.159 | ||||
| Covariance | -0.008 | ||||
| r | -0.208 | ||||
| b (slope, estimate of beta) | -0.143 | ||||
| a (intercept, estimate of alpha) | 0.060 | ||||
| Mean Square Error | 0.025 | ||||
| DF error | 57.000 | ||||
| t(b) | -1.603 | ||||
| p(b) | 0.943 | ||||
| t(a) | 0.756 | ||||
| p(a) | 0.226 | ||||
| Lowerbound of 95% confidence interval for beta | -0.322 | ||||
| Upperbound of 95% confidence interval for beta | 0.036 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | 0.219 | ||||
| Treynor index (mean / b) | -0.017 | ||||
| Jensen alpha (a) | 0.060 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.010 | ||||
| SD | 0.162 | ||||
| Sharpe ratio (Glass type estimate) | -0.064 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.063 | ||||
| df | 58.000 | ||||
| t | -0.141 | ||||
| p | 0.556 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.948 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.820 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.947 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.821 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.082 | ||||
| Upside Potential Ratio | 1.493 | ||||
| Upside part of mean | 0.188 | ||||
| Downside part of mean | -0.198 | ||||
| Upside SD | 0.100 | ||||
| Downside SD | 0.126 | ||||
| N nonnegative terms | 30.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 59.000 | ||||
| Mean of predictor | 0.371 | ||||
| Mean of criterion | -0.010 | ||||
| SD of predictor | 0.223 | ||||
| SD of criterion | 0.162 | ||||
| Covariance | -0.007 | ||||
| r | -0.205 | ||||
| b (slope, estimate of beta) | -0.149 | ||||
| a (intercept, estimate of alpha) | 0.045 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 57.000 | ||||
| t(b) | -1.583 | ||||
| p(b) | 0.941 | ||||
| t(a) | 0.561 | ||||
| p(a) | 0.289 | ||||
| Lowerbound of 95% confidence interval for beta | -0.338 | ||||
| Upperbound of 95% confidence interval for beta | 0.040 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.116 | ||||
| Upperbound of 95% confidence interval for alpha | 0.206 | ||||
| Treynor index (mean / b) | 0.069 | ||||
| Jensen alpha (a) | 0.045 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.075 | ||||
| Expected Shortfall on VaR | 0.093 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.072 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 59.000 | ||||
| Minimum | 0.814 | ||||
| Quartile 1 | 0.979 | ||||
| Median | 1.004 | ||||
| Quartile 3 | 1.032 | ||||
| Maximum | 1.155 | ||||
| Mean of quarter 1 | 0.951 | ||||
| Mean of quarter 2 | 0.994 | ||||
| Mean of quarter 3 | 1.018 | ||||
| Mean of quarter 4 | 1.054 | ||||
| Inter Quartile Range | 0.053 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.017 | ||||
| Mean of outliers low | 0.814 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.017 | ||||
| Mean of outliers high | 1.155 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.478 | ||||
| VaR(95%) (moments method) | 0.056 | ||||
| Expected Shortfall (moments method) | 0.113 | ||||
| Extreme Value Index (regression method) | 0.745 | ||||
| VaR(95%) (regression method) | 0.052 | ||||
| Expected Shortfall (regression method) | 0.174 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.282 | ||||
| Quartile 1 | 0.282 | ||||
| Median | 0.282 | ||||
| Quartile 3 | 0.282 | ||||
| Maximum | 0.282 | ||||
| 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) | 0.037 | ||||
| Compounded annual return (geometric extrapolation) | 0.034 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.121 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.369 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.010 | ||||
| SD | 0.259 | ||||
| Sharpe ratio (Glass type estimate) | 0.037 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.037 | ||||
| df | 1300.000 | ||||
| t | 0.082 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.843 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.916 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.843 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.916 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.054 | ||||
| Upside Potential Ratio | 5.698 | ||||
| Upside part of mean | 0.995 | ||||
| Downside part of mean | -0.985 | ||||
| Upside SD | 0.191 | ||||
| Downside SD | 0.175 | ||||
| N nonnegative terms | 646.000 | ||||
| N negative terms | 655.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1301.000 | ||||
| Mean of predictor | 0.454 | ||||
| Mean of criterion | 0.010 | ||||
| SD of predictor | 0.354 | ||||
| SD of criterion | 0.259 | ||||
| Covariance | -0.006 | ||||
| r | -0.071 | ||||
| b (slope, estimate of beta) | -0.052 | ||||
| a (intercept, estimate of alpha) | 0.033 | ||||
| Mean Square Error | 0.067 | ||||
| DF error | 1299.000 | ||||
| t(b) | -2.559 | ||||
| p(b) | 0.545 | ||||
| t(a) | 0.284 | ||||
| p(a) | 0.495 | ||||
| Lowerbound of 95% confidence interval for beta | -0.091 | ||||
| Upperbound of 95% confidence interval for beta | -0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.195 | ||||
| Upperbound of 95% confidence interval for alpha | 0.261 | ||||
| Treynor index (mean / b) | -0.184 | ||||
| Jensen alpha (a) | 0.033 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.024 | ||||
| SD | 0.258 | ||||
| Sharpe ratio (Glass type estimate) | -0.092 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.092 | ||||
| df | 1300.000 | ||||
| t | -0.205 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.972 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.787 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.972 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.787 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.130 | ||||
| Upside Potential Ratio | 5.363 | ||||
| Upside part of mean | 0.978 | ||||
| Downside part of mean | -1.001 | ||||
| Upside SD | 0.182 | ||||
| Downside SD | 0.182 | ||||
| N nonnegative terms | 646.000 | ||||
| N negative terms | 655.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1301.000 | ||||
| Mean of predictor | 0.389 | ||||
| Mean of criterion | -0.024 | ||||
| SD of predictor | 0.363 | ||||
| SD of criterion | 0.258 | ||||
| Covariance | -0.006 | ||||
| r | -0.064 | ||||
| b (slope, estimate of beta) | -0.045 | ||||
| a (intercept, estimate of alpha) | -0.006 | ||||
| Mean Square Error | 0.066 | ||||
| DF error | 1299.000 | ||||
| t(b) | -2.296 | ||||
| p(b) | 0.540 | ||||
| t(a) | -0.054 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | -0.084 | ||||
| Upperbound of 95% confidence interval for beta | -0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.233 | ||||
| Upperbound of 95% confidence interval for alpha | 0.221 | ||||
| Treynor index (mean / b) | 0.527 | ||||
| Jensen alpha (a) | -0.006 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.032 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.019 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1301.000 | ||||
| Minimum | 0.830 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.004 | ||||
| Maximum | 1.192 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.014 | ||||
| Inter Quartile Range | 0.008 | ||||
| Number outliers low | 73.000 | ||||
| Percentage of outliers low | 0.056 | ||||
| Mean of outliers low | 0.966 | ||||
| Number of outliers high | 68.000 | ||||
| Percentage of outliers high | 0.052 | ||||
| Mean of outliers high | 1.036 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.607 | ||||
| VaR(95%) (moments method) | 0.013 | ||||
| Expected Shortfall (moments method) | 0.036 | ||||
| Extreme Value Index (regression method) | 0.473 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.023 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.020 | ||||
| Median | 0.057 | ||||
| Quartile 3 | 0.117 | ||||
| Maximum | 0.309 | ||||
| Mean of quarter 1 | 0.012 | ||||
| Mean of quarter 2 | 0.027 | ||||
| Mean of quarter 3 | 0.080 | ||||
| Mean of quarter 4 | 0.269 | ||||
| Inter Quartile Range | 0.097 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.309 | ||||
| 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) | 0.021 | ||||
| Compounded annual return (geometric extrapolation) | 0.020 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.066 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.076 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.632 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.398 | ||||
| SD | 0.198 | ||||
| Sharpe ratio (Glass type estimate) | 2.011 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.999 | ||||
| df | 130.000 | ||||
| t | 1.422 | ||||
| p | 0.438 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.775 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.790 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.783 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.782 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.960 | ||||
| Upside Potential Ratio | 9.777 | ||||
| Upside part of mean | 1.315 | ||||
| Downside part of mean | -0.917 | ||||
| Upside SD | 0.146 | ||||
| Downside SD | 0.135 | ||||
| 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 | 1.086 | ||||
| Mean of criterion | 0.398 | ||||
| SD of predictor | 0.321 | ||||
| SD of criterion | 0.198 | ||||
| Covariance | 0.013 | ||||
| r | 0.197 | ||||
| b (slope, estimate of beta) | 0.121 | ||||
| a (intercept, estimate of alpha) | 0.267 | ||||
| Mean Square Error | 0.038 | ||||
| DF error | 129.000 | ||||
| t(b) | 2.277 | ||||
| p(b) | 0.376 | ||||
| t(a) | 0.947 | ||||
| p(a) | 0.447 | ||||
| Lowerbound of 95% confidence interval for beta | 0.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.226 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.290 | ||||
| Upperbound of 95% confidence interval for alpha | 0.824 | ||||
| Treynor index (mean / b) | 3.288 | ||||
| Jensen alpha (a) | 0.267 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.378 | ||||
| SD | 0.198 | ||||
| Sharpe ratio (Glass type estimate) | 1.908 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.897 | ||||
| df | 130.000 | ||||
| t | 1.349 | ||||
| p | 0.441 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.877 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.686 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.884 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.679 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.774 | ||||
| Upside Potential Ratio | 9.562 | ||||
| Upside part of mean | 1.304 | ||||
| Downside part of mean | -0.926 | ||||
| Upside SD | 0.145 | ||||
| Downside SD | 0.136 | ||||
| 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 | 1.032 | ||||
| Mean of criterion | 0.378 | ||||
| SD of predictor | 0.322 | ||||
| SD of criterion | 0.198 | ||||
| Covariance | 0.013 | ||||
| r | 0.197 | ||||
| b (slope, estimate of beta) | 0.121 | ||||
| a (intercept, estimate of alpha) | 0.253 | ||||
| Mean Square Error | 0.038 | ||||
| DF error | 129.000 | ||||
| t(b) | 2.278 | ||||
| p(b) | 0.376 | ||||
| t(a) | 0.900 | ||||
| p(a) | 0.450 | ||||
| Lowerbound of 95% confidence interval for beta | 0.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.226 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.303 | ||||
| Upperbound of 95% confidence interval for alpha | 0.810 | ||||
| Treynor index (mean / b) | 3.124 | ||||
| Jensen alpha (a) | 0.253 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.963 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.008 | ||||
| Maximum | 1.037 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.012 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.038 | ||||
| Mean of outliers low | 0.966 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.034 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.484 | ||||
| VaR(95%) (moments method) | 0.013 | ||||
| Expected Shortfall (moments method) | 0.029 | ||||
| Extreme Value Index (regression method) | -0.040 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.015 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 17.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.009 | ||||
| Quartile 3 | 0.024 | ||||
| Maximum | 0.080 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.018 | ||||
| Mean of quarter 4 | 0.042 | ||||
| Inter Quartile Range | 0.020 | ||||
| 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 | 0.059 | ||||
| Mean of outliers high | 0.080 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.435 | ||||
| VaR(95%) (moments method) | 0.048 | ||||
| Expected Shortfall (moments method) | 0.086 | ||||
| Extreme Value Index (regression method) | 1.397 | ||||
| VaR(95%) (regression method) | 0.055 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.470 | ||||
| Compounded annual return (geometric extrapolation) | 0.526 | ||||
| Calmar ratio (compounded annual return / max draw down) | 6.600 | ||||
| Compounded annual return / average of 25% largest draw downs | 12.501 | ||||
| Compounded annual return / Expected Shortfall lognormal | 22.336 | ||||