Advanced Statistics: constantine
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 | 0.327 | ||||
| SD | 0.650 | ||||
| Sharpe ratio (Glass type estimate) | 0.503 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.497 | ||||
| df | 69.000 | ||||
| t | 1.215 | ||||
| p | 0.114 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.315 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.317 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.318 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.313 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.954 | ||||
| Upside Potential Ratio | 2.523 | ||||
| Upside part of mean | 0.865 | ||||
| Downside part of mean | -0.538 | ||||
| Upside SD | 0.555 | ||||
| Downside SD | 0.343 | ||||
| N nonnegative terms | 39.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.273 | ||||
| Mean of criterion | 0.327 | ||||
| SD of predictor | 0.276 | ||||
| SD of criterion | 0.650 | ||||
| Covariance | -0.067 | ||||
| r | -0.372 | ||||
| b (slope, estimate of beta) | -0.875 | ||||
| a (intercept, estimate of alpha) | 0.566 | ||||
| Mean Square Error | 0.370 | ||||
| DF error | 68.000 | ||||
| t(b) | -3.300 | ||||
| p(b) | 0.999 | ||||
| t(a) | 2.161 | ||||
| p(a) | 0.017 | ||||
| Lowerbound of 95% confidence interval for beta | -1.404 | ||||
| Upperbound of 95% confidence interval for beta | -0.346 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.043 | ||||
| Upperbound of 95% confidence interval for alpha | 1.089 | ||||
| Treynor index (mean / b) | -0.374 | ||||
| Jensen alpha (a) | 0.566 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.132 | ||||
| SD | 0.627 | ||||
| Sharpe ratio (Glass type estimate) | 0.211 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.208 | ||||
| df | 69.000 | ||||
| t | 0.509 | ||||
| p | 0.306 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.602 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.022 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.604 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.021 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.298 | ||||
| Upside Potential Ratio | 1.693 | ||||
| Upside part of mean | 0.750 | ||||
| Downside part of mean | -0.618 | ||||
| Upside SD | 0.439 | ||||
| Downside SD | 0.443 | ||||
| N nonnegative terms | 39.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.234 | ||||
| Mean of criterion | 0.132 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.627 | ||||
| Covariance | -0.062 | ||||
| r | -0.366 | ||||
| b (slope, estimate of beta) | -0.848 | ||||
| a (intercept, estimate of alpha) | 0.330 | ||||
| Mean Square Error | 0.346 | ||||
| DF error | 68.000 | ||||
| t(b) | -3.239 | ||||
| p(b) | 0.999 | ||||
| t(a) | 1.316 | ||||
| p(a) | 0.096 | ||||
| Lowerbound of 95% confidence interval for beta | -1.371 | ||||
| Upperbound of 95% confidence interval for beta | -0.326 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.171 | ||||
| Upperbound of 95% confidence interval for alpha | 0.831 | ||||
| Treynor index (mean / b) | -0.156 | ||||
| Jensen alpha (a) | 0.330 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.249 | ||||
| Expected Shortfall on VaR | 0.303 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.095 | ||||
| Expected Shortfall on VaR | 0.195 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 70.000 | ||||
| Minimum | 0.437 | ||||
| Quartile 1 | 0.942 | ||||
| Median | 1.026 | ||||
| Quartile 3 | 1.094 | ||||
| Maximum | 1.895 | ||||
| Mean of quarter 1 | 0.854 | ||||
| Mean of quarter 2 | 0.979 | ||||
| Mean of quarter 3 | 1.054 | ||||
| Mean of quarter 4 | 1.234 | ||||
| Inter Quartile Range | 0.152 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.562 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.572 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.491 | ||||
| VaR(95%) (moments method) | 0.162 | ||||
| Expected Shortfall (moments method) | 0.344 | ||||
| Extreme Value Index (regression method) | 0.661 | ||||
| VaR(95%) (regression method) | 0.168 | ||||
| Expected Shortfall (regression method) | 0.486 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.032 | ||||
| Quartile 1 | 0.132 | ||||
| Median | 0.179 | ||||
| Quartile 3 | 0.395 | ||||
| Maximum | 0.728 | ||||
| Mean of quarter 1 | 0.082 | ||||
| Mean of quarter 2 | 0.179 | ||||
| Mean of quarter 3 | 0.395 | ||||
| Mean of quarter 4 | 0.728 | ||||
| Inter Quartile Range | 0.263 | ||||
| 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) | 0.308 | ||||
| Compounded annual return (geometric extrapolation) | 0.193 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.265 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.265 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.637 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 3.669 | ||||
| SD | 4.035 | ||||
| Sharpe ratio (Glass type estimate) | 0.909 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.909 | ||||
| df | 1539.000 | ||||
| t | 2.205 | ||||
| p | 0.464 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.100 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.718 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.100 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.718 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.343 | ||||
| Upside Potential Ratio | 7.788 | ||||
| Upside part of mean | 8.547 | ||||
| Downside part of mean | -4.879 | ||||
| Upside SD | 3.888 | ||||
| Downside SD | 1.097 | ||||
| N nonnegative terms | 756.000 | ||||
| N negative terms | 784.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1540.000 | ||||
| Mean of predictor | 0.410 | ||||
| Mean of criterion | 3.669 | ||||
| SD of predictor | 0.574 | ||||
| SD of criterion | 4.035 | ||||
| Covariance | -0.871 | ||||
| r | -0.376 | ||||
| b (slope, estimate of beta) | -2.644 | ||||
| a (intercept, estimate of alpha) | 4.754 | ||||
| Mean Square Error | 13.983 | ||||
| DF error | 1538.000 | ||||
| t(b) | -15.921 | ||||
| p(b) | 0.688 | ||||
| t(a) | 3.079 | ||||
| p(a) | 0.461 | ||||
| Lowerbound of 95% confidence interval for beta | -2.969 | ||||
| Upperbound of 95% confidence interval for beta | -2.318 | ||||
| Lowerbound of 95% confidence interval for alpha | 1.725 | ||||
| Upperbound of 95% confidence interval for alpha | 7.782 | ||||
| Treynor index (mean / b) | -1.388 | ||||
| Jensen alpha (a) | 4.754 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.131 | ||||
| SD | 2.424 | ||||
| Sharpe ratio (Glass type estimate) | 0.054 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.054 | ||||
| df | 1539.000 | ||||
| t | 0.131 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.754 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.862 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.754 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.862 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.079 | ||||
| Upside Potential Ratio | 3.636 | ||||
| Upside part of mean | 6.023 | ||||
| Downside part of mean | -5.892 | ||||
| Upside SD | 1.768 | ||||
| Downside SD | 1.657 | ||||
| N nonnegative terms | 756.000 | ||||
| N negative terms | 784.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1540.000 | ||||
| Mean of predictor | 0.250 | ||||
| Mean of criterion | 0.131 | ||||
| SD of predictor | 0.565 | ||||
| SD of criterion | 2.424 | ||||
| Covariance | -0.641 | ||||
| r | -0.468 | ||||
| b (slope, estimate of beta) | -2.006 | ||||
| a (intercept, estimate of alpha) | 0.632 | ||||
| Mean Square Error | 4.591 | ||||
| DF error | 1538.000 | ||||
| t(b) | -20.767 | ||||
| p(b) | 0.734 | ||||
| t(a) | 0.715 | ||||
| p(a) | 0.491 | ||||
| Lowerbound of 95% confidence interval for beta | -2.196 | ||||
| Upperbound of 95% confidence interval for beta | -1.817 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.102 | ||||
| Upperbound of 95% confidence interval for alpha | 2.366 | ||||
| Treynor index (mean / b) | -0.065 | ||||
| Jensen alpha (a) | 0.632 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.218 | ||||
| Expected Shortfall on VaR | 0.264 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.096 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1540.000 | ||||
| Minimum | 0.130 | ||||
| Quartile 1 | 0.985 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.016 | ||||
| Maximum | 7.686 | ||||
| Mean of quarter 1 | 0.932 | ||||
| Mean of quarter 2 | 0.994 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.124 | ||||
| Inter Quartile Range | 0.031 | ||||
| Number outliers low | 76.000 | ||||
| Percentage of outliers low | 0.049 | ||||
| Mean of outliers low | 0.773 | ||||
| Number of outliers high | 79.000 | ||||
| Percentage of outliers high | 0.051 | ||||
| Mean of outliers high | 1.477 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.849 | ||||
| VaR(95%) (moments method) | 0.063 | ||||
| Expected Shortfall (moments method) | 0.431 | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 16.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.061 | ||||
| Median | 0.130 | ||||
| Quartile 3 | 0.312 | ||||
| Maximum | 0.879 | ||||
| Mean of quarter 1 | 0.028 | ||||
| Mean of quarter 2 | 0.108 | ||||
| Mean of quarter 3 | 0.213 | ||||
| Mean of quarter 4 | 0.722 | ||||
| Inter Quartile Range | 0.251 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.188 | ||||
| Mean of outliers high | 0.808 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -38.496 | ||||
| VaR(95%) (moments method) | 0.728 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -1.623 | ||||
| VaR(95%) (regression method) | 0.758 | ||||
| Expected Shortfall (regression method) | 0.774 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.305 | ||||
| Compounded annual return (geometric extrapolation) | 0.191 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.217 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.264 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.723 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.013 | ||||
| SD | 0.305 | ||||
| Sharpe ratio (Glass type estimate) | 0.042 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.042 | ||||
| df | 130.000 | ||||
| t | 0.030 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.730 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.814 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.730 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.814 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.061 | ||||
| Upside Potential Ratio | 8.257 | ||||
| Upside part of mean | 1.734 | ||||
| Downside part of mean | -1.721 | ||||
| Upside SD | 0.219 | ||||
| Downside SD | 0.210 | ||||
| N nonnegative terms | 61.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.967 | ||||
| Mean of criterion | 0.013 | ||||
| SD of predictor | 0.431 | ||||
| SD of criterion | 0.305 | ||||
| Covariance | -0.054 | ||||
| r | -0.410 | ||||
| b (slope, estimate of beta) | -0.290 | ||||
| a (intercept, estimate of alpha) | 0.293 | ||||
| Mean Square Error | 0.078 | ||||
| DF error | 129.000 | ||||
| t(b) | -5.104 | ||||
| p(b) | 0.753 | ||||
| t(a) | 0.735 | ||||
| p(a) | 0.459 | ||||
| Lowerbound of 95% confidence interval for beta | -0.402 | ||||
| Upperbound of 95% confidence interval for beta | -0.177 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.495 | ||||
| Upperbound of 95% confidence interval for alpha | 1.081 | ||||
| Treynor index (mean / b) | -0.044 | ||||
| Jensen alpha (a) | 0.293 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.033 | ||||
| SD | 0.304 | ||||
| Sharpe ratio (Glass type estimate) | -0.109 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.108 | ||||
| df | 130.000 | ||||
| t | -0.077 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.881 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.663 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.880 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.664 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.155 | ||||
| Upside Potential Ratio | 7.998 | ||||
| Upside part of mean | 1.710 | ||||
| Downside part of mean | -1.743 | ||||
| Upside SD | 0.215 | ||||
| Downside SD | 0.214 | ||||
| N nonnegative terms | 61.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.872 | ||||
| Mean of criterion | -0.033 | ||||
| SD of predictor | 0.432 | ||||
| SD of criterion | 0.304 | ||||
| Covariance | -0.054 | ||||
| r | -0.411 | ||||
| b (slope, estimate of beta) | -0.290 | ||||
| a (intercept, estimate of alpha) | 0.220 | ||||
| Mean Square Error | 0.078 | ||||
| DF error | 129.000 | ||||
| t(b) | -5.124 | ||||
| p(b) | 0.754 | ||||
| t(a) | 0.553 | ||||
| p(a) | 0.469 | ||||
| Lowerbound of 95% confidence interval for beta | -0.402 | ||||
| Upperbound of 95% confidence interval for beta | -0.178 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.566 | ||||
| Upperbound of 95% confidence interval for alpha | 1.005 | ||||
| Treynor index (mean / b) | 0.114 | ||||
| Jensen alpha (a) | 0.220 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.939 | ||||
| Quartile 1 | 0.990 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.008 | ||||
| Maximum | 1.056 | ||||
| Mean of quarter 1 | 0.978 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.024 | ||||
| Inter Quartile Range | 0.019 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.947 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.038 | ||||
| Mean of outliers high | 1.049 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.081 | ||||
| VaR(95%) (moments method) | 0.022 | ||||
| Expected Shortfall (moments method) | 0.031 | ||||
| Extreme Value Index (regression method) | 0.152 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.029 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.022 | ||||
| Median | 0.028 | ||||
| Quartile 3 | 0.037 | ||||
| Maximum | 0.229 | ||||
| Mean of quarter 1 | 0.018 | ||||
| Mean of quarter 2 | 0.028 | ||||
| Mean of quarter 3 | 0.037 | ||||
| Mean of quarter 4 | 0.229 | ||||
| Inter Quartile Range | 0.016 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.229 | ||||
| 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) | 0.011 | ||||
| Compounded annual return (geometric extrapolation) | 0.011 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.048 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.048 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.286 | ||||