Advanced Statistics: test
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.208 | ||||
| SD | 0.404 | ||||
| Sharpe ratio (Glass type estimate) | 0.514 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.503 | ||||
| df | 33.000 | ||||
| t | 0.866 | ||||
| p | 0.196 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.660 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.682 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.668 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.673 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.999 | ||||
| Upside Potential Ratio | 3.027 | ||||
| Upside part of mean | 0.630 | ||||
| Downside part of mean | -0.422 | ||||
| Upside SD | 0.344 | ||||
| Downside SD | 0.208 | ||||
| N nonnegative terms | 16.000 | ||||
| N negative terms | 18.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.614 | ||||
| Mean of criterion | 0.208 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.404 | ||||
| Covariance | 0.048 | ||||
| r | 0.401 | ||||
| b (slope, estimate of beta) | 0.542 | ||||
| a (intercept, estimate of alpha) | -0.125 | ||||
| Mean Square Error | 0.141 | ||||
| DF error | 32.000 | ||||
| t(b) | 2.478 | ||||
| p(b) | 0.009 | ||||
| t(a) | -0.479 | ||||
| p(a) | 0.682 | ||||
| Lowerbound of 95% confidence interval for beta | 0.096 | ||||
| Upperbound of 95% confidence interval for beta | 0.987 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.655 | ||||
| Upperbound of 95% confidence interval for alpha | 0.406 | ||||
| Treynor index (mean / b) | 0.383 | ||||
| Jensen alpha (a) | -0.125 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.132 | ||||
| SD | 0.385 | ||||
| Sharpe ratio (Glass type estimate) | 0.344 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.336 | ||||
| df | 33.000 | ||||
| t | 0.579 | ||||
| p | 0.283 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.826 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.509 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.831 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.503 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.594 | ||||
| Upside Potential Ratio | 2.591 | ||||
| Upside part of mean | 0.577 | ||||
| Downside part of mean | -0.444 | ||||
| Upside SD | 0.309 | ||||
| Downside SD | 0.223 | ||||
| N nonnegative terms | 16.000 | ||||
| N negative terms | 18.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.558 | ||||
| Mean of criterion | 0.132 | ||||
| SD of predictor | 0.281 | ||||
| SD of criterion | 0.385 | ||||
| Covariance | 0.041 | ||||
| r | 0.384 | ||||
| b (slope, estimate of beta) | 0.525 | ||||
| a (intercept, estimate of alpha) | -0.161 | ||||
| Mean Square Error | 0.130 | ||||
| DF error | 32.000 | ||||
| t(b) | 2.350 | ||||
| p(b) | 0.013 | ||||
| t(a) | -0.649 | ||||
| p(a) | 0.739 | ||||
| Lowerbound of 95% confidence interval for beta | 0.070 | ||||
| Upperbound of 95% confidence interval for beta | 0.981 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.666 | ||||
| Upperbound of 95% confidence interval for alpha | 0.344 | ||||
| Treynor index (mean / b) | 0.252 | ||||
| Jensen alpha (a) | -0.161 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.158 | ||||
| Expected Shortfall on VaR | 0.195 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.085 | ||||
| Expected Shortfall on VaR | 0.147 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.808 | ||||
| Quartile 1 | 0.947 | ||||
| Median | 0.999 | ||||
| Quartile 3 | 1.096 | ||||
| Maximum | 1.325 | ||||
| Mean of quarter 1 | 0.900 | ||||
| Mean of quarter 2 | 0.971 | ||||
| Mean of quarter 3 | 1.031 | ||||
| Mean of quarter 4 | 1.178 | ||||
| Inter Quartile Range | 0.148 | ||||
| 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 | 0.029 | ||||
| Mean of outliers high | 1.325 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.262 | ||||
| VaR(95%) (moments method) | 0.105 | ||||
| Expected Shortfall (moments method) | 0.127 | ||||
| Extreme Value Index (regression method) | 0.025 | ||||
| VaR(95%) (regression method) | 0.132 | ||||
| Expected Shortfall (regression method) | 0.182 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.072 | ||||
| Quartile 1 | 0.078 | ||||
| Median | 0.084 | ||||
| Quartile 3 | 0.209 | ||||
| Maximum | 0.334 | ||||
| Mean of quarter 1 | 0.072 | ||||
| Mean of quarter 2 | 0.084 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.334 | ||||
| Inter Quartile Range | 0.131 | ||||
| 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) | 0.229 | ||||
| Compounded annual return (geometric extrapolation) | 0.193 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.576 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.576 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.988 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.355 | ||||
| SD | 0.518 | ||||
| Sharpe ratio (Glass type estimate) | 0.685 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.684 | ||||
| df | 743.000 | ||||
| t | 1.154 | ||||
| p | 0.124 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.479 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.848 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.479 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.848 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.059 | ||||
| Upside Potential Ratio | 8.774 | ||||
| Upside part of mean | 2.940 | ||||
| Downside part of mean | -2.585 | ||||
| Upside SD | 0.395 | ||||
| Downside SD | 0.335 | ||||
| N nonnegative terms | 368.000 | ||||
| N negative terms | 376.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 744.000 | ||||
| Mean of predictor | 0.619 | ||||
| Mean of criterion | 0.355 | ||||
| SD of predictor | 0.321 | ||||
| SD of criterion | 0.518 | ||||
| Covariance | 0.076 | ||||
| r | 0.458 | ||||
| b (slope, estimate of beta) | 0.740 | ||||
| a (intercept, estimate of alpha) | -0.103 | ||||
| Mean Square Error | 0.212 | ||||
| DF error | 742.000 | ||||
| t(b) | 14.023 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.374 | ||||
| p(a) | 0.646 | ||||
| Lowerbound of 95% confidence interval for beta | 0.636 | ||||
| Upperbound of 95% confidence interval for beta | 0.843 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.644 | ||||
| Upperbound of 95% confidence interval for alpha | 0.438 | ||||
| Treynor index (mean / b) | 0.480 | ||||
| Jensen alpha (a) | -0.103 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.223 | ||||
| SD | 0.512 | ||||
| Sharpe ratio (Glass type estimate) | 0.436 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.435 | ||||
| df | 743.000 | ||||
| t | 0.734 | ||||
| p | 0.231 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.728 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.599 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.728 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.599 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.643 | ||||
| Upside Potential Ratio | 8.263 | ||||
| Upside part of mean | 2.866 | ||||
| Downside part of mean | -2.643 | ||||
| Upside SD | 0.376 | ||||
| Downside SD | 0.347 | ||||
| N nonnegative terms | 368.000 | ||||
| N negative terms | 376.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 744.000 | ||||
| Mean of predictor | 0.567 | ||||
| Mean of criterion | 0.223 | ||||
| SD of predictor | 0.322 | ||||
| SD of criterion | 0.512 | ||||
| Covariance | 0.076 | ||||
| r | 0.462 | ||||
| b (slope, estimate of beta) | 0.735 | ||||
| a (intercept, estimate of alpha) | -0.194 | ||||
| Mean Square Error | 0.206 | ||||
| DF error | 742.000 | ||||
| t(b) | 14.203 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.714 | ||||
| p(a) | 0.762 | ||||
| Lowerbound of 95% confidence interval for beta | 0.633 | ||||
| Upperbound of 95% confidence interval for beta | 0.836 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.726 | ||||
| Upperbound of 95% confidence interval for alpha | 0.339 | ||||
| Treynor index (mean / b) | 0.303 | ||||
| Jensen alpha (a) | -0.194 | ||||
| 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%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.045 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 744.000 | ||||
| Minimum | 0.865 | ||||
| Quartile 1 | 0.987 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.015 | ||||
| Maximum | 1.299 | ||||
| Mean of quarter 1 | 0.966 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.039 | ||||
| Inter Quartile Range | 0.028 | ||||
| Number outliers low | 25.000 | ||||
| Percentage of outliers low | 0.034 | ||||
| Mean of outliers low | 0.919 | ||||
| Number of outliers high | 31.000 | ||||
| Percentage of outliers high | 0.042 | ||||
| Mean of outliers high | 1.086 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.242 | ||||
| VaR(95%) (moments method) | 0.033 | ||||
| Expected Shortfall (moments method) | 0.053 | ||||
| Extreme Value Index (regression method) | 0.077 | ||||
| VaR(95%) (regression method) | 0.031 | ||||
| Expected Shortfall (regression method) | 0.045 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 13.000 | ||||
| Minimum | 0.010 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.083 | ||||
| Quartile 3 | 0.138 | ||||
| Maximum | 0.461 | ||||
| Mean of quarter 1 | 0.020 | ||||
| Mean of quarter 2 | 0.070 | ||||
| Mean of quarter 3 | 0.119 | ||||
| Mean of quarter 4 | 0.282 | ||||
| Inter Quartile Range | 0.106 | ||||
| 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 | 0.077 | ||||
| Mean of outliers high | 0.461 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.201 | ||||
| VaR(95%) (moments method) | 0.289 | ||||
| Expected Shortfall (moments method) | 0.432 | ||||
| Extreme Value Index (regression method) | 1.332 | ||||
| VaR(95%) (regression method) | 0.426 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.400 | ||||
| Compounded annual return (geometric extrapolation) | 0.306 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.664 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.086 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.915 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.899 | ||||
| SD | 0.745 | ||||
| Sharpe ratio (Glass type estimate) | 2.549 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.534 | ||||
| df | 130.000 | ||||
| t | 1.802 | ||||
| p | 0.422 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.245 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 5.333 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.255 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 5.323 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4.940 | ||||
| Upside Potential Ratio | 13.181 | ||||
| Upside part of mean | 5.067 | ||||
| Downside part of mean | -3.168 | ||||
| Upside SD | 0.646 | ||||
| Downside SD | 0.384 | ||||
| N nonnegative terms | 72.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.040 | ||||
| Mean of criterion | 1.899 | ||||
| SD of predictor | 0.463 | ||||
| SD of criterion | 0.745 | ||||
| Covariance | 0.107 | ||||
| r | 0.310 | ||||
| b (slope, estimate of beta) | 0.498 | ||||
| a (intercept, estimate of alpha) | 1.381 | ||||
| Mean Square Error | 0.506 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.703 | ||||
| p(b) | 0.306 | ||||
| t(a) | 1.360 | ||||
| p(a) | 0.425 | ||||
| Lowerbound of 95% confidence interval for beta | 0.232 | ||||
| Upperbound of 95% confidence interval for beta | 0.765 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.628 | ||||
| Upperbound of 95% confidence interval for alpha | 3.390 | ||||
| Treynor index (mean / b) | 3.810 | ||||
| Jensen alpha (a) | 1.381 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.633 | ||||
| SD | 0.715 | ||||
| Sharpe ratio (Glass type estimate) | 2.285 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.272 | ||||
| df | 130.000 | ||||
| t | 1.616 | ||||
| p | 0.430 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.505 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 5.066 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.514 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 5.057 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4.110 | ||||
| Upside Potential Ratio | 12.276 | ||||
| Upside part of mean | 4.878 | ||||
| Downside part of mean | -3.245 | ||||
| Upside SD | 0.599 | ||||
| Downside SD | 0.397 | ||||
| N nonnegative terms | 72.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.931 | ||||
| Mean of criterion | 1.633 | ||||
| SD of predictor | 0.466 | ||||
| SD of criterion | 0.715 | ||||
| Covariance | 0.106 | ||||
| r | 0.319 | ||||
| b (slope, estimate of beta) | 0.489 | ||||
| a (intercept, estimate of alpha) | 1.178 | ||||
| Mean Square Error | 0.462 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.823 | ||||
| p(b) | 0.300 | ||||
| t(a) | 1.216 | ||||
| p(a) | 0.432 | ||||
| Lowerbound of 95% confidence interval for beta | 0.236 | ||||
| Upperbound of 95% confidence interval for beta | 0.742 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.739 | ||||
| Upperbound of 95% confidence interval for alpha | 3.095 | ||||
| Treynor index (mean / b) | 3.340 | ||||
| Jensen alpha (a) | 1.178 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.064 | ||||
| Expected Shortfall on VaR | 0.081 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.051 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.890 | ||||
| Quartile 1 | 0.981 | ||||
| Median | 1.005 | ||||
| Quartile 3 | 1.025 | ||||
| Maximum | 1.299 | ||||
| Mean of quarter 1 | 0.959 | ||||
| Mean of quarter 2 | 0.994 | ||||
| Mean of quarter 3 | 1.017 | ||||
| Mean of quarter 4 | 1.061 | ||||
| Inter Quartile Range | 0.044 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.902 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.172 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.053 | ||||
| VaR(95%) (moments method) | 0.039 | ||||
| Expected Shortfall (moments method) | 0.051 | ||||
| Extreme Value Index (regression method) | 0.163 | ||||
| VaR(95%) (regression method) | 0.040 | ||||
| Expected Shortfall (regression method) | 0.058 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 13.000 | ||||
| Minimum | 0.010 | ||||
| Quartile 1 | 0.045 | ||||
| Median | 0.083 | ||||
| Quartile 3 | 0.138 | ||||
| Maximum | 0.231 | ||||
| Mean of quarter 1 | 0.031 | ||||
| Mean of quarter 2 | 0.078 | ||||
| Mean of quarter 3 | 0.119 | ||||
| Mean of quarter 4 | 0.175 | ||||
| Inter Quartile Range | 0.093 | ||||
| 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) | 0.219 | ||||
| VaR(95%) (moments method) | 0.192 | ||||
| Expected Shortfall (moments method) | 0.245 | ||||
| Extreme Value Index (regression method) | 2.023 | ||||
| VaR(95%) (regression method) | 0.221 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 2.626 | ||||
| Compounded annual return (geometric extrapolation) | 4.350 | ||||
| Calmar ratio (compounded annual return / max draw down) | 18.847 | ||||
| Compounded annual return / average of 25% largest draw downs | 24.825 | ||||
| Compounded annual return / Expected Shortfall lognormal | 53.558 | ||||