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 | 0.006 | ||||
| SD | 0.093 | ||||
| Sharpe ratio (Glass type estimate) | 0.062 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.061 | ||||
| df | 70.000 | ||||
| t | 0.151 | ||||
| p | 0.440 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.744 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.868 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.745 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.867 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.216 | ||||
| Upside Potential Ratio | 2.335 | ||||
| Upside part of mean | 0.062 | ||||
| Downside part of mean | -0.057 | ||||
| Upside SD | 0.089 | ||||
| Downside SD | 0.027 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.253 | ||||
| Mean of criterion | 0.006 | ||||
| SD of predictor | 0.297 | ||||
| SD of criterion | 0.093 | ||||
| Covariance | -0.008 | ||||
| r | -0.284 | ||||
| b (slope, estimate of beta) | -0.090 | ||||
| a (intercept, estimate of alpha) | 0.028 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 69.000 | ||||
| t(b) | -2.462 | ||||
| p(b) | 0.992 | ||||
| t(a) | 0.744 | ||||
| p(a) | 0.230 | ||||
| Lowerbound of 95% confidence interval for beta | -0.162 | ||||
| Upperbound of 95% confidence interval for beta | -0.017 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.048 | ||||
| Upperbound of 95% confidence interval for alpha | 0.105 | ||||
| Treynor index (mean / b) | -0.065 | ||||
| Jensen alpha (a) | 0.028 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.002 | ||||
| SD | 0.087 | ||||
| Sharpe ratio (Glass type estimate) | 0.021 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.021 | ||||
| df | 70.000 | ||||
| t | 0.051 | ||||
| p | 0.480 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.785 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.827 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.785 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.827 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.068 | ||||
| Upside Potential Ratio | 2.170 | ||||
| Upside part of mean | 0.059 | ||||
| Downside part of mean | -0.057 | ||||
| Upside SD | 0.082 | ||||
| Downside SD | 0.027 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.206 | ||||
| Mean of criterion | 0.002 | ||||
| SD of predictor | 0.301 | ||||
| SD of criterion | 0.087 | ||||
| Covariance | -0.008 | ||||
| r | -0.306 | ||||
| b (slope, estimate of beta) | -0.089 | ||||
| a (intercept, estimate of alpha) | 0.020 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 69.000 | ||||
| t(b) | -2.672 | ||||
| p(b) | 0.995 | ||||
| t(a) | 0.575 | ||||
| p(a) | 0.284 | ||||
| Lowerbound of 95% confidence interval for beta | -0.155 | ||||
| Upperbound of 95% confidence interval for beta | -0.023 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.050 | ||||
| Upperbound of 95% confidence interval for alpha | 0.090 | ||||
| Treynor index (mean / b) | -0.021 | ||||
| Jensen alpha (a) | 0.020 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.040 | ||||
| Expected Shortfall on VaR | 0.050 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 71.000 | ||||
| Minimum | 0.962 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.187 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.113 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.155 | ||||
| Mean of outliers high | 1.036 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -22.214 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | -0.787 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.020 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.023 | ||||
| Quartile 1 | 0.028 | ||||
| Median | 0.034 | ||||
| Quartile 3 | 0.038 | ||||
| Maximum | 0.042 | ||||
| Mean of quarter 1 | 0.023 | ||||
| Mean of quarter 2 | 0.034 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.042 | ||||
| Inter Quartile Range | 0.009 | ||||
| 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) | 0.053 | ||||
| Compounded annual return (geometric extrapolation) | 0.047 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.120 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.120 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.930 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.101 | ||||
| SD | 0.452 | ||||
| Sharpe ratio (Glass type estimate) | 0.222 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.222 | ||||
| df | 1568.000 | ||||
| t | 0.544 | ||||
| p | 0.493 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.579 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.023 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.579 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.023 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.358 | ||||
| Upside Potential Ratio | 2.951 | ||||
| Upside part of mean | 0.829 | ||||
| Downside part of mean | -0.728 | ||||
| Upside SD | 0.354 | ||||
| Downside SD | 0.281 | ||||
| N nonnegative terms | 121.000 | ||||
| N negative terms | 1448.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1569.000 | ||||
| Mean of predictor | 0.427 | ||||
| Mean of criterion | 0.101 | ||||
| SD of predictor | 0.621 | ||||
| SD of criterion | 0.452 | ||||
| Covariance | -0.013 | ||||
| r | -0.047 | ||||
| b (slope, estimate of beta) | -0.034 | ||||
| a (intercept, estimate of alpha) | 0.115 | ||||
| Mean Square Error | 0.204 | ||||
| DF error | 1567.000 | ||||
| t(b) | -1.868 | ||||
| p(b) | 0.530 | ||||
| t(a) | 0.623 | ||||
| p(a) | 0.490 | ||||
| Lowerbound of 95% confidence interval for beta | -0.070 | ||||
| Upperbound of 95% confidence interval for beta | 0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.247 | ||||
| Upperbound of 95% confidence interval for alpha | 0.478 | ||||
| Treynor index (mean / b) | -2.930 | ||||
| Jensen alpha (a) | 0.115 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.001 | ||||
| SD | 0.444 | ||||
| Sharpe ratio (Glass type estimate) | 0.003 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.003 | ||||
| df | 1568.000 | ||||
| t | 0.007 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.798 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.804 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.798 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.804 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.004 | ||||
| Upside Potential Ratio | 2.504 | ||||
| Upside part of mean | 0.774 | ||||
| Downside part of mean | -0.773 | ||||
| Upside SD | 0.319 | ||||
| Downside SD | 0.309 | ||||
| N nonnegative terms | 121.000 | ||||
| N negative terms | 1448.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1569.000 | ||||
| Mean of predictor | 0.235 | ||||
| Mean of criterion | 0.001 | ||||
| SD of predictor | 0.621 | ||||
| SD of criterion | 0.444 | ||||
| Covariance | -0.013 | ||||
| r | -0.048 | ||||
| b (slope, estimate of beta) | -0.034 | ||||
| a (intercept, estimate of alpha) | 0.009 | ||||
| Mean Square Error | 0.197 | ||||
| DF error | 1567.000 | ||||
| t(b) | -1.903 | ||||
| p(b) | 0.531 | ||||
| t(a) | 0.052 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | -0.070 | ||||
| Upperbound of 95% confidence interval for beta | 0.001 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.346 | ||||
| Upperbound of 95% confidence interval for alpha | 0.365 | ||||
| Treynor index (mean / b) | -0.038 | ||||
| Jensen alpha (a) | 0.009 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.044 | ||||
| Expected Shortfall on VaR | 0.055 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1569.000 | ||||
| Minimum | 0.727 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.388 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 142.000 | ||||
| Percentage of outliers low | 0.091 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 151.000 | ||||
| Percentage of outliers high | 0.096 | ||||
| Mean of outliers high | 1.033 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.364 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.607 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.034 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.060 | ||||
| Median | 0.229 | ||||
| Quartile 3 | 0.252 | ||||
| Maximum | 0.273 | ||||
| Mean of quarter 1 | 0.034 | ||||
| Mean of quarter 2 | 0.218 | ||||
| Mean of quarter 3 | 0.245 | ||||
| Mean of quarter 4 | 0.272 | ||||
| Inter Quartile Range | 0.192 | ||||
| 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) | -296.061 | ||||
| VaR(95%) (moments method) | 0.272 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -4.489 | ||||
| VaR(95%) (regression method) | 0.305 | ||||
| Expected Shortfall (regression method) | 0.305 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.052 | ||||
| Compounded annual return (geometric extrapolation) | 0.046 | ||||
| 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 | 0.843 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.112 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.514 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.977 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.519 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | 0.000 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8740318071539106.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | -4460956803289584668058748580790272.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| 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 for a one-period unit investment (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 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| 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 | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||