Advanced Statistics: eminiglobex
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 | 0.044 | ||||
| SD | 0.050 | ||||
| Sharpe ratio (Glass type estimate) | 0.879 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.871 | ||||
| df | 80.000 | ||||
| t | 2.285 | ||||
| p | 0.012 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.110 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.643 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.105 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.637 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.730 | ||||
| Upside Potential Ratio | 4.430 | ||||
| Upside part of mean | 0.071 | ||||
| Downside part of mean | -0.027 | ||||
| Upside SD | 0.049 | ||||
| Downside SD | 0.016 | ||||
| N nonnegative terms | 39.000 | ||||
| N negative terms | 42.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 81.000 | ||||
| Mean of predictor | 0.240 | ||||
| Mean of criterion | 0.044 | ||||
| SD of predictor | 0.197 | ||||
| SD of criterion | 0.050 | ||||
| Covariance | -0.000 | ||||
| r | -0.005 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | 0.044 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 79.000 | ||||
| t(b) | -0.047 | ||||
| p(b) | 0.519 | ||||
| t(a) | 2.156 | ||||
| p(a) | 0.017 | ||||
| Lowerbound of 95% confidence interval for beta | -0.058 | ||||
| Upperbound of 95% confidence interval for beta | 0.056 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.003 | ||||
| Upperbound of 95% confidence interval for alpha | 0.085 | ||||
| Treynor index (mean / b) | -32.653 | ||||
| Jensen alpha (a) | 0.044 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.043 | ||||
| SD | 0.049 | ||||
| Sharpe ratio (Glass type estimate) | 0.870 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.862 | ||||
| df | 80.000 | ||||
| t | 2.261 | ||||
| p | 0.013 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.101 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.634 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.096 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.628 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.628 | ||||
| Upside Potential Ratio | 4.322 | ||||
| Upside part of mean | 0.070 | ||||
| Downside part of mean | -0.027 | ||||
| Upside SD | 0.047 | ||||
| Downside SD | 0.016 | ||||
| N nonnegative terms | 39.000 | ||||
| N negative terms | 42.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 81.000 | ||||
| Mean of predictor | 0.218 | ||||
| Mean of criterion | 0.043 | ||||
| SD of predictor | 0.190 | ||||
| SD of criterion | 0.049 | ||||
| Covariance | 0.000 | ||||
| r | 0.004 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | 0.042 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 79.000 | ||||
| t(b) | 0.037 | ||||
| p(b) | 0.485 | ||||
| t(a) | 2.120 | ||||
| p(a) | 0.019 | ||||
| Lowerbound of 95% confidence interval for beta | -0.056 | ||||
| Upperbound of 95% confidence interval for beta | 0.059 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.003 | ||||
| Upperbound of 95% confidence interval for alpha | 0.082 | ||||
| Treynor index (mean / b) | 39.514 | ||||
| Jensen alpha (a) | 0.042 | ||||
| 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 | 0.025 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 81.000 | ||||
| Minimum | 0.980 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.003 | ||||
| Quartile 3 | 1.008 | ||||
| Maximum | 1.074 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.001 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.026 | ||||
| Inter Quartile Range | 0.008 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.037 | ||||
| Mean of outliers low | 0.983 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.099 | ||||
| Mean of outliers high | 1.043 | ||||
| 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) | -0.863 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | 0.009 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.026 | ||||
| Quartile 3 | 0.032 | ||||
| Maximum | 0.037 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.037 | ||||
| Inter Quartile Range | 0.011 | ||||
| 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) | 0.118 | ||||
| Compounded annual return (geometric extrapolation) | 0.090 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.448 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.448 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.584 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.046 | ||||
| SD | 0.087 | ||||
| Sharpe ratio (Glass type estimate) | 0.530 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.530 | ||||
| df | 1776.000 | ||||
| t | 1.381 | ||||
| p | 0.484 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.223 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.283 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.223 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.283 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.850 | ||||
| Upside Potential Ratio | 3.896 | ||||
| Upside part of mean | 0.210 | ||||
| Downside part of mean | -0.164 | ||||
| Upside SD | 0.068 | ||||
| Downside SD | 0.054 | ||||
| N nonnegative terms | 199.000 | ||||
| N negative terms | 1578.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1777.000 | ||||
| Mean of predictor | 0.267 | ||||
| Mean of criterion | 0.046 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.087 | ||||
| Covariance | 0.005 | ||||
| r | 0.212 | ||||
| b (slope, estimate of beta) | 0.069 | ||||
| a (intercept, estimate of alpha) | 0.027 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 1775.000 | ||||
| t(b) | 9.149 | ||||
| p(b) | 0.366 | ||||
| t(a) | 0.843 | ||||
| p(a) | 0.487 | ||||
| Lowerbound of 95% confidence interval for beta | 0.054 | ||||
| Upperbound of 95% confidence interval for beta | 0.084 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.036 | ||||
| Upperbound of 95% confidence interval for alpha | 0.091 | ||||
| Treynor index (mean / b) | 0.664 | ||||
| Jensen alpha (a) | 0.027 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.042 | ||||
| SD | 0.086 | ||||
| Sharpe ratio (Glass type estimate) | 0.491 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.491 | ||||
| df | 1776.000 | ||||
| t | 1.278 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.262 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.244 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.262 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.243 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.765 | ||||
| Upside Potential Ratio | 3.774 | ||||
| Upside part of mean | 0.208 | ||||
| Downside part of mean | -0.166 | ||||
| Upside SD | 0.066 | ||||
| Downside SD | 0.055 | ||||
| N nonnegative terms | 199.000 | ||||
| N negative terms | 1578.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1777.000 | ||||
| Mean of predictor | 0.230 | ||||
| Mean of criterion | 0.042 | ||||
| SD of predictor | 0.274 | ||||
| SD of criterion | 0.086 | ||||
| Covariance | 0.005 | ||||
| r | 0.203 | ||||
| b (slope, estimate of beta) | 0.063 | ||||
| a (intercept, estimate of alpha) | 0.028 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 1775.000 | ||||
| t(b) | 8.725 | ||||
| p(b) | 0.372 | ||||
| t(a) | 0.851 | ||||
| p(a) | 0.487 | ||||
| Lowerbound of 95% confidence interval for beta | 0.049 | ||||
| Upperbound of 95% confidence interval for beta | 0.078 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.036 | ||||
| Upperbound of 95% confidence interval for alpha | 0.091 | ||||
| Treynor index (mean / b) | 0.664 | ||||
| Jensen alpha (a) | 0.028 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1777.000 | ||||
| Minimum | 0.923 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.107 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 103.000 | ||||
| Percentage of outliers low | 0.058 | ||||
| Mean of outliers low | 0.992 | ||||
| Number of outliers high | 202.000 | ||||
| Percentage of outliers high | 0.114 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.652 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.335 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.007 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 37.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.004 | ||||
| Quartile 3 | 0.013 | ||||
| Maximum | 0.124 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.007 | ||||
| Mean of quarter 4 | 0.037 | ||||
| Inter Quartile Range | 0.010 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.108 | ||||
| Mean of outliers high | 0.064 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.664 | ||||
| VaR(95%) (moments method) | 0.041 | ||||
| Expected Shortfall (moments method) | 0.126 | ||||
| Extreme Value Index (regression method) | 1.096 | ||||
| VaR(95%) (regression method) | 0.042 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.117 | ||||
| Compounded annual return (geometric extrapolation) | 0.090 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.728 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.401 | ||||
| Compounded annual return / Expected Shortfall lognormal | 8.393 | ||||
| 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 | 1.463 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.322 | ||||
| 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 | 1.408 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.320 | ||||
| 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) | -8489469994650091.000 | ||||
| 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) | -156455102529401398336605598515200.000 | ||||
| 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 | ||||