Advanced Statistics: TEWASYS
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 | 0.051 | ||||
| SD | 0.129 | ||||
| Sharpe ratio (Glass type estimate) | 0.391 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.383 | ||||
| df | 34.000 | ||||
| t | 0.668 | ||||
| p | 0.254 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.763 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.540 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.769 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.534 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.043 | ||||
| Upside Potential Ratio | 2.588 | ||||
| Upside part of mean | 0.126 | ||||
| Downside part of mean | -0.075 | ||||
| Upside SD | 0.119 | ||||
| Downside SD | 0.049 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.548 | ||||
| Mean of criterion | 0.051 | ||||
| SD of predictor | 0.306 | ||||
| SD of criterion | 0.129 | ||||
| Covariance | 0.002 | ||||
| r | 0.058 | ||||
| b (slope, estimate of beta) | 0.025 | ||||
| a (intercept, estimate of alpha) | 0.037 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 33.000 | ||||
| t(b) | 0.335 | ||||
| p(b) | 0.370 | ||||
| t(a) | 0.429 | ||||
| p(a) | 0.335 | ||||
| Lowerbound of 95% confidence interval for beta | -0.125 | ||||
| Upperbound of 95% confidence interval for beta | 0.174 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.139 | ||||
| Upperbound of 95% confidence interval for alpha | 0.214 | ||||
| Treynor index (mean / b) | 2.058 | ||||
| Jensen alpha (a) | 0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.043 | ||||
| SD | 0.124 | ||||
| Sharpe ratio (Glass type estimate) | 0.346 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.338 | ||||
| df | 34.000 | ||||
| t | 0.590 | ||||
| p | 0.279 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.807 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.494 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.812 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.488 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.858 | ||||
| Upside Potential Ratio | 2.384 | ||||
| Upside part of mean | 0.119 | ||||
| Downside part of mean | -0.076 | ||||
| Upside SD | 0.112 | ||||
| Downside SD | 0.050 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.495 | ||||
| Mean of criterion | 0.043 | ||||
| SD of predictor | 0.280 | ||||
| SD of criterion | 0.124 | ||||
| Covariance | 0.003 | ||||
| r | 0.082 | ||||
| b (slope, estimate of beta) | 0.036 | ||||
| a (intercept, estimate of alpha) | 0.025 | ||||
| Mean Square Error | 0.016 | ||||
| DF error | 33.000 | ||||
| t(b) | 0.471 | ||||
| p(b) | 0.320 | ||||
| t(a) | 0.302 | ||||
| p(a) | 0.382 | ||||
| Lowerbound of 95% confidence interval for beta | -0.120 | ||||
| Upperbound of 95% confidence interval for beta | 0.192 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.143 | ||||
| Upperbound of 95% confidence interval for alpha | 0.193 | ||||
| Treynor index (mean / b) | 1.184 | ||||
| Jensen alpha (a) | 0.025 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.054 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.938 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.143 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.042 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.057 | ||||
| Mean of outliers low | 0.947 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.114 | ||||
| Mean of outliers high | 1.095 | ||||
| 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) | -2.219 | ||||
| VaR(95%) (regression method) | 0.065 | ||||
| Expected Shortfall (regression method) | 0.086 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.043 | ||||
| Quartile 1 | 0.048 | ||||
| Median | 0.053 | ||||
| Quartile 3 | 0.057 | ||||
| Maximum | 0.062 | ||||
| Mean of quarter 1 | 0.043 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.062 | ||||
| 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) | 0.099 | ||||
| Compounded annual return (geometric extrapolation) | 0.091 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.466 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.466 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.341 | ||||
| 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 | 0.102 | ||||
| Sharpe ratio (Glass type estimate) | 0.455 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.455 | ||||
| df | 778.000 | ||||
| t | 0.785 | ||||
| p | 0.216 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.682 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.592 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.682 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.592 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.754 | ||||
| Upside Potential Ratio | 4.744 | ||||
| Upside part of mean | 0.291 | ||||
| Downside part of mean | -0.245 | ||||
| Upside SD | 0.081 | ||||
| Downside SD | 0.061 | ||||
| N nonnegative terms | 61.000 | ||||
| N negative terms | 718.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 779.000 | ||||
| Mean of predictor | 0.587 | ||||
| Mean of criterion | 0.046 | ||||
| SD of predictor | 0.350 | ||||
| SD of criterion | 0.102 | ||||
| Covariance | 0.000 | ||||
| r | 0.007 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | 0.045 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 777.000 | ||||
| t(b) | 0.200 | ||||
| p(b) | 0.421 | ||||
| t(a) | 0.759 | ||||
| p(a) | 0.224 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.023 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.071 | ||||
| Upperbound of 95% confidence interval for alpha | 0.161 | ||||
| Treynor index (mean / b) | 22.201 | ||||
| Jensen alpha (a) | 0.045 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.041 | ||||
| SD | 0.101 | ||||
| Sharpe ratio (Glass type estimate) | 0.407 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.407 | ||||
| df | 778.000 | ||||
| t | 0.702 | ||||
| p | 0.242 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.730 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.544 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.730 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.543 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.662 | ||||
| Upside Potential Ratio | 4.635 | ||||
| Upside part of mean | 0.288 | ||||
| Downside part of mean | -0.247 | ||||
| Upside SD | 0.080 | ||||
| Downside SD | 0.062 | ||||
| N nonnegative terms | 61.000 | ||||
| N negative terms | 718.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 779.000 | ||||
| Mean of predictor | 0.526 | ||||
| Mean of criterion | 0.041 | ||||
| SD of predictor | 0.347 | ||||
| SD of criterion | 0.101 | ||||
| Covariance | 0.000 | ||||
| r | 0.008 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | 0.040 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 777.000 | ||||
| t(b) | 0.219 | ||||
| p(b) | 0.413 | ||||
| t(a) | 0.678 | ||||
| p(a) | 0.249 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.023 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.076 | ||||
| Upperbound of 95% confidence interval for alpha | 0.155 | ||||
| Treynor index (mean / b) | 17.959 | ||||
| Jensen alpha (a) | 0.040 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 779.000 | ||||
| Minimum | 0.964 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.066 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 57.000 | ||||
| Percentage of outliers low | 0.073 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 61.000 | ||||
| Percentage of outliers high | 0.078 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.822 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -0.310 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | 0.009 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.013 | ||||
| Quartile 1 | 0.034 | ||||
| Median | 0.071 | ||||
| Quartile 3 | 0.088 | ||||
| Maximum | 0.096 | ||||
| Mean of quarter 1 | 0.019 | ||||
| Mean of quarter 2 | 0.058 | ||||
| Mean of quarter 3 | 0.084 | ||||
| Mean of quarter 4 | 0.093 | ||||
| Inter Quartile Range | 0.055 | ||||
| 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) | 0.097 | ||||
| Compounded annual return (geometric extrapolation) | 0.089 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.929 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.959 | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.033 | ||||
| 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 | 1.079 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.462 | ||||
| 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 | 0.971 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.464 | ||||
| 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) | -8726652605332657.000 | ||||
| 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) | -173598742179256238264900355358720.000 | ||||
| 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 | ||||