Advanced Statistics: VT26
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 | 0.023 | ||||
| SD | 0.214 | ||||
| Sharpe ratio (Glass type estimate) | 0.109 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.108 | ||||
| df | 71.000 | ||||
| t | 0.268 | ||||
| p | 0.395 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.691 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.909 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.692 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.909 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.146 | ||||
| Upside Potential Ratio | 1.036 | ||||
| Upside part of mean | 0.166 | ||||
| Downside part of mean | -0.143 | ||||
| Upside SD | 0.139 | ||||
| Downside SD | 0.160 | ||||
| N nonnegative terms | 25.000 | ||||
| N negative terms | 47.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 72.000 | ||||
| Mean of predictor | 0.378 | ||||
| Mean of criterion | 0.023 | ||||
| SD of predictor | 0.384 | ||||
| SD of criterion | 0.214 | ||||
| Covariance | -0.050 | ||||
| r | -0.606 | ||||
| b (slope, estimate of beta) | -0.337 | ||||
| a (intercept, estimate of alpha) | 0.151 | ||||
| Mean Square Error | 0.029 | ||||
| DF error | 70.000 | ||||
| t(b) | -6.380 | ||||
| p(b) | 1.000 | ||||
| t(a) | 2.076 | ||||
| p(a) | 0.021 | ||||
| Lowerbound of 95% confidence interval for beta | -0.443 | ||||
| Upperbound of 95% confidence interval for beta | -0.232 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.006 | ||||
| Upperbound of 95% confidence interval for alpha | 0.296 | ||||
| Treynor index (mean / b) | -0.069 | ||||
| Jensen alpha (a) | 0.151 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 0.237 | ||||
| Sharpe ratio (Glass type estimate) | -0.010 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.010 | ||||
| df | 71.000 | ||||
| t | -0.024 | ||||
| p | 0.509 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.810 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.791 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.810 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.791 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.012 | ||||
| Upside Potential Ratio | 0.792 | ||||
| Upside part of mean | 0.157 | ||||
| Downside part of mean | -0.159 | ||||
| Upside SD | 0.128 | ||||
| Downside SD | 0.198 | ||||
| N nonnegative terms | 25.000 | ||||
| N negative terms | 47.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 72.000 | ||||
| Mean of predictor | 0.307 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.355 | ||||
| SD of criterion | 0.237 | ||||
| Covariance | -0.049 | ||||
| r | -0.581 | ||||
| b (slope, estimate of beta) | -0.389 | ||||
| a (intercept, estimate of alpha) | 0.117 | ||||
| Mean Square Error | 0.038 | ||||
| DF error | 70.000 | ||||
| t(b) | -5.969 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.429 | ||||
| p(a) | 0.079 | ||||
| Lowerbound of 95% confidence interval for beta | -0.518 | ||||
| Upperbound of 95% confidence interval for beta | -0.259 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | 0.280 | ||||
| Treynor index (mean / b) | 0.006 | ||||
| Jensen alpha (a) | 0.117 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.107 | ||||
| Expected Shortfall on VaR | 0.132 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.071 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 72.000 | ||||
| Minimum | 0.626 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.011 | ||||
| Maximum | 1.230 | ||||
| Mean of quarter 1 | 0.962 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.058 | ||||
| Inter Quartile Range | 0.014 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.069 | ||||
| Mean of outliers low | 0.896 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.139 | ||||
| Mean of outliers high | 1.087 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.742 | ||||
| VaR(95%) (moments method) | 0.026 | ||||
| Expected Shortfall (moments method) | 0.112 | ||||
| Extreme Value Index (regression method) | 0.719 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.082 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.028 | ||||
| Quartile 1 | 0.041 | ||||
| Median | 0.092 | ||||
| Quartile 3 | 0.197 | ||||
| Maximum | 0.374 | ||||
| Mean of quarter 1 | 0.028 | ||||
| Mean of quarter 2 | 0.046 | ||||
| Mean of quarter 3 | 0.138 | ||||
| Mean of quarter 4 | 0.374 | ||||
| Inter Quartile Range | 0.155 | ||||
| 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) | 0.047 | ||||
| Compounded annual return (geometric extrapolation) | 0.043 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.114 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.114 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.324 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.238 | ||||
| SD | 0.712 | ||||
| Sharpe ratio (Glass type estimate) | 0.335 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.334 | ||||
| df | 1572.000 | ||||
| t | 0.820 | ||||
| p | 0.490 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.466 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.134 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.466 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.134 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.555 | ||||
| Upside Potential Ratio | 3.397 | ||||
| Upside part of mean | 1.458 | ||||
| Downside part of mean | -1.219 | ||||
| Upside SD | 0.568 | ||||
| Downside SD | 0.429 | ||||
| N nonnegative terms | 458.000 | ||||
| N negative terms | 1115.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1573.000 | ||||
| Mean of predictor | 0.499 | ||||
| Mean of criterion | 0.238 | ||||
| SD of predictor | 0.630 | ||||
| SD of criterion | 0.712 | ||||
| Covariance | -0.219 | ||||
| r | -0.489 | ||||
| b (slope, estimate of beta) | -0.552 | ||||
| a (intercept, estimate of alpha) | 0.513 | ||||
| Mean Square Error | 0.386 | ||||
| DF error | 1571.000 | ||||
| t(b) | -22.196 | ||||
| p(b) | 0.798 | ||||
| t(a) | 2.022 | ||||
| p(a) | 0.468 | ||||
| Lowerbound of 95% confidence interval for beta | -0.601 | ||||
| Upperbound of 95% confidence interval for beta | -0.503 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.015 | ||||
| Upperbound of 95% confidence interval for alpha | 1.011 | ||||
| Treynor index (mean / b) | -0.432 | ||||
| Jensen alpha (a) | 0.513 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 0.693 | ||||
| Sharpe ratio (Glass type estimate) | -0.003 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.003 | ||||
| df | 1572.000 | ||||
| t | -0.008 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.803 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.797 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.803 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.797 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.005 | ||||
| Upside Potential Ratio | 2.625 | ||||
| Upside part of mean | 1.332 | ||||
| Downside part of mean | -1.334 | ||||
| Upside SD | 0.473 | ||||
| Downside SD | 0.507 | ||||
| N nonnegative terms | 458.000 | ||||
| N negative terms | 1115.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1573.000 | ||||
| Mean of predictor | 0.310 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.609 | ||||
| SD of criterion | 0.693 | ||||
| Covariance | -0.216 | ||||
| r | -0.513 | ||||
| b (slope, estimate of beta) | -0.584 | ||||
| a (intercept, estimate of alpha) | 0.179 | ||||
| Mean Square Error | 0.355 | ||||
| DF error | 1571.000 | ||||
| t(b) | -23.671 | ||||
| p(b) | 0.811 | ||||
| t(a) | 0.735 | ||||
| p(a) | 0.488 | ||||
| Lowerbound of 95% confidence interval for beta | -0.632 | ||||
| Upperbound of 95% confidence interval for beta | -0.536 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.298 | ||||
| Upperbound of 95% confidence interval for alpha | 0.656 | ||||
| Treynor index (mean / b) | 0.004 | ||||
| Jensen alpha (a) | 0.179 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.068 | ||||
| Expected Shortfall on VaR | 0.084 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1573.000 | ||||
| Minimum | 0.547 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.800 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 239.000 | ||||
| Percentage of outliers low | 0.152 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 272.000 | ||||
| Percentage of outliers high | 0.173 | ||||
| Mean of outliers high | 1.032 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.359 | ||||
| VaR(95%) (moments method) | 0.010 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.986 | ||||
| VaR(95%) (regression method) | 0.008 | ||||
| Expected Shortfall (regression method) | 0.652 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 13.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.034 | ||||
| Quartile 3 | 0.149 | ||||
| Maximum | 0.457 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.020 | ||||
| Mean of quarter 3 | 0.110 | ||||
| Mean of quarter 4 | 0.449 | ||||
| Inter Quartile Range | 0.139 | ||||
| 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 | 0.231 | ||||
| Mean of outliers high | 0.449 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -4062.643 | ||||
| VaR(95%) (moments method) | 0.314 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -3.424 | ||||
| VaR(95%) (regression method) | 0.291 | ||||
| Expected Shortfall (regression method) | 0.291 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.047 | ||||
| Compounded annual return (geometric extrapolation) | 0.043 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.093 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.095 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.504 | ||||
| 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 | 0.972 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.445 | ||||
| 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 | 0.872 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.446 | ||||
| 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) | -8735673936237167.000 | ||||
| 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) | -174751719464248058709553178476544.000 | ||||
| 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 | ||||