Advanced Statistics: Test System 3
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
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| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.443 | ||||
| SD | 0.917 | ||||
| Sharpe ratio (Glass type estimate) | 0.483 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.475 | ||||
| df | 45.000 | ||||
| t | 0.945 | ||||
| p | 0.175 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.526 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.486 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.531 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.481 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.928 | ||||
| Upside Potential Ratio | 2.861 | ||||
| Upside part of mean | 1.364 | ||||
| Downside part of mean | -0.922 | ||||
| Upside SD | 0.782 | ||||
| Downside SD | 0.477 | ||||
| N nonnegative terms | 24.000 | ||||
| N negative terms | 22.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 46.000 | ||||
| Mean of predictor | 0.414 | ||||
| Mean of criterion | 0.443 | ||||
| SD of predictor | 0.236 | ||||
| SD of criterion | 0.917 | ||||
| Covariance | -0.049 | ||||
| r | -0.225 | ||||
| b (slope, estimate of beta) | -0.875 | ||||
| a (intercept, estimate of alpha) | 0.805 | ||||
| Mean Square Error | 0.816 | ||||
| DF error | 44.000 | ||||
| t(b) | -1.535 | ||||
| p(b) | 0.934 | ||||
| t(a) | 1.553 | ||||
| p(a) | 0.064 | ||||
| Lowerbound of 95% confidence interval for beta | -2.024 | ||||
| Upperbound of 95% confidence interval for beta | 0.274 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.239 | ||||
| Upperbound of 95% confidence interval for alpha | 1.849 | ||||
| Treynor index (mean / b) | -0.506 | ||||
| Jensen alpha (a) | 0.805 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.075 | ||||
| SD | 0.850 | ||||
| Sharpe ratio (Glass type estimate) | 0.088 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.087 | ||||
| df | 45.000 | ||||
| t | 0.173 | ||||
| p | 0.432 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.913 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.089 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.914 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.088 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.132 | ||||
| Upside Potential Ratio | 1.994 | ||||
| Upside part of mean | 1.137 | ||||
| Downside part of mean | -1.062 | ||||
| Upside SD | 0.618 | ||||
| Downside SD | 0.570 | ||||
| N nonnegative terms | 24.000 | ||||
| N negative terms | 22.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 46.000 | ||||
| Mean of predictor | 0.381 | ||||
| Mean of criterion | 0.075 | ||||
| SD of predictor | 0.223 | ||||
| SD of criterion | 0.850 | ||||
| Covariance | -0.044 | ||||
| r | -0.232 | ||||
| b (slope, estimate of beta) | -0.886 | ||||
| a (intercept, estimate of alpha) | 0.413 | ||||
| Mean Square Error | 0.699 | ||||
| DF error | 44.000 | ||||
| t(b) | -1.585 | ||||
| p(b) | 0.940 | ||||
| t(a) | 0.865 | ||||
| p(a) | 0.196 | ||||
| Lowerbound of 95% confidence interval for beta | -2.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.241 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.549 | ||||
| Upperbound of 95% confidence interval for alpha | 1.375 | ||||
| Treynor index (mean / b) | -0.085 | ||||
| Jensen alpha (a) | 0.413 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.328 | ||||
| Expected Shortfall on VaR | 0.391 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.174 | ||||
| Expected Shortfall on VaR | 0.317 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 46.000 | ||||
| Minimum | 0.602 | ||||
| Quartile 1 | 0.888 | ||||
| Median | 1.012 | ||||
| Quartile 3 | 1.104 | ||||
| Maximum | 1.895 | ||||
| Mean of quarter 1 | 0.763 | ||||
| Mean of quarter 2 | 0.946 | ||||
| Mean of quarter 3 | 1.061 | ||||
| Mean of quarter 4 | 1.386 | ||||
| Inter Quartile Range | 0.216 | ||||
| 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 | 0.065 | ||||
| Mean of outliers high | 1.695 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.323 | ||||
| VaR(95%) (moments method) | 0.243 | ||||
| Expected Shortfall (moments method) | 0.291 | ||||
| Extreme Value Index (regression method) | -0.973 | ||||
| VaR(95%) (regression method) | 0.303 | ||||
| Expected Shortfall (regression method) | 0.327 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.089 | ||||
| Quartile 1 | 0.099 | ||||
| Median | 0.217 | ||||
| Quartile 3 | 0.443 | ||||
| Maximum | 0.725 | ||||
| Mean of quarter 1 | 0.090 | ||||
| Mean of quarter 2 | 0.121 | ||||
| Mean of quarter 3 | 0.313 | ||||
| Mean of quarter 4 | 0.606 | ||||
| Inter Quartile Range | 0.344 | ||||
| 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) | 0.151 | ||||
| Compounded annual return (geometric extrapolation) | 0.126 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.174 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.209 | ||||
| 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 | 0.371 | ||||
| SD | 0.778 | ||||
| Sharpe ratio (Glass type estimate) | 0.477 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.476 | ||||
| df | 1013.000 | ||||
| t | 0.938 | ||||
| p | 0.481 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.520 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.473 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.520 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.473 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.729 | ||||
| Upside Potential Ratio | 8.047 | ||||
| Upside part of mean | 4.091 | ||||
| Downside part of mean | -3.720 | ||||
| Upside SD | 0.588 | ||||
| Downside SD | 0.508 | ||||
| N nonnegative terms | 479.000 | ||||
| N negative terms | 535.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1014.000 | ||||
| Mean of predictor | 0.414 | ||||
| Mean of criterion | 0.371 | ||||
| SD of predictor | 0.280 | ||||
| SD of criterion | 0.778 | ||||
| Covariance | -0.014 | ||||
| r | -0.066 | ||||
| b (slope, estimate of beta) | -0.183 | ||||
| a (intercept, estimate of alpha) | 0.446 | ||||
| Mean Square Error | 0.602 | ||||
| DF error | 1012.000 | ||||
| t(b) | -2.100 | ||||
| p(b) | 0.533 | ||||
| t(a) | 1.126 | ||||
| p(a) | 0.482 | ||||
| Lowerbound of 95% confidence interval for beta | -0.353 | ||||
| Upperbound of 95% confidence interval for beta | -0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.331 | ||||
| Upperbound of 95% confidence interval for alpha | 1.224 | ||||
| Treynor index (mean / b) | -2.030 | ||||
| Jensen alpha (a) | 0.446 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.074 | ||||
| SD | 0.770 | ||||
| Sharpe ratio (Glass type estimate) | 0.096 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.096 | ||||
| df | 1013.000 | ||||
| t | 0.189 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.900 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.092 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.900 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.092 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.135 | ||||
| Upside Potential Ratio | 7.196 | ||||
| Upside part of mean | 3.936 | ||||
| Downside part of mean | -3.862 | ||||
| Upside SD | 0.541 | ||||
| Downside SD | 0.547 | ||||
| N nonnegative terms | 479.000 | ||||
| N negative terms | 535.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1014.000 | ||||
| Mean of predictor | 0.374 | ||||
| Mean of criterion | 0.074 | ||||
| SD of predictor | 0.282 | ||||
| SD of criterion | 0.770 | ||||
| Covariance | -0.014 | ||||
| r | -0.066 | ||||
| b (slope, estimate of beta) | -0.181 | ||||
| a (intercept, estimate of alpha) | 0.142 | ||||
| Mean Square Error | 0.590 | ||||
| DF error | 1012.000 | ||||
| t(b) | -2.118 | ||||
| p(b) | 0.533 | ||||
| t(a) | 0.362 | ||||
| p(a) | 0.494 | ||||
| Lowerbound of 95% confidence interval for beta | -0.349 | ||||
| Upperbound of 95% confidence interval for beta | -0.013 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.627 | ||||
| Upperbound of 95% confidence interval for alpha | 0.911 | ||||
| Treynor index (mean / b) | -0.408 | ||||
| Jensen alpha (a) | 0.142 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.075 | ||||
| Expected Shortfall on VaR | 0.093 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1014.000 | ||||
| Minimum | 0.690 | ||||
| Quartile 1 | 0.980 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.020 | ||||
| Maximum | 1.505 | ||||
| Mean of quarter 1 | 0.951 | ||||
| Mean of quarter 2 | 0.993 | ||||
| Mean of quarter 3 | 1.008 | ||||
| Mean of quarter 4 | 1.055 | ||||
| Inter Quartile Range | 0.039 | ||||
| Number outliers low | 37.000 | ||||
| Percentage of outliers low | 0.036 | ||||
| Mean of outliers low | 0.882 | ||||
| Number of outliers high | 44.000 | ||||
| Percentage of outliers high | 0.043 | ||||
| Mean of outliers high | 1.125 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.267 | ||||
| VaR(95%) (moments method) | 0.049 | ||||
| Expected Shortfall (moments method) | 0.080 | ||||
| Extreme Value Index (regression method) | 0.182 | ||||
| VaR(95%) (regression method) | 0.045 | ||||
| Expected Shortfall (regression method) | 0.068 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 12.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.028 | ||||
| Median | 0.075 | ||||
| Quartile 3 | 0.311 | ||||
| Maximum | 0.787 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.055 | ||||
| Mean of quarter 3 | 0.180 | ||||
| Mean of quarter 4 | 0.584 | ||||
| Inter Quartile Range | 0.283 | ||||
| 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 | 0.083 | ||||
| Mean of outliers high | 0.787 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.722 | ||||
| VaR(95%) (moments method) | 0.669 | ||||
| Expected Shortfall (moments method) | 0.738 | ||||
| Extreme Value Index (regression method) | 0.775 | ||||
| VaR(95%) (regression method) | 0.776 | ||||
| Expected Shortfall (regression method) | 2.428 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.150 | ||||
| Compounded annual return (geometric extrapolation) | 0.125 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.159 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.214 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.346 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.110 | ||||
| SD | 0.585 | ||||
| Sharpe ratio (Glass type estimate) | -0.189 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.188 | ||||
| df | 130.000 | ||||
| t | -0.133 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.960 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.584 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.960 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.584 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.248 | ||||
| Upside Potential Ratio | 7.238 | ||||
| Upside part of mean | 3.214 | ||||
| Downside part of mean | -3.324 | ||||
| Upside SD | 0.377 | ||||
| Downside SD | 0.444 | ||||
| N nonnegative terms | 52.000 | ||||
| N negative terms | 79.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.768 | ||||
| Mean of criterion | -0.110 | ||||
| SD of predictor | 0.463 | ||||
| SD of criterion | 0.585 | ||||
| Covariance | -0.028 | ||||
| r | -0.102 | ||||
| b (slope, estimate of beta) | -0.129 | ||||
| a (intercept, estimate of alpha) | -0.011 | ||||
| Mean Square Error | 0.341 | ||||
| DF error | 129.000 | ||||
| t(b) | -1.169 | ||||
| p(b) | 0.565 | ||||
| t(a) | -0.013 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | -0.348 | ||||
| Upperbound of 95% confidence interval for beta | 0.090 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.653 | ||||
| Upperbound of 95% confidence interval for alpha | 1.631 | ||||
| Treynor index (mean / b) | 0.852 | ||||
| Jensen alpha (a) | -0.011 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.284 | ||||
| SD | 0.596 | ||||
| Sharpe ratio (Glass type estimate) | -0.477 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.474 | ||||
| df | 130.000 | ||||
| t | -0.337 | ||||
| p | 0.515 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.249 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.296 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.247 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.298 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.610 | ||||
| Upside Potential Ratio | 6.747 | ||||
| Upside part of mean | 3.145 | ||||
| Downside part of mean | -3.429 | ||||
| Upside SD | 0.367 | ||||
| Downside SD | 0.466 | ||||
| N nonnegative terms | 52.000 | ||||
| N negative terms | 79.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.659 | ||||
| Mean of criterion | -0.284 | ||||
| SD of predictor | 0.469 | ||||
| SD of criterion | 0.596 | ||||
| Covariance | -0.025 | ||||
| r | -0.091 | ||||
| b (slope, estimate of beta) | -0.116 | ||||
| a (intercept, estimate of alpha) | -0.208 | ||||
| Mean Square Error | 0.354 | ||||
| DF error | 129.000 | ||||
| t(b) | -1.039 | ||||
| p(b) | 0.558 | ||||
| t(a) | -0.246 | ||||
| p(a) | 0.514 | ||||
| Lowerbound of 95% confidence interval for beta | -0.336 | ||||
| Upperbound of 95% confidence interval for beta | 0.105 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.880 | ||||
| Upperbound of 95% confidence interval for alpha | 1.464 | ||||
| Treynor index (mean / b) | 2.453 | ||||
| Jensen alpha (a) | -0.208 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.060 | ||||
| Expected Shortfall on VaR | 0.074 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.064 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.836 | ||||
| Quartile 1 | 0.983 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.020 | ||||
| Maximum | 1.082 | ||||
| Mean of quarter 1 | 0.955 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.043 | ||||
| Inter Quartile Range | 0.037 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.902 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.008 | ||||
| Mean of outliers high | 1.082 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.065 | ||||
| VaR(95%) (moments method) | 0.041 | ||||
| Expected Shortfall (moments method) | 0.058 | ||||
| Extreme Value Index (regression method) | 0.056 | ||||
| VaR(95%) (regression method) | 0.048 | ||||
| Expected Shortfall (regression method) | 0.069 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.008 | ||||
| Quartile 1 | 0.012 | ||||
| Median | 0.017 | ||||
| Quartile 3 | 0.054 | ||||
| Maximum | 0.443 | ||||
| Mean of quarter 1 | 0.010 | ||||
| Mean of quarter 2 | 0.015 | ||||
| Mean of quarter 3 | 0.033 | ||||
| Mean of quarter 4 | 0.259 | ||||
| Inter Quartile Range | 0.042 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.443 | ||||
| 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) | -0.226 | ||||
| Compounded annual return (geometric extrapolation) | -0.213 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.482 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.823 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.884 | ||||