Advanced Statistics: Test System 1
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 | 0.502 | ||||
| SD | 0.883 | ||||
| Sharpe ratio (Glass type estimate) | 0.568 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.560 | ||||
| df | 55.000 | ||||
| t | 1.227 | ||||
| p | 0.113 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.348 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.479 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.353 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.473 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.818 | ||||
| Upside Potential Ratio | 4.742 | ||||
| Upside part of mean | 0.623 | ||||
| Downside part of mean | -0.121 | ||||
| Upside SD | 0.878 | ||||
| Downside SD | 0.131 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 56.000 | ||||
| Mean of predictor | 0.386 | ||||
| Mean of criterion | 0.502 | ||||
| SD of predictor | 0.267 | ||||
| SD of criterion | 0.883 | ||||
| Covariance | -0.033 | ||||
| r | -0.138 | ||||
| b (slope, estimate of beta) | -0.458 | ||||
| a (intercept, estimate of alpha) | 0.678 | ||||
| Mean Square Error | 0.780 | ||||
| DF error | 54.000 | ||||
| t(b) | -1.025 | ||||
| p(b) | 0.845 | ||||
| t(a) | 1.529 | ||||
| p(a) | 0.066 | ||||
| Lowerbound of 95% confidence interval for beta | -1.352 | ||||
| Upperbound of 95% confidence interval for beta | 0.437 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.211 | ||||
| Upperbound of 95% confidence interval for alpha | 1.568 | ||||
| Treynor index (mean / b) | -1.096 | ||||
| Jensen alpha (a) | 0.678 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.284 | ||||
| SD | 0.571 | ||||
| Sharpe ratio (Glass type estimate) | 0.498 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.491 | ||||
| df | 55.000 | ||||
| t | 1.076 | ||||
| p | 0.143 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.416 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.408 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.421 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.403 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.879 | ||||
| Upside Potential Ratio | 2.747 | ||||
| Upside part of mean | 0.415 | ||||
| Downside part of mean | -0.131 | ||||
| Upside SD | 0.551 | ||||
| Downside SD | 0.151 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 56.000 | ||||
| Mean of predictor | 0.345 | ||||
| Mean of criterion | 0.284 | ||||
| SD of predictor | 0.262 | ||||
| SD of criterion | 0.571 | ||||
| Covariance | -0.024 | ||||
| r | -0.161 | ||||
| b (slope, estimate of beta) | -0.350 | ||||
| a (intercept, estimate of alpha) | 0.405 | ||||
| Mean Square Error | 0.323 | ||||
| DF error | 54.000 | ||||
| t(b) | -1.200 | ||||
| p(b) | 0.882 | ||||
| t(a) | 1.438 | ||||
| p(a) | 0.078 | ||||
| Lowerbound of 95% confidence interval for beta | -0.936 | ||||
| Upperbound of 95% confidence interval for beta | 0.235 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.160 | ||||
| Upperbound of 95% confidence interval for alpha | 0.970 | ||||
| Treynor index (mean / b) | -0.811 | ||||
| Jensen alpha (a) | 0.405 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.219 | ||||
| Expected Shortfall on VaR | 0.270 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.073 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 56.000 | ||||
| Minimum | 0.732 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.691 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.209 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.107 | ||||
| Mean of outliers low | 0.937 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 1.418 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.683 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| Extreme Value Index (regression method) | 1.617 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.346 | ||||
| Quartile 1 | 0.346 | ||||
| Median | 0.346 | ||||
| Quartile 3 | 0.346 | ||||
| Maximum | 0.346 | ||||
| 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 | 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) | 0.777 | ||||
| Compounded annual return (geometric extrapolation) | 0.388 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.122 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.440 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.531 | ||||
| SD | 0.923 | ||||
| Sharpe ratio (Glass type estimate) | 0.575 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.574 | ||||
| df | 1234.000 | ||||
| t | 1.248 | ||||
| p | 0.482 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.328 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.478 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.329 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.478 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.495 | ||||
| Upside Potential Ratio | 4.460 | ||||
| Upside part of mean | 0.949 | ||||
| Downside part of mean | -0.418 | ||||
| Upside SD | 0.899 | ||||
| Downside SD | 0.213 | ||||
| N nonnegative terms | 87.000 | ||||
| N negative terms | 1148.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1235.000 | ||||
| Mean of predictor | 0.423 | ||||
| Mean of criterion | 0.531 | ||||
| SD of predictor | 0.338 | ||||
| SD of criterion | 0.923 | ||||
| Covariance | -0.036 | ||||
| r | -0.115 | ||||
| b (slope, estimate of beta) | -0.314 | ||||
| a (intercept, estimate of alpha) | 0.664 | ||||
| Mean Square Error | 0.842 | ||||
| DF error | 1233.000 | ||||
| t(b) | -4.068 | ||||
| p(b) | 0.573 | ||||
| t(a) | 1.566 | ||||
| p(a) | 0.472 | ||||
| Lowerbound of 95% confidence interval for beta | -0.466 | ||||
| Upperbound of 95% confidence interval for beta | -0.163 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.168 | ||||
| Upperbound of 95% confidence interval for alpha | 1.495 | ||||
| Treynor index (mean / b) | -1.690 | ||||
| Jensen alpha (a) | 0.664 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.281 | ||||
| SD | 0.628 | ||||
| Sharpe ratio (Glass type estimate) | 0.447 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.447 | ||||
| df | 1234.000 | ||||
| t | 0.970 | ||||
| p | 0.486 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.456 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.350 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.456 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.350 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.152 | ||||
| Upside Potential Ratio | 2.978 | ||||
| Upside part of mean | 0.726 | ||||
| Downside part of mean | -0.445 | ||||
| Upside SD | 0.579 | ||||
| Downside SD | 0.244 | ||||
| N nonnegative terms | 87.000 | ||||
| N negative terms | 1148.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1235.000 | ||||
| Mean of predictor | 0.364 | ||||
| Mean of criterion | 0.281 | ||||
| SD of predictor | 0.344 | ||||
| SD of criterion | 0.628 | ||||
| Covariance | -0.032 | ||||
| r | -0.147 | ||||
| b (slope, estimate of beta) | -0.269 | ||||
| a (intercept, estimate of alpha) | 0.379 | ||||
| Mean Square Error | 0.387 | ||||
| DF error | 1233.000 | ||||
| t(b) | -5.221 | ||||
| p(b) | 0.593 | ||||
| t(a) | 1.320 | ||||
| p(a) | 0.476 | ||||
| Lowerbound of 95% confidence interval for beta | -0.370 | ||||
| Upperbound of 95% confidence interval for beta | -0.168 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.184 | ||||
| Upperbound of 95% confidence interval for alpha | 0.942 | ||||
| Treynor index (mean / b) | -1.044 | ||||
| Jensen alpha (a) | 0.379 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.061 | ||||
| Expected Shortfall on VaR | 0.076 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1235.000 | ||||
| Minimum | 0.669 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.691 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 71.000 | ||||
| Percentage of outliers low | 0.057 | ||||
| Mean of outliers low | 0.975 | ||||
| Number of outliers high | 93.000 | ||||
| Percentage of outliers high | 0.075 | ||||
| Mean of outliers high | 1.048 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.541 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.605 | ||||
| VaR(95%) (regression method) | -0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 13.000 | ||||
| Minimum | 0.010 | ||||
| Quartile 1 | 0.015 | ||||
| Median | 0.039 | ||||
| Quartile 3 | 0.050 | ||||
| Maximum | 0.425 | ||||
| Mean of quarter 1 | 0.012 | ||||
| Mean of quarter 2 | 0.031 | ||||
| Mean of quarter 3 | 0.044 | ||||
| Mean of quarter 4 | 0.280 | ||||
| Inter Quartile Range | 0.035 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.154 | ||||
| Mean of outliers high | 0.393 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.750 | ||||
| VaR(95%) (moments method) | 0.251 | ||||
| Expected Shortfall (moments method) | 1.136 | ||||
| Extreme Value Index (regression method) | 0.780 | ||||
| VaR(95%) (regression method) | 0.222 | ||||
| Expected Shortfall (regression method) | 1.043 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.769 | ||||
| Compounded annual return (geometric extrapolation) | 0.384 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.903 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.369 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.059 | ||||
| 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 | 1.034 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.496 | ||||
| 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 | 0.910 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.498 | ||||
| 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) | -8743749322300231.000 | ||||
| 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) | -179640609380027681825835471339520.000 | ||||
| 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 | ||||