Advanced Statistics: Doubleday Advanced Small Cap
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 | -0.020 | ||||
| SD | 0.715 | ||||
| Sharpe ratio (Glass type estimate) | -0.029 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.028 | ||||
| df | 85.000 | ||||
| t | -0.076 | ||||
| p | 0.530 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.761 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.704 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.760 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.704 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.055 | ||||
| Upside Potential Ratio | 1.858 | ||||
| Upside part of mean | 0.683 | ||||
| Downside part of mean | -0.704 | ||||
| Upside SD | 0.608 | ||||
| Downside SD | 0.368 | ||||
| N nonnegative terms | 31.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 86.000 | ||||
| Mean of predictor | 0.226 | ||||
| Mean of criterion | -0.020 | ||||
| SD of predictor | 0.326 | ||||
| SD of criterion | 0.715 | ||||
| Covariance | 0.010 | ||||
| r | 0.043 | ||||
| b (slope, estimate of beta) | 0.094 | ||||
| a (intercept, estimate of alpha) | -0.042 | ||||
| Mean Square Error | 0.516 | ||||
| DF error | 84.000 | ||||
| t(b) | 0.392 | ||||
| p(b) | 0.348 | ||||
| t(a) | -0.152 | ||||
| p(a) | 0.560 | ||||
| Lowerbound of 95% confidence interval for beta | -0.382 | ||||
| Upperbound of 95% confidence interval for beta | 0.570 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.586 | ||||
| Upperbound of 95% confidence interval for alpha | 0.503 | ||||
| Treynor index (mean / b) | -0.217 | ||||
| Jensen alpha (a) | -0.042 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.221 | ||||
| SD | 0.613 | ||||
| Sharpe ratio (Glass type estimate) | -0.361 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.358 | ||||
| df | 85.000 | ||||
| t | -0.966 | ||||
| p | 0.832 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.094 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.374 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.092 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.376 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.519 | ||||
| Upside Potential Ratio | 1.317 | ||||
| Upside part of mean | 0.562 | ||||
| Downside part of mean | -0.783 | ||||
| Upside SD | 0.440 | ||||
| Downside SD | 0.427 | ||||
| N nonnegative terms | 31.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 86.000 | ||||
| Mean of predictor | 0.177 | ||||
| Mean of criterion | -0.221 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.613 | ||||
| Covariance | 0.013 | ||||
| r | 0.069 | ||||
| b (slope, estimate of beta) | 0.142 | ||||
| a (intercept, estimate of alpha) | -0.246 | ||||
| Mean Square Error | 0.379 | ||||
| DF error | 84.000 | ||||
| t(b) | 0.634 | ||||
| p(b) | 0.264 | ||||
| t(a) | -1.056 | ||||
| p(a) | 0.853 | ||||
| Lowerbound of 95% confidence interval for beta | -0.302 | ||||
| Upperbound of 95% confidence interval for beta | 0.585 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.710 | ||||
| Upperbound of 95% confidence interval for alpha | 0.217 | ||||
| Treynor index (mean / b) | -1.563 | ||||
| Jensen alpha (a) | -0.246 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.266 | ||||
| Expected Shortfall on VaR | 0.317 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.157 | ||||
| Expected Shortfall on VaR | 0.277 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 86.000 | ||||
| Minimum | 0.591 | ||||
| Quartile 1 | 0.923 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.043 | ||||
| Maximum | 2.289 | ||||
| Mean of quarter 1 | 0.819 | ||||
| Mean of quarter 2 | 0.959 | ||||
| Mean of quarter 3 | 1.008 | ||||
| Mean of quarter 4 | 1.220 | ||||
| Inter Quartile Range | 0.120 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.047 | ||||
| Mean of outliers low | 0.672 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.058 | ||||
| Mean of outliers high | 1.597 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.247 | ||||
| VaR(95%) (moments method) | 0.177 | ||||
| Expected Shortfall (moments method) | 0.218 | ||||
| Extreme Value Index (regression method) | 0.083 | ||||
| VaR(95%) (regression method) | 0.193 | ||||
| Expected Shortfall (regression method) | 0.274 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.877 | ||||
| Quartile 1 | 0.877 | ||||
| Median | 0.877 | ||||
| Quartile 3 | 0.877 | ||||
| Maximum | 0.877 | ||||
| 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) | -0.100 | ||||
| Compounded annual return (geometric extrapolation) | -0.162 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.185 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.512 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.561 | ||||
| SD | 1.391 | ||||
| Sharpe ratio (Glass type estimate) | 0.403 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.403 | ||||
| df | 1885.000 | ||||
| t | 1.082 | ||||
| p | 0.484 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.328 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.134 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.328 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.134 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.807 | ||||
| Upside Potential Ratio | 7.306 | ||||
| Upside part of mean | 5.072 | ||||
| Downside part of mean | -4.512 | ||||
| Upside SD | 1.205 | ||||
| Downside SD | 0.694 | ||||
| N nonnegative terms | 681.000 | ||||
| N negative terms | 1205.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1886.000 | ||||
| Mean of predictor | 0.315 | ||||
| Mean of criterion | 0.561 | ||||
| SD of predictor | 0.509 | ||||
| SD of criterion | 1.391 | ||||
| Covariance | 0.116 | ||||
| r | 0.163 | ||||
| b (slope, estimate of beta) | 0.446 | ||||
| a (intercept, estimate of alpha) | 0.420 | ||||
| Mean Square Error | 1.883 | ||||
| DF error | 1884.000 | ||||
| t(b) | 7.185 | ||||
| p(b) | 0.418 | ||||
| t(a) | 0.821 | ||||
| p(a) | 0.491 | ||||
| Lowerbound of 95% confidence interval for beta | 0.324 | ||||
| Upperbound of 95% confidence interval for beta | 0.568 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.584 | ||||
| Upperbound of 95% confidence interval for alpha | 1.424 | ||||
| Treynor index (mean / b) | 1.256 | ||||
| Jensen alpha (a) | 0.420 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.220 | ||||
| SD | 1.218 | ||||
| Sharpe ratio (Glass type estimate) | -0.181 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.181 | ||||
| df | 1885.000 | ||||
| t | -0.485 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.911 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.550 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.911 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.550 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.269 | ||||
| Upside Potential Ratio | 5.592 | ||||
| Upside part of mean | 4.588 | ||||
| Downside part of mean | -4.809 | ||||
| Upside SD | 0.900 | ||||
| Downside SD | 0.821 | ||||
| N nonnegative terms | 681.000 | ||||
| N negative terms | 1205.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1886.000 | ||||
| Mean of predictor | 0.186 | ||||
| Mean of criterion | -0.220 | ||||
| SD of predictor | 0.508 | ||||
| SD of criterion | 1.218 | ||||
| Covariance | 0.116 | ||||
| r | 0.187 | ||||
| b (slope, estimate of beta) | 0.449 | ||||
| a (intercept, estimate of alpha) | -0.304 | ||||
| Mean Square Error | 1.433 | ||||
| DF error | 1884.000 | ||||
| t(b) | 8.280 | ||||
| p(b) | 0.406 | ||||
| t(a) | -0.681 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | 0.343 | ||||
| Upperbound of 95% confidence interval for beta | 0.556 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.179 | ||||
| Upperbound of 95% confidence interval for alpha | 0.571 | ||||
| Treynor index (mean / b) | -0.491 | ||||
| Jensen alpha (a) | -0.304 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.117 | ||||
| Expected Shortfall on VaR | 0.144 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.094 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1886.000 | ||||
| Minimum | 0.351 | ||||
| Quartile 1 | 0.981 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.014 | ||||
| Maximum | 2.885 | ||||
| Mean of quarter 1 | 0.938 | ||||
| Mean of quarter 2 | 0.993 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.074 | ||||
| Inter Quartile Range | 0.033 | ||||
| Number outliers low | 122.000 | ||||
| Percentage of outliers low | 0.065 | ||||
| Mean of outliers low | 0.869 | ||||
| Number of outliers high | 153.000 | ||||
| Percentage of outliers high | 0.081 | ||||
| Mean of outliers high | 1.164 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.379 | ||||
| VaR(95%) (moments method) | 0.058 | ||||
| Expected Shortfall (moments method) | 0.111 | ||||
| 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 | 5.000 | ||||
| Minimum | 0.062 | ||||
| Quartile 1 | 0.110 | ||||
| Median | 0.165 | ||||
| Quartile 3 | 0.267 | ||||
| Maximum | 0.906 | ||||
| Mean of quarter 1 | 0.086 | ||||
| Mean of quarter 2 | 0.165 | ||||
| Mean of quarter 3 | 0.267 | ||||
| Mean of quarter 4 | 0.906 | ||||
| Inter Quartile Range | 0.157 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.906 | ||||
| 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) | -0.100 | ||||
| Compounded annual return (geometric extrapolation) | -0.162 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.179 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.179 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.122 | ||||
| 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 | 0.989 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.500 | ||||
| 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 | 0.865 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.496 | ||||
| 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) | -8748832952776670.000 | ||||
| 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) | 148819061403240265015489630044160.000 | ||||
| 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 | ||||