Advanced Statistics: Dividend Growth
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 | 0.088 | ||||
| SD | 0.212 | ||||
| Sharpe ratio (Glass type estimate) | 0.415 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.411 | ||||
| df | 72.000 | ||||
| t | 1.025 | ||||
| p | 0.154 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.384 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.212 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.386 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.209 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.797 | ||||
| Upside Potential Ratio | 2.431 | ||||
| Upside part of mean | 0.269 | ||||
| Downside part of mean | -0.181 | ||||
| Upside SD | 0.181 | ||||
| Downside SD | 0.111 | ||||
| N nonnegative terms | 43.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.254 | ||||
| Mean of criterion | 0.088 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 0.212 | ||||
| Covariance | 0.029 | ||||
| r | 0.433 | ||||
| b (slope, estimate of beta) | 0.296 | ||||
| a (intercept, estimate of alpha) | 0.013 | ||||
| Mean Square Error | 0.037 | ||||
| DF error | 71.000 | ||||
| t(b) | 4.048 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.161 | ||||
| p(a) | 0.436 | ||||
| Lowerbound of 95% confidence interval for beta | 0.150 | ||||
| Upperbound of 95% confidence interval for beta | 0.442 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.147 | ||||
| Upperbound of 95% confidence interval for alpha | 0.173 | ||||
| Treynor index (mean / b) | 0.298 | ||||
| Jensen alpha (a) | 0.013 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.067 | ||||
| SD | 0.199 | ||||
| Sharpe ratio (Glass type estimate) | 0.338 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.334 | ||||
| df | 72.000 | ||||
| t | 0.833 | ||||
| p | 0.204 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.460 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.133 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.462 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.131 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.583 | ||||
| Upside Potential Ratio | 2.199 | ||||
| Upside part of mean | 0.254 | ||||
| Downside part of mean | -0.187 | ||||
| Upside SD | 0.162 | ||||
| Downside SD | 0.116 | ||||
| N nonnegative terms | 43.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.208 | ||||
| Mean of criterion | 0.067 | ||||
| SD of predictor | 0.291 | ||||
| SD of criterion | 0.199 | ||||
| Covariance | 0.027 | ||||
| r | 0.468 | ||||
| b (slope, estimate of beta) | 0.321 | ||||
| a (intercept, estimate of alpha) | 0.001 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 71.000 | ||||
| t(b) | 4.462 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.009 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | 0.177 | ||||
| Upperbound of 95% confidence interval for beta | 0.464 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.146 | ||||
| Upperbound of 95% confidence interval for alpha | 0.147 | ||||
| Treynor index (mean / b) | 0.210 | ||||
| Jensen alpha (a) | 0.001 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.085 | ||||
| Expected Shortfall on VaR | 0.107 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 73.000 | ||||
| Minimum | 0.881 | ||||
| Quartile 1 | 0.986 | ||||
| Median | 1.010 | ||||
| Quartile 3 | 1.031 | ||||
| Maximum | 1.355 | ||||
| Mean of quarter 1 | 0.950 | ||||
| Mean of quarter 2 | 1.001 | ||||
| Mean of quarter 3 | 1.021 | ||||
| Mean of quarter 4 | 1.076 | ||||
| Inter Quartile Range | 0.045 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.055 | ||||
| Mean of outliers low | 0.896 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.041 | ||||
| Mean of outliers high | 1.214 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.206 | ||||
| VaR(95%) (moments method) | 0.040 | ||||
| Expected Shortfall (moments method) | 0.051 | ||||
| Extreme Value Index (regression method) | -0.351 | ||||
| VaR(95%) (regression method) | 0.042 | ||||
| Expected Shortfall (regression method) | 0.051 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.023 | ||||
| Quartile 1 | 0.029 | ||||
| Median | 0.065 | ||||
| Quartile 3 | 0.170 | ||||
| Maximum | 0.250 | ||||
| Mean of quarter 1 | 0.023 | ||||
| Mean of quarter 2 | 0.049 | ||||
| Mean of quarter 3 | 0.081 | ||||
| Mean of quarter 4 | 0.225 | ||||
| Inter Quartile Range | 0.141 | ||||
| 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) | 0.159 | ||||
| Compounded annual return (geometric extrapolation) | 0.118 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.471 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.524 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.103 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.138 | ||||
| SD | 0.333 | ||||
| Sharpe ratio (Glass type estimate) | 0.414 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.414 | ||||
| df | 1602.000 | ||||
| t | 1.024 | ||||
| p | 0.487 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.379 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.206 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.379 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.206 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.667 | ||||
| Upside Potential Ratio | 7.238 | ||||
| Upside part of mean | 1.499 | ||||
| Downside part of mean | -1.361 | ||||
| Upside SD | 0.261 | ||||
| Downside SD | 0.207 | ||||
| N nonnegative terms | 807.000 | ||||
| N negative terms | 796.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1603.000 | ||||
| Mean of predictor | 0.428 | ||||
| Mean of criterion | 0.138 | ||||
| SD of predictor | 0.609 | ||||
| SD of criterion | 0.333 | ||||
| Covariance | 0.111 | ||||
| r | 0.544 | ||||
| b (slope, estimate of beta) | 0.298 | ||||
| a (intercept, estimate of alpha) | 0.010 | ||||
| Mean Square Error | 0.078 | ||||
| DF error | 1601.000 | ||||
| t(b) | 25.972 | ||||
| p(b) | 0.171 | ||||
| t(a) | 0.092 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | 0.276 | ||||
| Upperbound of 95% confidence interval for beta | 0.321 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.212 | ||||
| Upperbound of 95% confidence interval for alpha | 0.233 | ||||
| Treynor index (mean / b) | 0.463 | ||||
| Jensen alpha (a) | 0.010 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.084 | ||||
| SD | 0.327 | ||||
| Sharpe ratio (Glass type estimate) | 0.256 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.256 | ||||
| df | 1602.000 | ||||
| t | 0.633 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.537 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.048 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.537 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.048 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.393 | ||||
| Upside Potential Ratio | 6.869 | ||||
| Upside part of mean | 1.467 | ||||
| Downside part of mean | -1.383 | ||||
| Upside SD | 0.248 | ||||
| Downside SD | 0.214 | ||||
| N nonnegative terms | 807.000 | ||||
| N negative terms | 796.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1603.000 | ||||
| Mean of predictor | 0.249 | ||||
| Mean of criterion | 0.084 | ||||
| SD of predictor | 0.596 | ||||
| SD of criterion | 0.327 | ||||
| Covariance | 0.105 | ||||
| r | 0.539 | ||||
| b (slope, estimate of beta) | 0.296 | ||||
| a (intercept, estimate of alpha) | 0.010 | ||||
| Mean Square Error | 0.076 | ||||
| DF error | 1601.000 | ||||
| t(b) | 25.608 | ||||
| p(b) | 0.174 | ||||
| t(a) | 0.090 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | 0.274 | ||||
| Upperbound of 95% confidence interval for beta | 0.319 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.209 | ||||
| Upperbound of 95% confidence interval for alpha | 0.229 | ||||
| Treynor index (mean / b) | 0.283 | ||||
| Jensen alpha (a) | 0.010 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.041 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.025 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1603.000 | ||||
| Minimum | 0.884 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.006 | ||||
| Maximum | 1.244 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.020 | ||||
| Inter Quartile Range | 0.011 | ||||
| Number outliers low | 94.000 | ||||
| Percentage of outliers low | 0.059 | ||||
| Mean of outliers low | 0.958 | ||||
| Number of outliers high | 91.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.052 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.451 | ||||
| VaR(95%) (moments method) | 0.018 | ||||
| Expected Shortfall (moments method) | 0.037 | ||||
| Extreme Value Index (regression method) | 0.221 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.025 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 37.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.019 | ||||
| Quartile 3 | 0.046 | ||||
| Maximum | 0.279 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.014 | ||||
| Mean of quarter 3 | 0.030 | ||||
| Mean of quarter 4 | 0.126 | ||||
| Inter Quartile Range | 0.039 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.108 | ||||
| Mean of outliers high | 0.211 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.612 | ||||
| VaR(95%) (moments method) | 0.140 | ||||
| Expected Shortfall (moments method) | 0.381 | ||||
| Extreme Value Index (regression method) | 0.298 | ||||
| VaR(95%) (regression method) | 0.117 | ||||
| Expected Shortfall (regression method) | 0.194 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.194 | ||||
| Compounded annual return (geometric extrapolation) | 0.136 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.489 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.086 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.364 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.247 | ||||
| SD | 0.461 | ||||
| Sharpe ratio (Glass type estimate) | 2.704 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.689 | ||||
| df | 130.000 | ||||
| t | 1.912 | ||||
| p | 0.417 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.092 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 5.490 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.102 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 5.480 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 5.932 | ||||
| Upside Potential Ratio | 12.781 | ||||
| Upside part of mean | 2.686 | ||||
| Downside part of mean | -1.440 | ||||
| Upside SD | 0.416 | ||||
| Downside SD | 0.210 | ||||
| N nonnegative terms | 76.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 2.077 | ||||
| Mean of criterion | 1.247 | ||||
| SD of predictor | 0.643 | ||||
| SD of criterion | 0.461 | ||||
| Covariance | 0.136 | ||||
| r | 0.460 | ||||
| b (slope, estimate of beta) | 0.330 | ||||
| a (intercept, estimate of alpha) | 0.562 | ||||
| Mean Square Error | 0.169 | ||||
| DF error | 129.000 | ||||
| t(b) | 5.878 | ||||
| p(b) | 0.218 | ||||
| t(a) | 0.948 | ||||
| p(a) | 0.447 | ||||
| Lowerbound of 95% confidence interval for beta | 0.219 | ||||
| Upperbound of 95% confidence interval for beta | 0.441 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.611 | ||||
| Upperbound of 95% confidence interval for alpha | 1.735 | ||||
| Treynor index (mean / b) | 3.781 | ||||
| Jensen alpha (a) | 0.562 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.145 | ||||
| SD | 0.439 | ||||
| Sharpe ratio (Glass type estimate) | 2.606 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.591 | ||||
| df | 130.000 | ||||
| t | 1.843 | ||||
| p | 0.420 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.189 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 5.391 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.199 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 5.380 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 5.326 | ||||
| Upside Potential Ratio | 12.126 | ||||
| Upside part of mean | 2.607 | ||||
| Downside part of mean | -1.462 | ||||
| Upside SD | 0.388 | ||||
| Downside SD | 0.215 | ||||
| N nonnegative terms | 76.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.863 | ||||
| Mean of criterion | 1.145 | ||||
| SD of predictor | 0.648 | ||||
| SD of criterion | 0.439 | ||||
| Covariance | 0.137 | ||||
| r | 0.482 | ||||
| b (slope, estimate of beta) | 0.327 | ||||
| a (intercept, estimate of alpha) | 0.536 | ||||
| Mean Square Error | 0.149 | ||||
| DF error | 129.000 | ||||
| t(b) | 6.253 | ||||
| p(b) | 0.205 | ||||
| t(a) | 0.965 | ||||
| p(a) | 0.446 | ||||
| Lowerbound of 95% confidence interval for beta | 0.224 | ||||
| Upperbound of 95% confidence interval for beta | 0.431 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.563 | ||||
| Upperbound of 95% confidence interval for alpha | 1.634 | ||||
| Treynor index (mean / b) | 3.500 | ||||
| Jensen alpha (a) | 0.536 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.039 | ||||
| Expected Shortfall on VaR | 0.050 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.929 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.003 | ||||
| Quartile 3 | 1.011 | ||||
| Maximum | 1.226 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.034 | ||||
| Inter Quartile Range | 0.016 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.951 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.061 | ||||
| Mean of outliers high | 1.076 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.127 | ||||
| VaR(95%) (moments method) | 0.016 | ||||
| Expected Shortfall (moments method) | 0.024 | ||||
| Extreme Value Index (regression method) | 0.213 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.036 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 15.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.014 | ||||
| Quartile 3 | 0.030 | ||||
| Maximum | 0.190 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.012 | ||||
| Mean of quarter 3 | 0.022 | ||||
| Mean of quarter 4 | 0.085 | ||||
| Inter Quartile Range | 0.022 | ||||
| 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 | 0.133 | ||||
| Mean of outliers high | 0.130 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.008 | ||||
| VaR(95%) (moments method) | 0.076 | ||||
| Expected Shortfall (moments method) | 0.108 | ||||
| Extreme Value Index (regression method) | 0.862 | ||||
| VaR(95%) (regression method) | 0.145 | ||||
| Expected Shortfall (regression method) | 1.089 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.624 | ||||
| Compounded annual return (geometric extrapolation) | 2.284 | ||||
| Calmar ratio (compounded annual return / max draw down) | 12.013 | ||||
| Compounded annual return / average of 25% largest draw downs | 26.774 | ||||
| Compounded annual return / Expected Shortfall lognormal | 45.436 | ||||