Advanced Statistics: Bompus Stocks B
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 | 0.515 | ||||
| SD | 0.477 | ||||
| Sharpe ratio (Glass type estimate) | 1.079 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.069 | ||||
| df | 77.000 | ||||
| t | 2.751 | ||||
| p | 0.004 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.288 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.863 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.281 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.856 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.008 | ||||
| Upside Potential Ratio | 3.203 | ||||
| Upside part of mean | 0.822 | ||||
| Downside part of mean | -0.307 | ||||
| Upside SD | 0.426 | ||||
| Downside SD | 0.257 | ||||
| N nonnegative terms | 53.000 | ||||
| N negative terms | 25.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 78.000 | ||||
| Mean of predictor | 0.216 | ||||
| Mean of criterion | 0.515 | ||||
| SD of predictor | 0.275 | ||||
| SD of criterion | 0.477 | ||||
| Covariance | 0.094 | ||||
| r | 0.713 | ||||
| b (slope, estimate of beta) | 1.238 | ||||
| a (intercept, estimate of alpha) | 0.248 | ||||
| Mean Square Error | 0.114 | ||||
| DF error | 76.000 | ||||
| t(b) | 8.861 | ||||
| p(b) | 0.000 | ||||
| t(a) | 1.826 | ||||
| p(a) | 0.036 | ||||
| Lowerbound of 95% confidence interval for beta | 0.960 | ||||
| Upperbound of 95% confidence interval for beta | 1.517 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.023 | ||||
| Upperbound of 95% confidence interval for alpha | 0.518 | ||||
| Treynor index (mean / b) | 0.416 | ||||
| Jensen alpha (a) | 0.248 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.400 | ||||
| SD | 0.460 | ||||
| Sharpe ratio (Glass type estimate) | 0.869 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.860 | ||||
| df | 77.000 | ||||
| t | 2.215 | ||||
| p | 0.015 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.085 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.647 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.080 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.641 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.327 | ||||
| Upside Potential Ratio | 2.475 | ||||
| Upside part of mean | 0.746 | ||||
| Downside part of mean | -0.346 | ||||
| Upside SD | 0.363 | ||||
| Downside SD | 0.301 | ||||
| N nonnegative terms | 53.000 | ||||
| N negative terms | 25.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 78.000 | ||||
| Mean of predictor | 0.178 | ||||
| Mean of criterion | 0.400 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.460 | ||||
| Covariance | 0.087 | ||||
| r | 0.702 | ||||
| b (slope, estimate of beta) | 1.195 | ||||
| a (intercept, estimate of alpha) | 0.188 | ||||
| Mean Square Error | 0.109 | ||||
| DF error | 76.000 | ||||
| t(b) | 8.591 | ||||
| p(b) | 0.000 | ||||
| t(a) | 1.424 | ||||
| p(a) | 0.079 | ||||
| Lowerbound of 95% confidence interval for beta | 0.918 | ||||
| Upperbound of 95% confidence interval for beta | 1.473 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.075 | ||||
| Upperbound of 95% confidence interval for alpha | 0.450 | ||||
| Treynor index (mean / b) | 0.335 | ||||
| Jensen alpha (a) | 0.188 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.169 | ||||
| Expected Shortfall on VaR | 0.213 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.041 | ||||
| Expected Shortfall on VaR | 0.098 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 78.000 | ||||
| Minimum | 0.646 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.038 | ||||
| Quartile 3 | 1.089 | ||||
| Maximum | 1.693 | ||||
| Mean of quarter 1 | 0.905 | ||||
| Mean of quarter 2 | 1.020 | ||||
| Mean of quarter 3 | 1.064 | ||||
| Mean of quarter 4 | 1.197 | ||||
| Inter Quartile Range | 0.094 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.064 | ||||
| Mean of outliers low | 0.732 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.077 | ||||
| Mean of outliers high | 1.340 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.140 | ||||
| VaR(95%) (moments method) | 0.058 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.469 | ||||
| VaR(95%) (regression method) | 0.071 | ||||
| Expected Shortfall (regression method) | 0.180 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.093 | ||||
| Median | 0.170 | ||||
| Quartile 3 | 0.237 | ||||
| Maximum | 0.417 | ||||
| Mean of quarter 1 | 0.033 | ||||
| Mean of quarter 2 | 0.124 | ||||
| Mean of quarter 3 | 0.197 | ||||
| Mean of quarter 4 | 0.386 | ||||
| Inter Quartile Range | 0.144 | ||||
| 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) | 2.602 | ||||
| Compounded annual return (geometric extrapolation) | 0.559 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.340 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.449 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.624 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.803 | ||||
| SD | 0.838 | ||||
| Sharpe ratio (Glass type estimate) | 0.959 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.958 | ||||
| df | 1722.000 | ||||
| t | 2.459 | ||||
| p | 0.470 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.194 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.724 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.193 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.723 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.539 | ||||
| Upside Potential Ratio | 7.366 | ||||
| Upside part of mean | 3.845 | ||||
| Downside part of mean | -3.042 | ||||
| Upside SD | 0.657 | ||||
| Downside SD | 0.522 | ||||
| N nonnegative terms | 904.000 | ||||
| N negative terms | 819.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1723.000 | ||||
| Mean of predictor | 0.366 | ||||
| Mean of criterion | 0.803 | ||||
| SD of predictor | 0.568 | ||||
| SD of criterion | 0.838 | ||||
| Covariance | 0.336 | ||||
| r | 0.706 | ||||
| b (slope, estimate of beta) | 1.041 | ||||
| a (intercept, estimate of alpha) | 0.423 | ||||
| Mean Square Error | 0.352 | ||||
| DF error | 1721.000 | ||||
| t(b) | 41.364 | ||||
| p(b) | 0.091 | ||||
| t(a) | 1.825 | ||||
| p(a) | 0.472 | ||||
| Lowerbound of 95% confidence interval for beta | 0.991 | ||||
| Upperbound of 95% confidence interval for beta | 1.090 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.032 | ||||
| Upperbound of 95% confidence interval for alpha | 0.877 | ||||
| Treynor index (mean / b) | 0.772 | ||||
| Jensen alpha (a) | 0.423 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.461 | ||||
| SD | 0.825 | ||||
| Sharpe ratio (Glass type estimate) | 0.558 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.558 | ||||
| df | 1722.000 | ||||
| t | 1.432 | ||||
| p | 0.483 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.206 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.323 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.206 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.323 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.804 | ||||
| Upside Potential Ratio | 6.379 | ||||
| Upside part of mean | 3.657 | ||||
| Downside part of mean | -3.196 | ||||
| Upside SD | 0.594 | ||||
| Downside SD | 0.573 | ||||
| N nonnegative terms | 904.000 | ||||
| N negative terms | 819.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1723.000 | ||||
| Mean of predictor | 0.206 | ||||
| Mean of criterion | 0.461 | ||||
| SD of predictor | 0.565 | ||||
| SD of criterion | 0.825 | ||||
| Covariance | 0.331 | ||||
| r | 0.709 | ||||
| b (slope, estimate of beta) | 1.034 | ||||
| a (intercept, estimate of alpha) | 0.248 | ||||
| Mean Square Error | 0.339 | ||||
| DF error | 1721.000 | ||||
| t(b) | 41.684 | ||||
| p(b) | 0.090 | ||||
| t(a) | 1.092 | ||||
| p(a) | 0.483 | ||||
| Lowerbound of 95% confidence interval for beta | 0.986 | ||||
| Upperbound of 95% confidence interval for beta | 1.083 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.197 | ||||
| Upperbound of 95% confidence interval for alpha | 0.693 | ||||
| Treynor index (mean / b) | 0.445 | ||||
| Jensen alpha (a) | 0.248 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.079 | ||||
| Expected Shortfall on VaR | 0.098 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.055 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1723.000 | ||||
| Minimum | 0.701 | ||||
| Quartile 1 | 0.989 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.015 | ||||
| Maximum | 1.427 | ||||
| Mean of quarter 1 | 0.958 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.051 | ||||
| Inter Quartile Range | 0.026 | ||||
| Number outliers low | 95.000 | ||||
| Percentage of outliers low | 0.055 | ||||
| Mean of outliers low | 0.889 | ||||
| Number of outliers high | 98.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.133 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.630 | ||||
| VaR(95%) (moments method) | 0.041 | ||||
| Expected Shortfall (moments method) | 0.122 | ||||
| Extreme Value Index (regression method) | 0.432 | ||||
| VaR(95%) (regression method) | 0.034 | ||||
| Expected Shortfall (regression method) | 0.068 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 73.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.011 | ||||
| Median | 0.030 | ||||
| Quartile 3 | 0.090 | ||||
| Maximum | 0.475 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.022 | ||||
| Mean of quarter 3 | 0.056 | ||||
| Mean of quarter 4 | 0.196 | ||||
| Inter Quartile Range | 0.079 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.082 | ||||
| Mean of outliers high | 0.322 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.230 | ||||
| VaR(95%) (moments method) | 0.204 | ||||
| Expected Shortfall (moments method) | 0.315 | ||||
| Extreme Value Index (regression method) | 0.262 | ||||
| VaR(95%) (regression method) | 0.223 | ||||
| Expected Shortfall (regression method) | 0.358 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 4.049 | ||||
| Compounded annual return (geometric extrapolation) | 0.656 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.381 | ||||
| Compounded annual return / average of 25% largest draw downs | 3.345 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.696 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.726 | ||||
| SD | 0.683 | ||||
| Sharpe ratio (Glass type estimate) | 2.527 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.513 | ||||
| df | 130.000 | ||||
| t | 1.787 | ||||
| p | 0.423 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.266 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 5.311 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.276 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 5.301 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4.076 | ||||
| Upside Potential Ratio | 11.670 | ||||
| Upside part of mean | 4.941 | ||||
| Downside part of mean | -3.215 | ||||
| Upside SD | 0.543 | ||||
| Downside SD | 0.423 | ||||
| N nonnegative terms | 70.000 | ||||
| N negative terms | 61.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.057 | ||||
| Mean of criterion | 1.726 | ||||
| SD of predictor | 0.497 | ||||
| SD of criterion | 0.683 | ||||
| Covariance | 0.241 | ||||
| r | 0.710 | ||||
| b (slope, estimate of beta) | 0.975 | ||||
| a (intercept, estimate of alpha) | 0.695 | ||||
| Mean Square Error | 0.233 | ||||
| DF error | 129.000 | ||||
| t(b) | 11.450 | ||||
| p(b) | 0.090 | ||||
| t(a) | 1.009 | ||||
| p(a) | 0.444 | ||||
| Lowerbound of 95% confidence interval for beta | 0.807 | ||||
| Upperbound of 95% confidence interval for beta | 1.144 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.667 | ||||
| Upperbound of 95% confidence interval for alpha | 2.058 | ||||
| Treynor index (mean / b) | 1.770 | ||||
| Jensen alpha (a) | 0.695 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.491 | ||||
| SD | 0.680 | ||||
| Sharpe ratio (Glass type estimate) | 2.192 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.180 | ||||
| df | 130.000 | ||||
| t | 1.550 | ||||
| p | 0.433 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.596 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.973 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.605 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.964 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.387 | ||||
| Upside Potential Ratio | 10.904 | ||||
| Upside part of mean | 4.800 | ||||
| Downside part of mean | -3.309 | ||||
| Upside SD | 0.523 | ||||
| Downside SD | 0.440 | ||||
| N nonnegative terms | 70.000 | ||||
| N negative terms | 61.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.931 | ||||
| Mean of criterion | 1.491 | ||||
| SD of predictor | 0.501 | ||||
| SD of criterion | 0.680 | ||||
| Covariance | 0.243 | ||||
| r | 0.714 | ||||
| b (slope, estimate of beta) | 0.969 | ||||
| a (intercept, estimate of alpha) | 0.589 | ||||
| Mean Square Error | 0.228 | ||||
| DF error | 129.000 | ||||
| t(b) | 11.591 | ||||
| p(b) | 0.088 | ||||
| t(a) | 0.865 | ||||
| p(a) | 0.452 | ||||
| Lowerbound of 95% confidence interval for beta | 0.804 | ||||
| Upperbound of 95% confidence interval for beta | 1.135 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.757 | ||||
| Upperbound of 95% confidence interval for alpha | 1.934 | ||||
| Treynor index (mean / b) | 1.538 | ||||
| Jensen alpha (a) | 0.589 | ||||
| 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 | 0.078 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.054 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.878 | ||||
| Quartile 1 | 0.985 | ||||
| Median | 1.003 | ||||
| Quartile 3 | 1.029 | ||||
| Maximum | 1.148 | ||||
| Mean of quarter 1 | 0.956 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.015 | ||||
| Mean of quarter 4 | 1.060 | ||||
| Inter Quartile Range | 0.044 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.903 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.008 | ||||
| Mean of outliers high | 1.148 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.207 | ||||
| VaR(95%) (moments method) | 0.043 | ||||
| Expected Shortfall (moments method) | 0.067 | ||||
| Extreme Value Index (regression method) | 0.175 | ||||
| VaR(95%) (regression method) | 0.044 | ||||
| Expected Shortfall (regression method) | 0.067 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 13.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.017 | ||||
| Median | 0.028 | ||||
| Quartile 3 | 0.091 | ||||
| Maximum | 0.239 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.025 | ||||
| Mean of quarter 3 | 0.070 | ||||
| Mean of quarter 4 | 0.166 | ||||
| Inter Quartile Range | 0.074 | ||||
| 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 | 0.077 | ||||
| Mean of outliers high | 0.239 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.019 | ||||
| VaR(95%) (moments method) | 0.166 | ||||
| Expected Shortfall (moments method) | 0.214 | ||||
| Extreme Value Index (regression method) | 1.080 | ||||
| VaR(95%) (regression method) | 0.215 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 2.309 | ||||
| Compounded annual return (geometric extrapolation) | 3.641 | ||||
| Calmar ratio (compounded annual return / max draw down) | 15.219 | ||||
| Compounded annual return / average of 25% largest draw downs | 21.881 | ||||
| Compounded annual return / Expected Shortfall lognormal | 46.878 | ||||