Advanced Statistics: Value Investing
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 | 0.656 | ||||
| SD | 0.384 | ||||
| Sharpe ratio (Glass type estimate) | 1.707 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.683 | ||||
| df | 55.000 | ||||
| t | 3.687 | ||||
| p | 0.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.738 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.661 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.723 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.644 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 6.231 | ||||
| Upside Potential Ratio | 7.702 | ||||
| Upside part of mean | 0.810 | ||||
| Downside part of mean | -0.155 | ||||
| Upside SD | 0.412 | ||||
| Downside SD | 0.105 | ||||
| N nonnegative terms | 39.000 | ||||
| N negative terms | 17.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 56.000 | ||||
| Mean of predictor | 0.335 | ||||
| Mean of criterion | 0.656 | ||||
| SD of predictor | 0.211 | ||||
| SD of criterion | 0.384 | ||||
| Covariance | 0.046 | ||||
| r | 0.569 | ||||
| b (slope, estimate of beta) | 1.038 | ||||
| a (intercept, estimate of alpha) | 0.308 | ||||
| Mean Square Error | 0.102 | ||||
| DF error | 54.000 | ||||
| t(b) | 5.089 | ||||
| p(b) | 0.000 | ||||
| t(a) | 1.892 | ||||
| p(a) | 0.032 | ||||
| Lowerbound of 95% confidence interval for beta | 0.629 | ||||
| Upperbound of 95% confidence interval for beta | 1.447 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.018 | ||||
| Upperbound of 95% confidence interval for alpha | 0.634 | ||||
| Treynor index (mean / b) | 0.631 | ||||
| Jensen alpha (a) | 0.308 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.576 | ||||
| SD | 0.342 | ||||
| Sharpe ratio (Glass type estimate) | 1.688 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.665 | ||||
| df | 55.000 | ||||
| t | 3.646 | ||||
| p | 0.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.721 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.641 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.706 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.624 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 5.232 | ||||
| Upside Potential Ratio | 6.685 | ||||
| Upside part of mean | 0.737 | ||||
| Downside part of mean | -0.160 | ||||
| Upside SD | 0.361 | ||||
| Downside SD | 0.110 | ||||
| N nonnegative terms | 39.000 | ||||
| N negative terms | 17.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 56.000 | ||||
| Mean of predictor | 0.309 | ||||
| Mean of criterion | 0.576 | ||||
| SD of predictor | 0.205 | ||||
| SD of criterion | 0.342 | ||||
| Covariance | 0.042 | ||||
| r | 0.599 | ||||
| b (slope, estimate of beta) | 0.996 | ||||
| a (intercept, estimate of alpha) | 0.269 | ||||
| Mean Square Error | 0.076 | ||||
| DF error | 54.000 | ||||
| t(b) | 5.493 | ||||
| p(b) | 0.000 | ||||
| t(a) | 1.927 | ||||
| p(a) | 0.030 | ||||
| Lowerbound of 95% confidence interval for beta | 0.633 | ||||
| Upperbound of 95% confidence interval for beta | 1.360 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.011 | ||||
| Upperbound of 95% confidence interval for alpha | 0.549 | ||||
| Treynor index (mean / b) | 0.579 | ||||
| Jensen alpha (a) | 0.269 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.108 | ||||
| Expected Shortfall on VaR | 0.143 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 56.000 | ||||
| Minimum | 0.869 | ||||
| Quartile 1 | 0.989 | ||||
| Median | 1.038 | ||||
| Quartile 3 | 1.083 | ||||
| Maximum | 1.462 | ||||
| Mean of quarter 1 | 0.953 | ||||
| Mean of quarter 2 | 1.017 | ||||
| Mean of quarter 3 | 1.057 | ||||
| Mean of quarter 4 | 1.206 | ||||
| Inter Quartile Range | 0.094 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.089 | ||||
| Mean of outliers high | 1.333 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.105 | ||||
| VaR(95%) (moments method) | 0.034 | ||||
| Expected Shortfall (moments method) | 0.046 | ||||
| Extreme Value Index (regression method) | -0.037 | ||||
| VaR(95%) (regression method) | 0.048 | ||||
| Expected Shortfall (regression method) | 0.069 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.012 | ||||
| Quartile 1 | 0.027 | ||||
| Median | 0.040 | ||||
| Quartile 3 | 0.110 | ||||
| Maximum | 0.131 | ||||
| Mean of quarter 1 | 0.018 | ||||
| Mean of quarter 2 | 0.034 | ||||
| Mean of quarter 3 | 0.046 | ||||
| Mean of quarter 4 | 0.131 | ||||
| Inter Quartile Range | 0.083 | ||||
| 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) | -25.601 | ||||
| VaR(95%) (moments method) | 0.131 | ||||
| Expected Shortfall (moments method) | 0.131 | ||||
| Extreme Value Index (regression method) | -2.634 | ||||
| VaR(95%) (regression method) | 0.131 | ||||
| Expected Shortfall (regression method) | 0.131 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 3.664 | ||||
| Compounded annual return (geometric extrapolation) | 0.860 | ||||
| Calmar ratio (compounded annual return / max draw down) | 6.574 | ||||
| Compounded annual return / average of 25% largest draw downs | 6.589 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.668 | ||||
| SD | 0.390 | ||||
| Sharpe ratio (Glass type estimate) | 1.712 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.711 | ||||
| df | 1234.000 | ||||
| t | 3.717 | ||||
| p | 0.447 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.806 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.617 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.806 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.616 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.991 | ||||
| Upside Potential Ratio | 9.534 | ||||
| Upside part of mean | 2.128 | ||||
| Downside part of mean | -1.461 | ||||
| Upside SD | 0.322 | ||||
| Downside SD | 0.223 | ||||
| N nonnegative terms | 674.000 | ||||
| N negative terms | 561.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1235.000 | ||||
| Mean of predictor | 0.366 | ||||
| Mean of criterion | 0.668 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 0.390 | ||||
| Covariance | 0.058 | ||||
| r | 0.530 | ||||
| b (slope, estimate of beta) | 0.741 | ||||
| a (intercept, estimate of alpha) | 0.397 | ||||
| Mean Square Error | 0.109 | ||||
| DF error | 1233.000 | ||||
| t(b) | 21.947 | ||||
| p(b) | 0.179 | ||||
| t(a) | 2.595 | ||||
| p(a) | 0.453 | ||||
| Lowerbound of 95% confidence interval for beta | 0.674 | ||||
| Upperbound of 95% confidence interval for beta | 0.807 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.097 | ||||
| Upperbound of 95% confidence interval for alpha | 0.697 | ||||
| Treynor index (mean / b) | 0.902 | ||||
| Jensen alpha (a) | 0.397 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.595 | ||||
| SD | 0.376 | ||||
| Sharpe ratio (Glass type estimate) | 1.581 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.580 | ||||
| df | 1234.000 | ||||
| t | 3.433 | ||||
| p | 0.451 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.676 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.486 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.675 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.485 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.588 | ||||
| Upside Potential Ratio | 9.055 | ||||
| Upside part of mean | 2.081 | ||||
| Downside part of mean | -1.486 | ||||
| Upside SD | 0.300 | ||||
| Downside SD | 0.230 | ||||
| N nonnegative terms | 674.000 | ||||
| N negative terms | 561.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1235.000 | ||||
| Mean of predictor | 0.327 | ||||
| Mean of criterion | 0.595 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 0.376 | ||||
| Covariance | 0.058 | ||||
| r | 0.552 | ||||
| b (slope, estimate of beta) | 0.744 | ||||
| a (intercept, estimate of alpha) | 0.352 | ||||
| Mean Square Error | 0.098 | ||||
| DF error | 1233.000 | ||||
| t(b) | 23.234 | ||||
| p(b) | 0.167 | ||||
| t(a) | 2.426 | ||||
| p(a) | 0.456 | ||||
| Lowerbound of 95% confidence interval for beta | 0.681 | ||||
| Upperbound of 95% confidence interval for beta | 0.807 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.067 | ||||
| Upperbound of 95% confidence interval for alpha | 0.636 | ||||
| Treynor index (mean / b) | 0.799 | ||||
| Jensen alpha (a) | 0.352 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.045 | ||||
| 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 | 1235.000 | ||||
| Minimum | 0.895 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.010 | ||||
| Maximum | 1.408 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.005 | ||||
| Mean of quarter 4 | 1.028 | ||||
| Inter Quartile Range | 0.015 | ||||
| Number outliers low | 61.000 | ||||
| Percentage of outliers low | 0.049 | ||||
| Mean of outliers low | 0.949 | ||||
| Number of outliers high | 71.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.058 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.459 | ||||
| VaR(95%) (moments method) | 0.019 | ||||
| Expected Shortfall (moments method) | 0.040 | ||||
| Extreme Value Index (regression method) | 0.213 | ||||
| VaR(95%) (regression method) | 0.017 | ||||
| Expected Shortfall (regression method) | 0.028 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 85.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.018 | ||||
| Quartile 3 | 0.057 | ||||
| Maximum | 0.223 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.012 | ||||
| Mean of quarter 3 | 0.030 | ||||
| Mean of quarter 4 | 0.123 | ||||
| Inter Quartile Range | 0.051 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.082 | ||||
| Mean of outliers high | 0.193 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.097 | ||||
| VaR(95%) (moments method) | 0.120 | ||||
| Expected Shortfall (moments method) | 0.153 | ||||
| Extreme Value Index (regression method) | -0.623 | ||||
| VaR(95%) (regression method) | 0.140 | ||||
| Expected Shortfall (regression method) | 0.158 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 4.094 | ||||
| Compounded annual return (geometric extrapolation) | 0.894 | ||||
| Calmar ratio (compounded annual return / max draw down) | 4.005 | ||||
| Compounded annual return / average of 25% largest draw downs | 7.252 | ||||
| Compounded annual return / Expected Shortfall lognormal | 20.048 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.265 | ||||
| SD | 0.663 | ||||
| Sharpe ratio (Glass type estimate) | 1.908 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.897 | ||||
| df | 130.000 | ||||
| t | 1.349 | ||||
| p | 0.441 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.877 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.686 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.884 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.679 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.866 | ||||
| Upside Potential Ratio | 10.802 | ||||
| Upside part of mean | 4.766 | ||||
| Downside part of mean | -3.502 | ||||
| Upside SD | 0.497 | ||||
| Downside SD | 0.441 | ||||
| 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 | 1.081 | ||||
| Mean of criterion | 1.265 | ||||
| SD of predictor | 0.496 | ||||
| SD of criterion | 0.663 | ||||
| Covariance | 0.225 | ||||
| r | 0.685 | ||||
| b (slope, estimate of beta) | 0.914 | ||||
| a (intercept, estimate of alpha) | 0.277 | ||||
| Mean Square Error | 0.235 | ||||
| DF error | 129.000 | ||||
| t(b) | 10.665 | ||||
| p(b) | 0.101 | ||||
| t(a) | 0.400 | ||||
| p(a) | 0.478 | ||||
| Lowerbound of 95% confidence interval for beta | 0.744 | ||||
| Upperbound of 95% confidence interval for beta | 1.083 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.093 | ||||
| Upperbound of 95% confidence interval for alpha | 1.646 | ||||
| Treynor index (mean / b) | 1.384 | ||||
| Jensen alpha (a) | 0.277 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.044 | ||||
| SD | 0.663 | ||||
| Sharpe ratio (Glass type estimate) | 1.574 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.565 | ||||
| df | 130.000 | ||||
| t | 1.113 | ||||
| p | 0.451 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.208 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.349 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.214 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.343 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.281 | ||||
| Upside Potential Ratio | 10.153 | ||||
| Upside part of mean | 4.647 | ||||
| Downside part of mean | -3.603 | ||||
| Upside SD | 0.481 | ||||
| Downside SD | 0.458 | ||||
| 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 | 0.958 | ||||
| Mean of criterion | 1.044 | ||||
| SD of predictor | 0.494 | ||||
| SD of criterion | 0.663 | ||||
| Covariance | 0.226 | ||||
| r | 0.689 | ||||
| b (slope, estimate of beta) | 0.926 | ||||
| a (intercept, estimate of alpha) | 0.158 | ||||
| Mean Square Error | 0.233 | ||||
| DF error | 129.000 | ||||
| t(b) | 10.804 | ||||
| p(b) | 0.099 | ||||
| t(a) | 0.229 | ||||
| p(a) | 0.487 | ||||
| Lowerbound of 95% confidence interval for beta | 0.756 | ||||
| Upperbound of 95% confidence interval for beta | 1.095 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.202 | ||||
| Upperbound of 95% confidence interval for alpha | 1.517 | ||||
| Treynor index (mean / b) | 1.128 | ||||
| Jensen alpha (a) | 0.158 | ||||
| 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 | 0.077 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.055 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.895 | ||||
| Quartile 1 | 0.980 | ||||
| Median | 1.005 | ||||
| Quartile 3 | 1.030 | ||||
| Maximum | 1.130 | ||||
| Mean of quarter 1 | 0.953 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.018 | ||||
| Mean of quarter 4 | 1.054 | ||||
| Inter Quartile Range | 0.050 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.896 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.008 | ||||
| Mean of outliers high | 1.130 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.085 | ||||
| VaR(95%) (moments method) | 0.046 | ||||
| Expected Shortfall (moments method) | 0.065 | ||||
| Extreme Value Index (regression method) | -0.119 | ||||
| VaR(95%) (regression method) | 0.049 | ||||
| Expected Shortfall (regression method) | 0.063 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.038 | ||||
| Median | 0.099 | ||||
| Quartile 3 | 0.141 | ||||
| Maximum | 0.216 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | 0.071 | ||||
| Mean of quarter 3 | 0.113 | ||||
| Mean of quarter 4 | 0.185 | ||||
| Inter Quartile Range | 0.103 | ||||
| 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) | -0.842 | ||||
| VaR(95%) (moments method) | 0.205 | ||||
| Expected Shortfall (moments method) | 0.215 | ||||
| Extreme Value Index (regression method) | 0.632 | ||||
| VaR(95%) (regression method) | 0.219 | ||||
| Expected Shortfall (regression method) | 0.371 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.446 | ||||
| Compounded annual return (geometric extrapolation) | 1.968 | ||||
| Calmar ratio (compounded annual return / max draw down) | 9.113 | ||||
| Compounded annual return / average of 25% largest draw downs | 10.660 | ||||
| Compounded annual return / Expected Shortfall lognormal | 25.467 | ||||