Advanced Statistics: Butterfly 100 Stocks
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 | 0.307 | ||||
| SD | 0.208 | ||||
| Sharpe ratio (Glass type estimate) | 1.475 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.459 | ||||
| df | 67.000 | ||||
| t | 3.512 | ||||
| p | 0.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.610 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.331 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.599 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.318 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4.389 | ||||
| Upside Potential Ratio | 5.494 | ||||
| Upside part of mean | 0.384 | ||||
| Downside part of mean | -0.077 | ||||
| Upside SD | 0.214 | ||||
| Downside SD | 0.070 | ||||
| N nonnegative terms | 49.000 | ||||
| N negative terms | 19.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.287 | ||||
| Mean of criterion | 0.307 | ||||
| SD of predictor | 0.224 | ||||
| SD of criterion | 0.208 | ||||
| Covariance | 0.035 | ||||
| r | 0.745 | ||||
| b (slope, estimate of beta) | 0.692 | ||||
| a (intercept, estimate of alpha) | 0.109 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 66.000 | ||||
| t(b) | 9.065 | ||||
| p(b) | 0.000 | ||||
| t(a) | 1.733 | ||||
| p(a) | 0.044 | ||||
| Lowerbound of 95% confidence interval for beta | 0.540 | ||||
| Upperbound of 95% confidence interval for beta | 0.844 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.017 | ||||
| Upperbound of 95% confidence interval for alpha | 0.234 | ||||
| Treynor index (mean / b) | 0.444 | ||||
| Jensen alpha (a) | 0.109 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.283 | ||||
| SD | 0.194 | ||||
| Sharpe ratio (Glass type estimate) | 1.458 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.441 | ||||
| df | 67.000 | ||||
| t | 3.470 | ||||
| p | 0.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.593 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.312 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.582 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.300 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.884 | ||||
| Upside Potential Ratio | 4.976 | ||||
| Upside part of mean | 0.363 | ||||
| Downside part of mean | -0.080 | ||||
| Upside SD | 0.196 | ||||
| Downside SD | 0.073 | ||||
| N nonnegative terms | 49.000 | ||||
| N negative terms | 19.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.260 | ||||
| Mean of criterion | 0.283 | ||||
| SD of predictor | 0.208 | ||||
| SD of criterion | 0.194 | ||||
| Covariance | 0.030 | ||||
| r | 0.745 | ||||
| b (slope, estimate of beta) | 0.695 | ||||
| a (intercept, estimate of alpha) | 0.102 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 66.000 | ||||
| t(b) | 9.063 | ||||
| p(b) | 0.000 | ||||
| t(a) | 1.748 | ||||
| p(a) | 0.043 | ||||
| Lowerbound of 95% confidence interval for beta | 0.542 | ||||
| Upperbound of 95% confidence interval for beta | 0.848 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.015 | ||||
| Upperbound of 95% confidence interval for alpha | 0.219 | ||||
| Treynor index (mean / b) | 0.407 | ||||
| Jensen alpha (a) | 0.102 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.066 | ||||
| Expected Shortfall on VaR | 0.088 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 68.000 | ||||
| Minimum | 0.896 | ||||
| Quartile 1 | 1.002 | ||||
| Median | 1.017 | ||||
| Quartile 3 | 1.039 | ||||
| Maximum | 1.241 | ||||
| Mean of quarter 1 | 0.978 | ||||
| Mean of quarter 2 | 1.009 | ||||
| Mean of quarter 3 | 1.027 | ||||
| Mean of quarter 4 | 1.103 | ||||
| Inter Quartile Range | 0.036 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.044 | ||||
| Mean of outliers low | 0.915 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.088 | ||||
| Mean of outliers high | 1.188 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.117 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.590 | ||||
| VaR(95%) (regression method) | 0.023 | ||||
| Expected Shortfall (regression method) | 0.078 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.017 | ||||
| Quartile 3 | 0.036 | ||||
| Maximum | 0.147 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.021 | ||||
| Mean of quarter 4 | 0.097 | ||||
| Inter Quartile Range | 0.028 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.125 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -19.926 | ||||
| VaR(95%) (moments method) | 0.087 | ||||
| Expected Shortfall (moments method) | 0.087 | ||||
| Extreme Value Index (regression method) | -1.584 | ||||
| VaR(95%) (regression method) | 0.183 | ||||
| Expected Shortfall (regression method) | 0.190 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.950 | ||||
| Compounded annual return (geometric extrapolation) | 0.387 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.638 | ||||
| Compounded annual return / average of 25% largest draw downs | 3.997 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.409 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.327 | ||||
| SD | 0.240 | ||||
| Sharpe ratio (Glass type estimate) | 1.363 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.363 | ||||
| df | 1499.000 | ||||
| t | 3.262 | ||||
| p | 0.447 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.543 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.184 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.542 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.183 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.959 | ||||
| Upside Potential Ratio | 6.781 | ||||
| Upside part of mean | 1.131 | ||||
| Downside part of mean | -0.804 | ||||
| Upside SD | 0.173 | ||||
| Downside SD | 0.167 | ||||
| N nonnegative terms | 830.000 | ||||
| N negative terms | 670.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1500.000 | ||||
| Mean of predictor | 0.316 | ||||
| Mean of criterion | 0.327 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 0.240 | ||||
| Covariance | 0.042 | ||||
| r | 0.722 | ||||
| b (slope, estimate of beta) | 0.713 | ||||
| a (intercept, estimate of alpha) | 0.101 | ||||
| Mean Square Error | 0.027 | ||||
| DF error | 1498.000 | ||||
| t(b) | 40.397 | ||||
| p(b) | 0.139 | ||||
| t(a) | 1.459 | ||||
| p(a) | 0.481 | ||||
| Lowerbound of 95% confidence interval for beta | 0.679 | ||||
| Upperbound of 95% confidence interval for beta | 0.748 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.035 | ||||
| Upperbound of 95% confidence interval for alpha | 0.238 | ||||
| Treynor index (mean / b) | 0.458 | ||||
| Jensen alpha (a) | 0.101 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.297 | ||||
| SD | 0.242 | ||||
| Sharpe ratio (Glass type estimate) | 1.229 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.228 | ||||
| df | 1499.000 | ||||
| t | 2.940 | ||||
| p | 0.452 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.408 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.049 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.408 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.048 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.704 | ||||
| Upside Potential Ratio | 6.397 | ||||
| Upside part of mean | 1.116 | ||||
| Downside part of mean | -0.819 | ||||
| Upside SD | 0.169 | ||||
| Downside SD | 0.174 | ||||
| N nonnegative terms | 830.000 | ||||
| N negative terms | 670.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1500.000 | ||||
| Mean of predictor | 0.286 | ||||
| Mean of criterion | 0.297 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 0.242 | ||||
| Covariance | 0.043 | ||||
| r | 0.724 | ||||
| b (slope, estimate of beta) | 0.720 | ||||
| a (intercept, estimate of alpha) | 0.091 | ||||
| Mean Square Error | 0.028 | ||||
| DF error | 1498.000 | ||||
| t(b) | 40.607 | ||||
| p(b) | 0.138 | ||||
| t(a) | 1.307 | ||||
| p(a) | 0.483 | ||||
| Lowerbound of 95% confidence interval for beta | 0.685 | ||||
| Upperbound of 95% confidence interval for beta | 0.755 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | 0.229 | ||||
| Treynor index (mean / b) | 0.413 | ||||
| Jensen alpha (a) | 0.091 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1500.000 | ||||
| Minimum | 0.825 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.004 | ||||
| Maximum | 1.144 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.006 | ||||
| Number outliers low | 109.000 | ||||
| Percentage of outliers low | 0.073 | ||||
| Mean of outliers low | 0.972 | ||||
| Number of outliers high | 154.000 | ||||
| Percentage of outliers high | 0.103 | ||||
| Mean of outliers high | 1.027 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.817 | ||||
| VaR(95%) (moments method) | 0.010 | ||||
| Expected Shortfall (moments method) | 0.059 | ||||
| Extreme Value Index (regression method) | 0.521 | ||||
| VaR(95%) (regression method) | 0.009 | ||||
| Expected Shortfall (regression method) | 0.022 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 138.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.019 | ||||
| Maximum | 0.274 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.011 | ||||
| Mean of quarter 4 | 0.063 | ||||
| Inter Quartile Range | 0.018 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 14.000 | ||||
| Percentage of outliers high | 0.101 | ||||
| Mean of outliers high | 0.113 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.616 | ||||
| VaR(95%) (moments method) | 0.066 | ||||
| Expected Shortfall (moments method) | 0.186 | ||||
| Extreme Value Index (regression method) | 0.623 | ||||
| VaR(95%) (regression method) | 0.062 | ||||
| Expected Shortfall (regression method) | 0.173 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.059 | ||||
| Compounded annual return (geometric extrapolation) | 0.407 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.483 | ||||
| Compounded annual return / average of 25% largest draw downs | 6.495 | ||||
| Compounded annual return / Expected Shortfall lognormal | 13.907 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.866 | ||||
| SD | 0.434 | ||||
| Sharpe ratio (Glass type estimate) | 1.997 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.985 | ||||
| df | 130.000 | ||||
| t | 1.412 | ||||
| p | 0.439 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.789 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.775 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.797 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.767 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.956 | ||||
| Upside Potential Ratio | 10.354 | ||||
| Upside part of mean | 3.032 | ||||
| Downside part of mean | -2.167 | ||||
| Upside SD | 0.322 | ||||
| Downside SD | 0.293 | ||||
| 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 | 1.407 | ||||
| Mean of criterion | 0.866 | ||||
| SD of predictor | 0.494 | ||||
| SD of criterion | 0.434 | ||||
| Covariance | 0.173 | ||||
| r | 0.810 | ||||
| b (slope, estimate of beta) | 0.711 | ||||
| a (intercept, estimate of alpha) | -0.134 | ||||
| Mean Square Error | 0.065 | ||||
| DF error | 129.000 | ||||
| t(b) | 15.692 | ||||
| p(b) | 0.048 | ||||
| t(a) | -0.367 | ||||
| p(a) | 0.521 | ||||
| Lowerbound of 95% confidence interval for beta | 0.621 | ||||
| Upperbound of 95% confidence interval for beta | 0.801 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.860 | ||||
| Upperbound of 95% confidence interval for alpha | 0.591 | ||||
| Treynor index (mean / b) | 1.217 | ||||
| Jensen alpha (a) | -0.134 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.771 | ||||
| SD | 0.435 | ||||
| Sharpe ratio (Glass type estimate) | 1.774 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.764 | ||||
| df | 130.000 | ||||
| t | 1.254 | ||||
| p | 0.445 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.010 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.551 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.016 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.544 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.564 | ||||
| Upside Potential Ratio | 9.915 | ||||
| Upside part of mean | 2.981 | ||||
| Downside part of mean | -2.211 | ||||
| Upside SD | 0.315 | ||||
| Downside SD | 0.301 | ||||
| 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 | 1.282 | ||||
| Mean of criterion | 0.771 | ||||
| SD of predictor | 0.495 | ||||
| SD of criterion | 0.435 | ||||
| Covariance | 0.175 | ||||
| r | 0.813 | ||||
| b (slope, estimate of beta) | 0.714 | ||||
| a (intercept, estimate of alpha) | -0.144 | ||||
| Mean Square Error | 0.064 | ||||
| DF error | 129.000 | ||||
| t(b) | 15.878 | ||||
| p(b) | 0.047 | ||||
| t(a) | -0.396 | ||||
| p(a) | 0.522 | ||||
| Lowerbound of 95% confidence interval for beta | 0.625 | ||||
| Upperbound of 95% confidence interval for beta | 0.803 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.863 | ||||
| Upperbound of 95% confidence interval for alpha | 0.575 | ||||
| Treynor index (mean / b) | 1.080 | ||||
| Jensen alpha (a) | -0.144 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.040 | ||||
| Expected Shortfall on VaR | 0.051 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.920 | ||||
| Quartile 1 | 0.990 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.019 | ||||
| Maximum | 1.076 | ||||
| Mean of quarter 1 | 0.970 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.011 | ||||
| Mean of quarter 4 | 1.036 | ||||
| Inter Quartile Range | 0.028 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.038 | ||||
| Mean of outliers low | 0.934 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.073 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.063 | ||||
| VaR(95%) (moments method) | 0.026 | ||||
| Expected Shortfall (moments method) | 0.037 | ||||
| Extreme Value Index (regression method) | 0.188 | ||||
| VaR(95%) (regression method) | 0.028 | ||||
| Expected Shortfall (regression method) | 0.044 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 13.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.035 | ||||
| Quartile 3 | 0.052 | ||||
| Maximum | 0.194 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.026 | ||||
| Mean of quarter 3 | 0.042 | ||||
| Mean of quarter 4 | 0.114 | ||||
| Inter Quartile Range | 0.038 | ||||
| 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 | 0.194 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.033 | ||||
| VaR(95%) (moments method) | 0.107 | ||||
| Expected Shortfall (moments method) | 0.146 | ||||
| Extreme Value Index (regression method) | 0.891 | ||||
| VaR(95%) (regression method) | 0.142 | ||||
| Expected Shortfall (regression method) | 1.078 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.006 | ||||
| Compounded annual return (geometric extrapolation) | 1.259 | ||||
| Calmar ratio (compounded annual return / max draw down) | 6.501 | ||||
| Compounded annual return / average of 25% largest draw downs | 11.020 | ||||
| Compounded annual return / Expected Shortfall lognormal | 24.666 | ||||