Advanced Statistics: Futurama
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 | 1763386.617 | ||||
| SD | 2595634.814 | ||||
| Sharpe ratio (Glass type estimate) | 0.679 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.659 | ||||
| df | 25.000 | ||||
| t | 1.000 | ||||
| p | 0.163 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.672 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.017 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.685 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.003 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2431423.073 | ||||
| Upside Potential Ratio | 2431424.130 | ||||
| Upside part of mean | 1763387.383 | ||||
| Downside part of mean | -0.766 | ||||
| Upside SD | 2595634.814 | ||||
| Downside SD | 0.725 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 23.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 26.000 | ||||
| Mean of predictor | 0.545 | ||||
| Mean of criterion | 1763386.617 | ||||
| SD of predictor | 0.488 | ||||
| SD of criterion | 2595634.814 | ||||
| Covariance | 99707.431 | ||||
| r | 0.079 | ||||
| b (slope, estimate of beta) | 419326.675 | ||||
| a (intercept, estimate of alpha) | 1534953.798 | ||||
| Mean Square Error | 6974489691519.891 | ||||
| DF error | 24.000 | ||||
| t(b) | 0.387 | ||||
| p(b) | 0.351 | ||||
| t(a) | 0.813 | ||||
| p(a) | 0.212 | ||||
| Lowerbound of 95% confidence interval for beta | -1816237.236 | ||||
| Upperbound of 95% confidence interval for beta | 2654890.585 | ||||
| Lowerbound of 95% confidence interval for alpha | -2363127.476 | ||||
| Upperbound of 95% confidence interval for alpha | 5433035.072 | ||||
| Treynor index (mean / b) | 4.205 | ||||
| Jensen alpha (a) | 1534953.798 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2.152 | ||||
| SD | 12.955 | ||||
| Sharpe ratio (Glass type estimate) | 0.166 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.161 | ||||
| df | 25.000 | ||||
| t | 0.245 | ||||
| p | 0.404 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.168 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.497 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.171 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.493 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.289 | ||||
| Upside Potential Ratio | 1.013 | ||||
| Upside part of mean | 7.546 | ||||
| Downside part of mean | -5.394 | ||||
| Upside SD | 10.311 | ||||
| Downside SD | 7.446 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 23.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 26.000 | ||||
| Mean of predictor | 0.448 | ||||
| Mean of criterion | 2.152 | ||||
| SD of predictor | 0.396 | ||||
| SD of criterion | 12.955 | ||||
| Covariance | 0.672 | ||||
| r | 0.131 | ||||
| b (slope, estimate of beta) | 4.289 | ||||
| a (intercept, estimate of alpha) | 0.233 | ||||
| Mean Square Error | 171.813 | ||||
| DF error | 24.000 | ||||
| t(b) | 0.648 | ||||
| p(b) | 0.262 | ||||
| t(a) | 0.025 | ||||
| p(a) | 0.490 | ||||
| Lowerbound of 95% confidence interval for beta | -9.381 | ||||
| Upperbound of 95% confidence interval for beta | 17.958 | ||||
| Lowerbound of 95% confidence interval for alpha | -19.137 | ||||
| Upperbound of 95% confidence interval for alpha | 19.603 | ||||
| Treynor index (mean / b) | 0.502 | ||||
| Jensen alpha (a) | 0.233 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.997 | ||||
| Expected Shortfall on VaR | 0.999 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.206 | ||||
| Expected Shortfall on VaR | 0.438 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 26.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 3820672.000 | ||||
| Mean of quarter 1 | 0.775 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 545811.382 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.154 | ||||
| Mean of outliers low | 0.606 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.115 | ||||
| Mean of outliers high | 1273558.558 | ||||
| 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) | 1.717 | ||||
| VaR(95%) (regression method) | 0.151 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.139 | ||||
| Quartile 1 | 0.219 | ||||
| Median | 0.299 | ||||
| Quartile 3 | 0.650 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.139 | ||||
| Mean of quarter 2 | 0.299 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.431 | ||||
| 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) | 53.364 | ||||
| Compounded annual return (geometric extrapolation) | 7.993 | ||||
| Calmar ratio (compounded annual return / max draw down) | 7.993 | ||||
| Compounded annual return / average of 25% largest draw downs | 7.993 | ||||
| Compounded annual return / Expected Shortfall lognormal | 8.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1532374.190 | ||||
| SD | 2293682.788 | ||||
| Sharpe ratio (Glass type estimate) | 0.668 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.667 | ||||
| df | 586.000 | ||||
| t | 1.000 | ||||
| p | 0.159 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.642 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.978 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.643 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.977 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1542783.922 | ||||
| Upside Potential Ratio | 1542786.075 | ||||
| Upside part of mean | 1532376.329 | ||||
| Downside part of mean | -2.139 | ||||
| Upside SD | 2293682.787 | ||||
| Downside SD | 0.993 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 519.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 587.000 | ||||
| Mean of predictor | 0.685 | ||||
| Mean of criterion | 1532374.190 | ||||
| SD of predictor | 0.353 | ||||
| SD of criterion | 2293682.788 | ||||
| Covariance | -9675.218 | ||||
| r | -0.012 | ||||
| b (slope, estimate of beta) | -77629.632 | ||||
| a (intercept, estimate of alpha) | 1585551.663 | ||||
| Mean Square Error | 5269221492058.454 | ||||
| DF error | 585.000 | ||||
| t(b) | -0.289 | ||||
| p(b) | 0.614 | ||||
| t(a) | 1.027 | ||||
| p(a) | 0.153 | ||||
| Lowerbound of 95% confidence interval for beta | -605169.621 | ||||
| Upperbound of 95% confidence interval for beta | 449910.358 | ||||
| Lowerbound of 95% confidence interval for alpha | -1448031.607 | ||||
| Upperbound of 95% confidence interval for alpha | 4619134.933 | ||||
| Treynor index (mean / b) | -19.740 | ||||
| Jensen alpha (a) | 1585551.663 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -4.526 | ||||
| SD | 15.950 | ||||
| Sharpe ratio (Glass type estimate) | -0.284 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.283 | ||||
| df | 586.000 | ||||
| t | -0.425 | ||||
| p | 0.664 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.593 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.026 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.593 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.026 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.366 | ||||
| Upside Potential Ratio | 0.673 | ||||
| Upside part of mean | 8.323 | ||||
| Downside part of mean | -12.849 | ||||
| Upside SD | 10.063 | ||||
| Downside SD | 12.361 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 519.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 587.000 | ||||
| Mean of predictor | 0.625 | ||||
| Mean of criterion | -4.526 | ||||
| SD of predictor | 0.342 | ||||
| SD of criterion | 15.950 | ||||
| Covariance | -0.179 | ||||
| r | -0.033 | ||||
| b (slope, estimate of beta) | -1.530 | ||||
| a (intercept, estimate of alpha) | -3.570 | ||||
| Mean Square Error | 254.577 | ||||
| DF error | 585.000 | ||||
| t(b) | -0.794 | ||||
| p(b) | 0.786 | ||||
| t(a) | -0.333 | ||||
| p(a) | 0.630 | ||||
| Lowerbound of 95% confidence interval for beta | -5.318 | ||||
| Upperbound of 95% confidence interval for beta | 2.257 | ||||
| Lowerbound of 95% confidence interval for alpha | -24.639 | ||||
| Upperbound of 95% confidence interval for alpha | 17.499 | ||||
| Treynor index (mean / b) | 2.958 | ||||
| Jensen alpha (a) | -3.570 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.806 | ||||
| Expected Shortfall on VaR | 0.864 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.060 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 587.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 3433222.000 | ||||
| Mean of quarter 1 | 0.968 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 23356.271 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 52.000 | ||||
| Percentage of outliers low | 0.089 | ||||
| Mean of outliers low | 0.910 | ||||
| Number of outliers high | 68.000 | ||||
| Percentage of outliers high | 0.116 | ||||
| Mean of outliers high | 50489.601 | ||||
| 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) | -0.399 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.034 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.008 | ||||
| Quartile 1 | 0.034 | ||||
| Median | 0.111 | ||||
| Quartile 3 | 0.272 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.017 | ||||
| Mean of quarter 2 | 0.062 | ||||
| Mean of quarter 3 | 0.187 | ||||
| Mean of quarter 4 | 0.761 | ||||
| Inter Quartile Range | 0.238 | ||||
| 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 | 1.000 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -19029910659.787 | ||||
| VaR(95%) (moments method) | 0.639 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -16.756 | ||||
| VaR(95%) (regression method) | 76.745 | ||||
| Expected Shortfall (regression method) | 76.745 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.446 | ||||
| Compounded annual return (geometric extrapolation) | -0.989 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.989 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.300 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.145 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 6866439.628 | ||||
| SD | 4855307.713 | ||||
| Sharpe ratio (Glass type estimate) | 1.414 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.406 | ||||
| df | 130.000 | ||||
| t | 1.000 | ||||
| p | 0.456 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.366 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.189 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.371 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.183 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4702622.785 | ||||
| Upside Potential Ratio | 4702625.439 | ||||
| Upside part of mean | 6866443.503 | ||||
| Downside part of mean | -3.875 | ||||
| Upside SD | 4855307.701 | ||||
| Downside SD | 1.460 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 114.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 2.126 | ||||
| Mean of criterion | 6866439.628 | ||||
| SD of predictor | 0.636 | ||||
| SD of criterion | 4855307.713 | ||||
| Covariance | -81659.033 | ||||
| r | -0.026 | ||||
| b (slope, estimate of beta) | -201752.461 | ||||
| a (intercept, estimate of alpha) | 7295293.752 | ||||
| Mean Square Error | 23740154656095.102 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.300 | ||||
| p(b) | 0.517 | ||||
| t(a) | 1.037 | ||||
| p(a) | 0.442 | ||||
| Lowerbound of 95% confidence interval for beta | -1530733.770 | ||||
| Upperbound of 95% confidence interval for beta | 1127228.849 | ||||
| Lowerbound of 95% confidence interval for alpha | -6627522.663 | ||||
| Upperbound of 95% confidence interval for alpha | 21218110.167 | ||||
| Treynor index (mean / b) | -34.034 | ||||
| Jensen alpha (a) | 7295293.752 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 29.994 | ||||
| Sharpe ratio (Glass type estimate) | -0.001 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.001 | ||||
| df | 130.000 | ||||
| t | -0.001 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.773 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.770 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.773 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.770 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.002 | ||||
| Upside Potential Ratio | 1.505 | ||||
| Upside part of mean | 31.551 | ||||
| Downside part of mean | -31.595 | ||||
| Upside SD | 21.285 | ||||
| Downside SD | 20.970 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 114.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.928 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.609 | ||||
| SD of criterion | 29.994 | ||||
| Covariance | -0.765 | ||||
| r | -0.042 | ||||
| b (slope, estimate of beta) | -2.059 | ||||
| a (intercept, estimate of alpha) | 3.927 | ||||
| Mean Square Error | 905.013 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.476 | ||||
| p(b) | 0.527 | ||||
| t(a) | 0.091 | ||||
| p(a) | 0.495 | ||||
| Lowerbound of 95% confidence interval for beta | -10.625 | ||||
| Upperbound of 95% confidence interval for beta | 6.506 | ||||
| Lowerbound of 95% confidence interval for alpha | -81.853 | ||||
| Upperbound of 95% confidence interval for alpha | 89.708 | ||||
| Treynor index (mean / b) | 0.021 | ||||
| Jensen alpha (a) | 3.927 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.953 | ||||
| Expected Shortfall on VaR | 0.974 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.047 | ||||
| Expected Shortfall on VaR | 0.106 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 3433222.000 | ||||
| Mean of quarter 1 | 0.942 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 104038.023 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 18.000 | ||||
| Percentage of outliers low | 0.137 | ||||
| Mean of outliers low | 0.893 | ||||
| Number of outliers high | 17.000 | ||||
| Percentage of outliers high | 0.130 | ||||
| Mean of outliers high | 201955.221 | ||||
| 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) | 0.341 | ||||
| VaR(95%) (regression method) | 0.029 | ||||
| Expected Shortfall (regression method) | 0.079 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.258 | ||||
| Median | 0.505 | ||||
| Quartile 3 | 0.753 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.011 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.495 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||