Advanced Statistics: ArayaFX
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 | 599.900 | ||||
| SD | 1038.344 | ||||
| Sharpe ratio (Glass type estimate) | 0.578 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.565 | ||||
| df | 35.000 | ||||
| t | 1.001 | ||||
| p | 0.162 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.566 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.713 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.574 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.705 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 617.088 | ||||
| Upside Potential Ratio | 618.862 | ||||
| Upside part of mean | 601.624 | ||||
| Downside part of mean | -1.724 | ||||
| Upside SD | 1038.363 | ||||
| Downside SD | 0.972 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 21.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.571 | ||||
| Mean of criterion | 599.900 | ||||
| SD of predictor | 0.304 | ||||
| SD of criterion | 1038.344 | ||||
| Covariance | -42.613 | ||||
| r | -0.135 | ||||
| b (slope, estimate of beta) | -461.181 | ||||
| a (intercept, estimate of alpha) | 863.012 | ||||
| Mean Square Error | 1089638.489 | ||||
| DF error | 34.000 | ||||
| t(b) | -0.795 | ||||
| p(b) | 0.784 | ||||
| t(a) | 1.255 | ||||
| p(a) | 0.109 | ||||
| Lowerbound of 95% confidence interval for beta | -1640.819 | ||||
| Upperbound of 95% confidence interval for beta | 718.456 | ||||
| Lowerbound of 95% confidence interval for alpha | -534.489 | ||||
| Upperbound of 95% confidence interval for alpha | 2260.513 | ||||
| Treynor index (mean / b) | -1.301 | ||||
| Jensen alpha (a) | 863.012 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.001 | ||||
| SD | 5.836 | ||||
| Sharpe ratio (Glass type estimate) | 0.000 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.000 | ||||
| df | 35.000 | ||||
| t | 0.000 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.131 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.132 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.131 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.132 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.000 | ||||
| Upside Potential Ratio | 1.099 | ||||
| Upside part of mean | 4.047 | ||||
| Downside part of mean | -4.046 | ||||
| Upside SD | 4.423 | ||||
| Downside SD | 3.681 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 21.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.517 | ||||
| Mean of criterion | 0.001 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 5.836 | ||||
| Covariance | -0.259 | ||||
| r | -0.159 | ||||
| b (slope, estimate of beta) | -3.335 | ||||
| a (intercept, estimate of alpha) | 1.725 | ||||
| Mean Square Error | 34.175 | ||||
| DF error | 34.000 | ||||
| t(b) | -0.941 | ||||
| p(b) | 0.823 | ||||
| t(a) | 0.449 | ||||
| p(a) | 0.328 | ||||
| Lowerbound of 95% confidence interval for beta | -10.540 | ||||
| Upperbound of 95% confidence interval for beta | 3.869 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.080 | ||||
| Upperbound of 95% confidence interval for alpha | 9.529 | ||||
| Treynor index (mean / b) | -0.000 | ||||
| Jensen alpha (a) | 1.725 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.937 | ||||
| Expected Shortfall on VaR | 0.964 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.365 | ||||
| Expected Shortfall on VaR | 0.682 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.799 | ||||
| Median | 0.998 | ||||
| Quartile 3 | 1.267 | ||||
| Maximum | 1799.500 | ||||
| Mean of quarter 1 | 0.526 | ||||
| Mean of quarter 2 | 0.908 | ||||
| Mean of quarter 3 | 1.104 | ||||
| Mean of quarter 4 | 201.444 | ||||
| Inter Quartile Range | 0.468 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.056 | ||||
| Mean of outliers low | 0.043 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.083 | ||||
| Mean of outliers high | 601.503 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.084 | ||||
| VaR(95%) (moments method) | 0.461 | ||||
| Expected Shortfall (moments method) | 0.657 | ||||
| Extreme Value Index (regression method) | 0.246 | ||||
| VaR(95%) (regression method) | 0.476 | ||||
| Expected Shortfall (regression method) | 0.745 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.023 | ||||
| Quartile 1 | 0.162 | ||||
| Median | 0.355 | ||||
| Quartile 3 | 0.648 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.084 | ||||
| Mean of quarter 2 | 0.210 | ||||
| Mean of quarter 3 | 0.499 | ||||
| Mean of quarter 4 | 0.849 | ||||
| Inter Quartile Range | 0.486 | ||||
| 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) | 0.048 | ||||
| Compounded annual return (geometric extrapolation) | 0.046 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.046 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.054 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.048 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 749.599 | ||||
| SD | 605.039 | ||||
| Sharpe ratio (Glass type estimate) | 1.239 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.238 | ||||
| df | 786.000 | ||||
| t | 2.147 | ||||
| p | 0.016 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.106 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.371 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.105 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.370 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 366.455 | ||||
| Upside Potential Ratio | 371.344 | ||||
| Upside part of mean | 759.599 | ||||
| Downside part of mean | -10.000 | ||||
| Upside SD | 606.422 | ||||
| Downside SD | 2.046 | ||||
| N nonnegative terms | 349.000 | ||||
| N negative terms | 438.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 787.000 | ||||
| Mean of predictor | 0.574 | ||||
| Mean of criterion | 749.599 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 605.039 | ||||
| Covariance | -2.423 | ||||
| r | -0.013 | ||||
| b (slope, estimate of beta) | -24.020 | ||||
| a (intercept, estimate of alpha) | 763.388 | ||||
| Mean Square Error | 366479.979 | ||||
| DF error | 785.000 | ||||
| t(b) | -0.353 | ||||
| p(b) | 0.638 | ||||
| t(a) | 2.172 | ||||
| p(a) | 0.015 | ||||
| Lowerbound of 95% confidence interval for beta | -157.487 | ||||
| Upperbound of 95% confidence interval for beta | 109.448 | ||||
| Lowerbound of 95% confidence interval for alpha | 73.464 | ||||
| Upperbound of 95% confidence interval for alpha | 1453.313 | ||||
| Treynor index (mean / b) | -31.208 | ||||
| Jensen alpha (a) | 763.388 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.001 | ||||
| SD | 12.573 | ||||
| Sharpe ratio (Glass type estimate) | 0.000 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.000 | ||||
| df | 786.000 | ||||
| t | 0.000 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.131 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.131 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.131 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.131 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.000 | ||||
| Upside Potential Ratio | 2.514 | ||||
| Upside part of mean | 22.765 | ||||
| Downside part of mean | -22.764 | ||||
| Upside SD | 8.712 | ||||
| Downside SD | 9.055 | ||||
| N nonnegative terms | 349.000 | ||||
| N negative terms | 438.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 787.000 | ||||
| Mean of predictor | 0.523 | ||||
| Mean of criterion | 0.001 | ||||
| SD of predictor | 0.319 | ||||
| SD of criterion | 12.573 | ||||
| Covariance | -0.131 | ||||
| r | -0.033 | ||||
| b (slope, estimate of beta) | -1.284 | ||||
| a (intercept, estimate of alpha) | 0.672 | ||||
| Mean Square Error | 158.126 | ||||
| DF error | 785.000 | ||||
| t(b) | -0.914 | ||||
| p(b) | 0.820 | ||||
| t(a) | 0.092 | ||||
| p(a) | 0.463 | ||||
| Lowerbound of 95% confidence interval for beta | -4.041 | ||||
| Upperbound of 95% confidence interval for beta | 1.473 | ||||
| Lowerbound of 95% confidence interval for alpha | -13.643 | ||||
| Upperbound of 95% confidence interval for alpha | 14.987 | ||||
| Treynor index (mean / b) | -0.001 | ||||
| Jensen alpha (a) | 0.672 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.721 | ||||
| Expected Shortfall on VaR | 0.791 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.091 | ||||
| Expected Shortfall on VaR | 0.204 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 787.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.966 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.037 | ||||
| Maximum | 811.000 | ||||
| Mean of quarter 1 | 0.859 | ||||
| Mean of quarter 2 | 0.989 | ||||
| Mean of quarter 3 | 1.013 | ||||
| Mean of quarter 4 | 12.569 | ||||
| Inter Quartile Range | 0.071 | ||||
| Number outliers low | 37.000 | ||||
| Percentage of outliers low | 0.047 | ||||
| Mean of outliers low | 0.558 | ||||
| Number of outliers high | 53.000 | ||||
| Percentage of outliers high | 0.067 | ||||
| Mean of outliers high | 43.787 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.701 | ||||
| VaR(95%) (moments method) | 0.134 | ||||
| Expected Shortfall (moments method) | 0.477 | ||||
| Extreme Value Index (regression method) | 0.066 | ||||
| VaR(95%) (regression method) | 0.091 | ||||
| Expected Shortfall (regression method) | 0.131 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.063 | ||||
| Median | 0.329 | ||||
| Quartile 3 | 0.551 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.032 | ||||
| Mean of quarter 2 | 0.173 | ||||
| Mean of quarter 3 | 0.414 | ||||
| Mean of quarter 4 | 0.781 | ||||
| Inter Quartile Range | 0.488 | ||||
| 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) | -2.917 | ||||
| VaR(95%) (moments method) | 0.891 | ||||
| Expected Shortfall (moments method) | 0.895 | ||||
| Extreme Value Index (regression method) | -0.432 | ||||
| VaR(95%) (regression method) | 1.063 | ||||
| Expected Shortfall (regression method) | 1.195 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.048 | ||||
| Compounded annual return (geometric extrapolation) | 0.046 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.046 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.059 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.058 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.145 | ||||
| SD | 1.065 | ||||
| Sharpe ratio (Glass type estimate) | 0.137 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.136 | ||||
| df | 130.000 | ||||
| t | 0.097 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.636 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.908 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.636 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.908 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.203 | ||||
| Upside Potential Ratio | 8.789 | ||||
| Upside part of mean | 6.295 | ||||
| Downside part of mean | -6.150 | ||||
| Upside SD | 0.783 | ||||
| Downside SD | 0.716 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 75.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.108 | ||||
| Mean of criterion | 0.145 | ||||
| SD of predictor | 0.443 | ||||
| SD of criterion | 1.065 | ||||
| Covariance | -0.174 | ||||
| r | -0.369 | ||||
| b (slope, estimate of beta) | -0.887 | ||||
| a (intercept, estimate of alpha) | 1.128 | ||||
| Mean Square Error | 0.987 | ||||
| DF error | 129.000 | ||||
| t(b) | -4.509 | ||||
| p(b) | 0.729 | ||||
| t(a) | 0.793 | ||||
| p(a) | 0.456 | ||||
| Lowerbound of 95% confidence interval for beta | -1.276 | ||||
| Upperbound of 95% confidence interval for beta | -0.498 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.686 | ||||
| Upperbound of 95% confidence interval for alpha | 3.942 | ||||
| Treynor index (mean / b) | -0.164 | ||||
| Jensen alpha (a) | 1.128 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.415 | ||||
| SD | 1.062 | ||||
| Sharpe ratio (Glass type estimate) | -0.390 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.388 | ||||
| df | 130.000 | ||||
| t | -0.276 | ||||
| p | 0.512 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.162 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.383 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.160 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.384 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.546 | ||||
| Upside Potential Ratio | 7.916 | ||||
| Upside part of mean | 6.011 | ||||
| Downside part of mean | -6.426 | ||||
| Upside SD | 0.737 | ||||
| Downside SD | 0.759 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 75.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.008 | ||||
| Mean of criterion | -0.415 | ||||
| SD of predictor | 0.446 | ||||
| SD of criterion | 1.062 | ||||
| Covariance | -0.174 | ||||
| r | -0.367 | ||||
| b (slope, estimate of beta) | -0.873 | ||||
| a (intercept, estimate of alpha) | 0.465 | ||||
| Mean Square Error | 0.984 | ||||
| DF error | 129.000 | ||||
| t(b) | -4.475 | ||||
| p(b) | 0.728 | ||||
| t(a) | 0.328 | ||||
| p(a) | 0.482 | ||||
| Lowerbound of 95% confidence interval for beta | -1.259 | ||||
| Upperbound of 95% confidence interval for beta | -0.487 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.338 | ||||
| Upperbound of 95% confidence interval for alpha | 3.268 | ||||
| Treynor index (mean / b) | 0.475 | ||||
| Jensen alpha (a) | 0.465 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.104 | ||||
| Expected Shortfall on VaR | 0.128 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.059 | ||||
| Expected Shortfall on VaR | 0.108 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.812 | ||||
| Quartile 1 | 0.964 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.034 | ||||
| Maximum | 1.197 | ||||
| Mean of quarter 1 | 0.922 | ||||
| Mean of quarter 2 | 0.985 | ||||
| Mean of quarter 3 | 1.012 | ||||
| Mean of quarter 4 | 1.084 | ||||
| Inter Quartile Range | 0.070 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.839 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.177 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.162 | ||||
| VaR(95%) (moments method) | 0.077 | ||||
| Expected Shortfall (moments method) | 0.096 | ||||
| Extreme Value Index (regression method) | 0.069 | ||||
| VaR(95%) (regression method) | 0.081 | ||||
| Expected Shortfall (regression method) | 0.111 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.030 | ||||
| Quartile 1 | 0.038 | ||||
| Median | 0.058 | ||||
| Quartile 3 | 0.099 | ||||
| Maximum | 0.590 | ||||
| Mean of quarter 1 | 0.034 | ||||
| Mean of quarter 2 | 0.048 | ||||
| Mean of quarter 3 | 0.091 | ||||
| Mean of quarter 4 | 0.349 | ||||
| Inter Quartile Range | 0.062 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.590 | ||||
| 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) | -0.338 | ||||
| Compounded annual return (geometric extrapolation) | -0.310 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.525 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.888 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.424 | ||||