Advanced Statistics: THESPECULATOR
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 | 0.243 | ||||
| SD | 0.824 | ||||
| Sharpe ratio (Glass type estimate) | 0.295 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.291 | ||||
| df | 67.000 | ||||
| t | 0.702 | ||||
| p | 0.243 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.531 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.118 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.533 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.116 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.918 | ||||
| Upside Potential Ratio | 1.745 | ||||
| Upside part of mean | 0.462 | ||||
| Downside part of mean | -0.219 | ||||
| Upside SD | 0.777 | ||||
| Downside SD | 0.265 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.263 | ||||
| Mean of criterion | 0.243 | ||||
| SD of predictor | 0.312 | ||||
| SD of criterion | 0.824 | ||||
| Covariance | 0.026 | ||||
| r | 0.102 | ||||
| b (slope, estimate of beta) | 0.270 | ||||
| a (intercept, estimate of alpha) | 0.172 | ||||
| Mean Square Error | 0.682 | ||||
| DF error | 66.000 | ||||
| t(b) | 0.835 | ||||
| p(b) | 0.203 | ||||
| t(a) | 0.481 | ||||
| p(a) | 0.316 | ||||
| Lowerbound of 95% confidence interval for beta | -0.376 | ||||
| Upperbound of 95% confidence interval for beta | 0.917 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.542 | ||||
| Upperbound of 95% confidence interval for alpha | 0.885 | ||||
| Treynor index (mean / b) | 0.898 | ||||
| Jensen alpha (a) | 0.172 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.038 | ||||
| SD | 0.605 | ||||
| Sharpe ratio (Glass type estimate) | 0.062 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.061 | ||||
| df | 67.000 | ||||
| t | 0.148 | ||||
| p | 0.441 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.762 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.885 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.762 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.885 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.093 | ||||
| Upside Potential Ratio | 0.787 | ||||
| Upside part of mean | 0.317 | ||||
| Downside part of mean | -0.279 | ||||
| Upside SD | 0.446 | ||||
| Downside SD | 0.402 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.215 | ||||
| Mean of criterion | 0.038 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.605 | ||||
| Covariance | 0.021 | ||||
| r | 0.117 | ||||
| b (slope, estimate of beta) | 0.235 | ||||
| a (intercept, estimate of alpha) | -0.013 | ||||
| Mean Square Error | 0.367 | ||||
| DF error | 66.000 | ||||
| t(b) | 0.953 | ||||
| p(b) | 0.172 | ||||
| t(a) | -0.050 | ||||
| p(a) | 0.520 | ||||
| Lowerbound of 95% confidence interval for beta | -0.258 | ||||
| Upperbound of 95% confidence interval for beta | 0.729 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.532 | ||||
| Upperbound of 95% confidence interval for alpha | 0.506 | ||||
| Treynor index (mean / b) | 0.160 | ||||
| Jensen alpha (a) | -0.013 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.247 | ||||
| Expected Shortfall on VaR | 0.299 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.097 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 68.000 | ||||
| Minimum | 0.389 | ||||
| Quartile 1 | 0.988 | ||||
| Median | 1.003 | ||||
| Quartile 3 | 1.013 | ||||
| Maximum | 2.839 | ||||
| Mean of quarter 1 | 0.938 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.008 | ||||
| Mean of quarter 4 | 1.154 | ||||
| Inter Quartile Range | 0.025 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.666 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.088 | ||||
| Mean of outliers high | 1.386 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.879 | ||||
| VaR(95%) (moments method) | 0.051 | ||||
| Expected Shortfall (moments method) | 0.421 | ||||
| Extreme Value Index (regression method) | 1.337 | ||||
| VaR(95%) (regression method) | 0.033 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.648 | ||||
| Quartile 1 | 0.648 | ||||
| Median | 0.648 | ||||
| Quartile 3 | 0.648 | ||||
| Maximum | 0.648 | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| 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) | 0.104 | ||||
| Compounded annual return (geometric extrapolation) | 0.085 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.131 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.284 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.637 | ||||
| SD | 1.198 | ||||
| Sharpe ratio (Glass type estimate) | 0.531 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.531 | ||||
| df | 1489.000 | ||||
| t | 1.267 | ||||
| p | 0.479 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.291 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.353 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.291 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.353 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.088 | ||||
| Upside Potential Ratio | 4.307 | ||||
| Upside part of mean | 2.519 | ||||
| Downside part of mean | -1.883 | ||||
| Upside SD | 1.046 | ||||
| Downside SD | 0.585 | ||||
| N nonnegative terms | 725.000 | ||||
| N negative terms | 765.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1490.000 | ||||
| Mean of predictor | 0.405 | ||||
| Mean of criterion | 0.637 | ||||
| SD of predictor | 0.570 | ||||
| SD of criterion | 1.198 | ||||
| Covariance | 0.126 | ||||
| r | 0.185 | ||||
| b (slope, estimate of beta) | 0.388 | ||||
| a (intercept, estimate of alpha) | 0.479 | ||||
| Mean Square Error | 1.388 | ||||
| DF error | 1488.000 | ||||
| t(b) | 7.244 | ||||
| p(b) | 0.408 | ||||
| t(a) | 0.969 | ||||
| p(a) | 0.487 | ||||
| Lowerbound of 95% confidence interval for beta | 0.283 | ||||
| Upperbound of 95% confidence interval for beta | 0.493 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.491 | ||||
| Upperbound of 95% confidence interval for alpha | 1.449 | ||||
| Treynor index (mean / b) | 1.641 | ||||
| Jensen alpha (a) | 0.479 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.037 | ||||
| SD | 1.071 | ||||
| Sharpe ratio (Glass type estimate) | 0.035 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.035 | ||||
| df | 1489.000 | ||||
| t | 0.083 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.787 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.857 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.787 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.857 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.051 | ||||
| Upside Potential Ratio | 2.935 | ||||
| Upside part of mean | 2.150 | ||||
| Downside part of mean | -2.112 | ||||
| Upside SD | 0.781 | ||||
| Downside SD | 0.733 | ||||
| N nonnegative terms | 725.000 | ||||
| N negative terms | 765.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1490.000 | ||||
| Mean of predictor | 0.244 | ||||
| Mean of criterion | 0.037 | ||||
| SD of predictor | 0.568 | ||||
| SD of criterion | 1.071 | ||||
| Covariance | 0.106 | ||||
| r | 0.174 | ||||
| b (slope, estimate of beta) | 0.328 | ||||
| a (intercept, estimate of alpha) | -0.043 | ||||
| Mean Square Error | 1.113 | ||||
| DF error | 1488.000 | ||||
| t(b) | 6.813 | ||||
| p(b) | 0.413 | ||||
| t(a) | -0.096 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | 0.234 | ||||
| Upperbound of 95% confidence interval for beta | 0.423 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.911 | ||||
| Upperbound of 95% confidence interval for alpha | 0.826 | ||||
| Treynor index (mean / b) | 0.114 | ||||
| Jensen alpha (a) | -0.043 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.103 | ||||
| Expected Shortfall on VaR | 0.127 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1490.000 | ||||
| Minimum | 0.523 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 2.108 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.037 | ||||
| Inter Quartile Range | 0.006 | ||||
| Number outliers low | 137.000 | ||||
| Percentage of outliers low | 0.092 | ||||
| Mean of outliers low | 0.935 | ||||
| Number of outliers high | 141.000 | ||||
| Percentage of outliers high | 0.095 | ||||
| Mean of outliers high | 1.089 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.122 | ||||
| VaR(95%) (moments method) | 0.020 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.863 | ||||
| VaR(95%) (regression method) | 0.014 | ||||
| Expected Shortfall (regression method) | 0.105 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.071 | ||||
| Median | 0.137 | ||||
| Quartile 3 | 0.402 | ||||
| Maximum | 0.666 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.137 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.666 | ||||
| Inter Quartile Range | 0.330 | ||||
| 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) | 0.104 | ||||
| Compounded annual return (geometric extrapolation) | 0.085 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.127 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.127 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.668 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.009 | ||||
| SD | 0.032 | ||||
| Sharpe ratio (Glass type estimate) | 0.269 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.267 | ||||
| df | 130.000 | ||||
| t | 0.190 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.503 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.041 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.505 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.039 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.436 | ||||
| Upside Potential Ratio | 8.945 | ||||
| Upside part of mean | 0.174 | ||||
| Downside part of mean | -0.166 | ||||
| Upside SD | 0.025 | ||||
| Downside SD | 0.020 | ||||
| N nonnegative terms | 58.000 | ||||
| N negative terms | 73.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.925 | ||||
| Mean of criterion | 0.009 | ||||
| SD of predictor | 0.727 | ||||
| SD of criterion | 0.032 | ||||
| Covariance | -0.011 | ||||
| r | -0.485 | ||||
| b (slope, estimate of beta) | -0.021 | ||||
| a (intercept, estimate of alpha) | 0.049 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 129.000 | ||||
| t(b) | -6.296 | ||||
| p(b) | 0.796 | ||||
| t(a) | 1.234 | ||||
| p(a) | 0.431 | ||||
| Lowerbound of 95% confidence interval for beta | -0.028 | ||||
| Upperbound of 95% confidence interval for beta | -0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.030 | ||||
| Upperbound of 95% confidence interval for alpha | 0.128 | ||||
| Treynor index (mean / b) | -0.403 | ||||
| Jensen alpha (a) | 0.049 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.008 | ||||
| SD | 0.032 | ||||
| Sharpe ratio (Glass type estimate) | 0.254 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.252 | ||||
| df | 130.000 | ||||
| t | 0.179 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.519 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.025 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.520 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.024 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.410 | ||||
| Upside Potential Ratio | 8.915 | ||||
| Upside part of mean | 0.174 | ||||
| Downside part of mean | -0.166 | ||||
| Upside SD | 0.025 | ||||
| Downside SD | 0.020 | ||||
| N nonnegative terms | 58.000 | ||||
| N negative terms | 73.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.652 | ||||
| Mean of criterion | 0.008 | ||||
| SD of predictor | 0.738 | ||||
| SD of criterion | 0.032 | ||||
| Covariance | -0.012 | ||||
| r | -0.500 | ||||
| b (slope, estimate of beta) | -0.021 | ||||
| a (intercept, estimate of alpha) | 0.043 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 129.000 | ||||
| t(b) | -6.558 | ||||
| p(b) | 0.805 | ||||
| t(a) | 1.106 | ||||
| p(a) | 0.438 | ||||
| Lowerbound of 95% confidence interval for beta | -0.028 | ||||
| Upperbound of 95% confidence interval for beta | -0.015 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.034 | ||||
| Upperbound of 95% confidence interval for alpha | 0.121 | ||||
| Treynor index (mean / b) | -0.374 | ||||
| Jensen alpha (a) | 0.043 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.994 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.008 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.996 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.076 | ||||
| Mean of outliers high | 1.005 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.354 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.248 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.002 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.002 | ||||
| Quartile 3 | 0.007 | ||||
| Maximum | 0.019 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.001 | ||||
| Mean of quarter 3 | 0.007 | ||||
| Mean of quarter 4 | 0.013 | ||||
| Inter Quartile Range | 0.007 | ||||
| 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 | 0.111 | ||||
| Mean of outliers high | 0.019 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.314 | ||||
| VaR(95%) (moments method) | 0.014 | ||||
| Expected Shortfall (moments method) | 0.023 | ||||
| Extreme Value Index (regression method) | 3.018 | ||||
| VaR(95%) (regression method) | 0.037 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.053 | ||||
| Compounded annual return (geometric extrapolation) | 0.053 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.841 | ||||
| Compounded annual return / average of 25% largest draw downs | 4.043 | ||||
| Compounded annual return / Expected Shortfall lognormal | 13.397 | ||||