Advanced Statistics: Chaos Trader
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 3.156 | ||||
| SD | 4.038 | ||||
| Sharpe ratio (Glass type estimate) | 0.781 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.772 | ||||
| df | 60.000 | ||||
| t | 1.762 | ||||
| p | 0.042 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.102 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.659 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.109 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.652 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.459 | ||||
| Upside Potential Ratio | 5.494 | ||||
| Upside part of mean | 5.012 | ||||
| Downside part of mean | -1.856 | ||||
| Upside SD | 4.005 | ||||
| Downside SD | 0.912 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.369 | ||||
| Mean of criterion | 3.156 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 4.038 | ||||
| Covariance | -0.660 | ||||
| r | -0.525 | ||||
| b (slope, estimate of beta) | -6.824 | ||||
| a (intercept, estimate of alpha) | 5.672 | ||||
| Mean Square Error | 12.007 | ||||
| DF error | 59.000 | ||||
| t(b) | -4.743 | ||||
| p(b) | 1.000 | ||||
| t(a) | 3.489 | ||||
| p(a) | 0.000 | ||||
| Lowerbound of 95% confidence interval for beta | -9.703 | ||||
| Upperbound of 95% confidence interval for beta | -3.945 | ||||
| Lowerbound of 95% confidence interval for alpha | 2.418 | ||||
| Upperbound of 95% confidence interval for alpha | 8.925 | ||||
| Treynor index (mean / b) | -0.462 | ||||
| Jensen alpha (a) | 5.672 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.073 | ||||
| SD | 2.189 | ||||
| Sharpe ratio (Glass type estimate) | 0.034 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.033 | ||||
| df | 60.000 | ||||
| t | 0.076 | ||||
| p | 0.470 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.836 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.903 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.836 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.902 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.051 | ||||
| Upside Potential Ratio | 1.857 | ||||
| Upside part of mean | 2.676 | ||||
| Downside part of mean | -2.602 | ||||
| Upside SD | 1.625 | ||||
| Downside SD | 1.441 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.311 | ||||
| Mean of criterion | 0.073 | ||||
| SD of predictor | 0.333 | ||||
| SD of criterion | 2.189 | ||||
| Covariance | -0.321 | ||||
| r | -0.441 | ||||
| b (slope, estimate of beta) | -2.898 | ||||
| a (intercept, estimate of alpha) | 0.975 | ||||
| Mean Square Error | 3.927 | ||||
| DF error | 59.000 | ||||
| t(b) | -3.772 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.071 | ||||
| p(a) | 0.144 | ||||
| Lowerbound of 95% confidence interval for beta | -4.435 | ||||
| Upperbound of 95% confidence interval for beta | -1.360 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.847 | ||||
| Upperbound of 95% confidence interval for alpha | 2.798 | ||||
| Treynor index (mean / b) | -0.025 | ||||
| Jensen alpha (a) | 0.975 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.644 | ||||
| Expected Shortfall on VaR | 0.720 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.378 | ||||
| Expected Shortfall on VaR | 0.649 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.256 | ||||
| Quartile 1 | 0.786 | ||||
| Median | 0.928 | ||||
| Quartile 3 | 1.362 | ||||
| Maximum | 6.714 | ||||
| Mean of quarter 1 | 0.551 | ||||
| Mean of quarter 2 | 0.861 | ||||
| Mean of quarter 3 | 1.131 | ||||
| Mean of quarter 4 | 2.571 | ||||
| Inter Quartile Range | 0.576 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.066 | ||||
| Mean of outliers high | 4.906 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.076 | ||||
| VaR(95%) (moments method) | 0.450 | ||||
| Expected Shortfall (moments method) | 0.580 | ||||
| Extreme Value Index (regression method) | -1.259 | ||||
| VaR(95%) (regression method) | 0.451 | ||||
| Expected Shortfall (regression method) | 0.470 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.989 | ||||
| Quartile 1 | 0.989 | ||||
| Median | 0.989 | ||||
| Quartile 3 | 0.989 | ||||
| Maximum | 0.989 | ||||
| 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) | 0.161 | ||||
| Compounded annual return (geometric extrapolation) | 0.125 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.126 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.173 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 63.715 | ||||
| SD | 127.208 | ||||
| Sharpe ratio (Glass type estimate) | 0.501 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.501 | ||||
| df | 1346.000 | ||||
| t | 1.136 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.364 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.365 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.364 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.365 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 38.404 | ||||
| Upside Potential Ratio | 45.108 | ||||
| Upside part of mean | 74.836 | ||||
| Downside part of mean | -11.122 | ||||
| Upside SD | 127.210 | ||||
| Downside SD | 1.659 | ||||
| N nonnegative terms | 668.000 | ||||
| N negative terms | 679.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1347.000 | ||||
| Mean of predictor | 0.393 | ||||
| Mean of criterion | 63.715 | ||||
| SD of predictor | 0.366 | ||||
| SD of criterion | 127.208 | ||||
| Covariance | -0.799 | ||||
| r | -0.017 | ||||
| b (slope, estimate of beta) | -5.964 | ||||
| a (intercept, estimate of alpha) | 66.061 | ||||
| Mean Square Error | 16189.021 | ||||
| DF error | 1345.000 | ||||
| t(b) | -0.629 | ||||
| p(b) | 0.511 | ||||
| t(a) | 1.175 | ||||
| p(a) | 0.480 | ||||
| Lowerbound of 95% confidence interval for beta | -24.555 | ||||
| Upperbound of 95% confidence interval for beta | 12.628 | ||||
| Lowerbound of 95% confidence interval for alpha | -44.264 | ||||
| Upperbound of 95% confidence interval for alpha | 176.386 | ||||
| Treynor index (mean / b) | -10.684 | ||||
| Jensen alpha (a) | 66.061 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.072 | ||||
| SD | 5.321 | ||||
| Sharpe ratio (Glass type estimate) | 0.014 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.014 | ||||
| df | 1346.000 | ||||
| t | 0.031 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.851 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.878 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.851 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.878 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.018 | ||||
| Upside Potential Ratio | 3.620 | ||||
| Upside part of mean | 14.373 | ||||
| Downside part of mean | -14.300 | ||||
| Upside SD | 3.539 | ||||
| Downside SD | 3.970 | ||||
| N nonnegative terms | 668.000 | ||||
| N negative terms | 679.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1347.000 | ||||
| Mean of predictor | 0.325 | ||||
| Mean of criterion | 0.072 | ||||
| SD of predictor | 0.372 | ||||
| SD of criterion | 5.321 | ||||
| Covariance | -0.316 | ||||
| r | -0.160 | ||||
| b (slope, estimate of beta) | -2.283 | ||||
| a (intercept, estimate of alpha) | 0.814 | ||||
| Mean Square Error | 27.610 | ||||
| DF error | 1345.000 | ||||
| t(b) | -5.928 | ||||
| p(b) | 0.601 | ||||
| t(a) | 0.351 | ||||
| p(a) | 0.494 | ||||
| Lowerbound of 95% confidence interval for beta | -3.039 | ||||
| Upperbound of 95% confidence interval for beta | -1.528 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.739 | ||||
| Upperbound of 95% confidence interval for alpha | 5.367 | ||||
| Treynor index (mean / b) | -0.032 | ||||
| Jensen alpha (a) | 0.814 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.417 | ||||
| Expected Shortfall on VaR | 0.489 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.097 | ||||
| Expected Shortfall on VaR | 0.203 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1347.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.956 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.049 | ||||
| Maximum | 289.000 | ||||
| Mean of quarter 1 | 0.849 | ||||
| Mean of quarter 2 | 0.982 | ||||
| Mean of quarter 3 | 1.021 | ||||
| Mean of quarter 4 | 2.121 | ||||
| Inter Quartile Range | 0.094 | ||||
| Number outliers low | 88.000 | ||||
| Percentage of outliers low | 0.065 | ||||
| Mean of outliers low | 0.673 | ||||
| Number of outliers high | 99.000 | ||||
| Percentage of outliers high | 0.073 | ||||
| Mean of outliers high | 4.584 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.519 | ||||
| VaR(95%) (moments method) | 0.151 | ||||
| Expected Shortfall (moments method) | 0.353 | ||||
| Extreme Value Index (regression method) | 0.323 | ||||
| VaR(95%) (regression method) | 0.132 | ||||
| Expected Shortfall (regression method) | 0.236 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.180 | ||||
| Quartile 1 | 0.196 | ||||
| Median | 0.212 | ||||
| Quartile 3 | 0.606 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.180 | ||||
| Mean of quarter 2 | 0.212 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.410 | ||||
| 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) | 0.159 | ||||
| Compounded annual return (geometric extrapolation) | 0.123 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.123 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.123 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.252 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.555 | ||||
| SD | 0.545 | ||||
| Sharpe ratio (Glass type estimate) | -1.019 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.013 | ||||
| df | 130.000 | ||||
| t | -0.720 | ||||
| p | 0.532 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.791 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.758 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.787 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.762 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.390 | ||||
| Upside Potential Ratio | 6.769 | ||||
| Upside part of mean | 2.706 | ||||
| Downside part of mean | -3.261 | ||||
| Upside SD | 0.369 | ||||
| Downside SD | 0.400 | ||||
| N nonnegative terms | 54.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.234 | ||||
| Mean of criterion | -0.555 | ||||
| SD of predictor | 0.355 | ||||
| SD of criterion | 0.545 | ||||
| Covariance | -0.076 | ||||
| r | -0.391 | ||||
| b (slope, estimate of beta) | -0.600 | ||||
| a (intercept, estimate of alpha) | 0.185 | ||||
| Mean Square Error | 0.254 | ||||
| DF error | 129.000 | ||||
| t(b) | -4.826 | ||||
| p(b) | 0.742 | ||||
| t(a) | 0.254 | ||||
| p(a) | 0.486 | ||||
| Lowerbound of 95% confidence interval for beta | -0.847 | ||||
| Upperbound of 95% confidence interval for beta | -0.354 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.257 | ||||
| Upperbound of 95% confidence interval for alpha | 1.627 | ||||
| Treynor index (mean / b) | 0.925 | ||||
| Jensen alpha (a) | 0.185 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.704 | ||||
| SD | 0.546 | ||||
| Sharpe ratio (Glass type estimate) | -1.290 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.283 | ||||
| df | 130.000 | ||||
| t | -0.912 | ||||
| p | 0.540 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.064 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.489 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.059 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.494 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.705 | ||||
| Upside Potential Ratio | 6.397 | ||||
| Upside part of mean | 2.640 | ||||
| Downside part of mean | -3.344 | ||||
| Upside SD | 0.356 | ||||
| Downside SD | 0.413 | ||||
| N nonnegative terms | 54.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.168 | ||||
| Mean of criterion | -0.704 | ||||
| SD of predictor | 0.355 | ||||
| SD of criterion | 0.546 | ||||
| Covariance | -0.074 | ||||
| r | -0.384 | ||||
| b (slope, estimate of beta) | -0.590 | ||||
| a (intercept, estimate of alpha) | -0.014 | ||||
| Mean Square Error | 0.256 | ||||
| DF error | 129.000 | ||||
| t(b) | -4.720 | ||||
| p(b) | 0.738 | ||||
| t(a) | -0.019 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | -0.838 | ||||
| Upperbound of 95% confidence interval for beta | -0.343 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.458 | ||||
| Upperbound of 95% confidence interval for alpha | 1.430 | ||||
| Treynor index (mean / b) | 1.192 | ||||
| Jensen alpha (a) | -0.014 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.056 | ||||
| Expected Shortfall on VaR | 0.070 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.060 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.895 | ||||
| Quartile 1 | 0.980 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.013 | ||||
| Maximum | 1.139 | ||||
| Mean of quarter 1 | 0.956 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.038 | ||||
| Inter Quartile Range | 0.033 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.906 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.090 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.605 | ||||
| VaR(95%) (moments method) | 0.044 | ||||
| Expected Shortfall (moments method) | 0.050 | ||||
| Extreme Value Index (regression method) | -0.216 | ||||
| VaR(95%) (regression method) | 0.042 | ||||
| Expected Shortfall (regression method) | 0.051 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.118 | ||||
| Median | 0.235 | ||||
| Quartile 3 | 0.351 | ||||
| Maximum | 0.467 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.467 | ||||
| Inter Quartile Range | 0.233 | ||||
| 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) | -0.562 | ||||
| Compounded annual return (geometric extrapolation) | -0.483 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.034 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.034 | ||||
| Compounded annual return / Expected Shortfall lognormal | -6.941 | ||||