Advanced Statistics: ES/TF Fund
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 | -0.017 | ||||
| SD | 0.056 | ||||
| Sharpe ratio (Glass type estimate) | -0.306 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.298 | ||||
| df | 31.000 | ||||
| t | -0.499 | ||||
| p | 0.689 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.506 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.899 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.501 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.904 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.977 | ||||
| Upside Potential Ratio | 1.835 | ||||
| Upside part of mean | 0.032 | ||||
| Downside part of mean | -0.049 | ||||
| Upside SD | 0.052 | ||||
| Downside SD | 0.017 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.676 | ||||
| Mean of criterion | -0.017 | ||||
| SD of predictor | 0.336 | ||||
| SD of criterion | 0.056 | ||||
| Covariance | -0.002 | ||||
| r | -0.086 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | -0.007 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.471 | ||||
| p(b) | 0.679 | ||||
| t(a) | -0.185 | ||||
| p(a) | 0.573 | ||||
| Lowerbound of 95% confidence interval for beta | -0.076 | ||||
| Upperbound of 95% confidence interval for beta | 0.047 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.089 | ||||
| Upperbound of 95% confidence interval for alpha | 0.074 | ||||
| Treynor index (mean / b) | 1.199 | ||||
| Jensen alpha (a) | -0.007 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 0.053 | ||||
| Sharpe ratio (Glass type estimate) | -0.344 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.336 | ||||
| df | 31.000 | ||||
| t | -0.562 | ||||
| p | 0.711 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.545 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.862 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.539 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.868 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.053 | ||||
| Upside Potential Ratio | 1.751 | ||||
| Upside part of mean | 0.030 | ||||
| Downside part of mean | -0.049 | ||||
| Upside SD | 0.050 | ||||
| Downside SD | 0.017 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.607 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 0.053 | ||||
| Covariance | -0.001 | ||||
| r | -0.081 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | -0.010 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.443 | ||||
| p(b) | 0.669 | ||||
| t(a) | -0.268 | ||||
| p(a) | 0.605 | ||||
| Lowerbound of 95% confidence interval for beta | -0.076 | ||||
| Upperbound of 95% confidence interval for beta | 0.049 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.088 | ||||
| Upperbound of 95% confidence interval for alpha | 0.067 | ||||
| Treynor index (mean / b) | 1.358 | ||||
| Jensen alpha (a) | -0.010 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.984 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.089 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.984 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.089 | ||||
| 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) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.016 | ||||
| Quartile 1 | 0.016 | ||||
| Median | 0.016 | ||||
| Quartile 3 | 0.016 | ||||
| Maximum | 0.016 | ||||
| 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) | 0.027 | ||||
| Compounded annual return (geometric extrapolation) | 0.026 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.597 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.796 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.017 | ||||
| SD | 0.043 | ||||
| Sharpe ratio (Glass type estimate) | -0.408 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.407 | ||||
| df | 699.000 | ||||
| t | -0.667 | ||||
| p | 0.747 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.607 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.791 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.607 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.792 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.723 | ||||
| Upside Potential Ratio | 2.417 | ||||
| Upside part of mean | 0.058 | ||||
| Downside part of mean | -0.076 | ||||
| Upside SD | 0.035 | ||||
| Downside SD | 0.024 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 685.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 700.000 | ||||
| Mean of predictor | 0.666 | ||||
| Mean of criterion | -0.017 | ||||
| SD of predictor | 0.357 | ||||
| SD of criterion | 0.043 | ||||
| Covariance | 0.001 | ||||
| r | 0.047 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.021 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 698.000 | ||||
| t(b) | 1.249 | ||||
| p(b) | 0.106 | ||||
| t(a) | -0.806 | ||||
| p(a) | 0.790 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.015 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.073 | ||||
| Upperbound of 95% confidence interval for alpha | 0.031 | ||||
| Treynor index (mean / b) | -3.081 | ||||
| Jensen alpha (a) | -0.021 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 0.043 | ||||
| Sharpe ratio (Glass type estimate) | -0.432 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.431 | ||||
| df | 699.000 | ||||
| t | -0.705 | ||||
| p | 0.760 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.631 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.768 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.630 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.768 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.752 | ||||
| Upside Potential Ratio | 2.365 | ||||
| Upside part of mean | 0.058 | ||||
| Downside part of mean | -0.076 | ||||
| Upside SD | 0.035 | ||||
| Downside SD | 0.024 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 685.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 700.000 | ||||
| Mean of predictor | 0.601 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.358 | ||||
| SD of criterion | 0.043 | ||||
| Covariance | 0.001 | ||||
| r | 0.047 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.022 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 698.000 | ||||
| t(b) | 1.240 | ||||
| p(b) | 0.108 | ||||
| t(a) | -0.830 | ||||
| p(a) | 0.797 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.073 | ||||
| Upperbound of 95% confidence interval for alpha | 0.030 | ||||
| Treynor index (mean / b) | -3.297 | ||||
| Jensen alpha (a) | -0.022 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 700.000 | ||||
| Minimum | 0.971 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.032 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.014 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.021 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.759 | ||||
| VaR(95%) (moments method) | -0.008 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.494 | ||||
| VaR(95%) (regression method) | -0.003 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.014 | ||||
| Quartile 3 | 0.029 | ||||
| Maximum | 0.058 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.008 | ||||
| Mean of quarter 3 | 0.020 | ||||
| Mean of quarter 4 | 0.058 | ||||
| Inter Quartile Range | 0.023 | ||||
| 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) | 0.027 | ||||
| Compounded annual return (geometric extrapolation) | 0.026 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.448 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.448 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.738 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.993 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.517 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.859 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.516 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.000 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8753337707619828.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | 249536207749731127583556096753664.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| 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 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) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| 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 | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| 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) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||