Advanced Statistics: UP!
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 | -0.043 | ||||
| SD | 0.057 | ||||
| Sharpe ratio (Glass type estimate) | -0.747 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.738 | ||||
| df | 67.000 | ||||
| t | -1.778 | ||||
| p | 0.960 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.577 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.089 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.571 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.094 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.062 | ||||
| Upside Potential Ratio | 0.664 | ||||
| Upside part of mean | 0.027 | ||||
| Downside part of mean | -0.069 | ||||
| Upside SD | 0.042 | ||||
| Downside SD | 0.040 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.316 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.315 | ||||
| SD of criterion | 0.057 | ||||
| Covariance | -0.002 | ||||
| r | -0.095 | ||||
| b (slope, estimate of beta) | -0.017 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 66.000 | ||||
| t(b) | -0.779 | ||||
| p(b) | 0.781 | ||||
| t(a) | -1.483 | ||||
| p(a) | 0.929 | ||||
| Lowerbound of 95% confidence interval for beta | -0.062 | ||||
| Upperbound of 95% confidence interval for beta | 0.027 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.087 | ||||
| Upperbound of 95% confidence interval for alpha | 0.013 | ||||
| Treynor index (mean / b) | 2.462 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.056 | ||||
| Sharpe ratio (Glass type estimate) | -0.782 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.773 | ||||
| df | 67.000 | ||||
| t | -1.862 | ||||
| p | 0.967 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.613 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.055 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.607 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.060 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.076 | ||||
| Upside Potential Ratio | 0.627 | ||||
| Upside part of mean | 0.026 | ||||
| Downside part of mean | -0.070 | ||||
| Upside SD | 0.040 | ||||
| Downside SD | 0.041 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.264 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.310 | ||||
| SD of criterion | 0.056 | ||||
| Covariance | -0.002 | ||||
| r | -0.089 | ||||
| b (slope, estimate of beta) | -0.016 | ||||
| a (intercept, estimate of alpha) | -0.040 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 66.000 | ||||
| t(b) | -0.728 | ||||
| p(b) | 0.765 | ||||
| t(a) | -1.626 | ||||
| p(a) | 0.946 | ||||
| Lowerbound of 95% confidence interval for beta | -0.061 | ||||
| Upperbound of 95% confidence interval for beta | 0.028 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.089 | ||||
| Upperbound of 95% confidence interval for alpha | 0.009 | ||||
| Treynor index (mean / b) | 2.720 | ||||
| Jensen alpha (a) | -0.040 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 68.000 | ||||
| Minimum | 0.938 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.091 | ||||
| Mean of quarter 1 | 0.991 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.103 | ||||
| Mean of outliers low | 0.978 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.088 | ||||
| Mean of outliers high | 1.027 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -49.946 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | -1.192 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.019 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.022 | ||||
| Maximum | 0.088 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | 0.000 | ||||
| Mean of quarter 4 | 0.088 | ||||
| Inter Quartile Range | 0.022 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 0.088 | ||||
| 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 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.004 | ||||
| SD | 0.283 | ||||
| Sharpe ratio (Glass type estimate) | -0.015 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.015 | ||||
| df | 1501.000 | ||||
| t | -0.035 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.833 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.804 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.833 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.804 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.021 | ||||
| Upside Potential Ratio | 2.444 | ||||
| Upside part of mean | 0.475 | ||||
| Downside part of mean | -0.479 | ||||
| Upside SD | 0.206 | ||||
| Downside SD | 0.194 | ||||
| N nonnegative terms | 75.000 | ||||
| N negative terms | 1427.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1502.000 | ||||
| Mean of predictor | 0.436 | ||||
| Mean of criterion | -0.004 | ||||
| SD of predictor | 0.561 | ||||
| SD of criterion | 0.283 | ||||
| Covariance | 0.009 | ||||
| r | 0.059 | ||||
| b (slope, estimate of beta) | 0.030 | ||||
| a (intercept, estimate of alpha) | -0.017 | ||||
| Mean Square Error | 0.080 | ||||
| DF error | 1500.000 | ||||
| t(b) | 2.296 | ||||
| p(b) | 0.470 | ||||
| t(a) | -0.145 | ||||
| p(a) | 0.502 | ||||
| Lowerbound of 95% confidence interval for beta | 0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.055 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.249 | ||||
| Upperbound of 95% confidence interval for alpha | 0.215 | ||||
| Treynor index (mean / b) | -0.140 | ||||
| Jensen alpha (a) | -0.017 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.282 | ||||
| Sharpe ratio (Glass type estimate) | -0.156 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.156 | ||||
| df | 1501.000 | ||||
| t | -0.373 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.974 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.663 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.974 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.663 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.214 | ||||
| Upside Potential Ratio | 2.218 | ||||
| Upside part of mean | 0.455 | ||||
| Downside part of mean | -0.499 | ||||
| Upside SD | 0.194 | ||||
| Downside SD | 0.205 | ||||
| N nonnegative terms | 75.000 | ||||
| N negative terms | 1427.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1502.000 | ||||
| Mean of predictor | 0.281 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.556 | ||||
| SD of criterion | 0.282 | ||||
| Covariance | 0.010 | ||||
| r | 0.062 | ||||
| b (slope, estimate of beta) | 0.032 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.079 | ||||
| DF error | 1500.000 | ||||
| t(b) | 2.425 | ||||
| p(b) | 0.469 | ||||
| t(a) | -0.449 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | 0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.057 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.284 | ||||
| Upperbound of 95% confidence interval for alpha | 0.178 | ||||
| Treynor index (mean / b) | -1.386 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1502.000 | ||||
| Minimum | 0.846 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.220 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 74.000 | ||||
| Percentage of outliers low | 0.049 | ||||
| Mean of outliers low | 0.966 | ||||
| Number of outliers high | 104.000 | ||||
| Percentage of outliers high | 0.069 | ||||
| Mean of outliers high | 1.026 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -4.164 | ||||
| VaR(95%) (moments method) | -0.018 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.164 | ||||
| VaR(95%) (regression method) | -0.015 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.106 | ||||
| Quartile 1 | 0.117 | ||||
| Median | 0.124 | ||||
| Quartile 3 | 0.135 | ||||
| Maximum | 0.189 | ||||
| Mean of quarter 1 | 0.112 | ||||
| Mean of quarter 2 | 0.124 | ||||
| Mean of quarter 3 | 0.135 | ||||
| Mean of quarter 4 | 0.189 | ||||
| Inter Quartile Range | 0.018 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.189 | ||||
| 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 | ||||
| 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 | 1.920 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.698 | ||||
| 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 | 1.677 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.687 | ||||
| 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) | -8700738920873009.000 | ||||
| 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) | -380934629477244767451740110848000.000 | ||||
| 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 | ||||