Advanced Statistics: test2
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 | -0.082 | ||||
| SD | 0.131 | ||||
| Sharpe ratio (Glass type estimate) | -0.628 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.616 | ||||
| df | 39.000 | ||||
| t | -1.146 | ||||
| p | 0.871 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.706 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.459 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.698 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.466 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.733 | ||||
| Upside Potential Ratio | 0.399 | ||||
| Upside part of mean | 0.045 | ||||
| Downside part of mean | -0.127 | ||||
| Upside SD | 0.069 | ||||
| Downside SD | 0.112 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.486 | ||||
| Mean of criterion | -0.082 | ||||
| SD of predictor | 0.313 | ||||
| SD of criterion | 0.131 | ||||
| Covariance | 0.001 | ||||
| r | 0.018 | ||||
| b (slope, estimate of beta) | 0.007 | ||||
| a (intercept, estimate of alpha) | -0.086 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 38.000 | ||||
| t(b) | 0.110 | ||||
| p(b) | 0.456 | ||||
| t(a) | -1.076 | ||||
| p(a) | 0.856 | ||||
| Lowerbound of 95% confidence interval for beta | -0.130 | ||||
| Upperbound of 95% confidence interval for beta | 0.145 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.248 | ||||
| Upperbound of 95% confidence interval for alpha | 0.076 | ||||
| Treynor index (mean / b) | -10.972 | ||||
| Jensen alpha (a) | -0.086 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.091 | ||||
| SD | 0.136 | ||||
| Sharpe ratio (Glass type estimate) | -0.668 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.655 | ||||
| df | 39.000 | ||||
| t | -1.220 | ||||
| p | 0.885 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.747 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.420 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.738 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.428 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.752 | ||||
| Upside Potential Ratio | 0.351 | ||||
| Upside part of mean | 0.042 | ||||
| Downside part of mean | -0.134 | ||||
| Upside SD | 0.065 | ||||
| Downside SD | 0.121 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.433 | ||||
| Mean of criterion | -0.091 | ||||
| SD of predictor | 0.289 | ||||
| SD of criterion | 0.136 | ||||
| Covariance | 0.001 | ||||
| r | 0.025 | ||||
| b (slope, estimate of beta) | 0.012 | ||||
| a (intercept, estimate of alpha) | -0.096 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 38.000 | ||||
| t(b) | 0.154 | ||||
| p(b) | 0.439 | ||||
| t(a) | -1.165 | ||||
| p(a) | 0.874 | ||||
| Lowerbound of 95% confidence interval for beta | -0.143 | ||||
| Upperbound of 95% confidence interval for beta | 0.167 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.263 | ||||
| Upperbound of 95% confidence interval for alpha | 0.071 | ||||
| Treynor index (mean / b) | -7.707 | ||||
| Jensen alpha (a) | -0.096 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.070 | ||||
| Expected Shortfall on VaR | 0.085 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.073 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 40.000 | ||||
| Minimum | 0.836 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.127 | ||||
| Mean of quarter 1 | 0.971 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.075 | ||||
| Mean of outliers low | 0.904 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.075 | ||||
| Mean of outliers high | 1.053 | ||||
| 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) | 0.070 | ||||
| VaR(95%) (regression method) | 0.047 | ||||
| Expected Shortfall (regression method) | 0.125 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.259 | ||||
| Quartile 1 | 0.259 | ||||
| Median | 0.259 | ||||
| Quartile 3 | 0.259 | ||||
| Maximum | 0.259 | ||||
| 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) | -0.044 | ||||
| Compounded annual return (geometric extrapolation) | -0.046 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.178 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.542 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.077 | ||||
| SD | 0.165 | ||||
| Sharpe ratio (Glass type estimate) | -0.469 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.468 | ||||
| df | 877.000 | ||||
| t | -0.858 | ||||
| p | 0.804 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.540 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.602 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.539 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.603 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.668 | ||||
| Upside Potential Ratio | 2.278 | ||||
| Upside part of mean | 0.264 | ||||
| Downside part of mean | -0.341 | ||||
| Upside SD | 0.117 | ||||
| Downside SD | 0.116 | ||||
| N nonnegative terms | 34.000 | ||||
| N negative terms | 844.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 878.000 | ||||
| Mean of predictor | 0.518 | ||||
| Mean of criterion | -0.077 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 0.165 | ||||
| Covariance | 0.000 | ||||
| r | 0.005 | ||||
| b (slope, estimate of beta) | 0.003 | ||||
| a (intercept, estimate of alpha) | -0.079 | ||||
| Mean Square Error | 0.027 | ||||
| DF error | 876.000 | ||||
| t(b) | 0.153 | ||||
| p(b) | 0.439 | ||||
| t(a) | -0.869 | ||||
| p(a) | 0.807 | ||||
| Lowerbound of 95% confidence interval for beta | -0.032 | ||||
| Upperbound of 95% confidence interval for beta | 0.037 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.257 | ||||
| Upperbound of 95% confidence interval for alpha | 0.099 | ||||
| Treynor index (mean / b) | -28.809 | ||||
| Jensen alpha (a) | -0.079 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.091 | ||||
| SD | 0.165 | ||||
| Sharpe ratio (Glass type estimate) | -0.552 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.552 | ||||
| df | 877.000 | ||||
| t | -1.011 | ||||
| p | 0.844 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.623 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.519 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.623 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.519 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.757 | ||||
| Upside Potential Ratio | 2.144 | ||||
| Upside part of mean | 0.257 | ||||
| Downside part of mean | -0.348 | ||||
| Upside SD | 0.113 | ||||
| Downside SD | 0.120 | ||||
| N nonnegative terms | 34.000 | ||||
| N negative terms | 844.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 878.000 | ||||
| Mean of predictor | 0.467 | ||||
| Mean of criterion | -0.091 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.165 | ||||
| Covariance | 0.000 | ||||
| r | 0.007 | ||||
| b (slope, estimate of beta) | 0.003 | ||||
| a (intercept, estimate of alpha) | -0.092 | ||||
| Mean Square Error | 0.027 | ||||
| DF error | 876.000 | ||||
| t(b) | 0.200 | ||||
| p(b) | 0.421 | ||||
| t(a) | -1.024 | ||||
| p(a) | 0.847 | ||||
| Lowerbound of 95% confidence interval for beta | -0.031 | ||||
| Upperbound of 95% confidence interval for beta | 0.038 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.270 | ||||
| Upperbound of 95% confidence interval for alpha | 0.085 | ||||
| Treynor index (mean / b) | -26.190 | ||||
| Jensen alpha (a) | -0.092 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 878.000 | ||||
| Minimum | 0.884 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.142 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 40.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.975 | ||||
| Number of outliers high | 34.000 | ||||
| Percentage of outliers high | 0.039 | ||||
| Mean of outliers high | 1.026 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -4.408 | ||||
| VaR(95%) (moments method) | -0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.078 | ||||
| VaR(95%) (regression method) | -0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.016 | ||||
| Median | 0.051 | ||||
| Quartile 3 | 0.148 | ||||
| Maximum | 0.348 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.021 | ||||
| Mean of quarter 3 | 0.081 | ||||
| Mean of quarter 4 | 0.348 | ||||
| Inter Quartile Range | 0.132 | ||||
| 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 | 0.348 | ||||
| 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) | -0.043 | ||||
| Compounded annual return (geometric extrapolation) | -0.046 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.131 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.131 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.169 | ||||
| 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 | 1.174 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.496 | ||||
| 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 | 1.049 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.499 | ||||
| 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) | -8725869298288166.000 | ||||
| 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) | -53065583677888834065803232935936.000 | ||||
| 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 | ||||