Advanced Statistics: TFG
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 | 0.062 | ||||
| SD | 0.301 | ||||
| Sharpe ratio (Glass type estimate) | 0.208 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.205 | ||||
| df | 70.000 | ||||
| t | 0.505 | ||||
| p | 0.308 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.600 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.013 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.601 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.012 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.434 | ||||
| Upside Potential Ratio | 1.274 | ||||
| Upside part of mean | 0.183 | ||||
| Downside part of mean | -0.121 | ||||
| Upside SD | 0.262 | ||||
| Downside SD | 0.144 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 63.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.256 | ||||
| Mean of criterion | 0.062 | ||||
| SD of predictor | 0.304 | ||||
| SD of criterion | 0.301 | ||||
| Covariance | -0.014 | ||||
| r | -0.158 | ||||
| b (slope, estimate of beta) | -0.156 | ||||
| a (intercept, estimate of alpha) | 0.103 | ||||
| Mean Square Error | 0.090 | ||||
| DF error | 69.000 | ||||
| t(b) | -1.331 | ||||
| p(b) | 0.906 | ||||
| t(a) | 0.809 | ||||
| p(a) | 0.211 | ||||
| Lowerbound of 95% confidence interval for beta | -0.391 | ||||
| Upperbound of 95% confidence interval for beta | 0.078 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.150 | ||||
| Upperbound of 95% confidence interval for alpha | 0.355 | ||||
| Treynor index (mean / b) | -0.399 | ||||
| Jensen alpha (a) | 0.103 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.023 | ||||
| SD | 0.275 | ||||
| Sharpe ratio (Glass type estimate) | 0.085 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.084 | ||||
| df | 70.000 | ||||
| t | 0.207 | ||||
| p | 0.418 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.721 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.891 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.722 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.890 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.135 | ||||
| Upside Potential Ratio | 0.906 | ||||
| Upside part of mean | 0.157 | ||||
| Downside part of mean | -0.134 | ||||
| Upside SD | 0.211 | ||||
| Downside SD | 0.173 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 63.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.208 | ||||
| Mean of criterion | 0.023 | ||||
| SD of predictor | 0.302 | ||||
| SD of criterion | 0.275 | ||||
| Covariance | -0.013 | ||||
| r | -0.156 | ||||
| b (slope, estimate of beta) | -0.142 | ||||
| a (intercept, estimate of alpha) | 0.053 | ||||
| Mean Square Error | 0.075 | ||||
| DF error | 69.000 | ||||
| t(b) | -1.311 | ||||
| p(b) | 0.903 | ||||
| t(a) | 0.461 | ||||
| p(a) | 0.323 | ||||
| Lowerbound of 95% confidence interval for beta | -0.358 | ||||
| Upperbound of 95% confidence interval for beta | 0.074 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.176 | ||||
| Upperbound of 95% confidence interval for alpha | 0.282 | ||||
| Treynor index (mean / b) | -0.164 | ||||
| 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%) | 0.121 | ||||
| Expected Shortfall on VaR | 0.149 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.071 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 71.000 | ||||
| Minimum | 0.665 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.599 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.062 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.155 | ||||
| Mean of outliers low | 0.956 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.155 | ||||
| Mean of outliers high | 1.101 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.098 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.493 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.016 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.044 | ||||
| Quartile 3 | 0.067 | ||||
| Maximum | 0.335 | ||||
| Mean of quarter 1 | 0.018 | ||||
| Mean of quarter 2 | 0.044 | ||||
| Mean of quarter 3 | 0.067 | ||||
| Mean of quarter 4 | 0.335 | ||||
| Inter Quartile Range | 0.046 | ||||
| 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 | 0.335 | ||||
| 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) | 0.083 | ||||
| Compounded annual return (geometric extrapolation) | 0.070 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.208 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.208 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.468 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.243 | ||||
| SD | 0.702 | ||||
| Sharpe ratio (Glass type estimate) | 0.346 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.346 | ||||
| df | 1570.000 | ||||
| t | 0.847 | ||||
| p | 0.489 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.455 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.146 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.455 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.146 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.642 | ||||
| Upside Potential Ratio | 3.077 | ||||
| Upside part of mean | 1.164 | ||||
| Downside part of mean | -0.921 | ||||
| Upside SD | 0.592 | ||||
| Downside SD | 0.378 | ||||
| N nonnegative terms | 115.000 | ||||
| N negative terms | 1456.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1571.000 | ||||
| Mean of predictor | 0.406 | ||||
| Mean of criterion | 0.243 | ||||
| SD of predictor | 0.574 | ||||
| SD of criterion | 0.702 | ||||
| Covariance | -0.051 | ||||
| r | -0.127 | ||||
| b (slope, estimate of beta) | -0.156 | ||||
| a (intercept, estimate of alpha) | 0.306 | ||||
| Mean Square Error | 0.486 | ||||
| DF error | 1569.000 | ||||
| t(b) | -5.090 | ||||
| p(b) | 0.581 | ||||
| t(a) | 1.075 | ||||
| p(a) | 0.483 | ||||
| Lowerbound of 95% confidence interval for beta | -0.216 | ||||
| Upperbound of 95% confidence interval for beta | -0.096 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.253 | ||||
| Upperbound of 95% confidence interval for alpha | 0.865 | ||||
| Treynor index (mean / b) | -1.558 | ||||
| Jensen alpha (a) | 0.306 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.022 | ||||
| SD | 0.654 | ||||
| Sharpe ratio (Glass type estimate) | 0.034 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.034 | ||||
| df | 1570.000 | ||||
| t | 0.084 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.766 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.835 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.766 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.835 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.051 | ||||
| Upside Potential Ratio | 2.350 | ||||
| Upside part of mean | 1.030 | ||||
| Downside part of mean | -1.008 | ||||
| Upside SD | 0.484 | ||||
| Downside SD | 0.439 | ||||
| N nonnegative terms | 115.000 | ||||
| N negative terms | 1456.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1571.000 | ||||
| Mean of predictor | 0.244 | ||||
| Mean of criterion | 0.022 | ||||
| SD of predictor | 0.568 | ||||
| SD of criterion | 0.654 | ||||
| Covariance | -0.050 | ||||
| r | -0.133 | ||||
| b (slope, estimate of beta) | -0.153 | ||||
| a (intercept, estimate of alpha) | 0.060 | ||||
| Mean Square Error | 0.420 | ||||
| DF error | 1569.000 | ||||
| t(b) | -5.334 | ||||
| p(b) | 0.585 | ||||
| t(a) | 0.226 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -0.210 | ||||
| Upperbound of 95% confidence interval for beta | -0.097 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.459 | ||||
| Upperbound of 95% confidence interval for alpha | 0.579 | ||||
| Treynor index (mean / b) | -0.146 | ||||
| Jensen alpha (a) | 0.060 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.064 | ||||
| Expected Shortfall on VaR | 0.080 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1571.000 | ||||
| Minimum | 0.588 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.847 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.018 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 163.000 | ||||
| Percentage of outliers low | 0.104 | ||||
| Mean of outliers low | 0.968 | ||||
| Number of outliers high | 159.000 | ||||
| Percentage of outliers high | 0.101 | ||||
| Mean of outliers high | 1.044 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.868 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| 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 | 8.000 | ||||
| Minimum | 0.034 | ||||
| Quartile 1 | 0.064 | ||||
| Median | 0.161 | ||||
| Quartile 3 | 0.342 | ||||
| Maximum | 0.506 | ||||
| Mean of quarter 1 | 0.034 | ||||
| Mean of quarter 2 | 0.085 | ||||
| Mean of quarter 3 | 0.267 | ||||
| Mean of quarter 4 | 0.478 | ||||
| Inter Quartile Range | 0.278 | ||||
| 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) | 0.082 | ||||
| Compounded annual return (geometric extrapolation) | 0.069 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.136 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.144 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.862 | ||||
| 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 | 1.077 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.475 | ||||
| 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 | 0.962 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.476 | ||||
| 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) | -8731518803304136.000 | ||||
| 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) | 99790654838473588937722400079872.000 | ||||
| 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 | ||||