Advanced Statistics: CL Dragon
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 | -0.104 | ||||
| SD | 0.082 | ||||
| Sharpe ratio (Glass type estimate) | -1.264 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.239 | ||||
| df | 38.000 | ||||
| t | -2.280 | ||||
| p | 0.986 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.380 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.133 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.362 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.117 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.201 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.104 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.086 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.544 | ||||
| Mean of criterion | -0.104 | ||||
| SD of predictor | 0.282 | ||||
| SD of criterion | 0.082 | ||||
| Covariance | 0.001 | ||||
| r | 0.030 | ||||
| b (slope, estimate of beta) | 0.009 | ||||
| a (intercept, estimate of alpha) | -0.108 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.183 | ||||
| p(b) | 0.428 | ||||
| t(a) | -2.050 | ||||
| p(a) | 0.976 | ||||
| Lowerbound of 95% confidence interval for beta | -0.088 | ||||
| Upperbound of 95% confidence interval for beta | 0.105 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.215 | ||||
| Upperbound of 95% confidence interval for alpha | -0.001 | ||||
| Treynor index (mean / b) | -11.872 | ||||
| Jensen alpha (a) | -0.108 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.107 | ||||
| SD | 0.088 | ||||
| Sharpe ratio (Glass type estimate) | -1.223 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.199 | ||||
| df | 38.000 | ||||
| t | -2.205 | ||||
| p | 0.983 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.337 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.094 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.319 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.079 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.167 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.107 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.092 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.496 | ||||
| Mean of criterion | -0.107 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.088 | ||||
| Covariance | 0.001 | ||||
| r | 0.023 | ||||
| b (slope, estimate of beta) | 0.007 | ||||
| a (intercept, estimate of alpha) | -0.111 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.137 | ||||
| p(b) | 0.446 | ||||
| t(a) | -1.977 | ||||
| p(a) | 0.972 | ||||
| Lowerbound of 95% confidence interval for beta | -0.102 | ||||
| Upperbound of 95% confidence interval for beta | 0.117 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.224 | ||||
| Upperbound of 95% confidence interval for alpha | 0.003 | ||||
| Treynor index (mean / b) | -14.457 | ||||
| Jensen alpha (a) | -0.111 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.049 | ||||
| Expected Shortfall on VaR | 0.059 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.061 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.861 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.981 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers low | 0.051 | ||||
| Mean of outliers low | 0.903 | ||||
| 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) | -0.377 | ||||
| VaR(95%) (regression method) | 0.048 | ||||
| Expected Shortfall (regression method) | 0.127 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.186 | ||||
| Quartile 1 | 0.186 | ||||
| Median | 0.186 | ||||
| Quartile 3 | 0.186 | ||||
| Maximum | 0.186 | ||||
| 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) | -0.057 | ||||
| Compounded annual return (geometric extrapolation) | -0.061 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.330 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.033 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.103 | ||||
| SD | 0.083 | ||||
| Sharpe ratio (Glass type estimate) | -1.233 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.232 | ||||
| df | 861.000 | ||||
| t | -2.236 | ||||
| p | 0.987 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.315 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.150 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.314 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.150 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.485 | ||||
| Upside Potential Ratio | 0.531 | ||||
| Upside part of mean | 0.037 | ||||
| Downside part of mean | -0.140 | ||||
| Upside SD | 0.047 | ||||
| Downside SD | 0.069 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 857.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 862.000 | ||||
| Mean of predictor | 0.579 | ||||
| Mean of criterion | -0.103 | ||||
| SD of predictor | 0.345 | ||||
| SD of criterion | 0.083 | ||||
| Covariance | -0.001 | ||||
| r | -0.039 | ||||
| b (slope, estimate of beta) | -0.009 | ||||
| a (intercept, estimate of alpha) | -0.097 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 860.000 | ||||
| t(b) | -1.134 | ||||
| p(b) | 0.871 | ||||
| t(a) | -2.108 | ||||
| p(a) | 0.982 | ||||
| Lowerbound of 95% confidence interval for beta | -0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.188 | ||||
| Upperbound of 95% confidence interval for alpha | -0.007 | ||||
| Treynor index (mean / b) | 11.016 | ||||
| Jensen alpha (a) | -0.097 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.106 | ||||
| SD | 0.085 | ||||
| Sharpe ratio (Glass type estimate) | -1.256 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.254 | ||||
| df | 861.000 | ||||
| t | -2.277 | ||||
| p | 0.988 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.337 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.173 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.337 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.172 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.478 | ||||
| Upside Potential Ratio | 0.497 | ||||
| Upside part of mean | 0.036 | ||||
| Downside part of mean | -0.142 | ||||
| Upside SD | 0.045 | ||||
| Downside SD | 0.072 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 857.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 862.000 | ||||
| Mean of predictor | 0.518 | ||||
| Mean of criterion | -0.106 | ||||
| SD of predictor | 0.351 | ||||
| SD of criterion | 0.085 | ||||
| Covariance | -0.001 | ||||
| r | -0.038 | ||||
| b (slope, estimate of beta) | -0.009 | ||||
| a (intercept, estimate of alpha) | -0.102 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 860.000 | ||||
| t(b) | -1.112 | ||||
| p(b) | 0.867 | ||||
| t(a) | -2.167 | ||||
| p(a) | 0.985 | ||||
| Lowerbound of 95% confidence interval for beta | -0.025 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.194 | ||||
| Upperbound of 95% confidence interval for alpha | -0.010 | ||||
| Treynor index (mean / b) | 11.620 | ||||
| Jensen alpha (a) | -0.102 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 862.000 | ||||
| Minimum | 0.902 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.082 | ||||
| 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 | 15.000 | ||||
| Percentage of outliers low | 0.017 | ||||
| Mean of outliers low | 0.979 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.006 | ||||
| Mean of outliers high | 1.024 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.738 | ||||
| VaR(95%) (moments method) | -0.085 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.640 | ||||
| VaR(95%) (regression method) | -0.006 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.194 | ||||
| Quartile 1 | 0.194 | ||||
| Median | 0.194 | ||||
| Quartile 3 | 0.194 | ||||
| Maximum | 0.194 | ||||
| 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) | -0.056 | ||||
| Compounded annual return (geometric extrapolation) | -0.060 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.312 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -5.429 | ||||
| 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 | 1.049 | ||||
| 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 | 0.924 | ||||
| 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) | -8742484362898938.000 | ||||
| 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) | -100588073367257971805353735618560.000 | ||||
| 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 | ||||