Advanced Statistics: Dragon Diversified
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 | -0.120 | ||||
| SD | 0.136 | ||||
| Sharpe ratio (Glass type estimate) | -0.887 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.868 | ||||
| df | 37.000 | ||||
| t | -1.578 | ||||
| p | 0.938 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.000 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.239 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.987 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.251 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.870 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.120 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.139 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.603 | ||||
| Mean of criterion | -0.120 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 0.136 | ||||
| Covariance | 0.003 | ||||
| r | 0.063 | ||||
| b (slope, estimate of beta) | 0.026 | ||||
| a (intercept, estimate of alpha) | -0.136 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 36.000 | ||||
| t(b) | 0.376 | ||||
| p(b) | 0.355 | ||||
| t(a) | -1.552 | ||||
| p(a) | 0.935 | ||||
| Lowerbound of 95% confidence interval for beta | -0.114 | ||||
| Upperbound of 95% confidence interval for beta | 0.165 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.314 | ||||
| Upperbound of 95% confidence interval for alpha | 0.042 | ||||
| Treynor index (mean / b) | -4.658 | ||||
| Jensen alpha (a) | -0.136 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.131 | ||||
| SD | 0.156 | ||||
| Sharpe ratio (Glass type estimate) | -0.845 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.828 | ||||
| df | 37.000 | ||||
| t | -1.504 | ||||
| p | 0.929 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.957 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.279 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.945 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.290 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.831 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.131 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.158 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.541 | ||||
| Mean of criterion | -0.131 | ||||
| SD of predictor | 0.303 | ||||
| SD of criterion | 0.156 | ||||
| Covariance | 0.003 | ||||
| r | 0.058 | ||||
| b (slope, estimate of beta) | 0.030 | ||||
| a (intercept, estimate of alpha) | -0.148 | ||||
| Mean Square Error | 0.025 | ||||
| DF error | 36.000 | ||||
| t(b) | 0.351 | ||||
| p(b) | 0.364 | ||||
| t(a) | -1.479 | ||||
| p(a) | 0.926 | ||||
| Lowerbound of 95% confidence interval for beta | -0.143 | ||||
| Upperbound of 95% confidence interval for beta | 0.203 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.350 | ||||
| Upperbound of 95% confidence interval for alpha | 0.055 | ||||
| Treynor index (mean / b) | -4.389 | ||||
| Jensen alpha (a) | -0.148 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.081 | ||||
| Expected Shortfall on VaR | 0.098 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.076 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 38.000 | ||||
| Minimum | 0.758 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.976 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.026 | ||||
| Mean of outliers low | 0.758 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.242 | ||||
| Quartile 1 | 0.242 | ||||
| Median | 0.242 | ||||
| Quartile 3 | 0.242 | ||||
| Maximum | 0.242 | ||||
| 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) | -0.076 | ||||
| Compounded annual return (geometric extrapolation) | -0.084 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.346 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.852 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.124 | ||||
| SD | 0.116 | ||||
| Sharpe ratio (Glass type estimate) | -1.078 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.077 | ||||
| df | 829.000 | ||||
| t | -1.918 | ||||
| p | 0.972 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.180 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.025 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.179 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.026 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.261 | ||||
| Upside Potential Ratio | 0.684 | ||||
| Upside part of mean | 0.068 | ||||
| Downside part of mean | -0.192 | ||||
| Upside SD | 0.060 | ||||
| Downside SD | 0.099 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 824.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 830.000 | ||||
| Mean of predictor | 0.599 | ||||
| Mean of criterion | -0.124 | ||||
| SD of predictor | 0.341 | ||||
| SD of criterion | 0.116 | ||||
| Covariance | -0.002 | ||||
| r | -0.039 | ||||
| b (slope, estimate of beta) | -0.013 | ||||
| a (intercept, estimate of alpha) | -0.117 | ||||
| Mean Square Error | 0.013 | ||||
| DF error | 828.000 | ||||
| t(b) | -1.119 | ||||
| p(b) | 0.868 | ||||
| t(a) | -1.786 | ||||
| p(a) | 0.963 | ||||
| Lowerbound of 95% confidence interval for beta | -0.036 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.245 | ||||
| Upperbound of 95% confidence interval for alpha | 0.012 | ||||
| Treynor index (mean / b) | 9.462 | ||||
| Jensen alpha (a) | -0.117 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.131 | ||||
| SD | 0.119 | ||||
| Sharpe ratio (Glass type estimate) | -1.107 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.106 | ||||
| df | 829.000 | ||||
| t | -1.970 | ||||
| p | 0.975 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.209 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.004 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.208 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.004 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.271 | ||||
| Upside Potential Ratio | 0.636 | ||||
| Upside part of mean | 0.066 | ||||
| Downside part of mean | -0.197 | ||||
| Upside SD | 0.059 | ||||
| Downside SD | 0.103 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 824.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 830.000 | ||||
| Mean of predictor | 0.541 | ||||
| Mean of criterion | -0.131 | ||||
| SD of predictor | 0.339 | ||||
| SD of criterion | 0.119 | ||||
| Covariance | -0.002 | ||||
| r | -0.039 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | -0.124 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 828.000 | ||||
| t(b) | -1.126 | ||||
| p(b) | 0.870 | ||||
| t(a) | -1.851 | ||||
| p(a) | 0.968 | ||||
| Lowerbound of 95% confidence interval for beta | -0.038 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.255 | ||||
| Upperbound of 95% confidence interval for alpha | 0.008 | ||||
| Treynor index (mean / b) | 9.609 | ||||
| Jensen alpha (a) | -0.124 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 830.000 | ||||
| Minimum | 0.875 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.071 | ||||
| Mean of quarter 1 | 0.998 | ||||
| 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 | 12.000 | ||||
| Percentage of outliers low | 0.014 | ||||
| Mean of outliers low | 0.961 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.007 | ||||
| Mean of outliers high | 1.036 | ||||
| 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) | -0.273 | ||||
| VaR(95%) (regression method) | -0.050 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.048 | ||||
| Quartile 1 | 0.103 | ||||
| Median | 0.158 | ||||
| Quartile 3 | 0.213 | ||||
| Maximum | 0.268 | ||||
| Mean of quarter 1 | 0.048 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.268 | ||||
| Inter Quartile Range | 0.110 | ||||
| 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) | -0.076 | ||||
| Compounded annual return (geometric extrapolation) | -0.084 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.312 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.312 | ||||
| Compounded annual return / Expected Shortfall lognormal | -5.397 | ||||
| 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 | 0.963 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.437 | ||||
| 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 | 0.866 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.438 | ||||
| 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) | -8734241941299515.000 | ||||
| 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) | 292843212317055451825440229949440.000 | ||||
| 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 | ||||