Advanced Statistics: DNTQ
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.159 | ||||
| SD | 0.332 | ||||
| Sharpe ratio (Glass type estimate) | 0.479 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.468 | ||||
| df | 31.000 | ||||
| t | 0.783 | ||||
| p | 0.220 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.730 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.682 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.738 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.674 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 12.693 | ||||
| Upside Potential Ratio | 16.103 | ||||
| Upside part of mean | 0.202 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.329 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.642 | ||||
| Mean of criterion | 0.159 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 0.332 | ||||
| Covariance | -0.005 | ||||
| r | -0.056 | ||||
| b (slope, estimate of beta) | -0.069 | ||||
| a (intercept, estimate of alpha) | 0.203 | ||||
| Mean Square Error | 0.113 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.308 | ||||
| p(b) | 0.620 | ||||
| t(a) | 0.809 | ||||
| p(a) | 0.212 | ||||
| Lowerbound of 95% confidence interval for beta | -0.524 | ||||
| Upperbound of 95% confidence interval for beta | 0.386 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.309 | ||||
| Upperbound of 95% confidence interval for alpha | 0.716 | ||||
| Treynor index (mean / b) | -2.316 | ||||
| Jensen alpha (a) | 0.203 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.118 | ||||
| SD | 0.265 | ||||
| Sharpe ratio (Glass type estimate) | 0.446 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.435 | ||||
| df | 31.000 | ||||
| t | 0.729 | ||||
| p | 0.236 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.763 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.648 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.770 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.641 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 9.460 | ||||
| Upside Potential Ratio | 12.870 | ||||
| Upside part of mean | 0.161 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.263 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.592 | ||||
| Mean of criterion | 0.118 | ||||
| SD of predictor | 0.254 | ||||
| SD of criterion | 0.265 | ||||
| Covariance | -0.003 | ||||
| r | -0.051 | ||||
| b (slope, estimate of beta) | -0.053 | ||||
| a (intercept, estimate of alpha) | 0.150 | ||||
| Mean Square Error | 0.072 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.280 | ||||
| p(b) | 0.609 | ||||
| t(a) | 0.750 | ||||
| p(a) | 0.229 | ||||
| Lowerbound of 95% confidence interval for beta | -0.442 | ||||
| Upperbound of 95% confidence interval for beta | 0.336 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.258 | ||||
| Upperbound of 95% confidence interval for alpha | 0.558 | ||||
| Treynor index (mean / b) | -2.222 | ||||
| Jensen alpha (a) | 0.150 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.110 | ||||
| Expected Shortfall on VaR | 0.137 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.542 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.068 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.542 | ||||
| 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) | 0.203 | ||||
| Compounded annual return (geometric extrapolation) | 0.176 | ||||
| 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 | 1.284 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.138 | ||||
| SD | 0.214 | ||||
| Sharpe ratio (Glass type estimate) | 0.644 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.643 | ||||
| df | 701.000 | ||||
| t | 1.054 | ||||
| p | 0.146 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.554 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.842 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.555 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.841 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.897 | ||||
| Upside Potential Ratio | 4.426 | ||||
| Upside part of mean | 0.210 | ||||
| Downside part of mean | -0.073 | ||||
| Upside SD | 0.208 | ||||
| Downside SD | 0.048 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 698.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 702.000 | ||||
| Mean of predictor | 0.669 | ||||
| Mean of criterion | 0.138 | ||||
| SD of predictor | 0.365 | ||||
| SD of criterion | 0.214 | ||||
| Covariance | 0.001 | ||||
| r | 0.008 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | 0.135 | ||||
| Mean Square Error | 0.046 | ||||
| DF error | 700.000 | ||||
| t(b) | 0.212 | ||||
| p(b) | 0.416 | ||||
| t(a) | 1.023 | ||||
| p(a) | 0.153 | ||||
| Lowerbound of 95% confidence interval for beta | -0.039 | ||||
| Upperbound of 95% confidence interval for beta | 0.048 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.124 | ||||
| Upperbound of 95% confidence interval for alpha | 0.393 | ||||
| Treynor index (mean / b) | 29.308 | ||||
| Jensen alpha (a) | 0.135 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.118 | ||||
| SD | 0.194 | ||||
| Sharpe ratio (Glass type estimate) | 0.605 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.604 | ||||
| df | 701.000 | ||||
| t | 0.990 | ||||
| p | 0.161 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.593 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.802 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.594 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.802 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.376 | ||||
| Upside Potential Ratio | 3.870 | ||||
| Upside part of mean | 0.191 | ||||
| Downside part of mean | -0.074 | ||||
| Upside SD | 0.188 | ||||
| Downside SD | 0.049 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 698.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 702.000 | ||||
| Mean of predictor | 0.600 | ||||
| Mean of criterion | 0.118 | ||||
| SD of predictor | 0.370 | ||||
| SD of criterion | 0.194 | ||||
| Covariance | 0.001 | ||||
| r | 0.009 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | 0.115 | ||||
| Mean Square Error | 0.038 | ||||
| DF error | 700.000 | ||||
| t(b) | 0.233 | ||||
| p(b) | 0.408 | ||||
| t(a) | 0.961 | ||||
| p(a) | 0.168 | ||||
| Lowerbound of 95% confidence interval for beta | -0.034 | ||||
| Upperbound of 95% confidence interval for beta | 0.044 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.120 | ||||
| Upperbound of 95% confidence interval for alpha | 0.349 | ||||
| Treynor index (mean / b) | 25.446 | ||||
| Jensen alpha (a) | 0.115 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 702.000 | ||||
| Minimum | 0.922 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.249 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.001 | ||||
| Mean of outliers low | 0.922 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.006 | ||||
| Mean of outliers high | 1.141 | ||||
| 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 | 0.078 | ||||
| Quartile 1 | 0.078 | ||||
| Median | 0.078 | ||||
| Quartile 3 | 0.078 | ||||
| Maximum | 0.078 | ||||
| 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) | 0.202 | ||||
| Compounded annual return (geometric extrapolation) | 0.175 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.262 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.301 | ||||
| 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 | 1.051 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.516 | ||||
| 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 | 0.917 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.515 | ||||
| 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) | -8746556950512880.000 | ||||
| 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) | -640851381660535304585248229031936.000 | ||||
| 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 | ||||