Advanced Statistics: expired YM Dynamic Duo(SM)
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 | -0.015 | ||||
| SD | 0.130 | ||||
| Sharpe ratio (Glass type estimate) | -0.112 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.110 | ||||
| df | 37.000 | ||||
| t | -0.200 | ||||
| p | 0.579 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.213 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.990 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.212 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.992 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.205 | ||||
| Upside Potential Ratio | 1.217 | ||||
| Upside part of mean | 0.087 | ||||
| Downside part of mean | -0.101 | ||||
| Upside SD | 0.107 | ||||
| Downside SD | 0.071 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.518 | ||||
| Mean of criterion | -0.015 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 0.130 | ||||
| Covariance | -0.005 | ||||
| r | -0.135 | ||||
| b (slope, estimate of beta) | -0.065 | ||||
| a (intercept, estimate of alpha) | 0.019 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.817 | ||||
| p(b) | 0.790 | ||||
| t(a) | 0.224 | ||||
| p(a) | 0.412 | ||||
| Lowerbound of 95% confidence interval for beta | -0.225 | ||||
| Upperbound of 95% confidence interval for beta | 0.096 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.151 | ||||
| Upperbound of 95% confidence interval for alpha | 0.189 | ||||
| Treynor index (mean / b) | 0.226 | ||||
| Jensen alpha (a) | 0.019 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.022 | ||||
| SD | 0.125 | ||||
| Sharpe ratio (Glass type estimate) | -0.179 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.175 | ||||
| df | 37.000 | ||||
| t | -0.318 | ||||
| p | 0.624 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.279 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.925 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.277 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.927 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.299 | ||||
| Upside Potential Ratio | 1.089 | ||||
| Upside part of mean | 0.081 | ||||
| Downside part of mean | -0.104 | ||||
| Upside SD | 0.099 | ||||
| Downside SD | 0.075 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.472 | ||||
| Mean of criterion | -0.022 | ||||
| SD of predictor | 0.259 | ||||
| SD of criterion | 0.125 | ||||
| Covariance | -0.004 | ||||
| r | -0.131 | ||||
| b (slope, estimate of beta) | -0.064 | ||||
| a (intercept, estimate of alpha) | 0.008 | ||||
| Mean Square Error | 0.016 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.795 | ||||
| p(b) | 0.784 | ||||
| t(a) | 0.096 | ||||
| p(a) | 0.462 | ||||
| Lowerbound of 95% confidence interval for beta | -0.226 | ||||
| Upperbound of 95% confidence interval for beta | 0.099 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.155 | ||||
| Upperbound of 95% confidence interval for alpha | 0.170 | ||||
| Treynor index (mean / b) | 0.352 | ||||
| Jensen alpha (a) | 0.008 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.059 | ||||
| Expected Shortfall on VaR | 0.074 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.055 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 38.000 | ||||
| Minimum | 0.891 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.179 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.029 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.105 | ||||
| Mean of outliers low | 0.952 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.079 | ||||
| Mean of outliers high | 1.095 | ||||
| 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) | 0.143 | ||||
| VaR(95%) (regression method) | 0.032 | ||||
| Expected Shortfall (regression method) | 0.074 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.049 | ||||
| Quartile 1 | 0.064 | ||||
| Median | 0.079 | ||||
| Quartile 3 | 0.094 | ||||
| Maximum | 0.109 | ||||
| Mean of quarter 1 | 0.049 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.109 | ||||
| Inter Quartile Range | 0.030 | ||||
| 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) | 0.022 | ||||
| Compounded annual return (geometric extrapolation) | 0.022 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.202 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.202 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.298 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 0.094 | ||||
| Sharpe ratio (Glass type estimate) | -0.194 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.194 | ||||
| df | 841.000 | ||||
| t | -0.349 | ||||
| p | 0.636 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.288 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.899 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.288 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.899 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.307 | ||||
| Upside Potential Ratio | 2.925 | ||||
| Upside part of mean | 0.174 | ||||
| Downside part of mean | -0.192 | ||||
| Upside SD | 0.073 | ||||
| Downside SD | 0.060 | ||||
| N nonnegative terms | 44.000 | ||||
| N negative terms | 798.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 842.000 | ||||
| Mean of predictor | 0.540 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 0.094 | ||||
| Covariance | -0.001 | ||||
| r | -0.047 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | -0.011 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 840.000 | ||||
| t(b) | -1.364 | ||||
| p(b) | 0.913 | ||||
| t(a) | -0.204 | ||||
| p(a) | 0.581 | ||||
| Lowerbound of 95% confidence interval for beta | -0.034 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.114 | ||||
| Upperbound of 95% confidence interval for alpha | 0.093 | ||||
| Treynor index (mean / b) | 1.316 | ||||
| Jensen alpha (a) | -0.011 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.023 | ||||
| SD | 0.093 | ||||
| Sharpe ratio (Glass type estimate) | -0.243 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.242 | ||||
| df | 841.000 | ||||
| t | -0.435 | ||||
| p | 0.668 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.336 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.851 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.336 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.851 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.375 | ||||
| Upside Potential Ratio | 2.841 | ||||
| Upside part of mean | 0.172 | ||||
| Downside part of mean | -0.194 | ||||
| Upside SD | 0.071 | ||||
| Downside SD | 0.060 | ||||
| N nonnegative terms | 44.000 | ||||
| N negative terms | 798.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 842.000 | ||||
| Mean of predictor | 0.488 | ||||
| Mean of criterion | -0.023 | ||||
| SD of predictor | 0.323 | ||||
| SD of criterion | 0.093 | ||||
| Covariance | -0.001 | ||||
| r | -0.046 | ||||
| b (slope, estimate of beta) | -0.013 | ||||
| a (intercept, estimate of alpha) | -0.016 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 840.000 | ||||
| t(b) | -1.323 | ||||
| p(b) | 0.907 | ||||
| t(a) | -0.310 | ||||
| p(a) | 0.622 | ||||
| Lowerbound of 95% confidence interval for beta | -0.033 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.119 | ||||
| Upperbound of 95% confidence interval for alpha | 0.086 | ||||
| Treynor index (mean / b) | 1.719 | ||||
| Jensen alpha (a) | -0.016 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 842.000 | ||||
| Minimum | 0.959 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.059 | ||||
| Mean of quarter 1 | 0.998 | ||||
| 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 | 33.000 | ||||
| Percentage of outliers low | 0.039 | ||||
| Mean of outliers low | 0.985 | ||||
| Number of outliers high | 44.000 | ||||
| Percentage of outliers high | 0.052 | ||||
| Mean of outliers high | 1.013 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.403 | ||||
| VaR(95%) (moments method) | -0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.269 | ||||
| VaR(95%) (regression method) | -0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.026 | ||||
| Quartile 3 | 0.057 | ||||
| Maximum | 0.144 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.026 | ||||
| Mean of quarter 3 | 0.057 | ||||
| Mean of quarter 4 | 0.144 | ||||
| Inter Quartile Range | 0.055 | ||||
| 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 | 0.144 | ||||
| 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) | 0.022 | ||||
| Compounded annual return (geometric extrapolation) | 0.022 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.149 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.149 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.809 | ||||
| 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 | 1.005 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.483 | ||||
| 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 | 0.888 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.481 | ||||
| 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) | -8742768766679186.000 | ||||
| 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) | -1034174841915610744562329128534016.000 | ||||
| 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 | ||||