Advanced Statistics: Asset Rotation Premium
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 | -0.035 | ||||
| SD | 0.073 | ||||
| Sharpe ratio (Glass type estimate) | -0.475 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.465 | ||||
| df | 37.000 | ||||
| t | -0.844 | ||||
| p | 0.798 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.578 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.635 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.571 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.642 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.679 | ||||
| Upside Potential Ratio | 1.008 | ||||
| Upside part of mean | 0.051 | ||||
| Downside part of mean | -0.086 | ||||
| Upside SD | 0.052 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.578 | ||||
| Mean of criterion | -0.035 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.073 | ||||
| Covariance | 0.002 | ||||
| r | 0.104 | ||||
| b (slope, estimate of beta) | 0.024 | ||||
| a (intercept, estimate of alpha) | -0.049 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 36.000 | ||||
| t(b) | 0.625 | ||||
| p(b) | 0.268 | ||||
| t(a) | -1.035 | ||||
| p(a) | 0.846 | ||||
| Lowerbound of 95% confidence interval for beta | -0.055 | ||||
| Upperbound of 95% confidence interval for beta | 0.104 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.144 | ||||
| Upperbound of 95% confidence interval for alpha | 0.047 | ||||
| Treynor index (mean / b) | -1.410 | ||||
| Jensen alpha (a) | -0.049 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.037 | ||||
| SD | 0.072 | ||||
| Sharpe ratio (Glass type estimate) | -0.512 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.501 | ||||
| df | 37.000 | ||||
| t | -0.911 | ||||
| p | 0.816 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.616 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.599 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.609 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.606 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.711 | ||||
| Upside Potential Ratio | 0.958 | ||||
| Upside part of mean | 0.050 | ||||
| Downside part of mean | -0.087 | ||||
| Upside SD | 0.050 | ||||
| Downside SD | 0.052 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.521 | ||||
| Mean of criterion | -0.037 | ||||
| SD of predictor | 0.290 | ||||
| SD of criterion | 0.072 | ||||
| Covariance | 0.002 | ||||
| r | 0.116 | ||||
| b (slope, estimate of beta) | 0.029 | ||||
| a (intercept, estimate of alpha) | -0.052 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 36.000 | ||||
| t(b) | 0.702 | ||||
| p(b) | 0.244 | ||||
| t(a) | -1.127 | ||||
| p(a) | 0.866 | ||||
| Lowerbound of 95% confidence interval for beta | -0.055 | ||||
| Upperbound of 95% confidence interval for beta | 0.113 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.146 | ||||
| Upperbound of 95% confidence interval for alpha | 0.042 | ||||
| Treynor index (mean / b) | -1.278 | ||||
| Jensen alpha (a) | -0.052 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.045 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.042 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 38.000 | ||||
| Minimum | 0.936 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.079 | ||||
| Mean of quarter 1 | 0.985 | ||||
| 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 | 4.000 | ||||
| Percentage of outliers low | 0.105 | ||||
| Mean of outliers low | 0.963 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.132 | ||||
| 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) | -0.620 | ||||
| VaR(95%) (regression method) | 0.038 | ||||
| Expected Shortfall (regression method) | 0.056 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.116 | ||||
| Quartile 1 | 0.116 | ||||
| Median | 0.116 | ||||
| Quartile 3 | 0.116 | ||||
| Maximum | 0.116 | ||||
| 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) | 0.007 | ||||
| Compounded annual return (geometric extrapolation) | 0.007 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.060 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.156 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.035 | ||||
| SD | 0.068 | ||||
| Sharpe ratio (Glass type estimate) | -0.509 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.509 | ||||
| df | 831.000 | ||||
| t | -0.908 | ||||
| p | 0.818 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.609 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.591 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.609 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.591 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.678 | ||||
| Upside Potential Ratio | 3.689 | ||||
| Upside part of mean | 0.189 | ||||
| Downside part of mean | -0.224 | ||||
| Upside SD | 0.045 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 92.000 | ||||
| N negative terms | 740.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 832.000 | ||||
| Mean of predictor | 0.574 | ||||
| Mean of criterion | -0.035 | ||||
| SD of predictor | 0.321 | ||||
| SD of criterion | 0.068 | ||||
| Covariance | 0.003 | ||||
| r | 0.115 | ||||
| b (slope, estimate of beta) | 0.024 | ||||
| a (intercept, estimate of alpha) | -0.049 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 830.000 | ||||
| t(b) | 3.341 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.274 | ||||
| p(a) | 0.899 | ||||
| Lowerbound of 95% confidence interval for beta | 0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.039 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.124 | ||||
| Upperbound of 95% confidence interval for alpha | 0.026 | ||||
| Treynor index (mean / b) | -1.421 | ||||
| Jensen alpha (a) | -0.049 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.037 | ||||
| SD | 0.068 | ||||
| Sharpe ratio (Glass type estimate) | -0.542 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.542 | ||||
| df | 831.000 | ||||
| t | -0.966 | ||||
| p | 0.833 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.642 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.558 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.642 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.558 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.716 | ||||
| Upside Potential Ratio | 3.634 | ||||
| Upside part of mean | 0.188 | ||||
| Downside part of mean | -0.225 | ||||
| Upside SD | 0.045 | ||||
| Downside SD | 0.052 | ||||
| N nonnegative terms | 92.000 | ||||
| N negative terms | 740.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 832.000 | ||||
| Mean of predictor | 0.521 | ||||
| Mean of criterion | -0.037 | ||||
| SD of predictor | 0.322 | ||||
| SD of criterion | 0.068 | ||||
| Covariance | 0.003 | ||||
| r | 0.116 | ||||
| b (slope, estimate of beta) | 0.025 | ||||
| a (intercept, estimate of alpha) | -0.050 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 830.000 | ||||
| t(b) | 3.353 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.301 | ||||
| p(a) | 0.903 | ||||
| Lowerbound of 95% confidence interval for beta | 0.010 | ||||
| Upperbound of 95% confidence interval for beta | 0.039 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.125 | ||||
| Upperbound of 95% confidence interval for alpha | 0.025 | ||||
| Treynor index (mean / b) | -1.511 | ||||
| Jensen alpha (a) | -0.050 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| 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 | 832.000 | ||||
| Minimum | 0.969 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.025 | ||||
| Mean of quarter 1 | 0.997 | ||||
| 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 | 89.000 | ||||
| Percentage of outliers low | 0.107 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 93.000 | ||||
| Percentage of outliers high | 0.112 | ||||
| Mean of outliers high | 1.007 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.424 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.152 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | 0.008 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.017 | ||||
| Quartile 3 | 0.024 | ||||
| Maximum | 0.147 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.008 | ||||
| Mean of quarter 3 | 0.021 | ||||
| Mean of quarter 4 | 0.071 | ||||
| Inter Quartile Range | 0.022 | ||||
| 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 | 0.100 | ||||
| Mean of outliers high | 0.147 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.126 | ||||
| VaR(95%) (moments method) | 0.065 | ||||
| Expected Shortfall (moments method) | 0.089 | ||||
| Extreme Value Index (regression method) | 1.524 | ||||
| VaR(95%) (regression method) | 0.182 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.007 | ||||
| Compounded annual return (geometric extrapolation) | 0.007 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.048 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.099 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.797 | ||||
| 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 | 0.979 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.489 | ||||
| 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 | 0.859 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.487 | ||||
| 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) | -8747588096308887.000 | ||||
| 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) | 250191146471687627716805179473920.000 | ||||
| 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 | ||||