Advanced Statistics: MFS-Cyclical-Options
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 | 0.258 | ||||
| SD | 0.706 | ||||
| Sharpe ratio (Glass type estimate) | 0.366 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.358 | ||||
| df | 33.000 | ||||
| t | 0.616 | ||||
| p | 0.271 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.804 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.531 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.810 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.525 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.692 | ||||
| Upside Potential Ratio | 2.656 | ||||
| Upside part of mean | 0.406 | ||||
| Downside part of mean | -0.147 | ||||
| Upside SD | 0.683 | ||||
| Downside SD | 0.153 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.571 | ||||
| Mean of criterion | 0.258 | ||||
| SD of predictor | 0.341 | ||||
| SD of criterion | 0.706 | ||||
| Covariance | -0.041 | ||||
| r | -0.169 | ||||
| b (slope, estimate of beta) | -0.349 | ||||
| a (intercept, estimate of alpha) | 0.458 | ||||
| Mean Square Error | 0.500 | ||||
| DF error | 32.000 | ||||
| t(b) | -0.968 | ||||
| p(b) | 0.830 | ||||
| t(a) | 0.979 | ||||
| p(a) | 0.168 | ||||
| Lowerbound of 95% confidence interval for beta | -1.083 | ||||
| Upperbound of 95% confidence interval for beta | 0.385 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.495 | ||||
| Upperbound of 95% confidence interval for alpha | 1.410 | ||||
| Treynor index (mean / b) | -0.741 | ||||
| Jensen alpha (a) | 0.458 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.109 | ||||
| SD | 0.492 | ||||
| Sharpe ratio (Glass type estimate) | 0.221 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.216 | ||||
| df | 33.000 | ||||
| t | 0.372 | ||||
| p | 0.356 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.946 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.385 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.949 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.382 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.625 | ||||
| Upside Potential Ratio | 1.546 | ||||
| Upside part of mean | 0.269 | ||||
| Downside part of mean | -0.160 | ||||
| Upside SD | 0.453 | ||||
| Downside SD | 0.174 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.505 | ||||
| Mean of criterion | 0.109 | ||||
| SD of predictor | 0.322 | ||||
| SD of criterion | 0.492 | ||||
| Covariance | -0.025 | ||||
| r | -0.160 | ||||
| b (slope, estimate of beta) | -0.244 | ||||
| a (intercept, estimate of alpha) | 0.232 | ||||
| Mean Square Error | 0.243 | ||||
| DF error | 32.000 | ||||
| t(b) | -0.914 | ||||
| p(b) | 0.816 | ||||
| t(a) | 0.719 | ||||
| p(a) | 0.239 | ||||
| Lowerbound of 95% confidence interval for beta | -0.786 | ||||
| Upperbound of 95% confidence interval for beta | 0.299 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.425 | ||||
| Upperbound of 95% confidence interval for alpha | 0.889 | ||||
| Treynor index (mean / b) | -0.447 | ||||
| Jensen alpha (a) | 0.232 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.201 | ||||
| Expected Shortfall on VaR | 0.246 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.090 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.753 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.153 | ||||
| Mean of quarter 1 | 0.967 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.128 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.059 | ||||
| Mean of outliers low | 0.852 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.029 | ||||
| Mean of outliers high | 2.153 | ||||
| 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) | 1.039 | ||||
| VaR(95%) (regression method) | 0.046 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.048 | ||||
| Quartile 1 | 0.098 | ||||
| Median | 0.148 | ||||
| Quartile 3 | 0.198 | ||||
| Maximum | 0.247 | ||||
| Mean of quarter 1 | 0.048 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.247 | ||||
| Inter Quartile Range | 0.099 | ||||
| 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) | 0.191 | ||||
| Compounded annual return (geometric extrapolation) | 0.165 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.668 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.668 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.671 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.314 | ||||
| SD | 0.756 | ||||
| Sharpe ratio (Glass type estimate) | 0.416 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.415 | ||||
| df | 745.000 | ||||
| t | 0.702 | ||||
| p | 0.242 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.746 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.577 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.746 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.577 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.186 | ||||
| Upside Potential Ratio | 4.041 | ||||
| Upside part of mean | 1.071 | ||||
| Downside part of mean | -0.757 | ||||
| Upside SD | 0.708 | ||||
| Downside SD | 0.265 | ||||
| N nonnegative terms | 27.000 | ||||
| N negative terms | 719.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 746.000 | ||||
| Mean of predictor | 0.603 | ||||
| Mean of criterion | 0.314 | ||||
| SD of predictor | 0.337 | ||||
| SD of criterion | 0.756 | ||||
| Covariance | -0.013 | ||||
| r | -0.051 | ||||
| b (slope, estimate of beta) | -0.114 | ||||
| a (intercept, estimate of alpha) | 0.383 | ||||
| Mean Square Error | 0.571 | ||||
| DF error | 744.000 | ||||
| t(b) | -1.385 | ||||
| p(b) | 0.917 | ||||
| t(a) | 0.850 | ||||
| p(a) | 0.198 | ||||
| Lowerbound of 95% confidence interval for beta | -0.275 | ||||
| Upperbound of 95% confidence interval for beta | 0.047 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.501 | ||||
| Upperbound of 95% confidence interval for alpha | 1.267 | ||||
| Treynor index (mean / b) | -2.763 | ||||
| Jensen alpha (a) | 0.383 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.108 | ||||
| SD | 0.598 | ||||
| Sharpe ratio (Glass type estimate) | 0.181 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.181 | ||||
| df | 745.000 | ||||
| t | 0.305 | ||||
| p | 0.380 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.981 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.342 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.981 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.342 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.382 | ||||
| Upside Potential Ratio | 3.189 | ||||
| Upside part of mean | 0.903 | ||||
| Downside part of mean | -0.795 | ||||
| Upside SD | 0.527 | ||||
| Downside SD | 0.283 | ||||
| N nonnegative terms | 27.000 | ||||
| N negative terms | 719.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 746.000 | ||||
| Mean of predictor | 0.545 | ||||
| Mean of criterion | 0.108 | ||||
| SD of predictor | 0.339 | ||||
| SD of criterion | 0.598 | ||||
| Covariance | -0.010 | ||||
| r | -0.050 | ||||
| b (slope, estimate of beta) | -0.088 | ||||
| a (intercept, estimate of alpha) | 0.156 | ||||
| Mean Square Error | 0.358 | ||||
| DF error | 744.000 | ||||
| t(b) | -1.364 | ||||
| p(b) | 0.914 | ||||
| t(a) | 0.438 | ||||
| p(a) | 0.331 | ||||
| Lowerbound of 95% confidence interval for beta | -0.215 | ||||
| Upperbound of 95% confidence interval for beta | 0.039 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.543 | ||||
| Upperbound of 95% confidence interval for alpha | 0.855 | ||||
| Treynor index (mean / b) | -1.228 | ||||
| Jensen alpha (a) | 0.156 | ||||
| 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 | 0.073 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.022 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 746.000 | ||||
| Minimum | 0.840 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.023 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 33.000 | ||||
| Percentage of outliers low | 0.044 | ||||
| Mean of outliers low | 0.938 | ||||
| Number of outliers high | 27.000 | ||||
| Percentage of outliers high | 0.036 | ||||
| Mean of outliers high | 1.113 | ||||
| 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) | -1.055 | ||||
| VaR(95%) (regression method) | -0.006 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.089 | ||||
| Median | 0.229 | ||||
| Quartile 3 | 0.363 | ||||
| Maximum | 0.430 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.117 | ||||
| Mean of quarter 3 | 0.340 | ||||
| Mean of quarter 4 | 0.430 | ||||
| Inter Quartile Range | 0.274 | ||||
| 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) | 0.190 | ||||
| Compounded annual return (geometric extrapolation) | 0.164 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.382 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.382 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.253 | ||||
| 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 | 1.046 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.477 | ||||
| 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 | 0.931 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.479 | ||||
| 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) | -8736581620933988.000 | ||||
| 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) | -266279242956794913025066576904192.000 | ||||
| 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 | ||||