Advanced Statistics: Options 787
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 | 0.171 | ||||
| SD | 0.361 | ||||
| Sharpe ratio (Glass type estimate) | 0.473 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.468 | ||||
| df | 65.000 | ||||
| t | 1.110 | ||||
| p | 0.135 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.368 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.311 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.372 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.308 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.285 | ||||
| Upside Potential Ratio | 2.774 | ||||
| Upside part of mean | 0.369 | ||||
| Downside part of mean | -0.198 | ||||
| Upside SD | 0.336 | ||||
| Downside SD | 0.133 | ||||
| N nonnegative terms | 36.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 66.000 | ||||
| Mean of predictor | 0.281 | ||||
| Mean of criterion | 0.171 | ||||
| SD of predictor | 0.230 | ||||
| SD of criterion | 0.361 | ||||
| Covariance | 0.045 | ||||
| r | 0.543 | ||||
| b (slope, estimate of beta) | 0.851 | ||||
| a (intercept, estimate of alpha) | -0.068 | ||||
| Mean Square Error | 0.093 | ||||
| DF error | 64.000 | ||||
| t(b) | 5.174 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.491 | ||||
| p(a) | 0.687 | ||||
| Lowerbound of 95% confidence interval for beta | 0.522 | ||||
| Upperbound of 95% confidence interval for beta | 1.179 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.344 | ||||
| Upperbound of 95% confidence interval for alpha | 0.208 | ||||
| Treynor index (mean / b) | 0.201 | ||||
| Jensen alpha (a) | -0.068 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.120 | ||||
| SD | 0.302 | ||||
| Sharpe ratio (Glass type estimate) | 0.397 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.392 | ||||
| df | 65.000 | ||||
| t | 0.930 | ||||
| p | 0.178 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.443 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.234 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.446 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.230 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.845 | ||||
| Upside Potential Ratio | 2.305 | ||||
| Upside part of mean | 0.326 | ||||
| Downside part of mean | -0.207 | ||||
| Upside SD | 0.266 | ||||
| Downside SD | 0.142 | ||||
| N nonnegative terms | 36.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 66.000 | ||||
| Mean of predictor | 0.252 | ||||
| Mean of criterion | 0.120 | ||||
| SD of predictor | 0.221 | ||||
| SD of criterion | 0.302 | ||||
| Covariance | 0.032 | ||||
| r | 0.486 | ||||
| b (slope, estimate of beta) | 0.664 | ||||
| a (intercept, estimate of alpha) | -0.048 | ||||
| Mean Square Error | 0.071 | ||||
| DF error | 64.000 | ||||
| t(b) | 4.450 | ||||
| p(b) | 0.000 | ||||
| t(a) | -0.401 | ||||
| p(a) | 0.655 | ||||
| Lowerbound of 95% confidence interval for beta | 0.366 | ||||
| Upperbound of 95% confidence interval for beta | 0.962 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.286 | ||||
| Upperbound of 95% confidence interval for alpha | 0.191 | ||||
| Treynor index (mean / b) | 0.180 | ||||
| Jensen alpha (a) | -0.048 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.125 | ||||
| Expected Shortfall on VaR | 0.156 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.074 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 66.000 | ||||
| Minimum | 0.811 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.007 | ||||
| Quartile 3 | 1.022 | ||||
| Maximum | 1.717 | ||||
| Mean of quarter 1 | 0.942 | ||||
| Mean of quarter 2 | 1.001 | ||||
| Mean of quarter 3 | 1.015 | ||||
| Mean of quarter 4 | 1.112 | ||||
| Inter Quartile Range | 0.026 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.136 | ||||
| Mean of outliers low | 0.913 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.136 | ||||
| Mean of outliers high | 1.178 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.421 | ||||
| VaR(95%) (moments method) | 0.019 | ||||
| Expected Shortfall (moments method) | 0.020 | ||||
| Extreme Value Index (regression method) | 0.056 | ||||
| VaR(95%) (regression method) | 0.045 | ||||
| Expected Shortfall (regression method) | 0.073 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.016 | ||||
| Median | 0.053 | ||||
| Quartile 3 | 0.166 | ||||
| Maximum | 0.238 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.051 | ||||
| Mean of quarter 3 | 0.055 | ||||
| Mean of quarter 4 | 0.220 | ||||
| Inter Quartile Range | 0.150 | ||||
| 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) | 0.265 | ||||
| Compounded annual return (geometric extrapolation) | 0.178 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.748 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.808 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.143 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.157 | ||||
| SD | 0.276 | ||||
| Sharpe ratio (Glass type estimate) | 0.568 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.568 | ||||
| df | 1442.000 | ||||
| t | 1.334 | ||||
| p | 0.482 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.267 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.404 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.267 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.404 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.892 | ||||
| Upside Potential Ratio | 5.950 | ||||
| Upside part of mean | 1.047 | ||||
| Downside part of mean | -0.890 | ||||
| Upside SD | 0.213 | ||||
| Downside SD | 0.176 | ||||
| N nonnegative terms | 670.000 | ||||
| N negative terms | 773.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1443.000 | ||||
| Mean of predictor | 0.288 | ||||
| Mean of criterion | 0.157 | ||||
| SD of predictor | 0.239 | ||||
| SD of criterion | 0.276 | ||||
| Covariance | 0.010 | ||||
| r | 0.146 | ||||
| b (slope, estimate of beta) | 0.169 | ||||
| a (intercept, estimate of alpha) | 0.108 | ||||
| Mean Square Error | 0.075 | ||||
| DF error | 1441.000 | ||||
| t(b) | 5.611 | ||||
| p(b) | 0.407 | ||||
| t(a) | 0.928 | ||||
| p(a) | 0.484 | ||||
| Lowerbound of 95% confidence interval for beta | 0.110 | ||||
| Upperbound of 95% confidence interval for beta | 0.228 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.121 | ||||
| Upperbound of 95% confidence interval for alpha | 0.337 | ||||
| Treynor index (mean / b) | 0.930 | ||||
| Jensen alpha (a) | 0.108 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.119 | ||||
| SD | 0.273 | ||||
| Sharpe ratio (Glass type estimate) | 0.438 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.438 | ||||
| df | 1442.000 | ||||
| t | 1.028 | ||||
| p | 0.486 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.397 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.273 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.398 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.273 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.658 | ||||
| Upside Potential Ratio | 5.648 | ||||
| Upside part of mean | 1.025 | ||||
| Downside part of mean | -0.906 | ||||
| Upside SD | 0.203 | ||||
| Downside SD | 0.182 | ||||
| N nonnegative terms | 670.000 | ||||
| N negative terms | 773.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1443.000 | ||||
| Mean of predictor | 0.259 | ||||
| Mean of criterion | 0.119 | ||||
| SD of predictor | 0.240 | ||||
| SD of criterion | 0.273 | ||||
| Covariance | 0.009 | ||||
| r | 0.143 | ||||
| b (slope, estimate of beta) | 0.163 | ||||
| a (intercept, estimate of alpha) | 0.077 | ||||
| Mean Square Error | 0.073 | ||||
| DF error | 1441.000 | ||||
| t(b) | 5.499 | ||||
| p(b) | 0.409 | ||||
| t(a) | 0.669 | ||||
| p(a) | 0.489 | ||||
| Lowerbound of 95% confidence interval for beta | 0.105 | ||||
| Upperbound of 95% confidence interval for beta | 0.221 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.149 | ||||
| Upperbound of 95% confidence interval for alpha | 0.303 | ||||
| Treynor index (mean / b) | 0.732 | ||||
| Jensen alpha (a) | 0.077 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1443.000 | ||||
| Minimum | 0.857 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.195 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 186.000 | ||||
| Percentage of outliers low | 0.129 | ||||
| Mean of outliers low | 0.977 | ||||
| Number of outliers high | 198.000 | ||||
| Percentage of outliers high | 0.137 | ||||
| Mean of outliers high | 1.025 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.072 | ||||
| VaR(95%) (moments method) | 0.009 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.428 | ||||
| VaR(95%) (regression method) | 0.010 | ||||
| Expected Shortfall (regression method) | 0.023 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 59.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.002 | ||||
| Quartile 3 | 0.010 | ||||
| Maximum | 0.308 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.001 | ||||
| Mean of quarter 3 | 0.005 | ||||
| Mean of quarter 4 | 0.073 | ||||
| Inter Quartile Range | 0.009 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.136 | ||||
| Mean of outliers high | 0.123 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.017 | ||||
| VaR(95%) (moments method) | 0.064 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.678 | ||||
| VaR(95%) (regression method) | 0.062 | ||||
| Expected Shortfall (regression method) | 0.226 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.265 | ||||
| Compounded annual return (geometric extrapolation) | 0.177 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.577 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.436 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.269 | ||||
| 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 | 1.091 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.425 | ||||
| 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 | 0.999 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.426 | ||||
| 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) | -8708138390922459.000 | ||||
| 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) | 219192088615177009869960901558272.000 | ||||
| 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 | ||||