Advanced Statistics: Options Trading
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 | 0.211 | ||||
| SD | 0.456 | ||||
| Sharpe ratio (Glass type estimate) | 0.462 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.452 | ||||
| df | 36.000 | ||||
| t | 0.811 | ||||
| p | 0.211 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.662 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.580 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.669 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.573 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.448 | ||||
| Upside Potential Ratio | 2.440 | ||||
| Upside part of mean | 0.355 | ||||
| Downside part of mean | -0.144 | ||||
| Upside SD | 0.430 | ||||
| Downside SD | 0.145 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.511 | ||||
| Mean of criterion | 0.211 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 0.456 | ||||
| Covariance | -0.027 | ||||
| r | -0.191 | ||||
| b (slope, estimate of beta) | -0.280 | ||||
| a (intercept, estimate of alpha) | 0.353 | ||||
| Mean Square Error | 0.206 | ||||
| DF error | 35.000 | ||||
| t(b) | -1.150 | ||||
| p(b) | 0.871 | ||||
| t(a) | 1.232 | ||||
| p(a) | 0.113 | ||||
| Lowerbound of 95% confidence interval for beta | -0.773 | ||||
| Upperbound of 95% confidence interval for beta | 0.214 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.229 | ||||
| Upperbound of 95% confidence interval for alpha | 0.936 | ||||
| Treynor index (mean / b) | -0.753 | ||||
| Jensen alpha (a) | 0.353 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.130 | ||||
| SD | 0.381 | ||||
| Sharpe ratio (Glass type estimate) | 0.342 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.334 | ||||
| df | 36.000 | ||||
| t | 0.600 | ||||
| p | 0.276 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.780 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.458 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.784 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.453 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.796 | ||||
| Upside Potential Ratio | 1.749 | ||||
| Upside part of mean | 0.286 | ||||
| Downside part of mean | -0.156 | ||||
| Upside SD | 0.340 | ||||
| Downside SD | 0.163 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.458 | ||||
| Mean of criterion | 0.130 | ||||
| SD of predictor | 0.285 | ||||
| SD of criterion | 0.381 | ||||
| Covariance | -0.022 | ||||
| r | -0.206 | ||||
| b (slope, estimate of beta) | -0.275 | ||||
| a (intercept, estimate of alpha) | 0.256 | ||||
| Mean Square Error | 0.143 | ||||
| DF error | 35.000 | ||||
| t(b) | -1.245 | ||||
| p(b) | 0.889 | ||||
| t(a) | 1.076 | ||||
| p(a) | 0.145 | ||||
| Lowerbound of 95% confidence interval for beta | -0.723 | ||||
| Upperbound of 95% confidence interval for beta | 0.173 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.227 | ||||
| Upperbound of 95% confidence interval for alpha | 0.739 | ||||
| Treynor index (mean / b) | -0.474 | ||||
| Jensen alpha (a) | 0.256 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.156 | ||||
| Expected Shortfall on VaR | 0.194 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.040 | ||||
| Expected Shortfall on VaR | 0.085 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 37.000 | ||||
| Minimum | 0.766 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.645 | ||||
| Mean of quarter 1 | 0.968 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.123 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.054 | ||||
| Mean of outliers low | 0.839 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.108 | ||||
| Mean of outliers high | 1.277 | ||||
| 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) | -0.283 | ||||
| VaR(95%) (regression method) | 0.085 | ||||
| Expected Shortfall (regression method) | 0.221 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.088 | ||||
| Quartile 1 | 0.125 | ||||
| Median | 0.161 | ||||
| Quartile 3 | 0.197 | ||||
| Maximum | 0.234 | ||||
| Mean of quarter 1 | 0.088 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.234 | ||||
| Inter Quartile Range | 0.073 | ||||
| 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) | 0.230 | ||||
| Compounded annual return (geometric extrapolation) | 0.190 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.814 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.814 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.983 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.158 | ||||
| SD | 0.257 | ||||
| Sharpe ratio (Glass type estimate) | 0.616 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.616 | ||||
| df | 822.000 | ||||
| t | 1.092 | ||||
| p | 0.138 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.490 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.722 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.491 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.722 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.187 | ||||
| Upside Potential Ratio | 3.885 | ||||
| Upside part of mean | 0.519 | ||||
| Downside part of mean | -0.360 | ||||
| Upside SD | 0.220 | ||||
| Downside SD | 0.134 | ||||
| N nonnegative terms | 62.000 | ||||
| N negative terms | 761.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 823.000 | ||||
| Mean of predictor | 0.545 | ||||
| Mean of criterion | 0.158 | ||||
| SD of predictor | 0.330 | ||||
| SD of criterion | 0.257 | ||||
| Covariance | 0.000 | ||||
| r | 0.001 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | 0.158 | ||||
| Mean Square Error | 0.066 | ||||
| DF error | 821.000 | ||||
| t(b) | 0.025 | ||||
| p(b) | 0.490 | ||||
| t(a) | 1.083 | ||||
| p(a) | 0.139 | ||||
| Lowerbound of 95% confidence interval for beta | -0.053 | ||||
| Upperbound of 95% confidence interval for beta | 0.054 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.128 | ||||
| Upperbound of 95% confidence interval for alpha | 0.445 | ||||
| Treynor index (mean / b) | 236.413 | ||||
| Jensen alpha (a) | 0.158 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.127 | ||||
| SD | 0.249 | ||||
| Sharpe ratio (Glass type estimate) | 0.510 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.510 | ||||
| df | 822.000 | ||||
| t | 0.904 | ||||
| p | 0.183 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.596 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.616 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.597 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.616 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.905 | ||||
| Upside Potential Ratio | 3.542 | ||||
| Upside part of mean | 0.496 | ||||
| Downside part of mean | -0.370 | ||||
| Upside SD | 0.205 | ||||
| Downside SD | 0.140 | ||||
| N nonnegative terms | 62.000 | ||||
| N negative terms | 761.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 823.000 | ||||
| Mean of predictor | 0.490 | ||||
| Mean of criterion | 0.127 | ||||
| SD of predictor | 0.330 | ||||
| SD of criterion | 0.249 | ||||
| Covariance | -0.000 | ||||
| r | -0.001 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | 0.127 | ||||
| Mean Square Error | 0.062 | ||||
| DF error | 821.000 | ||||
| t(b) | -0.026 | ||||
| p(b) | 0.511 | ||||
| t(a) | 0.902 | ||||
| p(a) | 0.184 | ||||
| Lowerbound of 95% confidence interval for beta | -0.052 | ||||
| Upperbound of 95% confidence interval for beta | 0.051 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.150 | ||||
| Upperbound of 95% confidence interval for alpha | 0.404 | ||||
| Treynor index (mean / b) | -182.648 | ||||
| Jensen alpha (a) | 0.127 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 823.000 | ||||
| Minimum | 0.870 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.231 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 54.000 | ||||
| Percentage of outliers low | 0.066 | ||||
| Mean of outliers low | 0.981 | ||||
| Number of outliers high | 63.000 | ||||
| Percentage of outliers high | 0.077 | ||||
| Mean of outliers high | 1.026 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.136 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.273 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | 0.017 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 15.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.023 | ||||
| Quartile 3 | 0.058 | ||||
| Maximum | 0.338 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.043 | ||||
| Mean of quarter 4 | 0.156 | ||||
| Inter Quartile Range | 0.054 | ||||
| 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 | 0.067 | ||||
| Mean of outliers high | 0.338 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.166 | ||||
| VaR(95%) (moments method) | 0.155 | ||||
| Expected Shortfall (moments method) | 0.242 | ||||
| Extreme Value Index (regression method) | 1.041 | ||||
| VaR(95%) (regression method) | 0.261 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.226 | ||||
| Compounded annual return (geometric extrapolation) | 0.186 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.552 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.197 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.067 | ||||
| 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 | 1.098 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.469 | ||||
| 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 | 0.987 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.471 | ||||
| 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) | -8726440034834371.000 | ||||
| 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) | 134094055551241319005659259207680.000 | ||||
| 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 | ||||