Advanced Statistics: Options Income
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 | 0.243 | ||||
| SD | 0.293 | ||||
| Sharpe ratio (Glass type estimate) | 0.828 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.821 | ||||
| df | 92.000 | ||||
| t | 2.304 | ||||
| p | 0.012 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.111 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.539 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.107 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.535 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.665 | ||||
| Upside Potential Ratio | 2.733 | ||||
| Upside part of mean | 0.398 | ||||
| Downside part of mean | -0.156 | ||||
| Upside SD | 0.262 | ||||
| Downside SD | 0.146 | ||||
| N nonnegative terms | 50.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 93.000 | ||||
| Mean of predictor | 0.249 | ||||
| Mean of criterion | 0.243 | ||||
| SD of predictor | 0.269 | ||||
| SD of criterion | 0.293 | ||||
| Covariance | 0.044 | ||||
| r | 0.551 | ||||
| b (slope, estimate of beta) | 0.600 | ||||
| a (intercept, estimate of alpha) | 0.094 | ||||
| Mean Square Error | 0.061 | ||||
| DF error | 91.000 | ||||
| t(b) | 6.301 | ||||
| p(b) | 0.000 | ||||
| t(a) | 1.022 | ||||
| p(a) | 0.155 | ||||
| Lowerbound of 95% confidence interval for beta | 0.411 | ||||
| Upperbound of 95% confidence interval for beta | 0.789 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.088 | ||||
| Upperbound of 95% confidence interval for alpha | 0.275 | ||||
| Treynor index (mean / b) | 0.405 | ||||
| Jensen alpha (a) | 0.094 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.201 | ||||
| SD | 0.276 | ||||
| Sharpe ratio (Glass type estimate) | 0.727 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.721 | ||||
| df | 92.000 | ||||
| t | 2.024 | ||||
| p | 0.023 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.013 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.437 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.009 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.433 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.224 | ||||
| Upside Potential Ratio | 2.244 | ||||
| Upside part of mean | 0.368 | ||||
| Downside part of mean | -0.167 | ||||
| Upside SD | 0.228 | ||||
| Downside SD | 0.164 | ||||
| N nonnegative terms | 50.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 93.000 | ||||
| Mean of predictor | 0.214 | ||||
| Mean of criterion | 0.201 | ||||
| SD of predictor | 0.248 | ||||
| SD of criterion | 0.276 | ||||
| Covariance | 0.037 | ||||
| r | 0.535 | ||||
| b (slope, estimate of beta) | 0.596 | ||||
| a (intercept, estimate of alpha) | 0.074 | ||||
| Mean Square Error | 0.055 | ||||
| DF error | 91.000 | ||||
| t(b) | 6.034 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.847 | ||||
| p(a) | 0.200 | ||||
| Lowerbound of 95% confidence interval for beta | 0.400 | ||||
| Upperbound of 95% confidence interval for beta | 0.792 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | 0.246 | ||||
| Treynor index (mean / b) | 0.337 | ||||
| Jensen alpha (a) | 0.074 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.108 | ||||
| Expected Shortfall on VaR | 0.137 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 93.000 | ||||
| Minimum | 0.727 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.008 | ||||
| Quartile 3 | 1.047 | ||||
| Maximum | 1.520 | ||||
| Mean of quarter 1 | 0.956 | ||||
| Mean of quarter 2 | 1.001 | ||||
| Mean of quarter 3 | 1.025 | ||||
| Mean of quarter 4 | 1.116 | ||||
| Inter Quartile Range | 0.047 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.032 | ||||
| Mean of outliers low | 0.790 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.065 | ||||
| Mean of outliers high | 1.237 | ||||
| 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) | 0.508 | ||||
| VaR(95%) (regression method) | 0.039 | ||||
| Expected Shortfall (regression method) | 0.112 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.060 | ||||
| Quartile 3 | 0.211 | ||||
| Maximum | 0.276 | ||||
| Mean of quarter 1 | 0.011 | ||||
| Mean of quarter 2 | 0.053 | ||||
| Mean of quarter 3 | 0.168 | ||||
| Mean of quarter 4 | 0.265 | ||||
| Inter Quartile Range | 0.179 | ||||
| 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) | 0.732 | ||||
| Compounded annual return (geometric extrapolation) | 0.278 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.007 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.049 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.025 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.274 | ||||
| SD | 0.388 | ||||
| Sharpe ratio (Glass type estimate) | 0.705 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.704 | ||||
| df | 2040.000 | ||||
| t | 1.967 | ||||
| p | 0.025 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.002 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.407 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.002 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.407 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.110 | ||||
| Upside Potential Ratio | 5.789 | ||||
| Upside part of mean | 1.427 | ||||
| Downside part of mean | -1.153 | ||||
| Upside SD | 0.300 | ||||
| Downside SD | 0.247 | ||||
| N nonnegative terms | 889.000 | ||||
| N negative terms | 1152.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2041.000 | ||||
| Mean of predictor | 0.272 | ||||
| Mean of criterion | 0.274 | ||||
| SD of predictor | 0.293 | ||||
| SD of criterion | 0.388 | ||||
| Covariance | 0.051 | ||||
| r | 0.447 | ||||
| b (slope, estimate of beta) | 0.592 | ||||
| a (intercept, estimate of alpha) | 0.113 | ||||
| Mean Square Error | 0.121 | ||||
| DF error | 2039.000 | ||||
| t(b) | 22.562 | ||||
| p(b) | -0.000 | ||||
| t(a) | 0.903 | ||||
| p(a) | 0.183 | ||||
| Lowerbound of 95% confidence interval for beta | 0.540 | ||||
| Upperbound of 95% confidence interval for beta | 0.643 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.132 | ||||
| Upperbound of 95% confidence interval for alpha | 0.357 | ||||
| Treynor index (mean / b) | 0.462 | ||||
| Jensen alpha (a) | 0.113 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.200 | ||||
| SD | 0.384 | ||||
| Sharpe ratio (Glass type estimate) | 0.520 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.520 | ||||
| df | 2040.000 | ||||
| t | 1.452 | ||||
| p | 0.073 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.182 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.223 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.182 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.222 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.746 | ||||
| Upside Potential Ratio | 5.179 | ||||
| Upside part of mean | 1.387 | ||||
| Downside part of mean | -1.187 | ||||
| Upside SD | 0.275 | ||||
| Downside SD | 0.268 | ||||
| N nonnegative terms | 889.000 | ||||
| N negative terms | 1152.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2041.000 | ||||
| Mean of predictor | 0.229 | ||||
| Mean of criterion | 0.200 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 0.384 | ||||
| Covariance | 0.050 | ||||
| r | 0.439 | ||||
| b (slope, estimate of beta) | 0.570 | ||||
| a (intercept, estimate of alpha) | 0.069 | ||||
| Mean Square Error | 0.119 | ||||
| DF error | 2039.000 | ||||
| t(b) | 22.038 | ||||
| p(b) | -0.000 | ||||
| t(a) | 0.561 | ||||
| p(a) | 0.287 | ||||
| Lowerbound of 95% confidence interval for beta | 0.519 | ||||
| Upperbound of 95% confidence interval for beta | 0.621 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.173 | ||||
| Upperbound of 95% confidence interval for alpha | 0.312 | ||||
| Treynor index (mean / b) | 0.350 | ||||
| Jensen alpha (a) | 0.069 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.038 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2041.000 | ||||
| Minimum | 0.673 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 1.476 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.020 | ||||
| Inter Quartile Range | 0.007 | ||||
| Number outliers low | 194.000 | ||||
| Percentage of outliers low | 0.095 | ||||
| Mean of outliers low | 0.965 | ||||
| Number of outliers high | 189.000 | ||||
| Percentage of outliers high | 0.093 | ||||
| Mean of outliers high | 1.041 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.801 | ||||
| VaR(95%) (moments method) | 0.013 | ||||
| Expected Shortfall (moments method) | 0.074 | ||||
| Extreme Value Index (regression method) | 0.402 | ||||
| VaR(95%) (regression method) | 0.013 | ||||
| Expected Shortfall (regression method) | 0.028 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 66.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.014 | ||||
| Quartile 3 | 0.055 | ||||
| Maximum | 0.420 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.032 | ||||
| Mean of quarter 4 | 0.173 | ||||
| Inter Quartile Range | 0.053 | ||||
| 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 | 0.121 | ||||
| Mean of outliers high | 0.272 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.285 | ||||
| VaR(95%) (moments method) | 0.165 | ||||
| Expected Shortfall (moments method) | 0.284 | ||||
| Extreme Value Index (regression method) | 0.156 | ||||
| VaR(95%) (regression method) | 0.170 | ||||
| Expected Shortfall (regression method) | 0.264 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.729 | ||||
| Compounded annual return (geometric extrapolation) | 0.276 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.657 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.595 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.875 | ||||
| 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 | 1.134 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.331 | ||||
| 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 | 1.077 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.333 | ||||
| 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) | -8627638833712433.000 | ||||
| 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) | 39186937157730756029317203886080.000 | ||||
| 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 | ||||