Advanced Statistics: Shorting 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 | 67.847 | ||||
| SD | 170.816 | ||||
| Sharpe ratio (Glass type estimate) | 0.397 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.393 | ||||
| df | 74.000 | ||||
| t | 0.993 | ||||
| p | 0.162 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.391 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.182 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.393 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.180 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 103.313 | ||||
| Upside Potential Ratio | 104.397 | ||||
| Upside part of mean | 68.559 | ||||
| Downside part of mean | -0.712 | ||||
| Upside SD | 170.799 | ||||
| Downside SD | 0.657 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 75.000 | ||||
| Mean of predictor | 0.327 | ||||
| Mean of criterion | 67.847 | ||||
| SD of predictor | 0.239 | ||||
| SD of criterion | 170.816 | ||||
| Covariance | -9.152 | ||||
| r | -0.224 | ||||
| b (slope, estimate of beta) | -159.970 | ||||
| a (intercept, estimate of alpha) | 120.158 | ||||
| Mean Square Error | 28093.603 | ||||
| DF error | 73.000 | ||||
| t(b) | -1.964 | ||||
| p(b) | 0.973 | ||||
| t(a) | 1.666 | ||||
| p(a) | 0.050 | ||||
| Lowerbound of 95% confidence interval for beta | -322.320 | ||||
| Upperbound of 95% confidence interval for beta | 2.380 | ||||
| Lowerbound of 95% confidence interval for alpha | -23.622 | ||||
| Upperbound of 95% confidence interval for alpha | 263.938 | ||||
| Treynor index (mean / b) | -0.424 | ||||
| Jensen alpha (a) | 120.158 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.536 | ||||
| SD | 4.715 | ||||
| Sharpe ratio (Glass type estimate) | -0.326 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.322 | ||||
| df | 74.000 | ||||
| t | -0.814 | ||||
| p | 0.791 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.110 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.461 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.108 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.463 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.381 | ||||
| Upside Potential Ratio | 0.297 | ||||
| Upside part of mean | 1.199 | ||||
| Downside part of mean | -2.735 | ||||
| Upside SD | 2.426 | ||||
| Downside SD | 4.031 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 75.000 | ||||
| Mean of predictor | 0.296 | ||||
| Mean of criterion | -1.536 | ||||
| SD of predictor | 0.225 | ||||
| SD of criterion | 4.715 | ||||
| Covariance | -0.528 | ||||
| r | -0.497 | ||||
| b (slope, estimate of beta) | -10.407 | ||||
| a (intercept, estimate of alpha) | 1.544 | ||||
| Mean Square Error | 16.966 | ||||
| DF error | 73.000 | ||||
| t(b) | -4.895 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.876 | ||||
| p(a) | 0.192 | ||||
| Lowerbound of 95% confidence interval for beta | -14.645 | ||||
| Upperbound of 95% confidence interval for beta | -6.169 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.971 | ||||
| Upperbound of 95% confidence interval for alpha | 5.059 | ||||
| Treynor index (mean / b) | 0.148 | ||||
| Jensen alpha (a) | 1.544 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.906 | ||||
| Expected Shortfall on VaR | 0.941 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.138 | ||||
| Expected Shortfall on VaR | 0.309 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 75.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.956 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.033 | ||||
| Maximum | 428.000 | ||||
| Mean of quarter 1 | 0.793 | ||||
| Mean of quarter 2 | 0.980 | ||||
| Mean of quarter 3 | 1.017 | ||||
| Mean of quarter 4 | 23.543 | ||||
| Inter Quartile Range | 0.076 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.040 | ||||
| Mean of outliers low | 0.086 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.027 | ||||
| Mean of outliers high | 214.606 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.996 | ||||
| VaR(95%) (moments method) | 0.196 | ||||
| Expected Shortfall (moments method) | 50.206 | ||||
| Extreme Value Index (regression method) | 0.599 | ||||
| VaR(95%) (regression method) | 0.104 | ||||
| Expected Shortfall (regression method) | 0.244 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.026 | ||||
| Median | 0.045 | ||||
| Quartile 3 | 0.099 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.035 | ||||
| Mean of quarter 3 | 0.052 | ||||
| Mean of quarter 4 | 0.614 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers high | 0.250 | ||||
| Mean of outliers high | 0.614 | ||||
| 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) | -0.160 | ||||
| Compounded annual return (geometric extrapolation) | -0.775 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.775 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.261 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.823 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 484.922 | ||||
| SD | 879.462 | ||||
| Sharpe ratio (Glass type estimate) | 0.551 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.551 | ||||
| df | 1638.000 | ||||
| t | 1.379 | ||||
| p | 0.483 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.233 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.335 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.233 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.335 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 428.568 | ||||
| Upside Potential Ratio | 431.562 | ||||
| Upside part of mean | 488.310 | ||||
| Downside part of mean | -3.387 | ||||
| Upside SD | 879.704 | ||||
| Downside SD | 1.131 | ||||
| N nonnegative terms | 747.000 | ||||
| N negative terms | 892.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1639.000 | ||||
| Mean of predictor | 0.358 | ||||
| Mean of criterion | 484.922 | ||||
| SD of predictor | 0.350 | ||||
| SD of criterion | 879.462 | ||||
| Covariance | -22.893 | ||||
| r | -0.074 | ||||
| b (slope, estimate of beta) | -187.241 | ||||
| a (intercept, estimate of alpha) | 551.885 | ||||
| Mean Square Error | 769637.506 | ||||
| DF error | 1637.000 | ||||
| t(b) | -3.020 | ||||
| p(b) | 0.547 | ||||
| t(a) | 1.570 | ||||
| p(a) | 0.475 | ||||
| Lowerbound of 95% confidence interval for beta | -308.831 | ||||
| Upperbound of 95% confidence interval for beta | -65.650 | ||||
| Lowerbound of 95% confidence interval for alpha | -137.465 | ||||
| Upperbound of 95% confidence interval for alpha | 1241.234 | ||||
| Treynor index (mean / b) | -2.590 | ||||
| Jensen alpha (a) | 551.885 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.535 | ||||
| SD | 7.016 | ||||
| Sharpe ratio (Glass type estimate) | -0.219 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.219 | ||||
| df | 1638.000 | ||||
| t | -0.547 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.002 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.565 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.002 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.565 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.296 | ||||
| Upside Potential Ratio | 1.106 | ||||
| Upside part of mean | 5.730 | ||||
| Downside part of mean | -7.265 | ||||
| Upside SD | 4.730 | ||||
| Downside SD | 5.180 | ||||
| N nonnegative terms | 747.000 | ||||
| N negative terms | 892.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1639.000 | ||||
| Mean of predictor | 0.296 | ||||
| Mean of criterion | -1.535 | ||||
| SD of predictor | 0.349 | ||||
| SD of criterion | 7.016 | ||||
| Covariance | -0.282 | ||||
| r | -0.115 | ||||
| b (slope, estimate of beta) | -2.316 | ||||
| a (intercept, estimate of alpha) | -0.848 | ||||
| Mean Square Error | 48.600 | ||||
| DF error | 1637.000 | ||||
| t(b) | -4.694 | ||||
| p(b) | 0.573 | ||||
| t(a) | -0.304 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | -3.283 | ||||
| Upperbound of 95% confidence interval for beta | -1.348 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.323 | ||||
| Upperbound of 95% confidence interval for alpha | 4.627 | ||||
| Treynor index (mean / b) | 0.663 | ||||
| Jensen alpha (a) | -0.848 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.513 | ||||
| Expected Shortfall on VaR | 0.588 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.071 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1639.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.994 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 2017.000 | ||||
| Mean of quarter 1 | 0.950 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 8.449 | ||||
| Inter Quartile Range | 0.011 | ||||
| Number outliers low | 150.000 | ||||
| Percentage of outliers low | 0.092 | ||||
| Mean of outliers low | 0.886 | ||||
| Number of outliers high | 135.000 | ||||
| Percentage of outliers high | 0.082 | ||||
| Mean of outliers high | 23.600 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.002 | ||||
| VaR(95%) (moments method) | 0.036 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.661 | ||||
| VaR(95%) (regression method) | 0.026 | ||||
| Expected Shortfall (regression method) | 0.086 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 82.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.019 | ||||
| Quartile 3 | 0.045 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.030 | ||||
| Mean of quarter 4 | 0.134 | ||||
| Inter Quartile Range | 0.041 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.073 | ||||
| Mean of outliers high | 0.299 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.668 | ||||
| VaR(95%) (moments method) | 0.139 | ||||
| Expected Shortfall (moments method) | 0.429 | ||||
| Extreme Value Index (regression method) | 1.158 | ||||
| VaR(95%) (regression method) | 0.093 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.160 | ||||
| Compounded annual return (geometric extrapolation) | -0.775 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.775 | ||||
| Compounded annual return / average of 25% largest draw downs | -5.791 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.316 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 6070.005 | ||||
| SD | 3100.825 | ||||
| Sharpe ratio (Glass type estimate) | 1.958 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.946 | ||||
| df | 130.000 | ||||
| t | 1.384 | ||||
| p | 0.440 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.828 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.736 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.836 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.728 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1813.445 | ||||
| Upside Potential Ratio | 1817.822 | ||||
| Upside part of mean | 6084.658 | ||||
| Downside part of mean | -14.652 | ||||
| Upside SD | 3111.645 | ||||
| Downside SD | 3.347 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 122.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.172 | ||||
| Mean of criterion | 6070.005 | ||||
| SD of predictor | 0.433 | ||||
| SD of criterion | 3100.825 | ||||
| Covariance | -307.593 | ||||
| r | -0.229 | ||||
| b (slope, estimate of beta) | -1643.081 | ||||
| a (intercept, estimate of alpha) | 7996.235 | ||||
| Mean Square Error | 9180332.108 | ||||
| DF error | 129.000 | ||||
| t(b) | -2.675 | ||||
| p(b) | 0.645 | ||||
| t(a) | 1.840 | ||||
| p(a) | 0.399 | ||||
| Lowerbound of 95% confidence interval for beta | -2858.260 | ||||
| Upperbound of 95% confidence interval for beta | -427.903 | ||||
| Lowerbound of 95% confidence interval for alpha | -600.472 | ||||
| Upperbound of 95% confidence interval for alpha | 16592.942 | ||||
| Treynor index (mean / b) | -3.694 | ||||
| Jensen alpha (a) | 7996.235 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 22.588 | ||||
| Sharpe ratio (Glass type estimate) | -0.002 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.002 | ||||
| df | 130.000 | ||||
| t | -0.001 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.774 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.770 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.774 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.770 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.003 | ||||
| Upside Potential Ratio | 3.235 | ||||
| Upside part of mean | 49.036 | ||||
| Downside part of mean | -49.080 | ||||
| Upside SD | 16.631 | ||||
| Downside SD | 15.157 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 122.000 | ||||
| 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 | 0.431 | ||||
| SD of criterion | 22.588 | ||||
| Covariance | -3.387 | ||||
| r | -0.348 | ||||
| b (slope, estimate of beta) | -18.256 | ||||
| a (intercept, estimate of alpha) | 19.627 | ||||
| Mean Square Error | 451.853 | ||||
| DF error | 129.000 | ||||
| t(b) | -4.218 | ||||
| p(b) | 0.717 | ||||
| t(a) | 0.645 | ||||
| p(a) | 0.464 | ||||
| Lowerbound of 95% confidence interval for beta | -26.820 | ||||
| Upperbound of 95% confidence interval for beta | -9.693 | ||||
| Lowerbound of 95% confidence interval for alpha | -40.562 | ||||
| Upperbound of 95% confidence interval for alpha | 79.816 | ||||
| Treynor index (mean / b) | 0.002 | ||||
| Jensen alpha (a) | 19.627 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.899 | ||||
| Expected Shortfall on VaR | 0.937 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.186 | ||||
| Expected Shortfall on VaR | 0.401 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2017.000 | ||||
| Mean of quarter 1 | 0.779 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 93.192 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.099 | ||||
| Mean of outliers low | 0.438 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.069 | ||||
| Mean of outliers high | 339.037 | ||||
| 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) | -1.840 | ||||
| VaR(95%) (regression method) | 0.430 | ||||
| Expected Shortfall (regression method) | 0.524 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| 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 | NA | ||||
| Mean of quarter 3 | NA | ||||
| 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 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) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||