Advanced Statistics: Selling Puts
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 | -0.050 | ||||
| SD | 0.058 | ||||
| Sharpe ratio (Glass type estimate) | -0.863 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.847 | ||||
| df | 41.000 | ||||
| t | -1.614 | ||||
| p | 0.943 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.922 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.206 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.910 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.217 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.946 | ||||
| Upside Potential Ratio | 0.496 | ||||
| Upside part of mean | 0.026 | ||||
| Downside part of mean | -0.076 | ||||
| Upside SD | 0.026 | ||||
| Downside SD | 0.052 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 42.000 | ||||
| Mean of predictor | 0.468 | ||||
| Mean of criterion | -0.050 | ||||
| SD of predictor | 0.228 | ||||
| SD of criterion | 0.058 | ||||
| Covariance | 0.002 | ||||
| r | 0.131 | ||||
| b (slope, estimate of beta) | 0.033 | ||||
| a (intercept, estimate of alpha) | -0.065 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 40.000 | ||||
| t(b) | 0.838 | ||||
| p(b) | 0.203 | ||||
| t(a) | -1.810 | ||||
| p(a) | 0.961 | ||||
| Lowerbound of 95% confidence interval for beta | -0.047 | ||||
| Upperbound of 95% confidence interval for beta | 0.113 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.138 | ||||
| Upperbound of 95% confidence interval for alpha | 0.008 | ||||
| Treynor index (mean / b) | -1.495 | ||||
| Jensen alpha (a) | -0.065 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.051 | ||||
| SD | 0.059 | ||||
| Sharpe ratio (Glass type estimate) | -0.872 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.856 | ||||
| df | 41.000 | ||||
| t | -1.631 | ||||
| p | 0.945 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.931 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.198 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.920 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.208 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.947 | ||||
| Upside Potential Ratio | 0.473 | ||||
| Upside part of mean | 0.026 | ||||
| Downside part of mean | -0.077 | ||||
| Upside SD | 0.026 | ||||
| Downside SD | 0.054 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 42.000 | ||||
| Mean of predictor | 0.434 | ||||
| Mean of criterion | -0.051 | ||||
| SD of predictor | 0.221 | ||||
| SD of criterion | 0.059 | ||||
| Covariance | 0.002 | ||||
| r | 0.135 | ||||
| b (slope, estimate of beta) | 0.036 | ||||
| a (intercept, estimate of alpha) | -0.067 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 40.000 | ||||
| t(b) | 0.863 | ||||
| p(b) | 0.197 | ||||
| t(a) | -1.839 | ||||
| p(a) | 0.963 | ||||
| Lowerbound of 95% confidence interval for beta | -0.048 | ||||
| Upperbound of 95% confidence interval for beta | 0.120 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.140 | ||||
| Upperbound of 95% confidence interval for alpha | 0.007 | ||||
| Treynor index (mean / b) | -1.423 | ||||
| Jensen alpha (a) | -0.067 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.040 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 42.000 | ||||
| Minimum | 0.925 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.041 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.071 | ||||
| Mean of outliers low | 0.957 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.119 | ||||
| Mean of outliers high | 1.022 | ||||
| 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) | 0.539 | ||||
| VaR(95%) (regression method) | 0.014 | ||||
| Expected Shortfall (regression method) | 0.069 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.109 | ||||
| Quartile 1 | 0.109 | ||||
| Median | 0.109 | ||||
| Quartile 3 | 0.109 | ||||
| Maximum | 0.109 | ||||
| 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 | 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) | -0.007 | ||||
| Compounded annual return (geometric extrapolation) | -0.007 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.066 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.186 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.050 | ||||
| SD | 0.053 | ||||
| Sharpe ratio (Glass type estimate) | -0.933 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.933 | ||||
| df | 924.000 | ||||
| t | -1.754 | ||||
| p | 0.960 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.977 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.111 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.977 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.111 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.185 | ||||
| Upside Potential Ratio | 2.202 | ||||
| Upside part of mean | 0.092 | ||||
| Downside part of mean | -0.142 | ||||
| Upside SD | 0.033 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 75.000 | ||||
| N negative terms | 850.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 925.000 | ||||
| Mean of predictor | 0.503 | ||||
| Mean of criterion | -0.050 | ||||
| SD of predictor | 0.312 | ||||
| SD of criterion | 0.053 | ||||
| Covariance | 0.000 | ||||
| r | 0.017 | ||||
| b (slope, estimate of beta) | 0.003 | ||||
| a (intercept, estimate of alpha) | -0.051 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 923.000 | ||||
| t(b) | 0.507 | ||||
| p(b) | 0.306 | ||||
| t(a) | -1.795 | ||||
| p(a) | 0.963 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.107 | ||||
| Upperbound of 95% confidence interval for alpha | 0.005 | ||||
| Treynor index (mean / b) | -17.435 | ||||
| Jensen alpha (a) | -0.051 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.051 | ||||
| SD | 0.054 | ||||
| Sharpe ratio (Glass type estimate) | -0.954 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.953 | ||||
| df | 924.000 | ||||
| t | -1.793 | ||||
| p | 0.963 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.998 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.090 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.997 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.091 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.200 | ||||
| Upside Potential Ratio | 2.155 | ||||
| Upside part of mean | 0.092 | ||||
| Downside part of mean | -0.143 | ||||
| Upside SD | 0.033 | ||||
| Downside SD | 0.043 | ||||
| N nonnegative terms | 75.000 | ||||
| N negative terms | 850.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 925.000 | ||||
| Mean of predictor | 0.453 | ||||
| Mean of criterion | -0.051 | ||||
| SD of predictor | 0.317 | ||||
| SD of criterion | 0.054 | ||||
| Covariance | 0.000 | ||||
| r | 0.016 | ||||
| b (slope, estimate of beta) | 0.003 | ||||
| a (intercept, estimate of alpha) | -0.052 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 923.000 | ||||
| t(b) | 0.495 | ||||
| p(b) | 0.310 | ||||
| t(a) | -1.829 | ||||
| p(a) | 0.966 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.109 | ||||
| Upperbound of 95% confidence interval for alpha | 0.004 | ||||
| Treynor index (mean / b) | -18.565 | ||||
| Jensen alpha (a) | -0.052 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 925.000 | ||||
| Minimum | 0.950 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.035 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 68.000 | ||||
| Percentage of outliers low | 0.074 | ||||
| Mean of outliers low | 0.995 | ||||
| Number of outliers high | 83.000 | ||||
| Percentage of outliers high | 0.090 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.606 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 0.488 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.004 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.003 | ||||
| Quartile 3 | 0.038 | ||||
| Maximum | 0.140 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.004 | ||||
| Mean of quarter 4 | 0.140 | ||||
| Inter Quartile Range | 0.036 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 0.140 | ||||
| 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) | -0.007 | ||||
| Compounded annual return (geometric extrapolation) | -0.007 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.051 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.051 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.012 | ||||
| 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 | 1.014 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.449 | ||||
| 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 | 0.913 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.449 | ||||
| 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) | -8730787709539240.000 | ||||
| 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) | 162729471343027350755271772209152.000 | ||||
| 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 | ||||