Advanced Statistics: 100% ROE 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 | -0.009 | ||||
| SD | 0.191 | ||||
| Sharpe ratio (Glass type estimate) | -0.045 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.045 | ||||
| df | 44.000 | ||||
| t | -0.088 | ||||
| p | 0.535 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.057 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.967 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.057 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.967 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.092 | ||||
| Upside Potential Ratio | 1.125 | ||||
| Upside part of mean | 0.106 | ||||
| Downside part of mean | -0.115 | ||||
| Upside SD | 0.163 | ||||
| Downside SD | 0.094 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.497 | ||||
| Mean of criterion | -0.009 | ||||
| SD of predictor | 0.299 | ||||
| SD of criterion | 0.191 | ||||
| Covariance | -0.006 | ||||
| r | -0.110 | ||||
| b (slope, estimate of beta) | -0.070 | ||||
| a (intercept, estimate of alpha) | 0.026 | ||||
| Mean Square Error | 0.037 | ||||
| DF error | 43.000 | ||||
| t(b) | -0.723 | ||||
| p(b) | 0.763 | ||||
| t(a) | 0.237 | ||||
| p(a) | 0.407 | ||||
| Lowerbound of 95% confidence interval for beta | -0.265 | ||||
| Upperbound of 95% confidence interval for beta | 0.125 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.196 | ||||
| Upperbound of 95% confidence interval for alpha | 0.248 | ||||
| Treynor index (mean / b) | 0.124 | ||||
| Jensen alpha (a) | 0.026 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.025 | ||||
| SD | 0.177 | ||||
| Sharpe ratio (Glass type estimate) | -0.139 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.137 | ||||
| df | 44.000 | ||||
| t | -0.270 | ||||
| p | 0.606 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.151 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.874 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.149 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.876 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.245 | ||||
| Upside Potential Ratio | 0.938 | ||||
| Upside part of mean | 0.094 | ||||
| Downside part of mean | -0.119 | ||||
| Upside SD | 0.144 | ||||
| Downside SD | 0.101 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.445 | ||||
| Mean of criterion | -0.025 | ||||
| SD of predictor | 0.290 | ||||
| SD of criterion | 0.177 | ||||
| Covariance | -0.005 | ||||
| r | -0.100 | ||||
| b (slope, estimate of beta) | -0.061 | ||||
| a (intercept, estimate of alpha) | 0.002 | ||||
| Mean Square Error | 0.032 | ||||
| DF error | 43.000 | ||||
| t(b) | -0.657 | ||||
| p(b) | 0.743 | ||||
| t(a) | 0.024 | ||||
| p(a) | 0.490 | ||||
| Lowerbound of 95% confidence interval for beta | -0.248 | ||||
| Upperbound of 95% confidence interval for beta | 0.126 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.201 | ||||
| Upperbound of 95% confidence interval for alpha | 0.206 | ||||
| Treynor index (mean / b) | 0.404 | ||||
| Jensen alpha (a) | 0.002 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.083 | ||||
| Expected Shortfall on VaR | 0.102 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.066 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 45.000 | ||||
| Minimum | 0.848 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.305 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.037 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.067 | ||||
| Mean of outliers low | 0.909 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.044 | ||||
| Mean of outliers high | 1.202 | ||||
| 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) | -0.412 | ||||
| VaR(95%) (regression method) | 0.058 | ||||
| Expected Shortfall (regression method) | 0.124 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.251 | ||||
| Quartile 1 | 0.251 | ||||
| Median | 0.251 | ||||
| Quartile 3 | 0.251 | ||||
| Maximum | 0.251 | ||||
| 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) | 0.020 | ||||
| Compounded annual return (geometric extrapolation) | 0.020 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.078 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.192 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.018 | ||||
| SD | 0.307 | ||||
| Sharpe ratio (Glass type estimate) | 0.058 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.058 | ||||
| df | 983.000 | ||||
| t | 0.112 | ||||
| p | 0.456 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.954 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.069 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.954 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.069 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.114 | ||||
| Upside Potential Ratio | 2.812 | ||||
| Upside part of mean | 0.434 | ||||
| Downside part of mean | -0.417 | ||||
| Upside SD | 0.265 | ||||
| Downside SD | 0.154 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 958.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 984.000 | ||||
| Mean of predictor | 0.508 | ||||
| Mean of criterion | 0.018 | ||||
| SD of predictor | 0.334 | ||||
| SD of criterion | 0.307 | ||||
| Covariance | -0.012 | ||||
| r | -0.122 | ||||
| b (slope, estimate of beta) | -0.112 | ||||
| a (intercept, estimate of alpha) | 0.075 | ||||
| Mean Square Error | 0.093 | ||||
| DF error | 982.000 | ||||
| t(b) | -3.857 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.474 | ||||
| p(a) | 0.318 | ||||
| Lowerbound of 95% confidence interval for beta | -0.169 | ||||
| Upperbound of 95% confidence interval for beta | -0.055 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.235 | ||||
| Upperbound of 95% confidence interval for alpha | 0.384 | ||||
| Treynor index (mean / b) | -0.157 | ||||
| Jensen alpha (a) | 0.075 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.025 | ||||
| SD | 0.285 | ||||
| Sharpe ratio (Glass type estimate) | -0.087 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.087 | ||||
| df | 983.000 | ||||
| t | -0.168 | ||||
| p | 0.567 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.098 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.925 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.098 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.925 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.153 | ||||
| Upside Potential Ratio | 2.508 | ||||
| Upside part of mean | 0.405 | ||||
| Downside part of mean | -0.429 | ||||
| Upside SD | 0.234 | ||||
| Downside SD | 0.161 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 958.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 984.000 | ||||
| Mean of predictor | 0.451 | ||||
| Mean of criterion | -0.025 | ||||
| SD of predictor | 0.336 | ||||
| SD of criterion | 0.285 | ||||
| Covariance | -0.012 | ||||
| r | -0.129 | ||||
| b (slope, estimate of beta) | -0.109 | ||||
| a (intercept, estimate of alpha) | 0.025 | ||||
| Mean Square Error | 0.080 | ||||
| DF error | 982.000 | ||||
| t(b) | -4.080 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.168 | ||||
| p(a) | 0.433 | ||||
| Lowerbound of 95% confidence interval for beta | -0.162 | ||||
| Upperbound of 95% confidence interval for beta | -0.057 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.262 | ||||
| Upperbound of 95% confidence interval for alpha | 0.312 | ||||
| Treynor index (mean / b) | 0.226 | ||||
| Jensen alpha (a) | 0.025 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 984.000 | ||||
| Minimum | 0.884 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.400 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 40.000 | ||||
| Percentage of outliers low | 0.041 | ||||
| Mean of outliers low | 0.965 | ||||
| Number of outliers high | 26.000 | ||||
| Percentage of outliers high | 0.026 | ||||
| Mean of outliers high | 1.063 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.632 | ||||
| VaR(95%) (moments method) | -0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.583 | ||||
| VaR(95%) (regression method) | -0.008 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.031 | ||||
| Median | 0.099 | ||||
| Quartile 3 | 0.119 | ||||
| Maximum | 0.366 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | 0.076 | ||||
| Mean of quarter 3 | 0.116 | ||||
| Mean of quarter 4 | 0.244 | ||||
| Inter Quartile Range | 0.089 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.366 | ||||
| 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) | 0.020 | ||||
| Compounded annual return (geometric extrapolation) | 0.020 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.053 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.080 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.547 | ||||
| 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 | 1.065 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.524 | ||||
| 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 | 0.925 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.530 | ||||
| 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) | -8748715191412986.000 | ||||
| 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) | -185220763498085577692823223795712.000 | ||||
| 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 | ||||