Advanced Statistics: Write/Call/Buy3x
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 | -0.054 | ||||
| SD | 0.013 | ||||
| Sharpe ratio (Glass type estimate) | -4.192 | ||||
| Sharpe ratio (Hedges UMVUE) | -4.108 | ||||
| df | 38.000 | ||||
| t | -7.557 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.612 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.739 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.535 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.682 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.708 | ||||
| Upside Potential Ratio | 0.073 | ||||
| Upside part of mean | 0.001 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.003 | ||||
| Downside SD | 0.020 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.510 | ||||
| Mean of criterion | -0.054 | ||||
| SD of predictor | 0.300 | ||||
| SD of criterion | 0.013 | ||||
| Covariance | 0.000 | ||||
| r | 0.127 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.057 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.781 | ||||
| p(b) | 0.220 | ||||
| t(a) | -7.081 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.009 | ||||
| Upperbound of 95% confidence interval for beta | 0.020 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.073 | ||||
| Upperbound of 95% confidence interval for alpha | -0.040 | ||||
| Treynor index (mean / b) | -9.882 | ||||
| Jensen alpha (a) | -0.057 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.054 | ||||
| SD | 0.013 | ||||
| Sharpe ratio (Glass type estimate) | -4.178 | ||||
| Sharpe ratio (Hedges UMVUE) | -4.094 | ||||
| df | 38.000 | ||||
| t | -7.531 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -5.596 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.727 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.519 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.670 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.704 | ||||
| Upside Potential Ratio | 0.073 | ||||
| Upside part of mean | 0.001 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.003 | ||||
| Downside SD | 0.020 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.460 | ||||
| Mean of criterion | -0.054 | ||||
| SD of predictor | 0.274 | ||||
| SD of criterion | 0.013 | ||||
| Covariance | 0.000 | ||||
| r | 0.130 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.057 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.795 | ||||
| p(b) | 0.216 | ||||
| t(a) | -7.077 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.009 | ||||
| Upperbound of 95% confidence interval for beta | 0.022 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.073 | ||||
| Upperbound of 95% confidence interval for alpha | -0.040 | ||||
| Treynor index (mean / b) | -8.818 | ||||
| Jensen alpha (a) | -0.057 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.987 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.008 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.077 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.026 | ||||
| Mean of outliers high | 1.008 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.003 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.142 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.010 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.048 | ||||
| Quartile 1 | 0.048 | ||||
| Median | 0.048 | ||||
| Quartile 3 | 0.048 | ||||
| Maximum | 0.048 | ||||
| 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) | -0.010 | ||||
| Compounded annual return (geometric extrapolation) | -0.010 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.205 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.814 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.054 | ||||
| SD | 0.022 | ||||
| Sharpe ratio (Glass type estimate) | -2.405 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.403 | ||||
| df | 854.000 | ||||
| t | -4.344 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.495 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.313 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.494 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.312 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.217 | ||||
| Upside Potential Ratio | 2.281 | ||||
| Upside part of mean | 0.038 | ||||
| Downside part of mean | -0.092 | ||||
| Upside SD | 0.015 | ||||
| Downside SD | 0.017 | ||||
| N nonnegative terms | 228.000 | ||||
| N negative terms | 627.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 855.000 | ||||
| Mean of predictor | 0.536 | ||||
| Mean of criterion | -0.054 | ||||
| SD of predictor | 0.344 | ||||
| SD of criterion | 0.022 | ||||
| Covariance | 0.000 | ||||
| r | 0.046 | ||||
| b (slope, estimate of beta) | 0.003 | ||||
| a (intercept, estimate of alpha) | -0.055 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 853.000 | ||||
| t(b) | 1.352 | ||||
| p(b) | 0.088 | ||||
| t(a) | -4.456 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.001 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.080 | ||||
| Upperbound of 95% confidence interval for alpha | -0.031 | ||||
| Treynor index (mean / b) | -17.899 | ||||
| Jensen alpha (a) | -0.055 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.054 | ||||
| SD | 0.022 | ||||
| Sharpe ratio (Glass type estimate) | -2.416 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.414 | ||||
| df | 854.000 | ||||
| t | -4.365 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.507 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.325 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.505 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.323 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.212 | ||||
| Upside Potential Ratio | 2.260 | ||||
| Upside part of mean | 0.038 | ||||
| Downside part of mean | -0.092 | ||||
| Upside SD | 0.015 | ||||
| Downside SD | 0.017 | ||||
| N nonnegative terms | 228.000 | ||||
| N negative terms | 627.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 855.000 | ||||
| Mean of predictor | 0.478 | ||||
| Mean of criterion | -0.054 | ||||
| SD of predictor | 0.338 | ||||
| SD of criterion | 0.022 | ||||
| Covariance | 0.000 | ||||
| r | 0.048 | ||||
| b (slope, estimate of beta) | 0.003 | ||||
| a (intercept, estimate of alpha) | -0.055 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 853.000 | ||||
| t(b) | 1.398 | ||||
| p(b) | 0.081 | ||||
| t(a) | -4.473 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.001 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.080 | ||||
| Upperbound of 95% confidence interval for alpha | -0.031 | ||||
| Treynor index (mean / b) | -17.088 | ||||
| Jensen alpha (a) | -0.055 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 855.000 | ||||
| Minimum | 0.983 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.018 | ||||
| Mean of quarter 1 | 0.999 | ||||
| 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 | 70.000 | ||||
| Percentage of outliers low | 0.082 | ||||
| Mean of outliers low | 0.998 | ||||
| Number of outliers high | 40.000 | ||||
| Percentage of outliers high | 0.047 | ||||
| Mean of outliers high | 1.002 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.505 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 0.157 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.002 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.004 | ||||
| Quartile 3 | 0.020 | ||||
| Maximum | 0.055 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.001 | ||||
| Mean of quarter 3 | 0.008 | ||||
| Mean of quarter 4 | 0.055 | ||||
| Inter Quartile Range | 0.019 | ||||
| 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 | 0.055 | ||||
| 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) | -0.010 | ||||
| Compounded annual return (geometric extrapolation) | -0.010 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.178 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.178 | ||||
| Compounded annual return / Expected Shortfall lognormal | -3.219 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 0.004 | ||||
| Sharpe ratio (Glass type estimate) | -10.312 | ||||
| Sharpe ratio (Hedges UMVUE) | -10.252 | ||||
| df | 130.000 | ||||
| t | -7.292 | ||||
| p | 0.769 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -13.337 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -7.254 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13.292 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -7.213 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -9.463 | ||||
| Upside Potential Ratio | 2.195 | ||||
| Upside part of mean | 0.009 | ||||
| Downside part of mean | -0.047 | ||||
| Upside SD | 0.002 | ||||
| Downside SD | 0.004 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 105.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.158 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.445 | ||||
| SD of criterion | 0.004 | ||||
| Covariance | 0.001 | ||||
| r | 0.632 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 9.263 | ||||
| p(b) | 0.126 | ||||
| t(a) | -10.730 | ||||
| p(a) | 0.900 | ||||
| Lowerbound of 95% confidence interval for beta | 0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.053 | ||||
| Upperbound of 95% confidence interval for alpha | -0.036 | ||||
| Treynor index (mean / b) | -7.259 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.038 | ||||
| SD | 0.004 | ||||
| Sharpe ratio (Glass type estimate) | -10.313 | ||||
| Sharpe ratio (Hedges UMVUE) | -10.254 | ||||
| df | 130.000 | ||||
| t | -7.293 | ||||
| p | 0.769 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -13.338 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -7.255 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13.293 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -7.214 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -9.463 | ||||
| Upside Potential Ratio | 2.194 | ||||
| Upside part of mean | 0.009 | ||||
| Downside part of mean | -0.047 | ||||
| Upside SD | 0.002 | ||||
| Downside SD | 0.004 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 105.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.057 | ||||
| Mean of criterion | -0.038 | ||||
| SD of predictor | 0.448 | ||||
| SD of criterion | 0.004 | ||||
| Covariance | 0.001 | ||||
| r | 0.632 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 9.259 | ||||
| p(b) | 0.126 | ||||
| t(a) | -10.615 | ||||
| p(a) | 0.898 | ||||
| Lowerbound of 95% confidence interval for beta | 0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.052 | ||||
| Upperbound of 95% confidence interval for alpha | -0.036 | ||||
| Treynor index (mean / b) | -7.306 | ||||
| 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%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.001 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.001 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.999 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.001 | ||||
| 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 | 4.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.999 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.001 | ||||
| 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 | 8.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.001 | ||||
| Quartile 3 | 0.001 | ||||
| Maximum | 0.001 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | 0.001 | ||||
| Mean of quarter 4 | 0.001 | ||||
| Inter Quartile Range | 0.001 | ||||
| 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) | 0.006 | ||||
| Compounded annual return (geometric extrapolation) | 0.006 | ||||
| Calmar ratio (compounded annual return / max draw down) | 4.186 | ||||
| Compounded annual return / average of 25% largest draw downs | 4.283 | ||||
| Compounded annual return / Expected Shortfall lognormal | 9.320 | ||||