Advanced Statistics: VIX Contango Play
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 | 6.396 | ||||
| SD | 6.518 | ||||
| Sharpe ratio (Glass type estimate) | 0.981 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.963 | ||||
| df | 41.000 | ||||
| t | 1.836 | ||||
| p | 0.037 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.093 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.044 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.105 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.031 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 57.587 | ||||
| Upside Potential Ratio | 58.863 | ||||
| Upside part of mean | 6.538 | ||||
| Downside part of mean | -0.142 | ||||
| Upside SD | 6.699 | ||||
| Downside SD | 0.111 | ||||
| N nonnegative terms | 18.000 | ||||
| N negative terms | 24.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 42.000 | ||||
| Mean of predictor | 0.451 | ||||
| Mean of criterion | 6.396 | ||||
| SD of predictor | 0.227 | ||||
| SD of criterion | 6.518 | ||||
| Covariance | 0.410 | ||||
| r | 0.278 | ||||
| b (slope, estimate of beta) | 7.997 | ||||
| a (intercept, estimate of alpha) | 2.792 | ||||
| Mean Square Error | 40.186 | ||||
| DF error | 40.000 | ||||
| t(b) | 1.830 | ||||
| p(b) | 0.037 | ||||
| t(a) | 0.712 | ||||
| p(a) | 0.240 | ||||
| Lowerbound of 95% confidence interval for beta | -0.837 | ||||
| Upperbound of 95% confidence interval for beta | 16.830 | ||||
| Lowerbound of 95% confidence interval for alpha | -5.130 | ||||
| Upperbound of 95% confidence interval for alpha | 10.713 | ||||
| Treynor index (mean / b) | 0.800 | ||||
| Jensen alpha (a) | 2.792 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2.128 | ||||
| SD | 1.867 | ||||
| Sharpe ratio (Glass type estimate) | 1.140 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.119 | ||||
| df | 41.000 | ||||
| t | 2.132 | ||||
| p | 0.020 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.057 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.209 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.043 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.194 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 18.128 | ||||
| Upside Potential Ratio | 19.387 | ||||
| Upside part of mean | 2.276 | ||||
| Downside part of mean | -0.148 | ||||
| Upside SD | 1.941 | ||||
| Downside SD | 0.117 | ||||
| N nonnegative terms | 18.000 | ||||
| N negative terms | 24.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 42.000 | ||||
| Mean of predictor | 0.418 | ||||
| Mean of criterion | 2.128 | ||||
| SD of predictor | 0.215 | ||||
| SD of criterion | 1.867 | ||||
| Covariance | 0.103 | ||||
| r | 0.256 | ||||
| b (slope, estimate of beta) | 2.221 | ||||
| a (intercept, estimate of alpha) | 1.199 | ||||
| Mean Square Error | 3.339 | ||||
| DF error | 40.000 | ||||
| t(b) | 1.677 | ||||
| p(b) | 0.051 | ||||
| t(a) | 1.068 | ||||
| p(a) | 0.146 | ||||
| Lowerbound of 95% confidence interval for beta | -0.455 | ||||
| Upperbound of 95% confidence interval for beta | 4.898 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.070 | ||||
| Upperbound of 95% confidence interval for alpha | 3.468 | ||||
| Treynor index (mean / b) | 0.958 | ||||
| Jensen alpha (a) | 1.199 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.508 | ||||
| Expected Shortfall on VaR | 0.600 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 42.000 | ||||
| Minimum | 0.858 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.048 | ||||
| Maximum | 9.909 | ||||
| Mean of quarter 1 | 0.962 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.013 | ||||
| Mean of quarter 4 | 3.075 | ||||
| Inter Quartile Range | 0.048 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.071 | ||||
| Mean of outliers low | 0.898 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.167 | ||||
| Mean of outliers high | 4.214 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -65.679 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.719 | ||||
| VaR(95%) (regression method) | 0.077 | ||||
| Expected Shortfall (regression method) | 0.107 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.037 | ||||
| Median | 0.074 | ||||
| Quartile 3 | 0.162 | ||||
| Maximum | 0.251 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.074 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.251 | ||||
| Inter Quartile Range | 0.126 | ||||
| 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) | 571.551 | ||||
| Compounded annual return (geometric extrapolation) | 7.775 | ||||
| Calmar ratio (compounded annual return / max draw down) | 30.973 | ||||
| Compounded annual return / average of 25% largest draw downs | 30.973 | ||||
| Compounded annual return / Expected Shortfall lognormal | 12.958 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 6.294 | ||||
| SD | 6.641 | ||||
| Sharpe ratio (Glass type estimate) | 0.948 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.947 | ||||
| df | 931.000 | ||||
| t | 1.788 | ||||
| p | 0.037 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.093 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.988 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.093 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.987 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 42.266 | ||||
| Upside Potential Ratio | 45.602 | ||||
| Upside part of mean | 6.791 | ||||
| Downside part of mean | -0.497 | ||||
| Upside SD | 6.647 | ||||
| Downside SD | 0.149 | ||||
| N nonnegative terms | 251.000 | ||||
| N negative terms | 681.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 932.000 | ||||
| Mean of predictor | 0.490 | ||||
| Mean of criterion | 6.294 | ||||
| SD of predictor | 0.296 | ||||
| SD of criterion | 6.641 | ||||
| Covariance | 0.007 | ||||
| r | 0.004 | ||||
| b (slope, estimate of beta) | 0.083 | ||||
| a (intercept, estimate of alpha) | 6.253 | ||||
| Mean Square Error | 44.149 | ||||
| DF error | 930.000 | ||||
| t(b) | 0.113 | ||||
| p(b) | 0.455 | ||||
| t(a) | 1.766 | ||||
| p(a) | 0.039 | ||||
| Lowerbound of 95% confidence interval for beta | -1.361 | ||||
| Upperbound of 95% confidence interval for beta | 1.528 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.697 | ||||
| Upperbound of 95% confidence interval for alpha | 13.203 | ||||
| Treynor index (mean / b) | 75.434 | ||||
| Jensen alpha (a) | 6.253 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2.093 | ||||
| SD | 1.931 | ||||
| Sharpe ratio (Glass type estimate) | 1.084 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.083 | ||||
| df | 931.000 | ||||
| t | 2.045 | ||||
| p | 0.021 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.044 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.124 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.043 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.124 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 13.499 | ||||
| Upside Potential Ratio | 16.777 | ||||
| Upside part of mean | 2.601 | ||||
| Downside part of mean | -0.508 | ||||
| Upside SD | 1.928 | ||||
| Downside SD | 0.155 | ||||
| N nonnegative terms | 251.000 | ||||
| N negative terms | 681.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 932.000 | ||||
| Mean of predictor | 0.445 | ||||
| Mean of criterion | 2.093 | ||||
| SD of predictor | 0.301 | ||||
| SD of criterion | 1.931 | ||||
| Covariance | 0.007 | ||||
| r | 0.011 | ||||
| b (slope, estimate of beta) | 0.072 | ||||
| a (intercept, estimate of alpha) | 2.061 | ||||
| Mean Square Error | 3.730 | ||||
| DF error | 930.000 | ||||
| t(b) | 0.342 | ||||
| p(b) | 0.366 | ||||
| t(a) | 2.004 | ||||
| p(a) | 0.023 | ||||
| Lowerbound of 95% confidence interval for beta | -0.341 | ||||
| Upperbound of 95% confidence interval for beta | 0.485 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.043 | ||||
| Upperbound of 95% confidence interval for alpha | 4.079 | ||||
| Treynor index (mean / b) | 29.071 | ||||
| Jensen alpha (a) | 2.061 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.172 | ||||
| Expected Shortfall on VaR | 0.211 | ||||
| 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 | 932.000 | ||||
| Minimum | 0.865 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 9.909 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.104 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 118.000 | ||||
| Percentage of outliers low | 0.127 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 180.000 | ||||
| Percentage of outliers high | 0.193 | ||||
| Mean of outliers high | 1.134 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.343 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.572 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.021 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 50.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.019 | ||||
| Maximum | 0.251 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | 0.003 | ||||
| Mean of quarter 4 | 0.083 | ||||
| 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 | 7.000 | ||||
| Percentage of outliers high | 0.140 | ||||
| Mean of outliers high | 0.126 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.360 | ||||
| VaR(95%) (moments method) | 0.069 | ||||
| Expected Shortfall (moments method) | 0.134 | ||||
| Extreme Value Index (regression method) | 0.348 | ||||
| VaR(95%) (regression method) | 0.099 | ||||
| Expected Shortfall (regression method) | 0.197 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 562.352 | ||||
| Compounded annual return (geometric extrapolation) | 7.473 | ||||
| Calmar ratio (compounded annual return / max draw down) | 29.772 | ||||
| Compounded annual return / average of 25% largest draw downs | 90.531 | ||||
| Compounded annual return / Expected Shortfall lognormal | 35.409 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 18.630 | ||||
| SD | 12.609 | ||||
| Sharpe ratio (Glass type estimate) | 1.478 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.469 | ||||
| df | 130.000 | ||||
| t | 1.045 | ||||
| p | 0.454 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.303 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.252 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.309 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.247 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 6903.915 | ||||
| Upside Potential Ratio | 6919.977 | ||||
| Upside part of mean | 18.674 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 12.614 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 129.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.019 | ||||
| Mean of criterion | 18.630 | ||||
| SD of predictor | 0.428 | ||||
| SD of criterion | 12.609 | ||||
| Covariance | -0.144 | ||||
| r | -0.027 | ||||
| b (slope, estimate of beta) | -0.784 | ||||
| a (intercept, estimate of alpha) | 19.429 | ||||
| Mean Square Error | 160.112 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.302 | ||||
| p(b) | 0.517 | ||||
| t(a) | 1.074 | ||||
| p(a) | 0.440 | ||||
| Lowerbound of 95% confidence interval for beta | -5.916 | ||||
| Upperbound of 95% confidence interval for beta | 4.348 | ||||
| Lowerbound of 95% confidence interval for alpha | -16.360 | ||||
| Upperbound of 95% confidence interval for alpha | 55.219 | ||||
| Treynor index (mean / b) | -23.762 | ||||
| Jensen alpha (a) | 19.429 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 5.256 | ||||
| SD | 3.279 | ||||
| Sharpe ratio (Glass type estimate) | 1.603 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.594 | ||||
| df | 130.000 | ||||
| t | 1.134 | ||||
| p | 0.451 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.179 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.379 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.185 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.372 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1947.751 | ||||
| Upside Potential Ratio | 1963.814 | ||||
| Upside part of mean | 5.299 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 3.282 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 129.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.926 | ||||
| Mean of criterion | 5.256 | ||||
| SD of predictor | 0.429 | ||||
| SD of criterion | 3.279 | ||||
| Covariance | -0.052 | ||||
| r | -0.037 | ||||
| b (slope, estimate of beta) | -0.281 | ||||
| a (intercept, estimate of alpha) | 5.516 | ||||
| Mean Square Error | 10.817 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.418 | ||||
| p(b) | 0.523 | ||||
| t(a) | 1.175 | ||||
| p(a) | 0.435 | ||||
| Lowerbound of 95% confidence interval for beta | -1.612 | ||||
| Upperbound of 95% confidence interval for beta | 1.049 | ||||
| Lowerbound of 95% confidence interval for alpha | -3.769 | ||||
| Upperbound of 95% confidence interval for alpha | 14.801 | ||||
| Treynor index (mean / b) | -18.678 | ||||
| Jensen alpha (a) | 5.516 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.269 | ||||
| Expected Shortfall on VaR | 0.326 | ||||
| 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 | 9.909 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.283 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.084 | ||||
| Mean of outliers low | 1.000 | ||||
| Number of outliers high | 23.000 | ||||
| Percentage of outliers high | 0.176 | ||||
| Mean of outliers high | 1.406 | ||||
| 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 | 14.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.000 | ||||
| Maximum | 0.000 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | 0.000 | ||||
| Mean of quarter 4 | 0.000 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers high | 0.143 | ||||
| Mean of outliers high | 0.000 | ||||
| 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) | 26.303 | ||||
| Compounded annual return (geometric extrapolation) | 199.266 | ||||
| Calmar ratio (compounded annual return / max draw down) | 176136715.377 | ||||
| Compounded annual return / average of 25% largest draw downs | 409742926.262 | ||||
| Compounded annual return / Expected Shortfall lognormal | 610.638 | ||||