Advanced Statistics: Super Oil
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 2.697 | ||||
| SD | 7.070 | ||||
| Sharpe ratio (Glass type estimate) | 0.382 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.377 | ||||
| df | 61.000 | ||||
| t | 0.867 | ||||
| p | 0.195 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.485 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.245 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.488 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.242 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 5.843 | ||||
| Upside Potential Ratio | 6.822 | ||||
| Upside part of mean | 3.150 | ||||
| Downside part of mean | -0.452 | ||||
| Upside SD | 7.041 | ||||
| Downside SD | 0.462 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 62.000 | ||||
| Mean of predictor | 0.312 | ||||
| Mean of criterion | 2.697 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 7.070 | ||||
| Covariance | -0.470 | ||||
| r | -0.253 | ||||
| b (slope, estimate of beta) | -6.804 | ||||
| a (intercept, estimate of alpha) | 4.817 | ||||
| Mean Square Error | 47.572 | ||||
| DF error | 60.000 | ||||
| t(b) | -2.024 | ||||
| p(b) | 0.976 | ||||
| t(a) | 1.501 | ||||
| p(a) | 0.069 | ||||
| Lowerbound of 95% confidence interval for beta | -13.528 | ||||
| Upperbound of 95% confidence interval for beta | -0.080 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.604 | ||||
| Upperbound of 95% confidence interval for alpha | 11.239 | ||||
| Treynor index (mean / b) | -0.396 | ||||
| Jensen alpha (a) | 4.817 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.045 | ||||
| SD | 1.451 | ||||
| Sharpe ratio (Glass type estimate) | -0.031 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.031 | ||||
| df | 61.000 | ||||
| t | -0.071 | ||||
| p | 0.528 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.893 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.831 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.893 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.832 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.063 | ||||
| Upside Potential Ratio | 0.832 | ||||
| Upside part of mean | 0.594 | ||||
| Downside part of mean | -0.639 | ||||
| Upside SD | 1.249 | ||||
| Downside SD | 0.714 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 59.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 62.000 | ||||
| Mean of predictor | 0.275 | ||||
| Mean of criterion | -0.045 | ||||
| SD of predictor | 0.250 | ||||
| SD of criterion | 1.451 | ||||
| Covariance | -0.067 | ||||
| r | -0.186 | ||||
| b (slope, estimate of beta) | -1.078 | ||||
| a (intercept, estimate of alpha) | 0.252 | ||||
| Mean Square Error | 2.066 | ||||
| DF error | 60.000 | ||||
| t(b) | -1.463 | ||||
| p(b) | 0.926 | ||||
| t(a) | 0.379 | ||||
| p(a) | 0.353 | ||||
| Lowerbound of 95% confidence interval for beta | -2.552 | ||||
| Upperbound of 95% confidence interval for beta | 0.396 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.076 | ||||
| Upperbound of 95% confidence interval for alpha | 1.580 | ||||
| Treynor index (mean / b) | 0.042 | ||||
| Jensen alpha (a) | 0.252 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.500 | ||||
| Expected Shortfall on VaR | 0.575 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.127 | ||||
| Expected Shortfall on VaR | 0.272 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 62.000 | ||||
| Minimum | 0.314 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 17.005 | ||||
| Mean of quarter 1 | 0.867 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 2.018 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.129 | ||||
| Mean of outliers low | 0.735 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.081 | ||||
| Mean of outliers high | 4.258 | ||||
| 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) | 0.572 | ||||
| VaR(95%) (regression method) | 0.131 | ||||
| Expected Shortfall (regression method) | 0.519 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.942 | ||||
| Quartile 1 | 0.942 | ||||
| Median | 0.942 | ||||
| Quartile 3 | 0.942 | ||||
| Maximum | 0.942 | ||||
| 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) | -0.001 | ||||
| Compounded annual return (geometric extrapolation) | -0.001 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.001 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.002 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 3.498 | ||||
| SD | 7.202 | ||||
| Sharpe ratio (Glass type estimate) | 0.486 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.485 | ||||
| df | 1372.000 | ||||
| t | 1.112 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.371 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.342 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.371 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.342 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4.487 | ||||
| Upside Potential Ratio | 7.141 | ||||
| Upside part of mean | 5.566 | ||||
| Downside part of mean | -2.069 | ||||
| Upside SD | 7.160 | ||||
| Downside SD | 0.779 | ||||
| N nonnegative terms | 84.000 | ||||
| N negative terms | 1289.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1373.000 | ||||
| Mean of predictor | 0.433 | ||||
| Mean of criterion | 3.498 | ||||
| SD of predictor | 0.490 | ||||
| SD of criterion | 7.202 | ||||
| Covariance | -0.266 | ||||
| r | -0.075 | ||||
| b (slope, estimate of beta) | -1.105 | ||||
| a (intercept, estimate of alpha) | 3.976 | ||||
| Mean Square Error | 51.615 | ||||
| DF error | 1371.000 | ||||
| t(b) | -2.794 | ||||
| p(b) | 0.548 | ||||
| t(a) | 1.265 | ||||
| p(a) | 0.478 | ||||
| Lowerbound of 95% confidence interval for beta | -1.882 | ||||
| Upperbound of 95% confidence interval for beta | -0.329 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.190 | ||||
| Upperbound of 95% confidence interval for alpha | 10.142 | ||||
| Treynor index (mean / b) | -3.164 | ||||
| Jensen alpha (a) | 3.976 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.045 | ||||
| SD | 1.881 | ||||
| Sharpe ratio (Glass type estimate) | -0.024 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.024 | ||||
| df | 1372.000 | ||||
| t | -0.055 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.880 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.832 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.880 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.832 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.042 | ||||
| Upside Potential Ratio | 2.324 | ||||
| Upside part of mean | 2.478 | ||||
| Downside part of mean | -2.523 | ||||
| Upside SD | 1.549 | ||||
| Downside SD | 1.066 | ||||
| N nonnegative terms | 84.000 | ||||
| N negative terms | 1289.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1373.000 | ||||
| Mean of predictor | 0.313 | ||||
| Mean of criterion | -0.045 | ||||
| SD of predictor | 0.488 | ||||
| SD of criterion | 1.881 | ||||
| Covariance | -0.181 | ||||
| r | -0.197 | ||||
| b (slope, estimate of beta) | -0.760 | ||||
| a (intercept, estimate of alpha) | 0.193 | ||||
| Mean Square Error | 3.403 | ||||
| DF error | 1371.000 | ||||
| t(b) | -7.454 | ||||
| p(b) | 0.625 | ||||
| t(a) | 0.239 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -0.960 | ||||
| Upperbound of 95% confidence interval for beta | -0.560 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.389 | ||||
| Upperbound of 95% confidence interval for alpha | 1.775 | ||||
| Treynor index (mean / b) | 0.059 | ||||
| Jensen alpha (a) | 0.193 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.174 | ||||
| Expected Shortfall on VaR | 0.213 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.059 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1373.000 | ||||
| Minimum | 0.273 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 17.063 | ||||
| Mean of quarter 1 | 0.969 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.085 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 90.000 | ||||
| Percentage of outliers low | 0.066 | ||||
| Mean of outliers low | 0.882 | ||||
| Number of outliers high | 84.000 | ||||
| Percentage of outliers high | 0.061 | ||||
| Mean of outliers high | 1.347 | ||||
| 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 | 5.000 | ||||
| Minimum | 0.044 | ||||
| Quartile 1 | 0.098 | ||||
| Median | 0.116 | ||||
| Quartile 3 | 0.152 | ||||
| Maximum | 0.953 | ||||
| Mean of quarter 1 | 0.071 | ||||
| Mean of quarter 2 | 0.116 | ||||
| Mean of quarter 3 | 0.152 | ||||
| Mean of quarter 4 | 0.953 | ||||
| Inter Quartile Range | 0.054 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.953 | ||||
| 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) | -0.001 | ||||
| Compounded annual return (geometric extrapolation) | -0.001 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.001 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.001 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.005 | ||||
| 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 | 1.091 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.505 | ||||
| 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 | 0.962 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.508 | ||||
| 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) | -8739866980847764.000 | ||||
| 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) | -234504090370267257355070888476672.000 | ||||
| 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 | ||||