Advanced Statistics: Crude Oil Swing Trade System
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 | -0.049 | ||||
| SD | 0.014 | ||||
| Sharpe ratio (Glass type estimate) | -3.422 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.366 | ||||
| df | 46.000 | ||||
| t | -6.773 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.621 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.198 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.572 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.160 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.539 | ||||
| Upside Potential Ratio | 0.139 | ||||
| Upside part of mean | 0.003 | ||||
| Downside part of mean | -0.052 | ||||
| Upside SD | 0.005 | ||||
| Downside SD | 0.019 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 46.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 47.000 | ||||
| Mean of predictor | 0.459 | ||||
| Mean of criterion | -0.049 | ||||
| SD of predictor | 0.253 | ||||
| SD of criterion | 0.014 | ||||
| Covariance | -0.000 | ||||
| r | -0.114 | ||||
| b (slope, estimate of beta) | -0.006 | ||||
| a (intercept, estimate of alpha) | -0.046 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 45.000 | ||||
| t(b) | -0.766 | ||||
| p(b) | 0.776 | ||||
| t(a) | -5.603 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.023 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.063 | ||||
| Upperbound of 95% confidence interval for alpha | -0.030 | ||||
| Treynor index (mean / b) | 7.640 | ||||
| Jensen alpha (a) | -0.046 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.049 | ||||
| SD | 0.014 | ||||
| Sharpe ratio (Glass type estimate) | -3.407 | ||||
| Sharpe ratio (Hedges UMVUE) | -3.351 | ||||
| df | 46.000 | ||||
| t | -6.743 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.604 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -2.185 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.555 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.147 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.531 | ||||
| Upside Potential Ratio | 0.138 | ||||
| Upside part of mean | 0.003 | ||||
| Downside part of mean | -0.052 | ||||
| Upside SD | 0.005 | ||||
| Downside SD | 0.019 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 46.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 47.000 | ||||
| Mean of predictor | 0.419 | ||||
| Mean of criterion | -0.049 | ||||
| SD of predictor | 0.248 | ||||
| SD of criterion | 0.014 | ||||
| Covariance | -0.000 | ||||
| r | -0.123 | ||||
| b (slope, estimate of beta) | -0.007 | ||||
| a (intercept, estimate of alpha) | -0.046 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 45.000 | ||||
| t(b) | -0.830 | ||||
| p(b) | 0.795 | ||||
| t(a) | -5.662 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.024 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.063 | ||||
| Upperbound of 95% confidence interval for alpha | -0.030 | ||||
| Treynor index (mean / b) | 6.891 | ||||
| Jensen alpha (a) | -0.046 | ||||
| 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 | 0.013 | ||||
| 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 | 47.000 | ||||
| Minimum | 0.980 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.014 | ||||
| Mean of quarter 1 | 0.997 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers low | 0.043 | ||||
| Mean of outliers low | 0.983 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.021 | ||||
| Mean of outliers high | 1.014 | ||||
| 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) | -2.156 | ||||
| VaR(95%) (regression method) | 0.012 | ||||
| Expected Shortfall (regression method) | 0.025 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.034 | ||||
| Quartile 1 | 0.034 | ||||
| Median | 0.034 | ||||
| Quartile 3 | 0.034 | ||||
| Maximum | 0.034 | ||||
| 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) | -0.005 | ||||
| Compounded annual return (geometric extrapolation) | -0.005 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.152 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.406 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.048 | ||||
| SD | 0.036 | ||||
| Sharpe ratio (Glass type estimate) | -1.350 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.349 | ||||
| df | 1036.000 | ||||
| t | -2.685 | ||||
| p | 0.542 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.336 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.362 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.336 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.362 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.853 | ||||
| Upside Potential Ratio | 1.393 | ||||
| Upside part of mean | 0.036 | ||||
| Downside part of mean | -0.085 | ||||
| Upside SD | 0.025 | ||||
| Downside SD | 0.026 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 1025.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1037.000 | ||||
| Mean of predictor | 0.483 | ||||
| Mean of criterion | -0.048 | ||||
| SD of predictor | 0.326 | ||||
| SD of criterion | 0.036 | ||||
| Covariance | -0.000 | ||||
| r | -0.008 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.048 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 1035.000 | ||||
| t(b) | -0.261 | ||||
| p(b) | 0.505 | ||||
| t(a) | -2.649 | ||||
| p(a) | 0.552 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.084 | ||||
| Upperbound of 95% confidence interval for alpha | -0.012 | ||||
| Treynor index (mean / b) | 54.222 | ||||
| Jensen alpha (a) | -0.048 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.049 | ||||
| SD | 0.036 | ||||
| Sharpe ratio (Glass type estimate) | -1.367 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.366 | ||||
| df | 1036.000 | ||||
| t | -2.721 | ||||
| p | 0.542 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.354 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.380 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.353 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.380 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.860 | ||||
| Upside Potential Ratio | 1.368 | ||||
| Upside part of mean | 0.036 | ||||
| Downside part of mean | -0.085 | ||||
| Upside SD | 0.024 | ||||
| Downside SD | 0.026 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 1025.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1037.000 | ||||
| Mean of predictor | 0.429 | ||||
| Mean of criterion | -0.049 | ||||
| SD of predictor | 0.330 | ||||
| SD of criterion | 0.036 | ||||
| Covariance | -0.000 | ||||
| r | -0.009 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.049 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 1035.000 | ||||
| t(b) | -0.298 | ||||
| p(b) | 0.506 | ||||
| t(a) | -2.687 | ||||
| p(a) | 0.553 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.084 | ||||
| Upperbound of 95% confidence interval for alpha | -0.013 | ||||
| Treynor index (mean / b) | 48.698 | ||||
| Jensen alpha (a) | -0.049 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| 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 | 1037.000 | ||||
| Minimum | 0.975 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.027 | ||||
| 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 | 14.000 | ||||
| Percentage of outliers low | 0.014 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.012 | ||||
| Mean of outliers high | 1.012 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -12.991 | ||||
| VaR(95%) (moments method) | -68747.219 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.760 | ||||
| VaR(95%) (regression method) | -0.030 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.019 | ||||
| Median | 0.026 | ||||
| Quartile 3 | 0.037 | ||||
| Maximum | 0.057 | ||||
| Mean of quarter 1 | 0.007 | ||||
| Mean of quarter 2 | 0.022 | ||||
| Mean of quarter 3 | 0.030 | ||||
| Mean of quarter 4 | 0.057 | ||||
| Inter Quartile Range | 0.018 | ||||
| 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) | -0.005 | ||||
| Compounded annual return (geometric extrapolation) | -0.005 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.088 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.088 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.066 | ||||
| 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 | 0.949 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.491 | ||||
| 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 | 0.827 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.494 | ||||
| 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) | -8752853715701793.000 | ||||
| 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) | -322610402381664710407233229291520.000 | ||||
| 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 | ||||