Advanced Statistics: Futures Trading Is Not Easy
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 | 0.028 | ||||
| SD | 0.118 | ||||
| Sharpe ratio (Glass type estimate) | 0.238 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.232 | ||||
| df | 31.000 | ||||
| t | 0.388 | ||||
| p | 0.350 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.966 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.437 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.970 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.433 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.232 | ||||
| Upside Potential Ratio | 5.642 | ||||
| Upside part of mean | 0.071 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.115 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.656 | ||||
| Mean of criterion | 0.028 | ||||
| SD of predictor | 0.260 | ||||
| SD of criterion | 0.118 | ||||
| Covariance | 0.004 | ||||
| r | 0.117 | ||||
| b (slope, estimate of beta) | 0.053 | ||||
| a (intercept, estimate of alpha) | -0.007 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 30.000 | ||||
| t(b) | 0.643 | ||||
| p(b) | 0.262 | ||||
| t(a) | -0.074 | ||||
| p(a) | 0.529 | ||||
| Lowerbound of 95% confidence interval for beta | -0.115 | ||||
| Upperbound of 95% confidence interval for beta | 0.221 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.192 | ||||
| Upperbound of 95% confidence interval for alpha | 0.178 | ||||
| Treynor index (mean / b) | 0.529 | ||||
| Jensen alpha (a) | -0.007 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.022 | ||||
| SD | 0.108 | ||||
| Sharpe ratio (Glass type estimate) | 0.203 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.198 | ||||
| df | 31.000 | ||||
| t | 0.332 | ||||
| p | 0.371 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.999 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.403 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.003 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.400 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.751 | ||||
| Upside Potential Ratio | 5.161 | ||||
| Upside part of mean | 0.065 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.105 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.607 | ||||
| Mean of criterion | 0.022 | ||||
| SD of predictor | 0.248 | ||||
| SD of criterion | 0.108 | ||||
| Covariance | 0.003 | ||||
| r | 0.119 | ||||
| b (slope, estimate of beta) | 0.052 | ||||
| a (intercept, estimate of alpha) | -0.009 | ||||
| Mean Square Error | 0.012 | ||||
| DF error | 30.000 | ||||
| t(b) | 0.656 | ||||
| p(b) | 0.258 | ||||
| t(a) | -0.115 | ||||
| p(a) | 0.545 | ||||
| Lowerbound of 95% confidence interval for beta | -0.109 | ||||
| Upperbound of 95% confidence interval for beta | 0.212 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.176 | ||||
| Upperbound of 95% confidence interval for alpha | 0.158 | ||||
| Treynor index (mean / b) | 0.425 | ||||
| Jensen alpha (a) | -0.009 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.048 | ||||
| Expected Shortfall on VaR | 0.060 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.192 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.024 | ||||
| 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 | 0.062 | ||||
| Mean of outliers high | 1.096 | ||||
| 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) | 0.072 | ||||
| Compounded annual return (geometric extrapolation) | 0.068 | ||||
| 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 | 1.130 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.028 | ||||
| SD | 0.123 | ||||
| Sharpe ratio (Glass type estimate) | 0.226 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.226 | ||||
| df | 716.000 | ||||
| t | 0.375 | ||||
| p | 0.354 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.958 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.411 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.959 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.411 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.347 | ||||
| Upside Potential Ratio | 1.585 | ||||
| Upside part of mean | 0.127 | ||||
| Downside part of mean | -0.099 | ||||
| Upside SD | 0.093 | ||||
| Downside SD | 0.080 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 709.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 717.000 | ||||
| Mean of predictor | 0.725 | ||||
| Mean of criterion | 0.028 | ||||
| SD of predictor | 0.387 | ||||
| SD of criterion | 0.123 | ||||
| Covariance | 0.001 | ||||
| r | 0.030 | ||||
| b (slope, estimate of beta) | 0.010 | ||||
| a (intercept, estimate of alpha) | 0.021 | ||||
| Mean Square Error | 0.015 | ||||
| DF error | 715.000 | ||||
| t(b) | 0.805 | ||||
| p(b) | 0.211 | ||||
| t(a) | 0.279 | ||||
| p(a) | 0.390 | ||||
| Lowerbound of 95% confidence interval for beta | -0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.033 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.126 | ||||
| Upperbound of 95% confidence interval for alpha | 0.168 | ||||
| Treynor index (mean / b) | 2.911 | ||||
| Jensen alpha (a) | 0.021 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.020 | ||||
| SD | 0.124 | ||||
| Sharpe ratio (Glass type estimate) | 0.163 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.163 | ||||
| df | 716.000 | ||||
| t | 0.269 | ||||
| p | 0.394 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.022 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.348 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.022 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.347 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.235 | ||||
| Upside Potential Ratio | 1.434 | ||||
| Upside part of mean | 0.123 | ||||
| Downside part of mean | -0.103 | ||||
| Upside SD | 0.090 | ||||
| Downside SD | 0.086 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 709.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 717.000 | ||||
| Mean of predictor | 0.652 | ||||
| Mean of criterion | 0.020 | ||||
| SD of predictor | 0.377 | ||||
| SD of criterion | 0.124 | ||||
| Covariance | 0.002 | ||||
| r | 0.033 | ||||
| b (slope, estimate of beta) | 0.011 | ||||
| a (intercept, estimate of alpha) | 0.013 | ||||
| Mean Square Error | 0.015 | ||||
| DF error | 715.000 | ||||
| t(b) | 0.885 | ||||
| p(b) | 0.188 | ||||
| t(a) | 0.174 | ||||
| p(a) | 0.431 | ||||
| Lowerbound of 95% confidence interval for beta | -0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.035 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.135 | ||||
| Upperbound of 95% confidence interval for alpha | 0.161 | ||||
| Treynor index (mean / b) | 1.857 | ||||
| Jensen alpha (a) | 0.013 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 717.000 | ||||
| Minimum | 0.869 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.108 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.003 | ||||
| Mean of outliers low | 0.924 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.013 | ||||
| Mean of outliers high | 1.039 | ||||
| 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) | 1.281 | ||||
| VaR(95%) (regression method) | -0.020 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.022 | ||||
| Quartile 1 | 0.049 | ||||
| Median | 0.076 | ||||
| Quartile 3 | 0.104 | ||||
| Maximum | 0.131 | ||||
| Mean of quarter 1 | 0.022 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.131 | ||||
| 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 | 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) | 0.070 | ||||
| Compounded annual return (geometric extrapolation) | 0.066 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.508 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.508 | ||||
| Compounded annual return / Expected Shortfall lognormal | 4.249 | ||||
| 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 | 1.011 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.441 | ||||
| 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 | 0.913 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.442 | ||||
| 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) | -8728675304570443.000 | ||||
| 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) | -109272983164312308373843244744704.000 | ||||
| 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 | ||||