Advanced Statistics: Precision Futures
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 | -0.204 | ||||
| SD | 0.509 | ||||
| Sharpe ratio (Glass type estimate) | -0.402 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.397 | ||||
| df | 60.000 | ||||
| t | -0.905 | ||||
| p | 0.816 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.272 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.472 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.269 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.476 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.422 | ||||
| Upside Potential Ratio | 0.288 | ||||
| Upside part of mean | 0.140 | ||||
| Downside part of mean | -0.344 | ||||
| Upside SD | 0.153 | ||||
| Downside SD | 0.485 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 54.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.372 | ||||
| Mean of criterion | -0.204 | ||||
| SD of predictor | 0.349 | ||||
| SD of criterion | 0.509 | ||||
| Covariance | 0.042 | ||||
| r | 0.235 | ||||
| b (slope, estimate of beta) | 0.343 | ||||
| a (intercept, estimate of alpha) | -0.332 | ||||
| Mean Square Error | 0.249 | ||||
| DF error | 59.000 | ||||
| t(b) | 1.857 | ||||
| p(b) | 0.034 | ||||
| t(a) | -1.432 | ||||
| p(a) | 0.921 | ||||
| Lowerbound of 95% confidence interval for beta | -0.027 | ||||
| Upperbound of 95% confidence interval for beta | 0.712 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.795 | ||||
| Upperbound of 95% confidence interval for alpha | 0.132 | ||||
| Treynor index (mean / b) | -0.597 | ||||
| Jensen alpha (a) | -0.332 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.992 | ||||
| SD | 4.403 | ||||
| Sharpe ratio (Glass type estimate) | -0.452 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.447 | ||||
| df | 60.000 | ||||
| t | -1.020 | ||||
| p | 0.844 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.324 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.422 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.320 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.426 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.453 | ||||
| Upside Potential Ratio | 0.029 | ||||
| Upside part of mean | 0.129 | ||||
| Downside part of mean | -2.121 | ||||
| Upside SD | 0.139 | ||||
| Downside SD | 4.402 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 54.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.308 | ||||
| Mean of criterion | -1.992 | ||||
| SD of predictor | 0.340 | ||||
| SD of criterion | 4.403 | ||||
| Covariance | 0.310 | ||||
| r | 0.207 | ||||
| b (slope, estimate of beta) | 2.673 | ||||
| a (intercept, estimate of alpha) | -2.816 | ||||
| Mean Square Error | 18.874 | ||||
| DF error | 59.000 | ||||
| t(b) | 1.623 | ||||
| p(b) | 0.055 | ||||
| t(a) | -1.413 | ||||
| p(a) | 0.919 | ||||
| Lowerbound of 95% confidence interval for beta | -0.623 | ||||
| Upperbound of 95% confidence interval for beta | 5.970 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.804 | ||||
| Upperbound of 95% confidence interval for alpha | 1.171 | ||||
| Treynor index (mean / b) | -0.745 | ||||
| Jensen alpha (a) | -2.816 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.895 | ||||
| Expected Shortfall on VaR | 0.933 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.092 | ||||
| Expected Shortfall on VaR | 0.206 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.250 | ||||
| Mean of quarter 1 | 0.903 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.049 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.131 | ||||
| Mean of outliers low | 0.806 | ||||
| Number of outliers high | 14.000 | ||||
| Percentage of outliers high | 0.230 | ||||
| Mean of outliers high | 1.053 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 3.003 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 2.400 | ||||
| VaR(95%) (regression method) | 0.031 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.206 | ||||
| Median | 0.413 | ||||
| Quartile 3 | 0.706 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.413 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.500 | ||||
| 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) | -0.197 | ||||
| Compounded annual return (geometric extrapolation) | -0.857 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.858 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.858 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.919 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.144 | ||||
| SD | 0.602 | ||||
| Sharpe ratio (Glass type estimate) | -0.239 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.239 | ||||
| df | 1341.000 | ||||
| t | -0.541 | ||||
| p | 0.509 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.105 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.627 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.105 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.627 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.269 | ||||
| Upside Potential Ratio | 1.421 | ||||
| Upside part of mean | 0.759 | ||||
| Downside part of mean | -0.902 | ||||
| Upside SD | 0.278 | ||||
| Downside SD | 0.534 | ||||
| N nonnegative terms | 142.000 | ||||
| N negative terms | 1200.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1342.000 | ||||
| Mean of predictor | 0.394 | ||||
| Mean of criterion | -0.144 | ||||
| SD of predictor | 0.378 | ||||
| SD of criterion | 0.602 | ||||
| Covariance | 0.015 | ||||
| r | 0.064 | ||||
| b (slope, estimate of beta) | 0.102 | ||||
| a (intercept, estimate of alpha) | -0.184 | ||||
| Mean Square Error | 0.361 | ||||
| DF error | 1340.000 | ||||
| t(b) | 2.351 | ||||
| p(b) | 0.468 | ||||
| t(a) | -0.692 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | 0.017 | ||||
| Upperbound of 95% confidence interval for beta | 0.187 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.706 | ||||
| Upperbound of 95% confidence interval for alpha | 0.338 | ||||
| Treynor index (mean / b) | -1.409 | ||||
| Jensen alpha (a) | -0.184 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -1.977 | ||||
| SD | 4.401 | ||||
| Sharpe ratio (Glass type estimate) | -0.449 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.449 | ||||
| df | 1341.000 | ||||
| t | -1.017 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.315 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.417 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.315 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.417 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.450 | ||||
| Upside Potential Ratio | 0.165 | ||||
| Upside part of mean | 0.723 | ||||
| Downside part of mean | -2.701 | ||||
| Upside SD | 0.258 | ||||
| Downside SD | 4.393 | ||||
| N nonnegative terms | 142.000 | ||||
| N negative terms | 1200.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1342.000 | ||||
| Mean of predictor | 0.321 | ||||
| Mean of criterion | -1.977 | ||||
| SD of predictor | 0.382 | ||||
| SD of criterion | 4.401 | ||||
| Covariance | 0.050 | ||||
| r | 0.030 | ||||
| b (slope, estimate of beta) | 0.342 | ||||
| a (intercept, estimate of alpha) | -2.087 | ||||
| Mean Square Error | 19.364 | ||||
| DF error | 1340.000 | ||||
| t(b) | 1.089 | ||||
| p(b) | 0.485 | ||||
| t(a) | -1.072 | ||||
| p(a) | 0.515 | ||||
| Lowerbound of 95% confidence interval for beta | -0.274 | ||||
| Upperbound of 95% confidence interval for beta | 0.959 | ||||
| Lowerbound of 95% confidence interval for alpha | -5.907 | ||||
| Upperbound of 95% confidence interval for alpha | 1.732 | ||||
| Treynor index (mean / b) | -5.781 | ||||
| Jensen alpha (a) | -2.087 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.365 | ||||
| Expected Shortfall on VaR | 0.431 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.025 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1342.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.227 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.012 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 172.000 | ||||
| Percentage of outliers low | 0.128 | ||||
| Mean of outliers low | 0.974 | ||||
| Number of outliers high | 181.000 | ||||
| Percentage of outliers high | 0.135 | ||||
| Mean of outliers high | 1.022 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.727 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.015 | ||||
| Extreme Value Index (regression method) | 0.574 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.039 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.003 | ||||
| Quartile 3 | 0.499 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.499 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.498 | ||||
| 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) | -0.195 | ||||
| Compounded annual return (geometric extrapolation) | -0.855 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.855 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.855 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.986 | ||||
| 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 | 1.080 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.394 | ||||
| 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 | 1.000 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.395 | ||||
| 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) | -8693113478465509.000 | ||||
| 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) | 67783821820653253227712325091328.000 | ||||
| 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 | ||||