Advanced Statistics: HiLo Futures
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 | -0.075 | ||||
| SD | 0.890 | ||||
| Sharpe ratio (Glass type estimate) | -0.085 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.083 | ||||
| df | 45.000 | ||||
| t | -0.166 | ||||
| p | 0.565 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.085 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.917 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.084 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.918 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.121 | ||||
| Upside Potential Ratio | 1.117 | ||||
| Upside part of mean | 0.697 | ||||
| Downside part of mean | -0.773 | ||||
| Upside SD | 0.621 | ||||
| Downside SD | 0.624 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 46.000 | ||||
| Mean of predictor | 0.423 | ||||
| Mean of criterion | -0.075 | ||||
| SD of predictor | 0.281 | ||||
| SD of criterion | 0.890 | ||||
| Covariance | 0.008 | ||||
| r | 0.033 | ||||
| b (slope, estimate of beta) | 0.103 | ||||
| a (intercept, estimate of alpha) | -0.119 | ||||
| Mean Square Error | 0.809 | ||||
| DF error | 44.000 | ||||
| t(b) | 0.216 | ||||
| p(b) | 0.415 | ||||
| t(a) | -0.237 | ||||
| p(a) | 0.593 | ||||
| Lowerbound of 95% confidence interval for beta | -0.857 | ||||
| Upperbound of 95% confidence interval for beta | 1.063 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.130 | ||||
| Upperbound of 95% confidence interval for alpha | 0.892 | ||||
| Treynor index (mean / b) | -0.731 | ||||
| Jensen alpha (a) | -0.119 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.579 | ||||
| SD | 1.126 | ||||
| Sharpe ratio (Glass type estimate) | -0.514 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.506 | ||||
| df | 45.000 | ||||
| t | -1.007 | ||||
| p | 0.840 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.518 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.495 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.512 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.501 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.569 | ||||
| Upside Potential Ratio | 0.548 | ||||
| Upside part of mean | 0.558 | ||||
| Downside part of mean | -1.137 | ||||
| Upside SD | 0.482 | ||||
| Downside SD | 1.018 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 46.000 | ||||
| Mean of predictor | 0.378 | ||||
| Mean of criterion | -0.579 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 1.126 | ||||
| Covariance | 0.032 | ||||
| r | 0.104 | ||||
| b (slope, estimate of beta) | 0.434 | ||||
| a (intercept, estimate of alpha) | -0.743 | ||||
| Mean Square Error | 1.283 | ||||
| DF error | 44.000 | ||||
| t(b) | 0.696 | ||||
| p(b) | 0.245 | ||||
| t(a) | -1.190 | ||||
| p(a) | 0.880 | ||||
| Lowerbound of 95% confidence interval for beta | -0.823 | ||||
| Upperbound of 95% confidence interval for beta | 1.691 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.002 | ||||
| Upperbound of 95% confidence interval for alpha | 0.516 | ||||
| Treynor index (mean / b) | -1.334 | ||||
| Jensen alpha (a) | -0.743 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.442 | ||||
| Expected Shortfall on VaR | 0.509 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.203 | ||||
| Expected Shortfall on VaR | 0.419 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 46.000 | ||||
| Minimum | 0.220 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.749 | ||||
| Mean of quarter 1 | 0.765 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.225 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 7.000 | ||||
| Percentage of outliers low | 0.152 | ||||
| Mean of outliers low | 0.597 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.174 | ||||
| Mean of outliers high | 1.337 | ||||
| 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) | -0.707 | ||||
| VaR(95%) (regression method) | 0.425 | ||||
| Expected Shortfall (regression method) | 0.553 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.883 | ||||
| Quartile 1 | 0.883 | ||||
| Median | 0.883 | ||||
| Quartile 3 | 0.883 | ||||
| Maximum | 0.883 | ||||
| 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) | -0.227 | ||||
| Compounded annual return (geometric extrapolation) | -0.414 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.469 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.814 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.166 | ||||
| SD | 0.871 | ||||
| Sharpe ratio (Glass type estimate) | -0.191 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.191 | ||||
| df | 1017.000 | ||||
| t | -0.377 | ||||
| p | 0.508 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.185 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.803 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.185 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.803 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.264 | ||||
| Upside Potential Ratio | 4.246 | ||||
| Upside part of mean | 2.672 | ||||
| Downside part of mean | -2.838 | ||||
| Upside SD | 0.602 | ||||
| Downside SD | 0.629 | ||||
| N nonnegative terms | 146.000 | ||||
| N negative terms | 872.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1018.000 | ||||
| Mean of predictor | 0.443 | ||||
| Mean of criterion | -0.166 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.871 | ||||
| Covariance | 0.022 | ||||
| r | 0.079 | ||||
| b (slope, estimate of beta) | 0.216 | ||||
| a (intercept, estimate of alpha) | -0.262 | ||||
| Mean Square Error | 0.755 | ||||
| DF error | 1016.000 | ||||
| t(b) | 2.535 | ||||
| p(b) | 0.460 | ||||
| t(a) | -0.593 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | 0.049 | ||||
| Upperbound of 95% confidence interval for beta | 0.383 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.130 | ||||
| Upperbound of 95% confidence interval for alpha | 0.606 | ||||
| Treynor index (mean / b) | -0.770 | ||||
| Jensen alpha (a) | -0.262 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.572 | ||||
| SD | 0.924 | ||||
| Sharpe ratio (Glass type estimate) | -0.619 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.619 | ||||
| df | 1017.000 | ||||
| t | -1.220 | ||||
| p | 0.524 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.614 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.376 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.613 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.376 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.771 | ||||
| Upside Potential Ratio | 3.384 | ||||
| Upside part of mean | 2.511 | ||||
| Downside part of mean | -3.083 | ||||
| Upside SD | 0.551 | ||||
| Downside SD | 0.742 | ||||
| N nonnegative terms | 146.000 | ||||
| N negative terms | 872.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1018.000 | ||||
| Mean of predictor | 0.391 | ||||
| Mean of criterion | -0.572 | ||||
| SD of predictor | 0.321 | ||||
| SD of criterion | 0.924 | ||||
| Covariance | 0.025 | ||||
| r | 0.084 | ||||
| b (slope, estimate of beta) | 0.242 | ||||
| a (intercept, estimate of alpha) | -0.667 | ||||
| Mean Square Error | 0.848 | ||||
| DF error | 1016.000 | ||||
| t(b) | 2.697 | ||||
| p(b) | 0.458 | ||||
| t(a) | -1.423 | ||||
| p(a) | 0.522 | ||||
| Lowerbound of 95% confidence interval for beta | 0.066 | ||||
| Upperbound of 95% confidence interval for beta | 0.419 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.586 | ||||
| Upperbound of 95% confidence interval for alpha | 0.253 | ||||
| Treynor index (mean / b) | -2.360 | ||||
| Jensen alpha (a) | -0.667 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.092 | ||||
| Expected Shortfall on VaR | 0.113 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.074 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1018.000 | ||||
| Minimum | 0.452 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.403 | ||||
| Mean of quarter 1 | 0.957 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.041 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 159.000 | ||||
| Percentage of outliers low | 0.156 | ||||
| Mean of outliers low | 0.932 | ||||
| Number of outliers high | 147.000 | ||||
| Percentage of outliers high | 0.144 | ||||
| Mean of outliers high | 1.071 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.206 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | -0.144 | ||||
| VaR(95%) (regression method) | 0.046 | ||||
| Expected Shortfall (regression method) | 0.079 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.098 | ||||
| Quartile 1 | 0.101 | ||||
| Median | 0.133 | ||||
| Quartile 3 | 0.135 | ||||
| Maximum | 0.938 | ||||
| Mean of quarter 1 | 0.100 | ||||
| Mean of quarter 2 | 0.133 | ||||
| Mean of quarter 3 | 0.135 | ||||
| Mean of quarter 4 | 0.938 | ||||
| Inter Quartile Range | 0.034 | ||||
| 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 | 0.938 | ||||
| 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) | -0.224 | ||||
| Compounded annual return (geometric extrapolation) | -0.410 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.437 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.437 | ||||
| Compounded annual return / Expected Shortfall lognormal | -3.636 | ||||
| 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 | 1.025 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.506 | ||||
| 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 | 0.895 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.511 | ||||
| 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) | -8748342670478011.000 | ||||
| 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) | 189428195442838199217767007125504.000 | ||||
| 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 | ||||