Advanced Statistics: Hemi 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 | 0.078 | ||||
| SD | 0.123 | ||||
| Sharpe ratio (Glass type estimate) | 0.635 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.626 | ||||
| df | 52.000 | ||||
| t | 1.334 | ||||
| p | 0.094 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.309 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.572 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.315 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.566 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.547 | ||||
| Upside Potential Ratio | 3.134 | ||||
| Upside part of mean | 0.158 | ||||
| Downside part of mean | -0.080 | ||||
| Upside SD | 0.113 | ||||
| Downside SD | 0.050 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.384 | ||||
| Mean of criterion | 0.078 | ||||
| SD of predictor | 0.346 | ||||
| SD of criterion | 0.123 | ||||
| Covariance | -0.001 | ||||
| r | -0.035 | ||||
| b (slope, estimate of beta) | -0.013 | ||||
| a (intercept, estimate of alpha) | 0.083 | ||||
| Mean Square Error | 0.015 | ||||
| DF error | 51.000 | ||||
| t(b) | -0.252 | ||||
| p(b) | 0.599 | ||||
| t(a) | 1.336 | ||||
| p(a) | 0.094 | ||||
| Lowerbound of 95% confidence interval for beta | -0.112 | ||||
| Upperbound of 95% confidence interval for beta | 0.087 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.042 | ||||
| Upperbound of 95% confidence interval for alpha | 0.207 | ||||
| Treynor index (mean / b) | -6.236 | ||||
| Jensen alpha (a) | 0.083 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.071 | ||||
| SD | 0.118 | ||||
| Sharpe ratio (Glass type estimate) | 0.598 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.589 | ||||
| df | 52.000 | ||||
| t | 1.256 | ||||
| p | 0.107 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.345 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.535 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.350 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.528 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.363 | ||||
| Upside Potential Ratio | 2.932 | ||||
| Upside part of mean | 0.152 | ||||
| Downside part of mean | -0.081 | ||||
| Upside SD | 0.107 | ||||
| Downside SD | 0.052 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.329 | ||||
| Mean of criterion | 0.071 | ||||
| SD of predictor | 0.301 | ||||
| SD of criterion | 0.118 | ||||
| Covariance | -0.001 | ||||
| r | -0.022 | ||||
| b (slope, estimate of beta) | -0.009 | ||||
| a (intercept, estimate of alpha) | 0.073 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 51.000 | ||||
| t(b) | -0.157 | ||||
| p(b) | 0.562 | ||||
| t(a) | 1.233 | ||||
| p(a) | 0.112 | ||||
| Lowerbound of 95% confidence interval for beta | -0.119 | ||||
| Upperbound of 95% confidence interval for beta | 0.102 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.046 | ||||
| Upperbound of 95% confidence interval for alpha | 0.193 | ||||
| Treynor index (mean / b) | -8.169 | ||||
| Jensen alpha (a) | 0.073 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.049 | ||||
| Expected Shortfall on VaR | 0.062 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 53.000 | ||||
| Minimum | 0.927 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.011 | ||||
| Maximum | 1.172 | ||||
| Mean of quarter 1 | 0.985 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.057 | ||||
| Inter Quartile Range | 0.011 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.094 | ||||
| Mean of outliers low | 0.963 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.208 | ||||
| Mean of outliers high | 1.064 | ||||
| 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) | 0.186 | ||||
| VaR(95%) (regression method) | 0.026 | ||||
| Expected Shortfall (regression method) | 0.054 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.026 | ||||
| Median | 0.032 | ||||
| Quartile 3 | 0.043 | ||||
| Maximum | 0.073 | ||||
| Mean of quarter 1 | 0.016 | ||||
| Mean of quarter 2 | 0.027 | ||||
| Mean of quarter 3 | 0.036 | ||||
| Mean of quarter 4 | 0.059 | ||||
| Inter Quartile Range | 0.017 | ||||
| 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 | 0.167 | ||||
| Mean of outliers high | 0.073 | ||||
| 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) | 0.149 | ||||
| Compounded annual return (geometric extrapolation) | 0.121 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.669 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.062 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.949 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.078 | ||||
| SD | 0.133 | ||||
| Sharpe ratio (Glass type estimate) | 0.588 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.588 | ||||
| df | 1166.000 | ||||
| t | 1.241 | ||||
| p | 0.482 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.341 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.517 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.341 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.517 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.875 | ||||
| Upside Potential Ratio | 4.168 | ||||
| Upside part of mean | 0.374 | ||||
| Downside part of mean | -0.295 | ||||
| Upside SD | 0.099 | ||||
| Downside SD | 0.090 | ||||
| N nonnegative terms | 117.000 | ||||
| N negative terms | 1050.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1167.000 | ||||
| Mean of predictor | 0.387 | ||||
| Mean of criterion | 0.078 | ||||
| SD of predictor | 0.300 | ||||
| SD of criterion | 0.133 | ||||
| Covariance | 0.006 | ||||
| r | 0.162 | ||||
| b (slope, estimate of beta) | 0.072 | ||||
| a (intercept, estimate of alpha) | 0.051 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 1165.000 | ||||
| t(b) | 5.607 | ||||
| p(b) | 0.397 | ||||
| t(a) | 0.808 | ||||
| p(a) | 0.485 | ||||
| Lowerbound of 95% confidence interval for beta | 0.047 | ||||
| Upperbound of 95% confidence interval for beta | 0.097 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.072 | ||||
| Upperbound of 95% confidence interval for alpha | 0.173 | ||||
| Treynor index (mean / b) | 1.089 | ||||
| Jensen alpha (a) | 0.051 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.070 | ||||
| SD | 0.134 | ||||
| Sharpe ratio (Glass type estimate) | 0.519 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.519 | ||||
| df | 1166.000 | ||||
| t | 1.096 | ||||
| p | 0.484 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.410 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.448 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.410 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.448 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.755 | ||||
| Upside Potential Ratio | 4.006 | ||||
| Upside part of mean | 0.369 | ||||
| Downside part of mean | -0.299 | ||||
| Upside SD | 0.097 | ||||
| Downside SD | 0.092 | ||||
| N nonnegative terms | 117.000 | ||||
| N negative terms | 1050.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1167.000 | ||||
| Mean of predictor | 0.342 | ||||
| Mean of criterion | 0.070 | ||||
| SD of predictor | 0.301 | ||||
| SD of criterion | 0.134 | ||||
| Covariance | 0.007 | ||||
| r | 0.165 | ||||
| b (slope, estimate of beta) | 0.073 | ||||
| a (intercept, estimate of alpha) | 0.045 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 1165.000 | ||||
| t(b) | 5.694 | ||||
| p(b) | 0.396 | ||||
| t(a) | 0.710 | ||||
| p(a) | 0.487 | ||||
| Lowerbound of 95% confidence interval for beta | 0.048 | ||||
| Upperbound of 95% confidence interval for beta | 0.098 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.079 | ||||
| Upperbound of 95% confidence interval for alpha | 0.168 | ||||
| Treynor index (mean / b) | 0.950 | ||||
| Jensen alpha (a) | 0.045 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1167.000 | ||||
| Minimum | 0.901 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.066 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 89.000 | ||||
| Percentage of outliers low | 0.076 | ||||
| Mean of outliers low | 0.987 | ||||
| Number of outliers high | 118.000 | ||||
| Percentage of outliers high | 0.101 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.515 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.227 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | 0.012 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 19.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.017 | ||||
| Quartile 3 | 0.056 | ||||
| Maximum | 0.175 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.011 | ||||
| Mean of quarter 3 | 0.044 | ||||
| Mean of quarter 4 | 0.098 | ||||
| Inter Quartile Range | 0.052 | ||||
| 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 | 0.053 | ||||
| Mean of outliers high | 0.175 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.248 | ||||
| VaR(95%) (moments method) | 0.107 | ||||
| Expected Shortfall (moments method) | 0.129 | ||||
| Extreme Value Index (regression method) | -0.029 | ||||
| VaR(95%) (regression method) | 0.094 | ||||
| Expected Shortfall (regression method) | 0.115 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.148 | ||||
| Compounded annual return (geometric extrapolation) | 0.120 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.686 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.229 | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.222 | ||||
| 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 | 0.979 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.490 | ||||
| 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 | 0.859 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.488 | ||||
| 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) | -8747796285723388.000 | ||||
| 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) | 657746567902036799351087263907840.000 | ||||
| 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 | ||||