Advanced Statistics: Futures fun
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 | -0.080 | ||||
| SD | 0.061 | ||||
| Sharpe ratio (Glass type estimate) | -1.310 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.281 | ||||
| df | 34.000 | ||||
| t | -2.237 | ||||
| p | 0.984 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.490 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.112 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.468 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.093 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.241 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.080 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.064 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.602 | ||||
| Mean of criterion | -0.080 | ||||
| SD of predictor | 0.337 | ||||
| SD of criterion | 0.061 | ||||
| Covariance | 0.000 | ||||
| r | 0.004 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.080 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 33.000 | ||||
| t(b) | 0.023 | ||||
| p(b) | 0.491 | ||||
| t(a) | -1.963 | ||||
| p(a) | 0.971 | ||||
| Lowerbound of 95% confidence interval for beta | -0.063 | ||||
| Upperbound of 95% confidence interval for beta | 0.065 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.163 | ||||
| Upperbound of 95% confidence interval for alpha | 0.003 | ||||
| Treynor index (mean / b) | -110.727 | ||||
| Jensen alpha (a) | -0.080 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.082 | ||||
| SD | 0.064 | ||||
| Sharpe ratio (Glass type estimate) | -1.270 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.242 | ||||
| df | 34.000 | ||||
| t | -2.169 | ||||
| p | 0.981 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.448 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.075 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.427 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.057 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.208 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.082 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.068 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.537 | ||||
| Mean of criterion | -0.082 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 0.064 | ||||
| Covariance | -0.000 | ||||
| r | -0.004 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.081 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 33.000 | ||||
| t(b) | -0.021 | ||||
| p(b) | 0.508 | ||||
| t(a) | -1.898 | ||||
| p(a) | 0.967 | ||||
| Lowerbound of 95% confidence interval for beta | -0.074 | ||||
| Upperbound of 95% confidence interval for beta | 0.072 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.168 | ||||
| Upperbound of 95% confidence interval for alpha | 0.006 | ||||
| Treynor index (mean / b) | 109.219 | ||||
| Jensen alpha (a) | -0.081 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.044 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.896 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.988 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.896 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.104 | ||||
| Quartile 1 | 0.104 | ||||
| Median | 0.104 | ||||
| Quartile 3 | 0.104 | ||||
| Maximum | 0.104 | ||||
| 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) | -0.036 | ||||
| Compounded annual return (geometric extrapolation) | -0.037 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.355 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.838 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.072 | ||||
| SD | 0.129 | ||||
| Sharpe ratio (Glass type estimate) | -0.561 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.560 | ||||
| df | 773.000 | ||||
| t | -0.964 | ||||
| p | 0.832 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.701 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.580 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.701 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.580 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.683 | ||||
| Upside Potential Ratio | 0.603 | ||||
| Upside part of mean | 0.064 | ||||
| Downside part of mean | -0.136 | ||||
| Upside SD | 0.074 | ||||
| Downside SD | 0.106 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 770.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 774.000 | ||||
| Mean of predictor | 0.639 | ||||
| Mean of criterion | -0.072 | ||||
| SD of predictor | 0.396 | ||||
| SD of criterion | 0.129 | ||||
| Covariance | -0.003 | ||||
| r | -0.055 | ||||
| b (slope, estimate of beta) | -0.018 | ||||
| a (intercept, estimate of alpha) | -0.061 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 772.000 | ||||
| t(b) | -1.524 | ||||
| p(b) | 0.936 | ||||
| t(a) | -0.809 | ||||
| p(a) | 0.791 | ||||
| Lowerbound of 95% confidence interval for beta | -0.041 | ||||
| Upperbound of 95% confidence interval for beta | 0.005 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.209 | ||||
| Upperbound of 95% confidence interval for alpha | 0.087 | ||||
| Treynor index (mean / b) | 4.052 | ||||
| Jensen alpha (a) | -0.061 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.081 | ||||
| SD | 0.135 | ||||
| Sharpe ratio (Glass type estimate) | -0.601 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.600 | ||||
| df | 773.000 | ||||
| t | -1.032 | ||||
| p | 0.849 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.741 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.540 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.741 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.541 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.702 | ||||
| Upside Potential Ratio | 0.530 | ||||
| Upside part of mean | 0.061 | ||||
| Downside part of mean | -0.143 | ||||
| Upside SD | 0.070 | ||||
| Downside SD | 0.116 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 770.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 774.000 | ||||
| Mean of predictor | 0.562 | ||||
| Mean of criterion | -0.081 | ||||
| SD of predictor | 0.390 | ||||
| SD of criterion | 0.135 | ||||
| Covariance | -0.003 | ||||
| r | -0.056 | ||||
| b (slope, estimate of beta) | -0.020 | ||||
| a (intercept, estimate of alpha) | -0.070 | ||||
| Mean Square Error | 0.018 | ||||
| DF error | 772.000 | ||||
| t(b) | -1.571 | ||||
| p(b) | 0.942 | ||||
| t(a) | -0.890 | ||||
| p(a) | 0.813 | ||||
| Lowerbound of 95% confidence interval for beta | -0.044 | ||||
| Upperbound of 95% confidence interval for beta | 0.005 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.225 | ||||
| Upperbound of 95% confidence interval for alpha | 0.085 | ||||
| Treynor index (mean / b) | 4.147 | ||||
| Jensen alpha (a) | -0.070 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 774.000 | ||||
| Minimum | 0.826 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.119 | ||||
| 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 | 6.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.954 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.005 | ||||
| Mean of outliers high | 1.047 | ||||
| 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) | 0.875 | ||||
| VaR(95%) (regression method) | -0.014 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.060 | ||||
| Median | 0.115 | ||||
| Quartile 3 | 0.171 | ||||
| Maximum | 0.226 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.226 | ||||
| Inter Quartile Range | 0.111 | ||||
| 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) | -0.035 | ||||
| Compounded annual return (geometric extrapolation) | -0.036 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.162 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.162 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.100 | ||||
| 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 | 1.083 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.525 | ||||
| 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 | 0.943 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.531 | ||||
| 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) | -8746974794823352.000 | ||||
| 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) | -204706051810852656975835381628928.000 | ||||
| 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 | ||||