Advanced Statistics: Steady-Profits Futures Mid-Term
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 | 0.085 | ||||
| Sharpe ratio (Glass type estimate) | 0.334 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.327 | ||||
| df | 36.000 | ||||
| t | 0.587 | ||||
| p | 0.280 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.787 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.451 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.791 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.446 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.131 | ||||
| Upside Potential Ratio | 3.192 | ||||
| Upside part of mean | 0.080 | ||||
| Downside part of mean | -0.052 | ||||
| Upside SD | 0.081 | ||||
| Downside SD | 0.025 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.515 | ||||
| Mean of criterion | 0.028 | ||||
| SD of predictor | 0.268 | ||||
| SD of criterion | 0.085 | ||||
| Covariance | -0.006 | ||||
| r | -0.256 | ||||
| b (slope, estimate of beta) | -0.081 | ||||
| a (intercept, estimate of alpha) | 0.070 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 35.000 | ||||
| t(b) | -1.567 | ||||
| p(b) | 0.937 | ||||
| t(a) | 1.289 | ||||
| p(a) | 0.103 | ||||
| Lowerbound of 95% confidence interval for beta | -0.187 | ||||
| Upperbound of 95% confidence interval for beta | 0.024 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.040 | ||||
| Upperbound of 95% confidence interval for alpha | 0.181 | ||||
| Treynor index (mean / b) | -0.350 | ||||
| Jensen alpha (a) | 0.070 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.025 | ||||
| SD | 0.082 | ||||
| Sharpe ratio (Glass type estimate) | 0.306 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.299 | ||||
| df | 36.000 | ||||
| t | 0.537 | ||||
| p | 0.297 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.815 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.422 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.819 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.418 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.983 | ||||
| Upside Potential Ratio | 3.026 | ||||
| Upside part of mean | 0.077 | ||||
| Downside part of mean | -0.052 | ||||
| Upside SD | 0.077 | ||||
| Downside SD | 0.025 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.470 | ||||
| Mean of criterion | 0.025 | ||||
| SD of predictor | 0.255 | ||||
| SD of criterion | 0.082 | ||||
| Covariance | -0.005 | ||||
| r | -0.258 | ||||
| b (slope, estimate of beta) | -0.083 | ||||
| a (intercept, estimate of alpha) | 0.064 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 35.000 | ||||
| t(b) | -1.579 | ||||
| p(b) | 0.938 | ||||
| t(a) | 1.233 | ||||
| p(a) | 0.113 | ||||
| Lowerbound of 95% confidence interval for beta | -0.189 | ||||
| Upperbound of 95% confidence interval for beta | 0.024 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.041 | ||||
| Upperbound of 95% confidence interval for alpha | 0.169 | ||||
| Treynor index (mean / b) | -0.302 | ||||
| Jensen alpha (a) | 0.064 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.046 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.022 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 37.000 | ||||
| Minimum | 0.966 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.104 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.030 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.135 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.189 | ||||
| Mean of outliers high | 1.039 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.951 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.085 | ||||
| Extreme Value Index (regression method) | 1.327 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.017 | ||||
| Quartile 3 | 0.026 | ||||
| Maximum | 0.034 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.034 | ||||
| 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 | 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) | 0.077 | ||||
| Compounded annual return (geometric extrapolation) | 0.071 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.106 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.106 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.570 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.025 | ||||
| SD | 0.054 | ||||
| Sharpe ratio (Glass type estimate) | 0.462 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.462 | ||||
| df | 823.000 | ||||
| t | 0.820 | ||||
| p | 0.206 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.643 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.568 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.644 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.567 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.068 | ||||
| Upside Potential Ratio | 6.711 | ||||
| Upside part of mean | 0.158 | ||||
| Downside part of mean | -0.133 | ||||
| Upside SD | 0.049 | ||||
| Downside SD | 0.024 | ||||
| N nonnegative terms | 157.000 | ||||
| N negative terms | 667.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 824.000 | ||||
| Mean of predictor | 0.556 | ||||
| Mean of criterion | 0.025 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.054 | ||||
| Covariance | -0.000 | ||||
| r | -0.026 | ||||
| b (slope, estimate of beta) | -0.004 | ||||
| a (intercept, estimate of alpha) | 0.028 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 822.000 | ||||
| t(b) | -0.759 | ||||
| p(b) | 0.776 | ||||
| t(a) | 0.894 | ||||
| p(a) | 0.186 | ||||
| Lowerbound of 95% confidence interval for beta | -0.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.033 | ||||
| Upperbound of 95% confidence interval for alpha | 0.088 | ||||
| Treynor index (mean / b) | -5.737 | ||||
| Jensen alpha (a) | 0.028 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.024 | ||||
| SD | 0.054 | ||||
| Sharpe ratio (Glass type estimate) | 0.441 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.441 | ||||
| df | 823.000 | ||||
| t | 0.782 | ||||
| p | 0.217 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.665 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.546 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.665 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.546 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.002 | ||||
| Upside Potential Ratio | 6.635 | ||||
| Upside part of mean | 0.157 | ||||
| Downside part of mean | -0.133 | ||||
| Upside SD | 0.048 | ||||
| Downside SD | 0.024 | ||||
| N nonnegative terms | 157.000 | ||||
| N negative terms | 667.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 824.000 | ||||
| Mean of predictor | 0.501 | ||||
| Mean of criterion | 0.024 | ||||
| SD of predictor | 0.332 | ||||
| SD of criterion | 0.054 | ||||
| Covariance | -0.000 | ||||
| r | -0.026 | ||||
| b (slope, estimate of beta) | -0.004 | ||||
| a (intercept, estimate of alpha) | 0.026 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 822.000 | ||||
| t(b) | -0.742 | ||||
| p(b) | 0.771 | ||||
| t(a) | 0.847 | ||||
| p(a) | 0.199 | ||||
| Lowerbound of 95% confidence interval for beta | -0.015 | ||||
| Upperbound of 95% confidence interval for beta | 0.007 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.034 | ||||
| Upperbound of 95% confidence interval for alpha | 0.085 | ||||
| Treynor index (mean / b) | -5.667 | ||||
| Jensen alpha (a) | 0.026 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 824.000 | ||||
| Minimum | 0.986 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.052 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 193.000 | ||||
| Percentage of outliers low | 0.234 | ||||
| Mean of outliers low | 0.998 | ||||
| Number of outliers high | 192.000 | ||||
| Percentage of outliers high | 0.233 | ||||
| Mean of outliers high | 1.003 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.224 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.065 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.004 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.004 | ||||
| Quartile 3 | 0.017 | ||||
| Maximum | 0.050 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.003 | ||||
| Mean of quarter 3 | 0.010 | ||||
| Mean of quarter 4 | 0.035 | ||||
| Inter Quartile Range | 0.015 | ||||
| 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 | 0.091 | ||||
| Mean of outliers high | 0.050 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -8.642 | ||||
| VaR(95%) (moments method) | 0.036 | ||||
| Expected Shortfall (moments method) | 0.036 | ||||
| Extreme Value Index (regression method) | -1.114 | ||||
| VaR(95%) (regression method) | 0.057 | ||||
| Expected Shortfall (regression method) | 0.061 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.075 | ||||
| Compounded annual return (geometric extrapolation) | 0.070 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.399 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.008 | ||||
| Compounded annual return / Expected Shortfall lognormal | 10.418 | ||||
| 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 | 1.016 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.533 | ||||
| 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 | 0.872 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.536 | ||||
| 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) | -8755443330846678.000 | ||||
| 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) | -278441089432887613955976609136640.000 | ||||
| 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 | ||||