Advanced Statistics: Freestyle ES/GC Trading
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 | -0.123 | ||||
| SD | 0.189 | ||||
| Sharpe ratio (Glass type estimate) | -0.648 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.633 | ||||
| df | 34.000 | ||||
| t | -1.106 | ||||
| p | 0.862 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.801 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.515 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.791 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.524 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.726 | ||||
| Upside Potential Ratio | 0.301 | ||||
| Upside part of mean | 0.051 | ||||
| Downside part of mean | -0.173 | ||||
| Upside SD | 0.087 | ||||
| Downside SD | 0.169 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.592 | ||||
| Mean of criterion | -0.123 | ||||
| SD of predictor | 0.311 | ||||
| SD of criterion | 0.189 | ||||
| Covariance | -0.006 | ||||
| r | -0.110 | ||||
| b (slope, estimate of beta) | -0.067 | ||||
| a (intercept, estimate of alpha) | -0.083 | ||||
| Mean Square Error | 0.036 | ||||
| DF error | 33.000 | ||||
| t(b) | -0.638 | ||||
| p(b) | 0.736 | ||||
| t(a) | -0.648 | ||||
| p(a) | 0.739 | ||||
| Lowerbound of 95% confidence interval for beta | -0.281 | ||||
| Upperbound of 95% confidence interval for beta | 0.147 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.343 | ||||
| Upperbound of 95% confidence interval for alpha | 0.178 | ||||
| Treynor index (mean / b) | 1.826 | ||||
| Jensen alpha (a) | -0.083 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.142 | ||||
| SD | 0.206 | ||||
| Sharpe ratio (Glass type estimate) | -0.690 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.674 | ||||
| df | 34.000 | ||||
| t | -1.178 | ||||
| p | 0.877 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.844 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.474 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.833 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.484 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.744 | ||||
| Upside Potential Ratio | 0.247 | ||||
| Upside part of mean | 0.047 | ||||
| Downside part of mean | -0.190 | ||||
| Upside SD | 0.081 | ||||
| Downside SD | 0.191 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 34.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 35.000 | ||||
| Mean of predictor | 0.536 | ||||
| Mean of criterion | -0.142 | ||||
| SD of predictor | 0.283 | ||||
| SD of criterion | 0.206 | ||||
| Covariance | -0.006 | ||||
| r | -0.111 | ||||
| b (slope, estimate of beta) | -0.081 | ||||
| a (intercept, estimate of alpha) | -0.099 | ||||
| Mean Square Error | 0.043 | ||||
| DF error | 33.000 | ||||
| t(b) | -0.642 | ||||
| p(b) | 0.737 | ||||
| t(a) | -0.710 | ||||
| p(a) | 0.759 | ||||
| Lowerbound of 95% confidence interval for beta | -0.338 | ||||
| Upperbound of 95% confidence interval for beta | 0.176 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.383 | ||||
| Upperbound of 95% confidence interval for alpha | 0.185 | ||||
| Treynor index (mean / b) | 1.756 | ||||
| Jensen alpha (a) | -0.099 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.104 | ||||
| Expected Shortfall on VaR | 0.126 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.049 | ||||
| Expected Shortfall on VaR | 0.105 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.749 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.152 | ||||
| Mean of quarter 1 | 0.958 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.057 | ||||
| Mean of outliers low | 0.809 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.029 | ||||
| Mean of outliers high | 1.152 | ||||
| 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) | -1.089 | ||||
| VaR(95%) (regression method) | 0.158 | ||||
| Expected Shortfall (regression method) | 0.269 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.348 | ||||
| Quartile 1 | 0.348 | ||||
| Median | 0.348 | ||||
| Quartile 3 | 0.348 | ||||
| Maximum | 0.348 | ||||
| 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) | -0.086 | ||||
| Compounded annual return (geometric extrapolation) | -0.094 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.269 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.744 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.067 | ||||
| SD | 0.371 | ||||
| Sharpe ratio (Glass type estimate) | -0.180 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.180 | ||||
| df | 784.000 | ||||
| t | -0.312 | ||||
| p | 0.623 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.313 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.952 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.313 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.952 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.232 | ||||
| Upside Potential Ratio | 1.365 | ||||
| Upside part of mean | 0.393 | ||||
| Downside part of mean | -0.460 | ||||
| Upside SD | 0.233 | ||||
| Downside SD | 0.288 | ||||
| N nonnegative terms | 21.000 | ||||
| N negative terms | 764.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 785.000 | ||||
| Mean of predictor | 0.639 | ||||
| Mean of criterion | -0.067 | ||||
| SD of predictor | 0.363 | ||||
| SD of criterion | 0.371 | ||||
| Covariance | -0.001 | ||||
| r | -0.004 | ||||
| b (slope, estimate of beta) | -0.004 | ||||
| a (intercept, estimate of alpha) | -0.064 | ||||
| Mean Square Error | 0.138 | ||||
| DF error | 783.000 | ||||
| t(b) | -0.121 | ||||
| p(b) | 0.548 | ||||
| t(a) | -0.297 | ||||
| p(a) | 0.617 | ||||
| Lowerbound of 95% confidence interval for beta | -0.076 | ||||
| Upperbound of 95% confidence interval for beta | 0.067 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.488 | ||||
| Upperbound of 95% confidence interval for alpha | 0.359 | ||||
| Treynor index (mean / b) | 15.194 | ||||
| Jensen alpha (a) | -0.064 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.140 | ||||
| SD | 0.389 | ||||
| Sharpe ratio (Glass type estimate) | -0.359 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.359 | ||||
| df | 784.000 | ||||
| t | -0.621 | ||||
| p | 0.733 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.491 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.773 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.491 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.774 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.427 | ||||
| Upside Potential Ratio | 1.129 | ||||
| Upside part of mean | 0.369 | ||||
| Downside part of mean | -0.509 | ||||
| Upside SD | 0.211 | ||||
| Downside SD | 0.327 | ||||
| N nonnegative terms | 21.000 | ||||
| N negative terms | 764.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 785.000 | ||||
| Mean of predictor | 0.573 | ||||
| Mean of criterion | -0.140 | ||||
| SD of predictor | 0.361 | ||||
| SD of criterion | 0.389 | ||||
| Covariance | -0.001 | ||||
| r | -0.008 | ||||
| b (slope, estimate of beta) | -0.008 | ||||
| a (intercept, estimate of alpha) | -0.135 | ||||
| Mean Square Error | 0.152 | ||||
| DF error | 783.000 | ||||
| t(b) | -0.219 | ||||
| p(b) | 0.587 | ||||
| t(a) | -0.597 | ||||
| p(a) | 0.725 | ||||
| Lowerbound of 95% confidence interval for beta | -0.084 | ||||
| Upperbound of 95% confidence interval for beta | 0.067 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.579 | ||||
| Upperbound of 95% confidence interval for alpha | 0.309 | ||||
| Treynor index (mean / b) | 16.546 | ||||
| Jensen alpha (a) | -0.135 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.039 | ||||
| Expected Shortfall on VaR | 0.049 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 785.000 | ||||
| Minimum | 0.718 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.318 | ||||
| Mean of quarter 1 | 0.994 | ||||
| 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 | 12.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.896 | ||||
| Number of outliers high | 21.000 | ||||
| Percentage of outliers high | 0.027 | ||||
| Mean of outliers high | 1.056 | ||||
| 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) | 0.936 | ||||
| VaR(95%) (regression method) | -0.011 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.087 | ||||
| Median | 0.137 | ||||
| Quartile 3 | 0.251 | ||||
| Maximum | 0.515 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.111 | ||||
| Mean of quarter 3 | 0.163 | ||||
| Mean of quarter 4 | 0.515 | ||||
| Inter Quartile Range | 0.164 | ||||
| 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 | 0.250 | ||||
| Mean of outliers high | 0.515 | ||||
| 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) | -0.083 | ||||
| Compounded annual return (geometric extrapolation) | -0.091 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.177 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.177 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.869 | ||||
| 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 | 0.971 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.466 | ||||
| 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 | 0.861 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.469 | ||||
| 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) | -8743292529136769.000 | ||||
| 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) | -111951340799326700947706117881856.000 | ||||
| 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 | ||||