Advanced Statistics: Battlecat Trading
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 | -0.052 | ||||
| SD | 0.026 | ||||
| Sharpe ratio (Glass type estimate) | -2.045 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.005 | ||||
| df | 38.000 | ||||
| t | -3.687 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.214 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.854 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.181 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.828 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.806 | ||||
| Upside Potential Ratio | 0.100 | ||||
| Upside part of mean | 0.003 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.005 | ||||
| Downside SD | 0.029 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.485 | ||||
| Mean of criterion | -0.052 | ||||
| SD of predictor | 0.249 | ||||
| SD of criterion | 0.026 | ||||
| Covariance | 0.001 | ||||
| r | 0.151 | ||||
| b (slope, estimate of beta) | 0.016 | ||||
| a (intercept, estimate of alpha) | -0.060 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.929 | ||||
| p(b) | 0.179 | ||||
| t(a) | -3.657 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.049 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.093 | ||||
| Upperbound of 95% confidence interval for alpha | -0.027 | ||||
| Treynor index (mean / b) | -3.370 | ||||
| Jensen alpha (a) | -0.060 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.053 | ||||
| SD | 0.026 | ||||
| Sharpe ratio (Glass type estimate) | -2.015 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.975 | ||||
| df | 38.000 | ||||
| t | -3.632 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.181 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.826 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.149 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.800 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.785 | ||||
| Upside Potential Ratio | 0.098 | ||||
| Upside part of mean | 0.003 | ||||
| Downside part of mean | -0.056 | ||||
| Upside SD | 0.005 | ||||
| Downside SD | 0.029 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.447 | ||||
| Mean of criterion | -0.053 | ||||
| SD of predictor | 0.238 | ||||
| SD of criterion | 0.026 | ||||
| Covariance | 0.001 | ||||
| r | 0.154 | ||||
| b (slope, estimate of beta) | 0.017 | ||||
| a (intercept, estimate of alpha) | -0.060 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 37.000 | ||||
| t(b) | 0.950 | ||||
| p(b) | 0.174 | ||||
| t(a) | -3.637 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.019 | ||||
| Upperbound of 95% confidence interval for beta | 0.053 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.094 | ||||
| Upperbound of 95% confidence interval for alpha | -0.027 | ||||
| Treynor index (mean / b) | -3.101 | ||||
| Jensen alpha (a) | -0.060 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.956 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.013 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.026 | ||||
| Mean of outliers low | 0.956 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.051 | ||||
| Mean of outliers high | 1.008 | ||||
| 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 | 0.044 | ||||
| Quartile 1 | 0.044 | ||||
| Median | 0.044 | ||||
| Quartile 3 | 0.044 | ||||
| Maximum | 0.044 | ||||
| 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) | -0.008 | ||||
| Compounded annual return (geometric extrapolation) | -0.009 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.196 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.435 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.052 | ||||
| SD | 0.022 | ||||
| Sharpe ratio (Glass type estimate) | -2.415 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.413 | ||||
| df | 866.000 | ||||
| t | -4.393 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.498 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.331 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.496 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.329 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.824 | ||||
| Upside Potential Ratio | 0.951 | ||||
| Upside part of mean | 0.018 | ||||
| Downside part of mean | -0.070 | ||||
| Upside SD | 0.012 | ||||
| Downside SD | 0.018 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 856.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 867.000 | ||||
| Mean of predictor | 0.526 | ||||
| Mean of criterion | -0.052 | ||||
| SD of predictor | 0.315 | ||||
| SD of criterion | 0.022 | ||||
| Covariance | 0.000 | ||||
| r | 0.009 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 865.000 | ||||
| t(b) | 0.272 | ||||
| p(b) | 0.393 | ||||
| t(a) | -4.395 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.005 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.076 | ||||
| Upperbound of 95% confidence interval for alpha | -0.029 | ||||
| Treynor index (mean / b) | -82.156 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.052 | ||||
| SD | 0.022 | ||||
| Sharpe ratio (Glass type estimate) | -2.417 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.414 | ||||
| df | 866.000 | ||||
| t | -4.396 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.499 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.332 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.498 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.331 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.817 | ||||
| Upside Potential Ratio | 0.940 | ||||
| Upside part of mean | 0.018 | ||||
| Downside part of mean | -0.070 | ||||
| Upside SD | 0.012 | ||||
| Downside SD | 0.019 | ||||
| N nonnegative terms | 11.000 | ||||
| N negative terms | 856.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 867.000 | ||||
| Mean of predictor | 0.475 | ||||
| Mean of criterion | -0.052 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.022 | ||||
| Covariance | 0.000 | ||||
| r | 0.009 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 865.000 | ||||
| t(b) | 0.260 | ||||
| p(b) | 0.397 | ||||
| t(a) | -4.399 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.005 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.076 | ||||
| Upperbound of 95% confidence interval for alpha | -0.029 | ||||
| Treynor index (mean / b) | -87.548 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 867.000 | ||||
| Minimum | 0.982 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.013 | ||||
| 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 | 10.000 | ||||
| Percentage of outliers low | 0.012 | ||||
| Mean of outliers low | 0.991 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.013 | ||||
| Mean of outliers high | 1.005 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -9.019 | ||||
| VaR(95%) (moments method) | -2581.848 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.557 | ||||
| VaR(95%) (regression method) | -0.015 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.036 | ||||
| Quartile 3 | 0.052 | ||||
| Maximum | 0.067 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.067 | ||||
| Inter Quartile Range | 0.031 | ||||
| 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) | -0.008 | ||||
| Compounded annual return (geometric extrapolation) | -0.008 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.125 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.125 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.844 | ||||
| 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 | 1.051 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.488 | ||||
| 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 | 0.931 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.491 | ||||
| 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) | -8739542836594534.000 | ||||
| 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) | -388205662317198108452230977814528.000 | ||||
| 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 | ||||