Advanced Statistics: BT - EarlyPattern
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 | -0.041 | ||||
| SD | 0.006 | ||||
| Sharpe ratio (Glass type estimate) | -7.443 | ||||
| Sharpe ratio (Hedges UMVUE) | -7.348 | ||||
| df | 59.000 | ||||
| t | -16.643 | ||||
| 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) | -8.937 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.759 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.238 | ||||
| Upside Potential Ratio | 0.154 | ||||
| Upside part of mean | 0.002 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.003 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.431 | ||||
| Mean of criterion | -0.041 | ||||
| SD of predictor | 0.296 | ||||
| SD of criterion | 0.006 | ||||
| Covariance | 0.000 | ||||
| r | 0.038 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.041 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 58.000 | ||||
| t(b) | 0.292 | ||||
| p(b) | 0.386 | ||||
| t(a) | -15.320 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.047 | ||||
| Upperbound of 95% confidence interval for alpha | -0.036 | ||||
| Treynor index (mean / b) | -57.560 | ||||
| Jensen alpha (a) | -0.041 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.041 | ||||
| SD | 0.006 | ||||
| Sharpe ratio (Glass type estimate) | -7.461 | ||||
| Sharpe ratio (Hedges UMVUE) | -7.366 | ||||
| df | 59.000 | ||||
| t | -16.683 | ||||
| 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) | -8.958 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -5.774 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.239 | ||||
| Upside Potential Ratio | 0.154 | ||||
| Upside part of mean | 0.002 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.003 | ||||
| Downside SD | 0.013 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.384 | ||||
| Mean of criterion | -0.041 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 0.006 | ||||
| Covariance | 0.000 | ||||
| r | 0.042 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.041 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 58.000 | ||||
| t(b) | 0.320 | ||||
| p(b) | 0.375 | ||||
| t(a) | -15.426 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.006 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.047 | ||||
| Upperbound of 95% confidence interval for alpha | -0.036 | ||||
| Treynor index (mean / b) | -48.220 | ||||
| Jensen alpha (a) | -0.041 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 60.000 | ||||
| Minimum | 0.997 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.009 | ||||
| Mean of quarter 1 | 1.000 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers low | 0.033 | ||||
| Mean of outliers low | 0.999 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.067 | ||||
| Mean of outliers high | 1.004 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.001 | ||||
| Quartile 3 | 0.002 | ||||
| Maximum | 0.003 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.003 | ||||
| Inter Quartile Range | 0.001 | ||||
| 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) | 0.003 | ||||
| Compounded annual return (geometric extrapolation) | 0.003 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.156 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.156 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.438 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.041 | ||||
| SD | 0.032 | ||||
| Sharpe ratio (Glass type estimate) | -1.283 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.282 | ||||
| df | 1327.000 | ||||
| t | -2.888 | ||||
| p | 0.550 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.154 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.411 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.154 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.410 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.824 | ||||
| Upside Potential Ratio | 1.439 | ||||
| Upside part of mean | 0.032 | ||||
| Downside part of mean | -0.073 | ||||
| Upside SD | 0.023 | ||||
| Downside SD | 0.022 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 1313.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1328.000 | ||||
| Mean of predictor | 0.467 | ||||
| Mean of criterion | -0.041 | ||||
| SD of predictor | 0.378 | ||||
| SD of criterion | 0.032 | ||||
| Covariance | -0.001 | ||||
| r | -0.054 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | -0.039 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 1326.000 | ||||
| t(b) | -1.972 | ||||
| p(b) | 0.527 | ||||
| t(a) | -2.733 | ||||
| p(a) | 0.537 | ||||
| Lowerbound of 95% confidence interval for beta | -0.009 | ||||
| Upperbound of 95% confidence interval for beta | -0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.066 | ||||
| Upperbound of 95% confidence interval for alpha | -0.011 | ||||
| Treynor index (mean / b) | 8.974 | ||||
| Jensen alpha (a) | -0.039 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.041 | ||||
| SD | 0.032 | ||||
| Sharpe ratio (Glass type estimate) | -1.298 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.297 | ||||
| df | 1327.000 | ||||
| t | -2.922 | ||||
| p | 0.551 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.169 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.426 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.169 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.425 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.827 | ||||
| Upside Potential Ratio | 1.412 | ||||
| Upside part of mean | 0.032 | ||||
| Downside part of mean | -0.073 | ||||
| Upside SD | 0.022 | ||||
| Downside SD | 0.023 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 1313.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1328.000 | ||||
| Mean of predictor | 0.396 | ||||
| Mean of criterion | -0.041 | ||||
| SD of predictor | 0.373 | ||||
| SD of criterion | 0.032 | ||||
| Covariance | -0.001 | ||||
| r | -0.055 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | -0.039 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 1326.000 | ||||
| t(b) | -1.989 | ||||
| p(b) | 0.527 | ||||
| t(a) | -2.788 | ||||
| p(a) | 0.538 | ||||
| Lowerbound of 95% confidence interval for beta | -0.009 | ||||
| Upperbound of 95% confidence interval for beta | -0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.067 | ||||
| Upperbound of 95% confidence interval for alpha | -0.012 | ||||
| Treynor index (mean / b) | 8.871 | ||||
| Jensen alpha (a) | -0.039 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| 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 | 1328.000 | ||||
| Minimum | 0.968 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.023 | ||||
| Mean of quarter 1 | 1.000 | ||||
| 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 | 44.000 | ||||
| Percentage of outliers low | 0.033 | ||||
| Mean of outliers low | 0.997 | ||||
| Number of outliers high | 44.000 | ||||
| Percentage of outliers high | 0.033 | ||||
| Mean of outliers high | 1.004 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -12.556 | ||||
| VaR(95%) (moments method) | -84484.199 | ||||
| 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 | 4.000 | ||||
| Minimum | 0.010 | ||||
| Quartile 1 | 0.019 | ||||
| Median | 0.024 | ||||
| Quartile 3 | 0.029 | ||||
| Maximum | 0.040 | ||||
| Mean of quarter 1 | 0.010 | ||||
| Mean of quarter 2 | 0.022 | ||||
| Mean of quarter 3 | 0.025 | ||||
| Mean of quarter 4 | 0.040 | ||||
| Inter Quartile Range | 0.010 | ||||
| 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) | 0.003 | ||||
| Compounded annual return (geometric extrapolation) | 0.003 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.071 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.071 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.689 | ||||
| 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 | 1.403 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.348 | ||||
| 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 | 1.339 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.349 | ||||
| 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) | -8560251740754734.000 | ||||
| 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) | -49314958761845683889645662765056.000 | ||||
| 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 | ||||