Advanced Statistics: BT - LateTrend
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 | -0.055 | ||||
| SD | 0.029 | ||||
| Sharpe ratio (Glass type estimate) | -1.894 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.870 | ||||
| df | 60.000 | ||||
| t | -4.270 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.820 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.954 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.802 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.939 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.735 | ||||
| Upside Potential Ratio | 0.122 | ||||
| Upside part of mean | 0.004 | ||||
| Downside part of mean | -0.059 | ||||
| Upside SD | 0.009 | ||||
| Downside SD | 0.032 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 60.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.405 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.231 | ||||
| SD of criterion | 0.029 | ||||
| Covariance | -0.000 | ||||
| r | -0.057 | ||||
| b (slope, estimate of beta) | -0.007 | ||||
| a (intercept, estimate of alpha) | -0.052 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 59.000 | ||||
| t(b) | -0.439 | ||||
| p(b) | 0.669 | ||||
| t(a) | -3.577 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.040 | ||||
| Upperbound of 95% confidence interval for beta | 0.026 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.081 | ||||
| Upperbound of 95% confidence interval for alpha | -0.023 | ||||
| Treynor index (mean / b) | 7.674 | ||||
| Jensen alpha (a) | -0.052 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.055 | ||||
| SD | 0.030 | ||||
| Sharpe ratio (Glass type estimate) | -1.865 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.841 | ||||
| df | 60.000 | ||||
| t | -4.204 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.789 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.927 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.771 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.911 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.710 | ||||
| Upside Potential Ratio | 0.118 | ||||
| Upside part of mean | 0.004 | ||||
| Downside part of mean | -0.059 | ||||
| Upside SD | 0.009 | ||||
| Downside SD | 0.032 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 60.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.373 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.225 | ||||
| SD of criterion | 0.030 | ||||
| Covariance | -0.000 | ||||
| r | -0.059 | ||||
| b (slope, estimate of beta) | -0.008 | ||||
| a (intercept, estimate of alpha) | -0.052 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 59.000 | ||||
| t(b) | -0.453 | ||||
| p(b) | 0.674 | ||||
| t(a) | -3.567 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.042 | ||||
| Upperbound of 95% confidence interval for beta | 0.026 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.082 | ||||
| Upperbound of 95% confidence interval for alpha | -0.023 | ||||
| Treynor index (mean / b) | 7.144 | ||||
| Jensen alpha (a) | -0.052 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.022 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.943 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.023 | ||||
| Mean of quarter 1 | 0.995 | ||||
| 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 | 2.000 | ||||
| Percentage of outliers low | 0.033 | ||||
| Mean of outliers low | 0.961 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.016 | ||||
| Mean of outliers high | 1.023 | ||||
| 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) | -0.277 | ||||
| VaR(95%) (regression method) | -0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.077 | ||||
| Quartile 1 | 0.077 | ||||
| Median | 0.077 | ||||
| Quartile 3 | 0.077 | ||||
| Maximum | 0.077 | ||||
| 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) | -0.011 | ||||
| Compounded annual return (geometric extrapolation) | -0.011 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.145 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.510 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.054 | ||||
| SD | 0.055 | ||||
| Sharpe ratio (Glass type estimate) | -0.970 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.969 | ||||
| df | 1337.000 | ||||
| t | -2.192 | ||||
| p | 0.538 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.838 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.102 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.837 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.101 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.356 | ||||
| Upside Potential Ratio | 1.426 | ||||
| Upside part of mean | 0.057 | ||||
| Downside part of mean | -0.110 | ||||
| Upside SD | 0.039 | ||||
| Downside SD | 0.040 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 1321.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1338.000 | ||||
| Mean of predictor | 0.447 | ||||
| Mean of criterion | -0.054 | ||||
| SD of predictor | 0.359 | ||||
| SD of criterion | 0.055 | ||||
| Covariance | -0.001 | ||||
| r | -0.059 | ||||
| b (slope, estimate of beta) | -0.009 | ||||
| a (intercept, estimate of alpha) | -0.050 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 1336.000 | ||||
| t(b) | -2.151 | ||||
| p(b) | 0.529 | ||||
| t(a) | -2.023 | ||||
| p(a) | 0.528 | ||||
| Lowerbound of 95% confidence interval for beta | -0.017 | ||||
| Upperbound of 95% confidence interval for beta | -0.001 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.098 | ||||
| Upperbound of 95% confidence interval for alpha | -0.002 | ||||
| Treynor index (mean / b) | 5.932 | ||||
| Jensen alpha (a) | -0.050 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.055 | ||||
| SD | 0.055 | ||||
| Sharpe ratio (Glass type estimate) | -0.999 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.998 | ||||
| df | 1337.000 | ||||
| t | -2.257 | ||||
| p | 0.539 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.867 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.130 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.866 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.130 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.374 | ||||
| Upside Potential Ratio | 1.386 | ||||
| Upside part of mean | 0.056 | ||||
| Downside part of mean | -0.111 | ||||
| Upside SD | 0.038 | ||||
| Downside SD | 0.040 | ||||
| N nonnegative terms | 17.000 | ||||
| N negative terms | 1321.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1338.000 | ||||
| Mean of predictor | 0.383 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.358 | ||||
| SD of criterion | 0.055 | ||||
| Covariance | -0.001 | ||||
| r | -0.059 | ||||
| b (slope, estimate of beta) | -0.009 | ||||
| a (intercept, estimate of alpha) | -0.052 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 1336.000 | ||||
| t(b) | -2.169 | ||||
| p(b) | 0.530 | ||||
| t(a) | -2.112 | ||||
| p(a) | 0.529 | ||||
| Lowerbound of 95% confidence interval for beta | -0.017 | ||||
| Upperbound of 95% confidence interval for beta | -0.001 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.100 | ||||
| Upperbound of 95% confidence interval for alpha | -0.004 | ||||
| Treynor index (mean / b) | 6.033 | ||||
| Jensen alpha (a) | -0.052 | ||||
| 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%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.003 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1338.000 | ||||
| Minimum | 0.960 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.058 | ||||
| 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 | 25.000 | ||||
| Percentage of outliers low | 0.019 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 17.000 | ||||
| Percentage of outliers high | 0.013 | ||||
| Mean of outliers high | 1.017 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.774 | ||||
| VaR(95%) (moments method) | -0.016 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.469 | ||||
| VaR(95%) (regression method) | -0.015 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.009 | ||||
| Quartile 1 | 0.042 | ||||
| Median | 0.074 | ||||
| Quartile 3 | 0.107 | ||||
| Maximum | 0.140 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.140 | ||||
| Inter Quartile Range | 0.066 | ||||
| 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) | -0.011 | ||||
| Compounded annual return (geometric extrapolation) | -0.011 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.080 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.080 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.545 | ||||
| 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 | ||||