Advanced Statistics: Beta TF System
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 | -0.140 | ||||
| SD | 0.127 | ||||
| Sharpe ratio (Glass type estimate) | -1.104 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.080 | ||||
| df | 34.000 | ||||
| t | -1.886 | ||||
| p | 0.966 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.274 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.080 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.256 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.096 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.075 | ||||
| Upside Potential Ratio | 0.076 | ||||
| Upside part of mean | 0.010 | ||||
| Downside part of mean | -0.150 | ||||
| Upside SD | 0.017 | ||||
| Downside SD | 0.130 | ||||
| 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 | 0.542 | ||||
| Mean of criterion | -0.140 | ||||
| SD of predictor | 0.265 | ||||
| SD of criterion | 0.127 | ||||
| Covariance | 0.005 | ||||
| r | 0.153 | ||||
| b (slope, estimate of beta) | 0.073 | ||||
| a (intercept, estimate of alpha) | -0.180 | ||||
| Mean Square Error | 0.016 | ||||
| DF error | 33.000 | ||||
| t(b) | 0.890 | ||||
| p(b) | 0.190 | ||||
| t(a) | -2.070 | ||||
| p(a) | 0.977 | ||||
| Lowerbound of 95% confidence interval for beta | -0.094 | ||||
| Upperbound of 95% confidence interval for beta | 0.241 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.357 | ||||
| Upperbound of 95% confidence interval for alpha | -0.003 | ||||
| Treynor index (mean / b) | -1.911 | ||||
| Jensen alpha (a) | -0.180 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.149 | ||||
| SD | 0.138 | ||||
| Sharpe ratio (Glass type estimate) | -1.083 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.059 | ||||
| df | 34.000 | ||||
| t | -1.850 | ||||
| p | 0.964 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.252 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.100 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.234 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.116 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.055 | ||||
| Upside Potential Ratio | 0.069 | ||||
| Upside part of mean | 0.010 | ||||
| Downside part of mean | -0.159 | ||||
| Upside SD | 0.017 | ||||
| Downside SD | 0.141 | ||||
| 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 | 0.497 | ||||
| Mean of criterion | -0.149 | ||||
| SD of predictor | 0.255 | ||||
| SD of criterion | 0.138 | ||||
| Covariance | 0.005 | ||||
| r | 0.151 | ||||
| b (slope, estimate of beta) | 0.082 | ||||
| a (intercept, estimate of alpha) | -0.190 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 33.000 | ||||
| t(b) | 0.879 | ||||
| p(b) | 0.193 | ||||
| t(a) | -2.037 | ||||
| p(a) | 0.975 | ||||
| Lowerbound of 95% confidence interval for beta | -0.107 | ||||
| Upperbound of 95% confidence interval for beta | 0.271 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.379 | ||||
| Upperbound of 95% confidence interval for alpha | -0.000 | ||||
| Treynor index (mean / b) | -1.828 | ||||
| Jensen alpha (a) | -0.190 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.075 | ||||
| Expected Shortfall on VaR | 0.090 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.043 | ||||
| Expected Shortfall on VaR | 0.089 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 35.000 | ||||
| Minimum | 0.828 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.033 | ||||
| Mean of quarter 1 | 0.965 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.086 | ||||
| Mean of outliers low | 0.896 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.029 | ||||
| Mean of outliers high | 1.033 | ||||
| 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) | -0.006 | ||||
| VaR(95%) (regression method) | 0.054 | ||||
| Expected Shortfall (regression method) | 0.121 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.264 | ||||
| Quartile 1 | 0.264 | ||||
| Median | 0.264 | ||||
| Quartile 3 | 0.264 | ||||
| Maximum | 0.264 | ||||
| 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) | -0.091 | ||||
| Compounded annual return (geometric extrapolation) | -0.100 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.378 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.109 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.141 | ||||
| SD | 0.098 | ||||
| Sharpe ratio (Glass type estimate) | -1.439 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.438 | ||||
| df | 784.000 | ||||
| t | -2.491 | ||||
| p | 0.994 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.573 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.304 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.572 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.303 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.549 | ||||
| Upside Potential Ratio | 0.632 | ||||
| Upside part of mean | 0.058 | ||||
| Downside part of mean | -0.199 | ||||
| Upside SD | 0.037 | ||||
| Downside SD | 0.091 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 777.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 785.000 | ||||
| Mean of predictor | 0.598 | ||||
| Mean of criterion | -0.141 | ||||
| SD of predictor | 0.335 | ||||
| SD of criterion | 0.098 | ||||
| Covariance | 0.001 | ||||
| r | 0.019 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.145 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 783.000 | ||||
| t(b) | 0.526 | ||||
| p(b) | 0.300 | ||||
| t(a) | -2.532 | ||||
| p(a) | 0.994 | ||||
| Lowerbound of 95% confidence interval for beta | -0.015 | ||||
| Upperbound of 95% confidence interval for beta | 0.026 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.257 | ||||
| Upperbound of 95% confidence interval for alpha | -0.033 | ||||
| Treynor index (mean / b) | -25.697 | ||||
| Jensen alpha (a) | -0.145 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.146 | ||||
| SD | 0.101 | ||||
| Sharpe ratio (Glass type estimate) | -1.445 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.443 | ||||
| df | 784.000 | ||||
| t | -2.501 | ||||
| p | 0.994 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.579 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.310 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.578 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.309 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.545 | ||||
| Upside Potential Ratio | 0.601 | ||||
| Upside part of mean | 0.057 | ||||
| Downside part of mean | -0.203 | ||||
| Upside SD | 0.037 | ||||
| Downside SD | 0.095 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 777.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 785.000 | ||||
| Mean of predictor | 0.540 | ||||
| Mean of criterion | -0.146 | ||||
| SD of predictor | 0.341 | ||||
| SD of criterion | 0.101 | ||||
| Covariance | 0.001 | ||||
| r | 0.018 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.149 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 783.000 | ||||
| t(b) | 0.496 | ||||
| p(b) | 0.310 | ||||
| t(a) | -2.536 | ||||
| p(a) | 0.994 | ||||
| Lowerbound of 95% confidence interval for beta | -0.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.026 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.265 | ||||
| Upperbound of 95% confidence interval for alpha | -0.034 | ||||
| Treynor index (mean / b) | -27.785 | ||||
| Jensen alpha (a) | -0.149 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.006 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 785.000 | ||||
| Minimum | 0.903 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.029 | ||||
| Mean of quarter 1 | 0.998 | ||||
| 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 | 18.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.974 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.010 | ||||
| Mean of outliers high | 1.022 | ||||
| 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) | 0.103 | ||||
| VaR(95%) (regression method) | -0.010 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.264 | ||||
| Quartile 1 | 0.264 | ||||
| Median | 0.264 | ||||
| Quartile 3 | 0.264 | ||||
| Maximum | 0.264 | ||||
| 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) | -0.088 | ||||
| Compounded annual return (geometric extrapolation) | -0.097 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.368 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -7.274 | ||||
| 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 | 0.990 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.474 | ||||
| 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 | 0.877 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.475 | ||||
| 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) | -8742652182402077.000 | ||||
| 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) | -107250083927677353385196129353728.000 | ||||
| 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 | ||||