Advanced Statistics: Beta 2
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 | -0.080 | ||||
| SD | 0.172 | ||||
| Sharpe ratio (Glass type estimate) | -0.468 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.457 | ||||
| df | 31.000 | ||||
| t | -0.765 | ||||
| p | 0.775 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.670 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.741 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.662 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.749 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.563 | ||||
| Upside Potential Ratio | 0.401 | ||||
| Upside part of mean | 0.057 | ||||
| Downside part of mean | -0.137 | ||||
| Upside SD | 0.093 | ||||
| Downside SD | 0.143 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.588 | ||||
| Mean of criterion | -0.080 | ||||
| SD of predictor | 0.285 | ||||
| SD of criterion | 0.172 | ||||
| Covariance | -0.005 | ||||
| r | -0.097 | ||||
| b (slope, estimate of beta) | -0.058 | ||||
| a (intercept, estimate of alpha) | -0.046 | ||||
| Mean Square Error | 0.030 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.531 | ||||
| p(b) | 0.700 | ||||
| t(a) | -0.372 | ||||
| p(a) | 0.644 | ||||
| Lowerbound of 95% confidence interval for beta | -0.281 | ||||
| Upperbound of 95% confidence interval for beta | 0.165 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.300 | ||||
| Upperbound of 95% confidence interval for alpha | 0.207 | ||||
| Treynor index (mean / b) | 1.382 | ||||
| Jensen alpha (a) | -0.046 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.096 | ||||
| SD | 0.184 | ||||
| Sharpe ratio (Glass type estimate) | -0.522 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.510 | ||||
| df | 31.000 | ||||
| t | -0.853 | ||||
| p | 0.800 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.725 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.689 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.716 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.697 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.596 | ||||
| Upside Potential Ratio | 0.329 | ||||
| Upside part of mean | 0.053 | ||||
| Downside part of mean | -0.149 | ||||
| Upside SD | 0.087 | ||||
| Downside SD | 0.161 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.537 | ||||
| Mean of criterion | -0.096 | ||||
| SD of predictor | 0.267 | ||||
| SD of criterion | 0.184 | ||||
| Covariance | -0.005 | ||||
| r | -0.093 | ||||
| b (slope, estimate of beta) | -0.064 | ||||
| a (intercept, estimate of alpha) | -0.062 | ||||
| Mean Square Error | 0.035 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.511 | ||||
| p(b) | 0.694 | ||||
| t(a) | -0.466 | ||||
| p(a) | 0.678 | ||||
| Lowerbound of 95% confidence interval for beta | -0.319 | ||||
| Upperbound of 95% confidence interval for beta | 0.191 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.331 | ||||
| Upperbound of 95% confidence interval for alpha | 0.208 | ||||
| Treynor index (mean / b) | 1.499 | ||||
| Jensen alpha (a) | -0.062 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.091 | ||||
| Expected Shortfall on VaR | 0.111 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.039 | ||||
| Expected Shortfall on VaR | 0.084 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.774 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.156 | ||||
| Mean of quarter 1 | 0.968 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.020 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.062 | ||||
| Mean of outliers low | 0.874 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.031 | ||||
| Mean of outliers high | 1.156 | ||||
| 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) | 1.935 | ||||
| VaR(95%) (regression method) | 0.027 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.247 | ||||
| Quartile 1 | 0.247 | ||||
| Median | 0.247 | ||||
| Quartile 3 | 0.247 | ||||
| Maximum | 0.247 | ||||
| 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) | -0.048 | ||||
| Compounded annual return (geometric extrapolation) | -0.051 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.205 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.457 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.078 | ||||
| SD | 0.177 | ||||
| Sharpe ratio (Glass type estimate) | -0.440 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.440 | ||||
| df | 712.000 | ||||
| t | -0.726 | ||||
| p | 0.766 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.629 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.748 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.628 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.748 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.489 | ||||
| Upside Potential Ratio | 1.227 | ||||
| Upside part of mean | 0.195 | ||||
| Downside part of mean | -0.273 | ||||
| Upside SD | 0.077 | ||||
| Downside SD | 0.159 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 678.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 713.000 | ||||
| Mean of predictor | 0.629 | ||||
| Mean of criterion | -0.078 | ||||
| SD of predictor | 0.376 | ||||
| SD of criterion | 0.177 | ||||
| Covariance | 0.001 | ||||
| r | 0.017 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | -0.083 | ||||
| Mean Square Error | 0.031 | ||||
| DF error | 711.000 | ||||
| t(b) | 0.443 | ||||
| p(b) | 0.329 | ||||
| t(a) | -0.768 | ||||
| p(a) | 0.779 | ||||
| Lowerbound of 95% confidence interval for beta | -0.027 | ||||
| Upperbound of 95% confidence interval for beta | 0.042 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.294 | ||||
| Upperbound of 95% confidence interval for alpha | 0.129 | ||||
| Treynor index (mean / b) | -9.955 | ||||
| Jensen alpha (a) | -0.083 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.095 | ||||
| SD | 0.189 | ||||
| Sharpe ratio (Glass type estimate) | -0.501 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.501 | ||||
| df | 712.000 | ||||
| t | -0.827 | ||||
| p | 0.796 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.689 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.687 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.689 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.688 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.547 | ||||
| Upside Potential Ratio | 1.107 | ||||
| Upside part of mean | 0.192 | ||||
| Downside part of mean | -0.287 | ||||
| Upside SD | 0.075 | ||||
| Downside SD | 0.173 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 678.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 713.000 | ||||
| Mean of predictor | 0.554 | ||||
| Mean of criterion | -0.095 | ||||
| SD of predictor | 0.391 | ||||
| SD of criterion | 0.189 | ||||
| Covariance | 0.001 | ||||
| r | 0.015 | ||||
| b (slope, estimate of beta) | 0.007 | ||||
| a (intercept, estimate of alpha) | -0.099 | ||||
| Mean Square Error | 0.036 | ||||
| DF error | 711.000 | ||||
| t(b) | 0.396 | ||||
| p(b) | 0.346 | ||||
| t(a) | -0.858 | ||||
| p(a) | 0.804 | ||||
| Lowerbound of 95% confidence interval for beta | -0.028 | ||||
| Upperbound of 95% confidence interval for beta | 0.043 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.325 | ||||
| Upperbound of 95% confidence interval for alpha | 0.127 | ||||
| Treynor index (mean / b) | -13.199 | ||||
| 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%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 713.000 | ||||
| Minimum | 0.812 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.058 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 24.000 | ||||
| Percentage of outliers low | 0.034 | ||||
| Mean of outliers low | 0.974 | ||||
| Number of outliers high | 35.000 | ||||
| Percentage of outliers high | 0.049 | ||||
| Mean of outliers high | 1.015 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.279 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.728 | ||||
| VaR(95%) (regression method) | -0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.013 | ||||
| Median | 0.023 | ||||
| Quartile 3 | 0.086 | ||||
| Maximum | 0.319 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.015 | ||||
| Mean of quarter 3 | 0.031 | ||||
| Mean of quarter 4 | 0.212 | ||||
| Inter Quartile Range | 0.073 | ||||
| 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 | 0.167 | ||||
| Mean of outliers high | 0.319 | ||||
| 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) | -0.047 | ||||
| Compounded annual return (geometric extrapolation) | -0.050 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.155 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.234 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.050 | ||||
| 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 | 1.088 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.450 | ||||
| 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 | 0.985 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.448 | ||||
| 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) | -8719105782825541.000 | ||||
| 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) | -161975252058806890487141042749440.000 | ||||
| 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 | ||||