Advanced Statistics: no name
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 | -0.004 | ||||
| SD | 0.467 | ||||
| Sharpe ratio (Glass type estimate) | -0.009 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.008 | ||||
| df | 38.000 | ||||
| t | -0.015 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.096 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.079 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.096 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.079 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.013 | ||||
| Upside Potential Ratio | 0.864 | ||||
| Upside part of mean | 0.273 | ||||
| Downside part of mean | -0.277 | ||||
| Upside SD | 0.336 | ||||
| Downside SD | 0.316 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.507 | ||||
| Mean of criterion | -0.004 | ||||
| SD of predictor | 0.303 | ||||
| SD of criterion | 0.467 | ||||
| Covariance | -0.009 | ||||
| r | -0.065 | ||||
| b (slope, estimate of beta) | -0.101 | ||||
| a (intercept, estimate of alpha) | 0.047 | ||||
| Mean Square Error | 0.223 | ||||
| DF error | 37.000 | ||||
| t(b) | -0.398 | ||||
| p(b) | 0.653 | ||||
| t(a) | 0.161 | ||||
| p(a) | 0.436 | ||||
| Lowerbound of 95% confidence interval for beta | -0.613 | ||||
| Upperbound of 95% confidence interval for beta | 0.412 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.544 | ||||
| Upperbound of 95% confidence interval for alpha | 0.638 | ||||
| Treynor index (mean / b) | 0.040 | ||||
| Jensen alpha (a) | 0.047 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.119 | ||||
| SD | 0.506 | ||||
| Sharpe ratio (Glass type estimate) | -0.235 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.231 | ||||
| df | 38.000 | ||||
| t | -0.425 | ||||
| p | 0.663 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.322 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.855 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.319 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.858 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.284 | ||||
| Upside Potential Ratio | 0.546 | ||||
| Upside part of mean | 0.229 | ||||
| Downside part of mean | -0.348 | ||||
| Upside SD | 0.273 | ||||
| Downside SD | 0.420 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.454 | ||||
| Mean of criterion | -0.119 | ||||
| SD of predictor | 0.286 | ||||
| SD of criterion | 0.506 | ||||
| Covariance | -0.002 | ||||
| r | -0.016 | ||||
| b (slope, estimate of beta) | -0.028 | ||||
| a (intercept, estimate of alpha) | -0.106 | ||||
| Mean Square Error | 0.263 | ||||
| DF error | 37.000 | ||||
| t(b) | -0.098 | ||||
| p(b) | 0.539 | ||||
| t(a) | -0.339 | ||||
| p(a) | 0.632 | ||||
| Lowerbound of 95% confidence interval for beta | -0.617 | ||||
| Upperbound of 95% confidence interval for beta | 0.561 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.742 | ||||
| Upperbound of 95% confidence interval for alpha | 0.529 | ||||
| Treynor index (mean / b) | 4.206 | ||||
| Jensen alpha (a) | -0.106 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.221 | ||||
| Expected Shortfall on VaR | 0.267 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.076 | ||||
| Expected Shortfall on VaR | 0.166 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.505 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.563 | ||||
| Mean of quarter 1 | 0.923 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.090 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.077 | ||||
| Mean of outliers low | 0.744 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.077 | ||||
| Mean of outliers high | 1.299 | ||||
| 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) | 2.528 | ||||
| VaR(95%) (regression method) | 0.026 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.270 | ||||
| Quartile 1 | 0.326 | ||||
| Median | 0.382 | ||||
| Quartile 3 | 0.439 | ||||
| Maximum | 0.495 | ||||
| Mean of quarter 1 | 0.270 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.495 | ||||
| Inter Quartile Range | 0.112 | ||||
| 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) | -0.067 | ||||
| Compounded annual return (geometric extrapolation) | -0.072 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.146 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.146 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.272 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.151 | ||||
| SD | 0.792 | ||||
| Sharpe ratio (Glass type estimate) | 0.191 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.190 | ||||
| df | 860.000 | ||||
| t | 0.346 | ||||
| p | 0.365 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.891 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.272 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.891 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.272 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.350 | ||||
| Upside Potential Ratio | 3.358 | ||||
| Upside part of mean | 1.447 | ||||
| Downside part of mean | -1.296 | ||||
| Upside SD | 0.664 | ||||
| Downside SD | 0.431 | ||||
| N nonnegative terms | 40.000 | ||||
| N negative terms | 821.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 861.000 | ||||
| Mean of predictor | 0.525 | ||||
| Mean of criterion | 0.151 | ||||
| SD of predictor | 0.363 | ||||
| SD of criterion | 0.792 | ||||
| Covariance | -0.004 | ||||
| r | -0.012 | ||||
| b (slope, estimate of beta) | -0.027 | ||||
| a (intercept, estimate of alpha) | 0.165 | ||||
| Mean Square Error | 0.627 | ||||
| DF error | 859.000 | ||||
| t(b) | -0.359 | ||||
| p(b) | 0.640 | ||||
| t(a) | 0.376 | ||||
| p(a) | 0.354 | ||||
| Lowerbound of 95% confidence interval for beta | -0.173 | ||||
| Upperbound of 95% confidence interval for beta | 0.119 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.696 | ||||
| Upperbound of 95% confidence interval for alpha | 1.026 | ||||
| Treynor index (mean / b) | -5.642 | ||||
| Jensen alpha (a) | 0.165 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.118 | ||||
| SD | 0.715 | ||||
| Sharpe ratio (Glass type estimate) | -0.166 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.165 | ||||
| df | 860.000 | ||||
| t | -0.300 | ||||
| p | 0.618 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.247 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.916 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.247 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.916 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.248 | ||||
| Upside Potential Ratio | 2.690 | ||||
| Upside part of mean | 1.284 | ||||
| Downside part of mean | -1.402 | ||||
| Upside SD | 0.532 | ||||
| Downside SD | 0.477 | ||||
| N nonnegative terms | 40.000 | ||||
| N negative terms | 821.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 861.000 | ||||
| Mean of predictor | 0.456 | ||||
| Mean of criterion | -0.118 | ||||
| SD of predictor | 0.375 | ||||
| SD of criterion | 0.715 | ||||
| Covariance | -0.002 | ||||
| r | -0.006 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | -0.113 | ||||
| Mean Square Error | 0.512 | ||||
| DF error | 859.000 | ||||
| t(b) | -0.171 | ||||
| p(b) | 0.568 | ||||
| t(a) | -0.286 | ||||
| p(a) | 0.613 | ||||
| Lowerbound of 95% confidence interval for beta | -0.139 | ||||
| Upperbound of 95% confidence interval for beta | 0.117 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.890 | ||||
| Upperbound of 95% confidence interval for alpha | 0.664 | ||||
| Treynor index (mean / b) | 10.655 | ||||
| Jensen alpha (a) | -0.113 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.071 | ||||
| Expected Shortfall on VaR | 0.087 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 861.000 | ||||
| Minimum | 0.730 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.909 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 47.000 | ||||
| Percentage of outliers low | 0.055 | ||||
| Mean of outliers low | 0.912 | ||||
| Number of outliers high | 40.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.119 | ||||
| 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 | 0.772 | ||||
| Quartile 1 | 0.772 | ||||
| Median | 0.772 | ||||
| Quartile 3 | 0.772 | ||||
| Maximum | 0.772 | ||||
| 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) | -0.066 | ||||
| Compounded annual return (geometric extrapolation) | -0.072 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.093 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.820 | ||||
| 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 | 1.046 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.451 | ||||
| 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 | 0.944 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.449 | ||||
| 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) | -8725811681243490.000 | ||||
| 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) | -1460401431577856822941430904258560.000 | ||||
| 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 | ||||