Advanced Statistics: Test 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 | -0.351 | ||||
| SD | 0.423 | ||||
| Sharpe ratio (Glass type estimate) | -0.829 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.815 | ||||
| df | 44.000 | ||||
| t | -1.606 | ||||
| p | 0.942 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.851 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.202 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.841 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.211 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.821 | ||||
| Upside Potential Ratio | 0.069 | ||||
| Upside part of mean | 0.029 | ||||
| Downside part of mean | -0.381 | ||||
| Upside SD | 0.052 | ||||
| Downside SD | 0.428 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.431 | ||||
| Mean of criterion | -0.351 | ||||
| SD of predictor | 0.258 | ||||
| SD of criterion | 0.423 | ||||
| Covariance | 0.007 | ||||
| r | 0.063 | ||||
| b (slope, estimate of beta) | 0.103 | ||||
| a (intercept, estimate of alpha) | -0.395 | ||||
| Mean Square Error | 0.183 | ||||
| DF error | 43.000 | ||||
| t(b) | 0.412 | ||||
| p(b) | 0.341 | ||||
| t(a) | -1.611 | ||||
| p(a) | 0.943 | ||||
| Lowerbound of 95% confidence interval for beta | -0.400 | ||||
| Upperbound of 95% confidence interval for beta | 0.606 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.891 | ||||
| Upperbound of 95% confidence interval for alpha | 0.100 | ||||
| Treynor index (mean / b) | -3.415 | ||||
| Jensen alpha (a) | -0.395 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.507 | ||||
| SD | 0.631 | ||||
| Sharpe ratio (Glass type estimate) | -0.803 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.789 | ||||
| df | 44.000 | ||||
| t | -1.554 | ||||
| p | 0.936 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.824 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.228 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.814 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.237 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.793 | ||||
| Upside Potential Ratio | 0.044 | ||||
| Upside part of mean | 0.028 | ||||
| Downside part of mean | -0.535 | ||||
| Upside SD | 0.049 | ||||
| Downside SD | 0.639 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 43.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.392 | ||||
| Mean of criterion | -0.507 | ||||
| SD of predictor | 0.247 | ||||
| SD of criterion | 0.631 | ||||
| Covariance | 0.009 | ||||
| r | 0.057 | ||||
| b (slope, estimate of beta) | 0.147 | ||||
| a (intercept, estimate of alpha) | -0.564 | ||||
| Mean Square Error | 0.407 | ||||
| DF error | 43.000 | ||||
| t(b) | 0.377 | ||||
| p(b) | 0.354 | ||||
| t(a) | -1.555 | ||||
| p(a) | 0.936 | ||||
| Lowerbound of 95% confidence interval for beta | -0.637 | ||||
| Upperbound of 95% confidence interval for beta | 0.930 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.296 | ||||
| Upperbound of 95% confidence interval for alpha | 0.167 | ||||
| Treynor index (mean / b) | -3.457 | ||||
| Jensen alpha (a) | -0.564 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.290 | ||||
| Expected Shortfall on VaR | 0.340 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.107 | ||||
| Expected Shortfall on VaR | 0.232 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 45.000 | ||||
| Minimum | 0.381 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.104 | ||||
| Mean of quarter 1 | 0.894 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.111 | ||||
| Mean of outliers low | 0.746 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.044 | ||||
| Mean of outliers high | 1.059 | ||||
| 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) | 0.977 | ||||
| VaR(95%) (regression method) | 0.079 | ||||
| Expected Shortfall (regression method) | 5.584 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.824 | ||||
| Quartile 1 | 0.824 | ||||
| Median | 0.824 | ||||
| Quartile 3 | 0.824 | ||||
| Maximum | 0.824 | ||||
| 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) | -0.220 | ||||
| Compounded annual return (geometric extrapolation) | -0.370 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.450 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.089 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.303 | ||||
| SD | 0.628 | ||||
| Sharpe ratio (Glass type estimate) | -0.483 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.482 | ||||
| df | 992.000 | ||||
| t | -0.940 | ||||
| p | 0.826 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.490 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.524 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.489 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.525 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.683 | ||||
| Upside Potential Ratio | 1.938 | ||||
| Upside part of mean | 0.861 | ||||
| Downside part of mean | -1.164 | ||||
| Upside SD | 0.444 | ||||
| Downside SD | 0.444 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 947.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 993.000 | ||||
| Mean of predictor | 0.475 | ||||
| Mean of criterion | -0.303 | ||||
| SD of predictor | 0.337 | ||||
| SD of criterion | 0.628 | ||||
| Covariance | 0.031 | ||||
| r | 0.147 | ||||
| b (slope, estimate of beta) | 0.273 | ||||
| a (intercept, estimate of alpha) | -0.433 | ||||
| Mean Square Error | 0.387 | ||||
| DF error | 991.000 | ||||
| t(b) | 4.665 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.351 | ||||
| p(a) | 0.912 | ||||
| Lowerbound of 95% confidence interval for beta | 0.158 | ||||
| Upperbound of 95% confidence interval for beta | 0.388 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.062 | ||||
| Upperbound of 95% confidence interval for alpha | 0.196 | ||||
| Treynor index (mean / b) | -1.110 | ||||
| Jensen alpha (a) | -0.433 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.502 | ||||
| SD | 0.636 | ||||
| Sharpe ratio (Glass type estimate) | -0.790 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.789 | ||||
| df | 992.000 | ||||
| t | -1.537 | ||||
| p | 0.938 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.797 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.218 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.796 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.218 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.988 | ||||
| Upside Potential Ratio | 1.535 | ||||
| Upside part of mean | 0.780 | ||||
| Downside part of mean | -1.282 | ||||
| Upside SD | 0.383 | ||||
| Downside SD | 0.508 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 947.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 993.000 | ||||
| Mean of predictor | 0.417 | ||||
| Mean of criterion | -0.502 | ||||
| SD of predictor | 0.343 | ||||
| SD of criterion | 0.636 | ||||
| Covariance | 0.031 | ||||
| r | 0.140 | ||||
| b (slope, estimate of beta) | 0.260 | ||||
| a (intercept, estimate of alpha) | -0.610 | ||||
| Mean Square Error | 0.396 | ||||
| DF error | 991.000 | ||||
| t(b) | 4.461 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.882 | ||||
| p(a) | 0.970 | ||||
| Lowerbound of 95% confidence interval for beta | 0.146 | ||||
| Upperbound of 95% confidence interval for beta | 0.375 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.247 | ||||
| Upperbound of 95% confidence interval for alpha | 0.026 | ||||
| Treynor index (mean / b) | -1.929 | ||||
| Jensen alpha (a) | -0.610 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.064 | ||||
| Expected Shortfall on VaR | 0.079 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 993.000 | ||||
| Minimum | 0.664 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.478 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 48.000 | ||||
| Percentage of outliers low | 0.048 | ||||
| Mean of outliers low | 0.911 | ||||
| Number of outliers high | 46.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.071 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.376 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.056 | ||||
| VaR(95%) (regression method) | -0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.013 | ||||
| Quartile 1 | 0.029 | ||||
| Median | 0.044 | ||||
| Quartile 3 | 0.442 | ||||
| Maximum | 0.839 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | 0.044 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.839 | ||||
| Inter Quartile Range | 0.413 | ||||
| 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) | -0.217 | ||||
| Compounded annual return (geometric extrapolation) | -0.367 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.438 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.438 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.622 | ||||
| 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 | 0.376 | ||||
| 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 | 1.329 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.376 | ||||
| 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) | -8595328726682286.000 | ||||
| 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) | 115390330839476483397136418865152.000 | ||||
| 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 | ||||