Advanced Statistics: System Fx2
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.471 | ||||
| SD | 1.173 | ||||
| Sharpe ratio (Glass type estimate) | -0.402 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.395 | ||||
| df | 44.000 | ||||
| t | -0.778 | ||||
| p | 0.780 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.415 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.616 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.410 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.620 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.520 | ||||
| Upside Potential Ratio | 0.719 | ||||
| Upside part of mean | 0.652 | ||||
| Downside part of mean | -1.124 | ||||
| Upside SD | 0.736 | ||||
| Downside SD | 0.907 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.507 | ||||
| Mean of criterion | -0.471 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 1.173 | ||||
| Covariance | 0.114 | ||||
| r | 0.349 | ||||
| b (slope, estimate of beta) | 1.464 | ||||
| a (intercept, estimate of alpha) | -1.214 | ||||
| Mean Square Error | 1.237 | ||||
| DF error | 43.000 | ||||
| t(b) | 2.440 | ||||
| p(b) | 0.009 | ||||
| t(a) | -1.868 | ||||
| p(a) | 0.966 | ||||
| Lowerbound of 95% confidence interval for beta | 0.254 | ||||
| Upperbound of 95% confidence interval for beta | 2.673 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.524 | ||||
| Upperbound of 95% confidence interval for alpha | 0.097 | ||||
| Treynor index (mean / b) | -0.322 | ||||
| Jensen alpha (a) | -1.214 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.114 | ||||
| SD | 3.951 | ||||
| Sharpe ratio (Glass type estimate) | -0.788 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.775 | ||||
| df | 44.000 | ||||
| t | -1.526 | ||||
| p | 0.933 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.809 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.242 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.800 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.250 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.784 | ||||
| Upside Potential Ratio | 0.120 | ||||
| Upside part of mean | 0.478 | ||||
| Downside part of mean | -3.592 | ||||
| Upside SD | 0.525 | ||||
| Downside SD | 3.974 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.460 | ||||
| Mean of criterion | -3.114 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 3.951 | ||||
| Covariance | 0.192 | ||||
| r | 0.180 | ||||
| b (slope, estimate of beta) | 2.629 | ||||
| a (intercept, estimate of alpha) | -4.322 | ||||
| Mean Square Error | 15.458 | ||||
| DF error | 43.000 | ||||
| t(b) | 1.198 | ||||
| p(b) | 0.119 | ||||
| t(a) | -1.907 | ||||
| p(a) | 0.968 | ||||
| Lowerbound of 95% confidence interval for beta | -1.796 | ||||
| Upperbound of 95% confidence interval for beta | 7.053 | ||||
| Lowerbound of 95% confidence interval for alpha | -8.894 | ||||
| Upperbound of 95% confidence interval for alpha | 0.249 | ||||
| Treynor index (mean / b) | -1.185 | ||||
| Jensen alpha (a) | -4.322 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.882 | ||||
| Expected Shortfall on VaR | 0.921 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.308 | ||||
| Expected Shortfall on VaR | 0.631 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 45.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.028 | ||||
| Mean of quarter 1 | 0.661 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.224 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.178 | ||||
| Mean of outliers low | 0.492 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.089 | ||||
| Mean of outliers high | 1.615 | ||||
| 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) | -1.103 | ||||
| VaR(95%) (regression method) | 0.690 | ||||
| Expected Shortfall (regression method) | 0.793 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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) | -0.267 | ||||
| Compounded annual return (geometric extrapolation) | -0.954 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.954 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.035 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 196.479 | ||||
| SD | 382.041 | ||||
| Sharpe ratio (Glass type estimate) | 0.514 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.514 | ||||
| df | 986.000 | ||||
| t | 0.998 | ||||
| p | 0.159 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.496 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.524 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.496 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.524 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 154.673 | ||||
| Upside Potential Ratio | 158.106 | ||||
| Upside part of mean | 200.839 | ||||
| Downside part of mean | -4.360 | ||||
| Upside SD | 382.038 | ||||
| Downside SD | 1.270 | ||||
| N nonnegative terms | 118.000 | ||||
| N negative terms | 869.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 987.000 | ||||
| Mean of predictor | 0.528 | ||||
| Mean of criterion | 196.479 | ||||
| SD of predictor | 0.327 | ||||
| SD of criterion | 382.041 | ||||
| Covariance | 1.444 | ||||
| r | 0.012 | ||||
| b (slope, estimate of beta) | 13.527 | ||||
| a (intercept, estimate of alpha) | 189.336 | ||||
| Mean Square Error | 146083.938 | ||||
| DF error | 985.000 | ||||
| t(b) | 0.363 | ||||
| p(b) | 0.358 | ||||
| t(a) | 0.957 | ||||
| p(a) | 0.169 | ||||
| Lowerbound of 95% confidence interval for beta | -59.592 | ||||
| Upperbound of 95% confidence interval for beta | 86.645 | ||||
| Lowerbound of 95% confidence interval for alpha | -199.022 | ||||
| Upperbound of 95% confidence interval for alpha | 577.694 | ||||
| Treynor index (mean / b) | 14.525 | ||||
| Jensen alpha (a) | 189.336 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.100 | ||||
| SD | 6.036 | ||||
| Sharpe ratio (Glass type estimate) | -0.514 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.513 | ||||
| df | 986.000 | ||||
| t | -0.997 | ||||
| p | 0.840 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.524 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.497 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.523 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.497 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.636 | ||||
| Upside Potential Ratio | 1.038 | ||||
| Upside part of mean | 5.057 | ||||
| Downside part of mean | -8.157 | ||||
| Upside SD | 3.564 | ||||
| Downside SD | 4.871 | ||||
| N nonnegative terms | 118.000 | ||||
| N negative terms | 869.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 987.000 | ||||
| Mean of predictor | 0.474 | ||||
| Mean of criterion | -3.100 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 6.036 | ||||
| Covariance | 0.130 | ||||
| r | 0.066 | ||||
| b (slope, estimate of beta) | 1.203 | ||||
| a (intercept, estimate of alpha) | -3.670 | ||||
| Mean Square Error | 36.310 | ||||
| DF error | 985.000 | ||||
| t(b) | 2.060 | ||||
| p(b) | 0.020 | ||||
| t(a) | -1.177 | ||||
| p(a) | 0.880 | ||||
| Lowerbound of 95% confidence interval for beta | 0.057 | ||||
| Upperbound of 95% confidence interval for beta | 2.348 | ||||
| Lowerbound of 95% confidence interval for alpha | -9.787 | ||||
| Upperbound of 95% confidence interval for alpha | 2.447 | ||||
| Treynor index (mean / b) | -2.578 | ||||
| Jensen alpha (a) | -3.670 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.465 | ||||
| Expected Shortfall on VaR | 0.538 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.053 | ||||
| Expected Shortfall on VaR | 0.119 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 987.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 742.500 | ||||
| Mean of quarter 1 | 0.934 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 4.063 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 122.000 | ||||
| Percentage of outliers low | 0.124 | ||||
| Mean of outliers low | 0.867 | ||||
| Number of outliers high | 118.000 | ||||
| Percentage of outliers high | 0.120 | ||||
| Mean of outliers high | 7.412 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.710 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.083 | ||||
| VaR(95%) (regression method) | 0.059 | ||||
| Expected Shortfall (regression method) | 0.134 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.066 | ||||
| Median | 0.071 | ||||
| Quartile 3 | 0.072 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.034 | ||||
| Mean of quarter 2 | 0.071 | ||||
| Mean of quarter 3 | 0.072 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.006 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.200 | ||||
| Mean of outliers low | 0.002 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| Mean of outliers high | 1.000 | ||||
| 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) | -0.265 | ||||
| Compounded annual return (geometric extrapolation) | -0.953 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.953 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.953 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.772 | ||||
| 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 | 1.413 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.356 | ||||
| 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 | 1.347 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.354 | ||||
| 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) | -8564720647791684.000 | ||||
| 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) | -160911748187581334279312396779520.000 | ||||
| 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 | ||||