Advanced Statistics: U0
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 | 0.107 | ||||
| SD | 0.858 | ||||
| Sharpe ratio (Glass type estimate) | 0.125 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.122 | ||||
| df | 31.000 | ||||
| t | 0.204 | ||||
| p | 0.420 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.077 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.325 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.079 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.322 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.217 | ||||
| Upside Potential Ratio | 1.135 | ||||
| Upside part of mean | 0.561 | ||||
| Downside part of mean | -0.454 | ||||
| Upside SD | 0.686 | ||||
| Downside SD | 0.494 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.591 | ||||
| Mean of criterion | 0.107 | ||||
| SD of predictor | 0.262 | ||||
| SD of criterion | 0.858 | ||||
| Covariance | -0.031 | ||||
| r | -0.138 | ||||
| b (slope, estimate of beta) | -0.453 | ||||
| a (intercept, estimate of alpha) | 0.375 | ||||
| Mean Square Error | 0.746 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.764 | ||||
| p(b) | 0.775 | ||||
| t(a) | 0.591 | ||||
| p(a) | 0.279 | ||||
| Lowerbound of 95% confidence interval for beta | -1.664 | ||||
| Upperbound of 95% confidence interval for beta | 0.758 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.921 | ||||
| Upperbound of 95% confidence interval for alpha | 1.671 | ||||
| Treynor index (mean / b) | -0.237 | ||||
| Jensen alpha (a) | 0.375 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.268 | ||||
| SD | 0.939 | ||||
| Sharpe ratio (Glass type estimate) | -0.285 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.278 | ||||
| df | 31.000 | ||||
| t | -0.466 | ||||
| p | 0.678 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.485 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.919 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.481 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.924 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.340 | ||||
| Upside Potential Ratio | 0.520 | ||||
| Upside part of mean | 0.409 | ||||
| Downside part of mean | -0.677 | ||||
| Upside SD | 0.490 | ||||
| Downside SD | 0.787 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 30.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 32.000 | ||||
| Mean of predictor | 0.545 | ||||
| Mean of criterion | -0.268 | ||||
| SD of predictor | 0.250 | ||||
| SD of criterion | 0.939 | ||||
| Covariance | -0.036 | ||||
| r | -0.154 | ||||
| b (slope, estimate of beta) | -0.578 | ||||
| a (intercept, estimate of alpha) | 0.047 | ||||
| Mean Square Error | 0.889 | ||||
| DF error | 30.000 | ||||
| t(b) | -0.853 | ||||
| p(b) | 0.800 | ||||
| t(a) | 0.069 | ||||
| p(a) | 0.473 | ||||
| Lowerbound of 95% confidence interval for beta | -1.963 | ||||
| Upperbound of 95% confidence interval for beta | 0.806 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.353 | ||||
| Upperbound of 95% confidence interval for alpha | 1.448 | ||||
| Treynor index (mean / b) | 0.463 | ||||
| Jensen alpha (a) | 0.047 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.374 | ||||
| Expected Shortfall on VaR | 0.438 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.126 | ||||
| Expected Shortfall on VaR | 0.273 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.311 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.011 | ||||
| Mean of quarter 1 | 0.863 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.188 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.062 | ||||
| Mean of outliers low | 0.450 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.062 | ||||
| Mean of outliers high | 1.751 | ||||
| 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) | -1.564 | ||||
| VaR(95%) (regression method) | 0.602 | ||||
| Expected Shortfall (regression method) | 0.839 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.411 | ||||
| Quartile 1 | 0.480 | ||||
| Median | 0.550 | ||||
| Quartile 3 | 0.619 | ||||
| Maximum | 0.689 | ||||
| Mean of quarter 1 | 0.411 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.689 | ||||
| Inter Quartile Range | 0.139 | ||||
| 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) | -0.169 | ||||
| Compounded annual return (geometric extrapolation) | -0.201 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.291 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.291 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.458 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.117 | ||||
| SD | 0.530 | ||||
| Sharpe ratio (Glass type estimate) | -0.221 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.221 | ||||
| df | 715.000 | ||||
| t | -0.365 | ||||
| p | 0.642 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.406 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.965 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.406 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.965 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.309 | ||||
| Upside Potential Ratio | 2.546 | ||||
| Upside part of mean | 0.965 | ||||
| Downside part of mean | -1.082 | ||||
| Upside SD | 0.369 | ||||
| Downside SD | 0.379 | ||||
| N nonnegative terms | 40.000 | ||||
| N negative terms | 676.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 716.000 | ||||
| Mean of predictor | 0.636 | ||||
| Mean of criterion | -0.117 | ||||
| SD of predictor | 0.325 | ||||
| SD of criterion | 0.530 | ||||
| Covariance | 0.010 | ||||
| r | 0.058 | ||||
| b (slope, estimate of beta) | 0.095 | ||||
| a (intercept, estimate of alpha) | -0.178 | ||||
| Mean Square Error | 0.280 | ||||
| DF error | 714.000 | ||||
| t(b) | 1.564 | ||||
| p(b) | 0.059 | ||||
| t(a) | -0.551 | ||||
| p(a) | 0.709 | ||||
| Lowerbound of 95% confidence interval for beta | -0.024 | ||||
| Upperbound of 95% confidence interval for beta | 0.215 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.811 | ||||
| Upperbound of 95% confidence interval for alpha | 0.455 | ||||
| Treynor index (mean / b) | -1.227 | ||||
| Jensen alpha (a) | -0.178 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.262 | ||||
| SD | 0.548 | ||||
| Sharpe ratio (Glass type estimate) | -0.479 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.479 | ||||
| df | 715.000 | ||||
| t | -0.792 | ||||
| p | 0.786 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.665 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.707 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.664 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.707 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.609 | ||||
| Upside Potential Ratio | 2.096 | ||||
| Upside part of mean | 0.904 | ||||
| Downside part of mean | -1.167 | ||||
| Upside SD | 0.338 | ||||
| Downside SD | 0.431 | ||||
| N nonnegative terms | 40.000 | ||||
| N negative terms | 676.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 716.000 | ||||
| Mean of predictor | 0.582 | ||||
| Mean of criterion | -0.262 | ||||
| SD of predictor | 0.327 | ||||
| SD of criterion | 0.548 | ||||
| Covariance | 0.010 | ||||
| r | 0.055 | ||||
| b (slope, estimate of beta) | 0.092 | ||||
| a (intercept, estimate of alpha) | -0.316 | ||||
| Mean Square Error | 0.300 | ||||
| DF error | 714.000 | ||||
| t(b) | 1.470 | ||||
| p(b) | 0.071 | ||||
| t(a) | -0.949 | ||||
| p(a) | 0.828 | ||||
| Lowerbound of 95% confidence interval for beta | -0.031 | ||||
| Upperbound of 95% confidence interval for beta | 0.215 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.970 | ||||
| Upperbound of 95% confidence interval for alpha | 0.338 | ||||
| Treynor index (mean / b) | -2.855 | ||||
| Jensen alpha (a) | -0.316 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.055 | ||||
| Expected Shortfall on VaR | 0.068 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 716.000 | ||||
| Minimum | 0.627 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.297 | ||||
| Mean of quarter 1 | 0.984 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.015 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 41.000 | ||||
| Percentage of outliers low | 0.057 | ||||
| Mean of outliers low | 0.931 | ||||
| Number of outliers high | 41.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.064 | ||||
| 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) | -0.082 | ||||
| VaR(95%) (regression method) | 0.009 | ||||
| Expected Shortfall (regression method) | 0.058 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.081 | ||||
| Quartile 1 | 0.209 | ||||
| Median | 0.338 | ||||
| Quartile 3 | 0.501 | ||||
| Maximum | 0.730 | ||||
| Mean of quarter 1 | 0.081 | ||||
| Mean of quarter 2 | 0.251 | ||||
| Mean of quarter 3 | 0.425 | ||||
| Mean of quarter 4 | 0.730 | ||||
| Inter Quartile Range | 0.292 | ||||
| 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) | -0.164 | ||||
| Compounded annual return (geometric extrapolation) | -0.196 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.269 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.269 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.874 | ||||
| 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 | 1.051 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.446 | ||||
| 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 | 0.950 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.447 | ||||
| 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) | -8724283826205143.000 | ||||
| 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) | -527035714875620536409143606509568.000 | ||||
| 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 | ||||