Advanced Statistics: System 30091398
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 | 0.056 | ||||
| SD | 0.493 | ||||
| Sharpe ratio (Glass type estimate) | 0.113 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.112 | ||||
| df | 68.000 | ||||
| t | 0.272 | ||||
| p | 0.393 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.705 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.931 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.705 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.930 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.203 | ||||
| Upside Potential Ratio | 0.777 | ||||
| Upside part of mean | 0.214 | ||||
| Downside part of mean | -0.158 | ||||
| Upside SD | 0.405 | ||||
| Downside SD | 0.275 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 69.000 | ||||
| Mean of predictor | 0.261 | ||||
| Mean of criterion | 0.056 | ||||
| SD of predictor | 0.288 | ||||
| SD of criterion | 0.493 | ||||
| Covariance | 0.010 | ||||
| r | 0.069 | ||||
| b (slope, estimate of beta) | 0.118 | ||||
| a (intercept, estimate of alpha) | 0.025 | ||||
| Mean Square Error | 0.245 | ||||
| DF error | 67.000 | ||||
| t(b) | 0.567 | ||||
| p(b) | 0.286 | ||||
| t(a) | 0.117 | ||||
| p(a) | 0.454 | ||||
| Lowerbound of 95% confidence interval for beta | -0.298 | ||||
| Upperbound of 95% confidence interval for beta | 0.535 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.401 | ||||
| Upperbound of 95% confidence interval for alpha | 0.451 | ||||
| Treynor index (mean / b) | 0.472 | ||||
| Jensen alpha (a) | 0.025 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.067 | ||||
| SD | 0.533 | ||||
| Sharpe ratio (Glass type estimate) | -0.126 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.125 | ||||
| df | 68.000 | ||||
| t | -0.303 | ||||
| p | 0.619 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.944 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.692 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.943 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.693 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.151 | ||||
| Upside Potential Ratio | 0.363 | ||||
| Upside part of mean | 0.162 | ||||
| Downside part of mean | -0.229 | ||||
| Upside SD | 0.285 | ||||
| Downside SD | 0.446 | ||||
| N nonnegative terms | 12.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 69.000 | ||||
| Mean of predictor | 0.217 | ||||
| Mean of criterion | -0.067 | ||||
| SD of predictor | 0.288 | ||||
| SD of criterion | 0.533 | ||||
| Covariance | 0.014 | ||||
| r | 0.092 | ||||
| b (slope, estimate of beta) | 0.170 | ||||
| a (intercept, estimate of alpha) | -0.104 | ||||
| Mean Square Error | 0.286 | ||||
| DF error | 67.000 | ||||
| t(b) | 0.757 | ||||
| p(b) | 0.226 | ||||
| t(a) | -0.457 | ||||
| p(a) | 0.676 | ||||
| Lowerbound of 95% confidence interval for beta | -0.279 | ||||
| Upperbound of 95% confidence interval for beta | 0.619 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.560 | ||||
| Upperbound of 95% confidence interval for alpha | 0.351 | ||||
| Treynor index (mean / b) | -0.395 | ||||
| Jensen alpha (a) | -0.104 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.228 | ||||
| Expected Shortfall on VaR | 0.275 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.041 | ||||
| Expected Shortfall on VaR | 0.092 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 69.000 | ||||
| Minimum | 0.345 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.964 | ||||
| Mean of quarter 1 | 0.961 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.075 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.072 | ||||
| Mean of outliers low | 0.860 | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.217 | ||||
| Mean of outliers high | 1.085 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.106 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 2.670 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.655 | ||||
| Quartile 1 | 0.655 | ||||
| Median | 0.655 | ||||
| Quartile 3 | 0.655 | ||||
| Maximum | 0.655 | ||||
| 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) | -0.022 | ||||
| Compounded annual return (geometric extrapolation) | -0.023 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.035 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.084 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 1.368 | ||||
| SD | 2.065 | ||||
| Sharpe ratio (Glass type estimate) | 0.663 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.662 | ||||
| df | 1527.000 | ||||
| t | 1.600 | ||||
| p | 0.474 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.149 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.474 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.150 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.474 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.789 | ||||
| Upside Potential Ratio | 3.539 | ||||
| Upside part of mean | 2.705 | ||||
| Downside part of mean | -1.337 | ||||
| Upside SD | 1.919 | ||||
| Downside SD | 0.764 | ||||
| N nonnegative terms | 176.000 | ||||
| N negative terms | 1352.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1528.000 | ||||
| Mean of predictor | 0.400 | ||||
| Mean of criterion | 1.368 | ||||
| SD of predictor | 0.551 | ||||
| SD of criterion | 2.065 | ||||
| Covariance | 0.039 | ||||
| r | 0.034 | ||||
| b (slope, estimate of beta) | 0.128 | ||||
| a (intercept, estimate of alpha) | 1.317 | ||||
| Mean Square Error | 4.262 | ||||
| DF error | 1526.000 | ||||
| t(b) | 1.338 | ||||
| p(b) | 0.483 | ||||
| t(a) | 1.539 | ||||
| p(a) | 0.480 | ||||
| Lowerbound of 95% confidence interval for beta | -0.060 | ||||
| Upperbound of 95% confidence interval for beta | 0.316 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.362 | ||||
| Upperbound of 95% confidence interval for alpha | 2.995 | ||||
| Treynor index (mean / b) | 10.660 | ||||
| Jensen alpha (a) | 1.317 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.067 | ||||
| SD | 1.656 | ||||
| Sharpe ratio (Glass type estimate) | -0.040 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.040 | ||||
| df | 1527.000 | ||||
| t | -0.098 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.852 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.771 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.852 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.771 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.055 | ||||
| Upside Potential Ratio | 1.491 | ||||
| Upside part of mean | 1.802 | ||||
| Downside part of mean | -1.869 | ||||
| Upside SD | 1.132 | ||||
| Downside SD | 1.208 | ||||
| N nonnegative terms | 176.000 | ||||
| N negative terms | 1352.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1528.000 | ||||
| Mean of predictor | 0.248 | ||||
| Mean of criterion | -0.067 | ||||
| SD of predictor | 0.553 | ||||
| SD of criterion | 1.656 | ||||
| Covariance | 0.030 | ||||
| r | 0.033 | ||||
| b (slope, estimate of beta) | 0.098 | ||||
| a (intercept, estimate of alpha) | -0.091 | ||||
| Mean Square Error | 2.743 | ||||
| DF error | 1526.000 | ||||
| t(b) | 1.276 | ||||
| p(b) | 0.484 | ||||
| t(a) | -0.133 | ||||
| p(a) | 0.502 | ||||
| Lowerbound of 95% confidence interval for beta | -0.053 | ||||
| Upperbound of 95% confidence interval for beta | 0.248 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.437 | ||||
| Upperbound of 95% confidence interval for alpha | 1.254 | ||||
| Treynor index (mean / b) | -0.686 | ||||
| Jensen alpha (a) | -0.091 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.155 | ||||
| Expected Shortfall on VaR | 0.190 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1528.000 | ||||
| Minimum | 0.243 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 3.476 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.041 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 165.000 | ||||
| Percentage of outliers low | 0.108 | ||||
| Mean of outliers low | 0.954 | ||||
| Number of outliers high | 201.000 | ||||
| Percentage of outliers high | 0.132 | ||||
| Mean of outliers high | 1.079 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.049 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.650 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.234 | ||||
| Quartile 1 | 0.402 | ||||
| Median | 0.570 | ||||
| Quartile 3 | 0.714 | ||||
| Maximum | 0.858 | ||||
| Mean of quarter 1 | 0.292 | ||||
| Mean of quarter 2 | 0.555 | ||||
| Mean of quarter 3 | 0.584 | ||||
| Mean of quarter 4 | 0.808 | ||||
| Inter Quartile Range | 0.312 | ||||
| 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) | -0.022 | ||||
| Compounded annual return (geometric extrapolation) | -0.023 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.026 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.028 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.120 | ||||
| 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 | 1.103 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.496 | ||||
| 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 | 0.981 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.487 | ||||
| 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) | -8732006557549866.000 | ||||
| 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) | 2299015633585630539155314428608512.000 | ||||
| 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 | ||||