Advanced Statistics: ZK
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 | -0.170 | ||||
| SD | 0.674 | ||||
| Sharpe ratio (Glass type estimate) | -0.252 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.246 | ||||
| df | 33.000 | ||||
| t | -0.424 | ||||
| p | 0.663 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.416 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.916 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.412 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.920 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.280 | ||||
| Upside Potential Ratio | 0.504 | ||||
| Upside part of mean | 0.306 | ||||
| Downside part of mean | -0.476 | ||||
| Upside SD | 0.273 | ||||
| Downside SD | 0.607 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.568 | ||||
| Mean of criterion | -0.170 | ||||
| SD of predictor | 0.402 | ||||
| SD of criterion | 0.674 | ||||
| Covariance | 0.021 | ||||
| r | 0.077 | ||||
| b (slope, estimate of beta) | 0.130 | ||||
| a (intercept, estimate of alpha) | -0.244 | ||||
| Mean Square Error | 0.466 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.439 | ||||
| p(b) | 0.332 | ||||
| t(a) | -0.555 | ||||
| p(a) | 0.709 | ||||
| Lowerbound of 95% confidence interval for beta | -0.472 | ||||
| Upperbound of 95% confidence interval for beta | 0.732 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.138 | ||||
| Upperbound of 95% confidence interval for alpha | 0.651 | ||||
| Treynor index (mean / b) | -1.307 | ||||
| Jensen alpha (a) | -0.244 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -3.050 | ||||
| SD | 5.392 | ||||
| Sharpe ratio (Glass type estimate) | -0.566 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.553 | ||||
| df | 33.000 | ||||
| t | -0.952 | ||||
| p | 0.826 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.734 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.611 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.725 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.619 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.567 | ||||
| Upside Potential Ratio | 0.051 | ||||
| Upside part of mean | 0.273 | ||||
| Downside part of mean | -3.324 | ||||
| Upside SD | 0.241 | ||||
| Downside SD | 5.379 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.488 | ||||
| Mean of criterion | -3.050 | ||||
| SD of predictor | 0.358 | ||||
| SD of criterion | 5.392 | ||||
| Covariance | 0.195 | ||||
| r | 0.101 | ||||
| b (slope, estimate of beta) | 1.522 | ||||
| a (intercept, estimate of alpha) | -3.793 | ||||
| Mean Square Error | 29.672 | ||||
| DF error | 32.000 | ||||
| t(b) | 0.575 | ||||
| p(b) | 0.285 | ||||
| t(a) | -1.089 | ||||
| p(a) | 0.858 | ||||
| Lowerbound of 95% confidence interval for beta | -3.872 | ||||
| Upperbound of 95% confidence interval for beta | 6.916 | ||||
| Lowerbound of 95% confidence interval for alpha | -10.892 | ||||
| Upperbound of 95% confidence interval for alpha | 3.305 | ||||
| Treynor index (mean / b) | -2.004 | ||||
| Jensen alpha (a) | -3.793 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.940 | ||||
| Expected Shortfall on VaR | 0.964 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.125 | ||||
| Expected Shortfall on VaR | 0.277 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.313 | ||||
| Mean of quarter 1 | 0.862 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.098 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.147 | ||||
| Mean of outliers low | 0.752 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.147 | ||||
| Mean of outliers high | 1.177 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.343 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 2.561 | ||||
| VaR(95%) (regression method) | 0.098 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.227 | ||||
| Quartile 1 | 0.421 | ||||
| Median | 0.614 | ||||
| Quartile 3 | 0.807 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.227 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.386 | ||||
| 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) | -0.353 | ||||
| Compounded annual return (geometric extrapolation) | -0.951 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.951 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.951 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.986 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.094 | ||||
| SD | 0.746 | ||||
| Sharpe ratio (Glass type estimate) | -0.126 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.126 | ||||
| df | 759.000 | ||||
| t | -0.215 | ||||
| p | 0.585 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.277 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.024 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.277 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.025 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.140 | ||||
| Upside Potential Ratio | 1.603 | ||||
| Upside part of mean | 1.077 | ||||
| Downside part of mean | -1.171 | ||||
| Upside SD | 0.323 | ||||
| Downside SD | 0.672 | ||||
| N nonnegative terms | 77.000 | ||||
| N negative terms | 683.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 760.000 | ||||
| Mean of predictor | 0.584 | ||||
| Mean of criterion | -0.094 | ||||
| SD of predictor | 0.326 | ||||
| SD of criterion | 0.746 | ||||
| Covariance | 0.005 | ||||
| r | 0.021 | ||||
| b (slope, estimate of beta) | 0.049 | ||||
| a (intercept, estimate of alpha) | -0.123 | ||||
| Mean Square Error | 0.557 | ||||
| DF error | 758.000 | ||||
| t(b) | 0.589 | ||||
| p(b) | 0.278 | ||||
| t(a) | -0.279 | ||||
| p(a) | 0.610 | ||||
| Lowerbound of 95% confidence interval for beta | -0.114 | ||||
| Upperbound of 95% confidence interval for beta | 0.212 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.988 | ||||
| Upperbound of 95% confidence interval for alpha | 0.742 | ||||
| Treynor index (mean / b) | -1.926 | ||||
| Jensen alpha (a) | -0.123 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.980 | ||||
| SD | 5.334 | ||||
| Sharpe ratio (Glass type estimate) | -0.559 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.558 | ||||
| df | 759.000 | ||||
| t | -0.952 | ||||
| p | 0.829 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.710 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.593 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.709 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.593 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.560 | ||||
| Upside Potential Ratio | 0.193 | ||||
| Upside part of mean | 1.029 | ||||
| Downside part of mean | -4.009 | ||||
| Upside SD | 0.304 | ||||
| Downside SD | 5.325 | ||||
| N nonnegative terms | 77.000 | ||||
| N negative terms | 683.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 760.000 | ||||
| Mean of predictor | 0.530 | ||||
| Mean of criterion | -2.980 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 5.334 | ||||
| Covariance | 0.064 | ||||
| r | 0.036 | ||||
| b (slope, estimate of beta) | 0.586 | ||||
| a (intercept, estimate of alpha) | -3.291 | ||||
| Mean Square Error | 28.457 | ||||
| DF error | 758.000 | ||||
| t(b) | 0.997 | ||||
| p(b) | 0.160 | ||||
| t(a) | -1.046 | ||||
| p(a) | 0.852 | ||||
| Lowerbound of 95% confidence interval for beta | -0.568 | ||||
| Upperbound of 95% confidence interval for beta | 1.741 | ||||
| Lowerbound of 95% confidence interval for alpha | -9.470 | ||||
| Upperbound of 95% confidence interval for alpha | 2.888 | ||||
| Treynor index (mean / b) | -5.082 | ||||
| Jensen alpha (a) | -3.291 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.425 | ||||
| Expected Shortfall on VaR | 0.495 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 760.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.186 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 52.000 | ||||
| Percentage of outliers low | 0.068 | ||||
| Mean of outliers low | 0.937 | ||||
| Number of outliers high | 77.000 | ||||
| Percentage of outliers high | 0.101 | ||||
| Mean of outliers high | 1.041 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.814 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.154 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 14.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.019 | ||||
| Quartile 3 | 0.071 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.008 | ||||
| Mean of quarter 3 | 0.033 | ||||
| Mean of quarter 4 | 0.433 | ||||
| Inter Quartile Range | 0.067 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.214 | ||||
| Mean of outliers high | 0.551 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.632 | ||||
| VaR(95%) (moments method) | 0.270 | ||||
| Expected Shortfall (moments method) | 0.273 | ||||
| Extreme Value Index (regression method) | 0.221 | ||||
| VaR(95%) (regression method) | 0.838 | ||||
| Expected Shortfall (regression method) | 1.533 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.345 | ||||
| Compounded annual return (geometric extrapolation) | -0.947 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.947 | ||||
| Compounded annual return / average of 25% largest draw downs | -2.185 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.911 | ||||
| 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 | 1.145 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.497 | ||||
| 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 | 1.020 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.497 | ||||
| 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) | -8729336888687865.000 | ||||
| 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) | 123534731860284780410087566999552.000 | ||||
| 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 | ||||