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Using the asymmetric LINEX loss function, we derive and numerically evaluate the exact risk function of the almost unbiased feasible generalized ridge regression estimator. Contrary to the properties of the (biased) feasible generalized ridge estimator, it is found that regardless of the loss asymmetry,the almost unbiased feasible generalized ridge estimator does not strictly dominate the traditional least squares estimator. Our numerical results show that over a wide range of parameter values, the almost unbiased feasible generalized ridge estimator is inferior to either the least squares or the feasible generalized ridge estimators.