Let's consider the Mean Square Error of an approximation of a parameter $\theta$ by $\hat{\theta}$.
$$\mathbb{E}(\theta-\hat{\theta})^2=Var(\hat{\theta})+(Bias(\hat{\theta}))^{2}$$
Usually, we say that there is a trade-off between the Variance and the Bias of the estimate, i.e. when the Bias is decreasing the Variance is increasing, and the opposite.
Is it possible to find an estimate that increases both the Variance and Bias?? In that case, we can say that the estimate is totally unworthy?