This paper deals with performance assessment of decentralized controllers using a minimum variance (MV) benchmark. The available MV benchmarks do not take the structure of the controller into account and can give overly optimistic estimates of achievable performance, when applied to systems under decentralized control. We propose an approximate solution to this problem obtained by explicitly solving simple linear matrix equations. As a special case of this general result, we also present an upper bound on the achievable performance for systems under multi-loop proportional-integral-derivative control. These results are useful for assessing the feasibility of significant performance improvement by retuning the decentralized controller and input-output pairing selection.