Many financial institutions employ outside portfolio managers to manage part or all of their investable assets. These institutions include pension funds, private endowments (e.g., colleges and charities), and private trusts. Pension funds are the largest and most likely organizations to employ several outside managers, each of whom manages a part of the overall portfolio. In this paper we will use the pension fund manager as the prototype of the centralized decision-maker trying to optimally manage a set of decentralized decision-makers but the analysts is general. If the centralized decision-maker (CDM) is a mean variance maximizer, the CDM could construct a portfolio using standard portfolio theory and estimates of mean return, variances, and covariances between the portfolios constructed by a group of decentralized managers. However, this overall portfolio is unlikely to be optimum since the individually managed portfolios themselves were constructed without taking into account the portfolios of the other managers. The purpose of this article is to set up a structure that leads to the optimum portfolio from the viewpoint of the CDM when there are multiple managers and their portfolios are constructed without reference to each other.
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