Government-sponsored inquiries into trustee competence, and legislation regarding the protocols and practice of trustee decision making, have raised questions about the competence of trustees to make investment decisions consistent with the long-term interest of defined benefit pension plan beneficiaries. In this paper, we report the results of an analysis of trustee competence in solving problems relevant to their investment responsibilities. Based upon a set of widely recognized problems drawn from the psychology literature, we assess their discount functions, their willingness to risk their own money and others' money, their appreciation of probability, and their use of evidence to solve problems. For comparison, where appropriate we report the results of the same testing regime applied to a group of Oxford undergraduates. Our goals are fourfold: first, to demonstrate the nature of trustee competence in decision making; second, to demonstrate the range of trustee responses to problems relevant to investment; third, to assess trustees' risk appetites in relation to their own and others' money; and fourth, to draw implications from these results for the governance of trustee boards and their relationships with advisers and service providers. It is shown that trustee competence is surprisingly heterogeneous, and the lack of common approaches to problems relevant to investment practice has significant implications for fund governance.