Using Portfolio Theory to Design Better Exams

Abstract

The mathematics behind many psychometric measures is similar to the mathematics in portfolio theory. Faculty often build exams based on judgment and experience and only use psychometric tools after an exam is administered. An obvious question is, can portfolio optimization models be used to design exams with desirable psychometric outcomes and content coverage? Although underlying variables (stock returns versus exam question scores) differ fundamentally, a portfolio approach to exam development can be used. The objective functions and underlying constraints will differ, but many faculty can readily apply the principles of portfolio theory to design more optimal exams. In this paper we contrast the objectives and mechanics of portfolio and exam development and use an integer programming model to develop the optimal set of exam questions given a realistic example.