Approximate portfolio analysis

This paper presents a portfolio selection model based on the idea of approximation. The model describes a portfolio by its decumulative distribution curve and a preference structure by a family of convex indi€erence curves. It prescribes the optimal portfolio as the one whose decumulative curve has the highest tangent indi€erence curve. The model extends the mean±variance model in the sense that it does not restrict the return distributions of assets to be normal. While under the assumption of normality, the model simpli®es to the mean±variance model. The model has a measure of risk attitudes that resembles the Arrow±Pratt measure while combining both wealth and probability attitudes. Using this measure, we show that the smaller the curvature of a value function and the larger the curvature of a weighting function, the more risk averse an agent. Ó 1999 Elsevier Science B.V. All rights reserved.