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 indifference curves. It prescribes the optimal portfolio as the one whose decumulative curve has the highest tangent indifference 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 simplifies 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.