Portfolio Theory for Independent Assets

This paper presents several new concepts for portfolio problems with independently distributed asset prices. A criterion is developed for including or excluding assets in an optimal portfolio for an investor maximizing the expected value of a von Neumann–Morgenstern utility function. The central concept of the generalized harmonic mean is introduced: it is shown to be the analogue of the riskless rate of return for problems without a riskless asset. A new ordering theorem is proven, showing that an optimal portfolio always consists of positive amounts of the assets with the largest mean values. Next, the concept of independence from irrelevant alternatives is introduced for portfolio problems; this is a property of utility functions and is proven to be true for most of the commonly used utility functions. Altogether, the results provide new insights and tools for portfolio problems with independent assets and extend earlier results by Samuelson, and Fishburn and Porter.