Log-Linear Relative Asset Demand

This paper studies the theoretical underpinnings of log-linear models of relative asset demand. It shows that log-linearity provides a poor approximation - in both a global and local sense - to asset demand functions implied by standard portfolio optimization theory. Instead, log-linearity is consistent with a model of portfolio choice in which the investor views the payoffs of different assets, within any state of the world, as being imperfectly substitutable. Equilibria in this model, and all other models that generate log-linear relative asset demand, are generically inconsistent with the existence of a positive stochastic discount factor. I argue that these results imply that the demand system asset pricing approach represents a radically new way to interpret financial market data.