On the interpretation of price adjustments and demand in asset pricing models with mean-variance optimization

With reference to the class of asset pricing models with a market maker and mean-variance optimization of speculative agents, the note seeks to clarify the concepts behind the price adjustment rule, which are often treated somewhat carelessly in this literature. Calling attention to the distinction between the agents’ desired holding of the risky asset and the desired change in their position, the following conclusion is drawn. If market prices are said to adjust in the direction of excess demand, then the story of the maximization of expected wealth should be dropped. On the other hand, the story could be perfectly maintained if the market maker were assumed to adjust prices inversely to his accumulated inventory. -- Expected wealth maximization ; market maker ; positions of speculative agents