Unreasonable Rationality?

This paper explores how fractional demands (the optimal fraction of wealth invested in a security) change upon exogenous changes in security returns and wealth. In the first part of the paper, the analysis is conducted in an Arrow-Debreu framework. Here we demonstrate the counterintuitive but completely rational result that fractional demands can remain unchanged or in fact decrease upon an exogenous increase in return. Furthermore, we show that this can occur without any offsetting wealth effect. In the second part of the paper, we apply these results to ordinary securities (those composed of fixed portfolios of Arrow-Debreu securities). Here we derive a complete analytical solution and show that portfolio managers should beware. Even correct information that the return from holding an underlying pure security will improve is not sufficient to conclude that one should increase (or decrease) one's holdings of any particular stock.