Income Taxation, Wealth Effects, and Uncertainty: Portfolio Adjustments with Isoelastic Utility and Discrete Probability

The expected utility formulation of the problem of a risk-averse agent’s allocating a portfolio between a safe and a risky asset is widely taken as standing for the proposition that if α* ε (0, 1) is the optimal allocation to the risky asset in the absence of tax, α*/(1-t) is the optimal allocation in the presence of tax at rate t, a finding obtained on the assumption that the return r to the riskless asset is (or is taxed as though it were) zero. In this paper I model the agent as exhibiting constant relative risk aversion and the probability distribution of the risky asset as binomial, and take the riskless rate to be greater than zero. With those assumptions the optimal solution α* depends on the all the parameters of the problem. The key finding of the paper, however, is that the optimal adjustment to taxation does not. That adjustment differs from what has been widely assumed, and depends on r, as well as t, but does not depend on anything else. It reflects in a natural way the response of the agent to the wealth effect of taxation