Certainty and Uncertainty in the Taxation of Risky Returns

I extend the general equilibrium techniques that have been applied to proportionate taxes to analyze the economic impact of non-proportionate taxes, including those with such commonly observed features as loss disallowances and progressivity. I analogize proportionate taxes to financial forwards and more general taxes to structured financial options. Option pricing theory and methods carry over naturally, and in general the burden of an income tax has a “certainty equivalent value” equal to the price of a corresponding complex option. A direct consequence is that non-proportionate taxes specifically burden the risk in risky investment returns, but not the expected level of these returns. If expected return levels are determined as a function of risk, then they may be burdened indirectly, but the existence of such a functional relationship depends on particular choices of market model and portfolio, such as an investment in the market portfolio under the CAPM. After developing the general theory, I apply it to the specific example of a tax that is proportionate on gains but disallows loss offsets. Such a tax burdens the risk of returns and therefore encourages portfolio diversification targeted at risk minimization, without regard to expected portfolio return. It also heavily burdens investment in put and call options, with such investments being more disfavored the more out of the money, and hence the more risky, the options are. In addition, it penalizes division of risky asset ownership across taxpayers using put-call parity, and interestingly this means that it penalizes the use of debt financing as well. Finally, I describe ways in which the general theory applies both to broader classes of taxes and also to particular aspects of the current U.S. tax system.