Arbitrage and the tax code

Abstract

We provide a detailed characterization of arbitrage-free asset prices in the presence of capital gains and income taxes. The distinguishing feature of our analysis is that we impose on the model two important features of the tax code: the limited use of capital losses and the inability to wash sell. We show that under remarkably mild conditions, the lack of pre-tax arbitrage implies the lack of post-tax arbitrage with the limited use of capital losses. The conditions are that the risk free interest rate be positive and that tax rates on interest income exceed capital gains tax rates. The result also holds when only a wash sale constraint is imposed and no investor holds a portfolio with a large capital loss. We allow investors to face different tax rates and have different bases for the calculation of capital gains taxes. The characterizations we provide have important implications for both asset pricing and portfolio choice. Our results imply that models that use arbitrage-free pre-tax models continue for derivative pricing and hedging are also arbitrage free in a world with taxes. Similarly, portfolio choice models with taxes typically specify pre-tax arbitrage free price processes and then analyze portfolio choice in the presence of taxes. In these models, it is unclear if portfolio recommendations are based on risk-return tradeoffs or on the arbitrage opportunities present in the model. Our results imply that if the above features of the tax code are modeled explicitly, then we can isolate the post-tax risk-return tradeoffs. © 2011 Springer-Verlag.