Arbitrage and the Tax Code

Abstract:     
We study the no arbitrage characterization of 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 that have received little attention in the academic literature: 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 for all investors when the limited use of capital losses is imposed. The result also holds when only a wash sale constraint is imposed and no investor holds a portfolio with a large capital loss. The results allow investors to face different tax rates and have different bases for the calculation of capital gains taxes. When the underlying assets are capital gain taxed Arrow-Debreu securities, the shadow riskless interest rate embedded in the prices must be positive to avoid post-tax arbitrage under either limited use of losses or no wash sales. When the security market also includes a taxable bond, arbitrage can exist with no wash sales for sufficiently large tax bases. Limiting the use of capital losses eliminates this arbitrage. When the price system consists of a capital gain taxed stock and a taxable bond, the pre-tax interest rate must be positive and the post-tax return of the bond cannot dominate the post-tax return of the stock to avoid post-tax arbitrage under limited capital losses. When the wash sale restriction is imposed with this price system, limited arbitrage opportunities can still arise if there exists a very large tax basis in the portfolio relative to the current stock price. We also demonstrate that allowing the full use of capital losses has strong implications for portfolio choice. When a capital loss tax rebate is disallowed, investors tend to optimally hold significantly smaller equity positions.

Keywords: capital gain taxation, no arbitrage, tax arbitrage

JEL Classifications: G11, G12, G13, H24

Working Paper Series