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.

Heuristic Portfolio Trading Rules with Capital Gain Taxes

“…From Constantinides (1983), an investor should realize all losses immediately when trading in a setting where no transaction costs apply and realized capital gains and losses are subject to the same tax treatment. Srivastava (2011) andMarekwica (2012) generalize this result to tax systems with limited use of losses. Once transaction costs are taken into account, the incentive to realize losses trades off against the incentive to avoid the trading costs from such trades.…”

“…Consistent with most tax codes, we assume the limited use of capital losses implying that realized capital losses can only be used to offset realized gains now or in the future implying that unused capital losses must be tracked over the portfolio's life. This more realistic feature of the tax code has been studied in a no-arbitrage context by Gallmeyer and Srivastava (2011) and an optimal portfolio choice context by Marekwica (2012) and Ehling, Gallmeyer, Srivastava, Tompaidis, and Yang (2014).…”

“…One complication is how to handle the realization of capital losses. With no transaction costs, Gallmeyer and Srivastava (2011) and Marekwica (2012) show that it is weakly optimal for an investor to always realize all capital losses even if they cannot be immediately used to offset realized capital gains as these losses can be carried forward. With a proportional transaction cost, this result breaks down given the desire to also minimize transaction costs.…”

How local in time is the no-arbitrage property under capital gains taxes?

“…In other systems, losses can also be carried forwards in time. Besides progressive tax rates, these restrictions are another source of nonlinearity that calls for a local arbitrage theory as developed in Ross [21] and Gallmeyer and Srivastava [11]. The concepts differ in detail, but the basic idea is as follows: the investor does not start -as usual in arbitrage theory -without an endowment and tries to attain a portfolio with nonnegative liquidation value, which is positive with positive probability.…”

“…In the US, a declaration of a loss is not possible if "substantially identical" securities are purchased within 30 days after the liquidation of the loss-making security. Under a limited use of losses or the prohibition of wash sales, and a positive interest rate, Gallmeyer and Srivastava [11] show that in a static Arrow-Debreu security model (i.e., in a model without redundant securities), no pre-tax arbitrage implies no local after-tax arbitrage. Under some parameter restrictions, similar results are obtained for the multi-period binomial model including dividends that are taxed at a different rate.…”