Our objective in this paper is to study the optimal dynamic portfolio policy in the presence of capital-gains tax when using the exact tax basis. This is an important problem given that most investors face taxes on their stock holdings. Moreover, the magnitude of the capital gains tax is quite large it typically ranges from twenty percent to forty percent and so is much larger than transactions costs, which are usually less than one percent.
In spite of the importance of this problem, the optimal portfolio policies in the presence of capital gains tax using the exact tax basis have not been studied in the literature. The main reason for this is that computing the optimal portfolio policy of an investor subject to capital gains taxes is a challenging task. The difficulty is that the tax to be paid depends not only on the selling price, but also on the price at which the securities were purchased, that is, the tax basis. As a consequence, the optimal policy is path dependent and the size of the problem grows exponentially with the number of time periods.
Constantinides (1983) shows that, if shortselling were costless and unconstrained, the optimal policy would be to realize all losses immediately and to defer all gains. The investor optimally defers all gains because, with costless shortselling, she prefers to short sell those securities with an embedded capital gain instead of selling them, avoiding any tax payment and thus capturing the time value of taxes. Also, an investor should realize all losses by selling any securities whose price falls below their tax basis in order to get a tax rebate, and then rebalance her portfolio by buying the securities at the current price; this operation is known as a wash sale. In essence, costless shortselling allows one to separate the portfolio problem from the tax timing problem. However, in practice short selling is not costless and it may also be prohibited by the tax authorities, and thus, in this paper we focus on the portfolio problem for the case where short sales are prohibited.
A popular approach adopted in the literature for dealing with the complexity of the portfolio problem in the presence of capital gains tax has been to use the weighted average purchase price as the tax basis in order to find an approximate solution to the problem with short-sale constraints – see for instance Dammon, Spatt, and Zhang (2001, 2002a,b), Garlappi, Naik, and Slive (2001) and Gallmeyer, Kaniel, and Tompaidis (2001). This is equivalent to forcing the investor to sell the same proportion of the shares she holds for each different tax basis whenever she sells stock. The resulting policies are obviously suboptimal because it is always better to sell those shares with the highest tax basis first. However, the advantage of using this approximation is that it makes the problem path-independent, and thus, allows one to solve problems with a large number of dates using dynamic programming.
Contents
1 Introduction
2 The model and optimization problem
2.1 The basic model
2.2 Extensions to the basic model
- 2.2.1 Transaction costs
2.2.2 Dividends
2.2.3 Intermediate consumption .
2.2.4 Labor income
2.2.5 Tax forgiveness
2.2.6 Wash-sale constraints
2.2.7 More than one stock
3 Characteristics of the optimization problem
4 Properties of the optimal portfolio policies
4.1 Optimal portfolio policy in basic model with benchmark parameters
- 4.1.1 Benchmark parameter values
4.1.2 The true tax basis policy
4.1.3 Comparison with suboptimal portfolio policies
4.2 Sensitivity to parameter values for stock returns and risk aversion
4.3 Sensitivity to model refinements
- 4.3.1 Transaction costs
4.3.2 Dividends
4.3.3 Intermediate consumption
4.3.4 Labor income
4.3.5 Tax reset provision at the last date
4.3.6 Asymmetric taxation
4.3.7 Wash-sale constraints
4.3.8 Summary of CEQ loss under various model refinements
4.4 Sensitivity to number of stocks and correlation
4.5 Sensitivity to number of periods
5 Conclusions
Tables
Figures
References
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Portfolio Investment with the Exact Tax Basis via Nonlinear Programming
