A Note on the Effects of Taxes on Optimal Investment

Abstract

We integrate two approaches to portfolio management problems: that of Morton and Pliska (1995) for a portfolio with risky and riskless assets under transaction costs, and that of Cadenillas and Pliska (1999) for a portfolio with a risky asset under taxes and transaction costs. In particular, we show that the two surprising results of the latter paper, results shown for a taxable market consisting of only a single security, extend to a financial market with one risky asset and one bond: it can be optimal to realize not only losses but also gains, and sometimes the investor prefers a positive tax rate.

Investors’ preference for a positive tax rate depends on the level of the interest rate

“…Those two results were obtained for investors maximizing the long-run growth-rate of the portfolio in a market with only one stock, whose price was modeled by a geometric Brownian motion. Those results were later generalized by Buescu et al [7] to a more realistic financial market which consisted not only of one stock, but also of one bank account with zero interest rate.…”

“…After presenting the model with multiple stocks and one bank account, we use numerical methods to obtain the solution in the case of one stock and one bank account. We show that the two main economic results of Buescu et al [7] are also valid in our financial market: it can be optimal to make a transaction when there is a gain, and sometimes investors prefer a positive tax rate. In addition, our model enables us to investigate how the level of the interest rate influences investors' preference for a positive tax rate.…”

“…The main difference between our paper and that of Buescu et al [7] is in the interest rate of the risk-free asset: they assume that the interest rate is zero, while we assume that it is positive. A positive interest rate makes the model more realistic, but increases the dimensionality of the problem and the difficulty of the analysis (we shall see the details below).…”

“…This analysis could not be done previously by Buescu et al. [7] because they assumed that the level of interest rate was zero. We show the existence of a threshold level of the interest rate beyond which a positive tax rate is no longer advantageous to the investor's portfolio growth.…”

“…The incorporation of taxes not only makes financial models more realistic, but also creates challenging mathematical and computational problems (surprisingly, taxation has received little attention in the financial mathematics literature). Important papers on portfolio management with taxes include the classical works of Constantinides [9,10], and the more recent works of Ben Tahar et al [3,4], Buescu et al [7], Cadenillas and Pliska [8], Dammon and Spatt [12], Dammon et al [13,14], DeMiguel and Uppal [15], Gallmeyer et al [18], Hur [19], Jouini et al [20], and Leland [23]. The works by Buescu et al [7] and Cadenillas and Pliska [8] are the closest to the present paper.…”