Two Stock Portfolio Choice with Capital Gain Taxes and Short Sales

Abstract

In this paper, we study the consumption-portfolio problem of an investor who faces realized capital gain taxes in a two stock setting with short sales. The investor finances consumption and a time of death bequest by trading in a money market and two stocks that he can short sell subject to margin constraints and a shorting the box restriction. When the correlation between the two stocks is low, the investor's optimal strategy is similar to the case of one risky asset with the notable exceptions that the investor may optimally hold an undiversified equity position. At higher levels of correlation, tax trading costs lead to significantly different trading strategies. With short sale restrictions, it is common for the investor to hold an undiversified equity portfolio. With short selling, the trading strategy is dramatically different. The investor is induced to short equity under two different incentives. The first incentive is an imperfect form of shorting the box used to reduce the aggregate equity exposure while the second incentive is a trading flexibility strategy. Under the trading flexibility incentive, the investor shorts stock while holding a positive aggregate equity position even when the current portfolio has no embedded gains. By doing so, the investor uses the tax loss selling option embedded in the short position to offset gains in the larger long stock position when rebalancing. This trading flexibility incentive also leads to the investor holding less equity when older in contrast to the two stock case with no short sales and the previously studied one stock case.