For what trading strategies is the tax payment stream of infinite variation?

ABSTRACT

For an Itô asset price process and under quite mild structural assumptions, we show that the accumulated payments of a linear tax on trading gains are of infinite variation if the quadratic covariation of the trading strategy and the asset price is negative. By contrast, if the strategy is a smooth function of the asset price and some finite variation processes with positive partial derivative with respect to the price variable, then accumulated tax payments are of finite variation. An interesting example are constant proportion portfolio insurance (CPPI) strategies which we extend to models with capital gains taxes. The associated tax payment stream is of finite variation if the tax-adjusted constant multiple of the cushion which is invested in the risky asset is bigger or equal to one. Otherwise, it is of infinite variation.

KEYWORDS:

• Capital gains taxes
• CPPI with taxes
• wash sales
• total variation
• pathwise suprema of killed Brownian motions

MATHEMATICS SUBJECT CLASSIFICATION:

• 91G10
• 91B60
• 60J60
• 60H20

Acknowledgments

The author thanks two anonymous referees for their valuable comments.