Portfolio Optimization with Concave Transaction Costs

FAME Working Paper No. 103

39 Pages Posted: 28 Dec 2003

Date Written: December 2002

Abstract

In this paper we study the optimal portfolio management for the constant relative-risk averse investor who maximizes an expected utility of his terminal wealth and who faces transaction costs during his trades. In our model the investor's portfolio consists of one risky and one risk-free asset, and we assume that the transaction cost is a concave function of the traded volume of the risky asset. We find that under such transaction cost formulation the optimal trading strategies and boundaries of the no-transaction region are different than those when transaction costs are proportional, i.e. when they are linear in the traded volume. When transaction costs are concave, we show that the no-transaction region is narrower than when transaction costs are proportional, and it is not a positive cone. Under our transaction cost formulation, when the investor's wealth is relatively high, the optimal trading strategy consists in bringing the post-trade portfolio position inside the no-transaction region, whereas proportional transaction costs induce the investor trading to the boundary of the no-transaction region. We also examine the impact of the risky asset volatility and the risk aversion parameter on the shape of the no-transaction region. When comparing different transaction cost structures, we show that the financial securities' market tends to be more liquid with concave transaction costs than with alternative cost specifications.

Keywords: Concave transaction costs, optimal trading strategy

JEL Classification: C61, G11

Suggested Citation

Demchuk, Andriy, Portfolio Optimization with Concave Transaction Costs (December 2002). FAME Working Paper No. 103, Available at SSRN: https://ssrn.com/abstract=481102 or http://dx.doi.org/10.2139/ssrn.481102

Andriy Demchuk (Contact Author)

International Center FAME ( email )

40, Boulevard du Pont-d'Arve
40, Bd du Pont-d'Arve
1211 Geneva 4, CH-6900
Switzerland

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