IJPAM: Volume 39, No. 2 (2007)

PORTFOLIO OPTIMIZATION UNDER LIQUIDITY COSTS

Rudi Zagst$^1$, Dieter Kalin$^2$
$^{1}$HVB-Institute of Mathematical Finance
Munich University of Technology
Boltzmannstr. 3, Garching, D-85748, GERMANY
e-mai: zagst@ma.tum.de
$^2$Insitute of Optimization and Operations Research
University of Ulm
Helmholtzstr. 18, Ulm, D-89069, GERMANY
e-mail: dieter.kalin@uni-ulm.de


Abstract.In this paper we examine the problem of optimally structuring a portfolio of assets with respect to transaction costs and liquidity effects. We claim that the intention of the portfolio manager is to maximize the expected net return of his portfolio, i.e. the expected return after costs, under a given limit for the portfolio risk. We show how this problem can be characterized by a convex optimization problem and that it can be solved by an equivalent quadratic optimization problem minimizing the portfolio risk under a given minimum level for the expected net return. The liquidity cost is estimated using intraday data of the German stock market. A case study shows how the results can be applied to practical trading problems.

Received: May 14, 2007

AMS Subject Classification: 91B28

Key Words and Phrases: portfolio optimization, transaction costs, liquidity effects

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 39
Issue: 2