Quantitative Financial Risk Management: Theory and Practice

CHAPTER 8

Portfolio Optimization and Transaction Costs

Renata Mansini

University of Brescia,Department of Information Engineering

Wlodzimierz Ogryczak

Warsaw University of Technology,Institute of Control and Computation Engineering

M. Grazia Speranza

University of Brescia,Department of Economics and Management

INTRODUCTION

In financial markets, expenses incurred when buying or selling securities are commonly defined as transaction costs and usually include brokers’ commissions and spreads (i.e., the difference between the price the dealer paid for a security and the price the buyer pays). Broadly speaking, the transaction costs are the payments that banks and brokers receive for performing transactions (buying or selling securities). In addition to brokerage fees/commissions, the transaction costs may represent capital gain taxes and thus be considered in portfolio rebalancing. Transaction costs are important to investors because they are one of the key determinants of their net returns. Transaction costs diminish returns and reduce the amount of capital available to future investments. Investors, in particular individual ones, are thus interested to the amount and structure of transaction costs and to how they will impact their portfolios.

The portfolio optimization problem we consider is based on a single-period model of investment, which is based on a single decision at the beginning of the investment horizon (buy and hold strategy). This model has played a crucial role in stock ...