Optimal Consumption and Investment with Transaction Costs and Multiple Risky Assets

We consider the optimal intertemporal consumption and investment policy of a constant absolute risk aversion (CARA) investor who faces fixed and proportional transaction costs when trading multiple risky assets. We show that when asset returns are uncorrelated, the optimal investment policy is to keep the dollar amount invested in each risky asset between two constant levels and upon reaching either of these thresholds, to trade to the corresponding optimal targets. An extensive analysis suggests that transaction cost is an important factor in affecting trading volume and that it can significantly diminish the importance of stock return predictability as reported in the literature. THIS PAPER STUDIES THE OPTIMAL INTERTEMPORAL CONSUMPTION and investment policy of an investor with a constant absolute risk aversion (CARA) preference and an infinite horizon. The investor can trade in one risk-free asset and n ≥ 1 risky assets. In contrast to the standard setting, the investor faces both fixed and proportional transaction costs in trading any of these risky assets. In the absence of transaction costs and when risky asset prices follow geometric Brownian motions, the optimal investment policy is to keep a constant dollar amount in each risky asset, as shown by Merton (1971). This trading strategy requires continuous trading in all the risky assets. In addition, the optimal consumption is affine in the total wealth. In the presence of transaction costs, however, trading continuously in a risky asset would incur infinite transaction costs. Therefore, risky assets are traded only infrequently in this case. The literature on optimal consumption and investment with multiple risky assets subject to transaction costs is limited. Leland (2000) examines a multiasset investment fund that is subject to transaction costs and capital gains taxes. Under the assumption that the fund has an exogenous target for each risky asset, he develops a relatively simple numerical procedure to compute the no-transaction region. Akian, Menaldi, and Sulem (1996) consider an optimal consumption and investment problem with proportional transaction costs for ∗Liu is from the John M. Olin School of Business, Washington University in St. Louis. I thank Domenico Cuoco, Sanjiv Das, Phil Dybvig, Bob Goldstein, Zhongfei Li, Mark Loewenstein, Mark Schroder, Dimitri Vayanos, Guofu Zhou, and participants in the 2002 WFA Conference, the 2002 International Finance Conference, the 2001 International Mathematical Finance Conference, and the University of Kentucky seminar for helpful comments. I am especially indebted to an anonymous referee, Rick Green (the Editor) and Kerry Back for very useful suggestions. Any remaining errors are of course mine.