Optimal Portfolio Implementation: Asset Management with Transactions Costs and Capital Gains Taxes

While there is an extensive literature, both theoretical and empirical, on determining optimal asset ratios for funds with alternative objectives, little has been written about an equally-important aspect of money management: how to implement these strategies optimally in the presence of transactions costs and capital gains taxes. Yet trading to implement investment objectives is regularly done in a highly inefficient manner. For example, standard rebalancing strategies (e.g. annually or quarterly to optimal asset ratios) result in trading costs double those which can be achieved by optimal trading strategies. Because there has been little theory, most dynamic investment strategies have been implemented in toocostly ways. For mutual funds alone, back-of-the-envelope calculations show that the $13tr US mutual fund market with average turnover of 85% and transactions costs of 25 bps incurs trading costs of approximately $25b. We consider a multi-asset investment fund that, in the absence of transactions costs and/or taxes, would hold assets in given target proportions. Trading is required as random price fluctuations change actual proportions. The fund seeks to minimize a weighted sum of expected trading costs and the expected cost of tracking error. Very frequent trading to maintain the target proportions will incur ruinous transactions costs, while infrequent trading will incur significant tracking error relative to the desired returns. As suggested by the pioneering work of Davis and Norman (1990), the optimal strategy is characterized by a no-trade region. But the problem is much more complicated in the multi-asset case when returns are correlated. In contrast with Liu (2004), whose multi-asset analysis considers only the case of uncorrelated assets, we develop a relatively simple means to compute the multi-dimensional no-trade region. In contrast with Dammon and Spatt (1996), we consider optimal realization of capital gains in the context of a full portfolio-choice model. The analysis has practical importance to asset management. The optimal trading strategy can be determined, given standard parameters (asset trading costs; tracking error bounds; and return variances and correlations). The expected turnover and tracking error of the optimal strategy can be determined. When new asset classes are introduced, the optimal initial allocation can also be calculated. Almost surely, the strategy will require trading just one risky asset at any moment, although which asset is traded varies stochastically through time. Compared to the common practice of periodically rebalancing assets to their target proportions, the optimal strategy with the same degree of tracking accuracy will reduce turnover by almost 50%.