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

/pdf/optimal-consumption-and-investment-with-transaction-costs-32ye3naf68.pdf

Optimal Consumption and Investment with Transaction Costs and Multiple Risky Assets

Standard literature concludes that transaction costs only have a second-order effect on liquidity premia. We show that this conclusion depends crucially on the assumption of a constant investment opportunity set. In a regime-switching model in which the investment opportunity set varies over time, we explicitly characterize the optimal consumption and investment strategy. In contrast to the standard literature, we find that transaction costs can have a first-order effect on liquidity premia. However, with reasonably calibrated parameters, the presence of transaction costs still cannot fully explain the equity premium puzzle. TRANSACTION COSTS ARE PREVALENT in almost all financial markets. Extensive research has been conducted on the optimal consumption and investment policy in the presence of transaction costs since the seminal work of Constantinides (1979, 1986). The presence of transaction costs significantly changes optimal consumption and investment strategies. For example, in the presence of transaction costs, continuous trade incurs infinite transaction costs, and thus even a small transaction cost can dramatically decrease the frequency of trade. However, most studies find that the utility loss due to the presence of transaction costs is small. In particular, Constantinides (1986) finds that the liquidity premium (i.e., the maximum expected return an investor is willing to exchange for zero transaction cost) is small relative to the transaction cost, even for a suboptimal trading strategy, and hence concludes that transaction costs only have a second-order effect for asset pricing. Indeed, in this framework it seems unlikely that transaction costs can have an important role in explaining the cross-sectional patterns of expected returns, the equity premium puzzle, or the small stock risk premia. This finding contrasts with many empirical studies that highlight the importance of transaction costs or related measures such as turnover in influencing the cross-sectional patterns of expected returns. 1

/pdf/liquidity-premia-and-transaction-costs-11b40o4ljx.pdf

Liquidity Premia and Transaction Costs

A portfolio9s asset allocation determines the portfolio9s risk and return characteristics. To maintain its original risk and return characteristics over time, the portfolio must be rebalanced. This paper identifies the factors that influence a rebalancing strategy. We present a conceptual framework for developing rebalancing strategies that can accommodate changes in the financial market environment and in asset class characteristics, as well as account for an institution9s unique risk tolerance and time horizon. We conduct simulations to analyze how these different factors and different rebalancing guidelines affect a portfolio9s risk and return characteristics. We conclude with a review of practical rebalancing considerations.

Portfolio Rebalancing in Theory and Practice

We compare the risk-adjusted performance of stock–bond portfolios between rebalancing and buy-and-hold across different asset allocations by reporting statistical significance levels. Our investigation is based on a 30-year dataset and incorporates the financial markets of the United States, the United Kingdom and Germany. To draw useful recommendations to investment management, we implement a history-based simulation approach which enables us to mimic realistic market conditions. Even if the portfolio weight of stocks is very low, our empirical results show that a frequent rebalancing significantly enhances risk-adjusted portfolio performance for all analysed countries and all risk-adjusted performance measures.

Testing rebalancing strategies for stock-bond portfolios across different asset allocations

Private wealth management is the investment management specialization focused on high-net-worth individuals and families. Portfolio design and investment solutions in private wealth management are customized to reflect the complexities of the investor’s unique circumstances. This literature review reflects the current best thinking on private wealth management.

Perspectives from the Literature of Private Wealth Management

We examine the optimal trading strategy for an investment fund which in the absence of transactions costs would like to maintain assets in exogenously fixed proportions, e.g. 60/30/10 in stocks, bonds and cash. Transactions costs are assumed to be proportional, but may differ with buying and selling, and may include a (positive) capital gains tax component. We show that the optimal policy involves a no-trade region about the target stock proportions. As long as the actual proportions remain inside this region, no trading should occur. When proportions are outside the region, trading should be undertaken to move the ratio to the region's boundary. We compute the optimal multi-asset no-trade region and resulting annual turnover and tracking error of the optimal strategy. 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 current practice of periodic rebalancing of all assets to their target proportions, the optimal strategy will reduce turnover by almost 50%. The optimal response to a capital gains tax is to allow proportions to substantially exceed their target levels before selling. When an asset's proportion exceeds a critical level, selling should occur to bring it back to that critical level. Capital gains taxes lead to lower optimal initial investment levels. Similarly, it is optimal to invest less initially in asset classes that have high transactions costs, such as emerging markets.

Research Program in Finance Working Paper RPF-290 Optimal Portfolio Management with Transactions Costs and Capital Gains Taxes

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Research Program in Finance Working Paper RPF-290 Optimal Portfolio Management with Transactions Costs and Capital Gains Taxes