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Nematrian Reference Library

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Abstract "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 with the same degree of tracking error 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, starting from a zero-investment position, it is optimal to invest less initially in asset classes that have high transactions costs, such as emerging markets. Our analysis makes precise the effects of transactions costs on optimal initial investment and subsequent trading"

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