Investment Strategies under Transaction Costs: The Finite Horizon Case

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Abstract
We examine the effect of proportional transaction costs on dynamic portfolio strategies for an agent who maximizes his expected utility of terminal wealth. For portfolios composed of a single risky asset and a single riskless asset, Constantinides (1979) shows that the optimal investment policy is described in terms of a no transaction region, where the optimal policy is to refrain from trading if initial portfolio holdings lie within the region, and to transact to the nearest boundary of the region if portfolio holdings lie outside the region. Because the boundaries could not be derived analytically, we developed an efficient and tractable algorithm to obtain the boundaries, which are expressed as the ratio of the dollar holdings in stocks and bonds. We considered two cases: the same transaction costs for the two assets, and costs incurred on only the risky asset. We derived the optimal trading strategies and utility levels for a large set of realistic parameters. In particular, we show that the no transaction region narrows and converges rapidly to the infinite horizon limit as the time horizon increases.

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