| Resumo: | We apply numerical stochastic dynamic programming to derive trading strategies that minimize the mean and variance of the costs of executing a large block of a security over a fixed exogenously defined time period. Financial markets are considered to be liquid if a large quantity can be traded quickly and with minimal price impact. Although, the trading costs associated with trading such large quantity of a single asset – often called execution or transaction costs – can be substantial significant that directly influence the return of the investment. To minimize the price impact, an investor would choose to split his order into many small pieces. However the time taken to transact introduces a risk component in execution costs that arise from unfavourable price movements during the execution of an order. The longer the trade duration, the higher the uncertainty of the realized prices. In this setting, the decision can be viewed as a risk/reward trade-off faced by the investor who not only cares about the expected value but also about the variance (or volatility) of his execution costs. Risk aversion in this context means that an investor is willing to trade lower risk for higher price impact costs. A numerical solution for minimizing a combination of the expected transaction costs and volatility (or price) risk is derived. The parameters of the price impact model are estimated based on real world stock data.
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