Algorithmic Trading, Optimal Execution, and Dyna Mic Port Folios

This article discusses the portfolio optimization with market impact costs, combining execution and portfolio risk, and dynamic portfolio analysis. A multi-period portfolio optimization model is proposed that incorporates permanent and temporary market impact costs, and alpha decay. There are five popular algorithmic trading strategies that include arrival price, market-on-close, participation, time-weighted average price (TWAP), and volume-weighted average price (VWAP). For a VWAP benchmark, the lowest risk execution is obtained by trading one's own shares in the same fractional volume pattern as the market. VWAP execution is expected to result in the lowest temporary market impact costs. The temporary market impact in a rate of trading model is a function of one's own rate of trading expressed as a fraction of the absolute trading activity of the market. One popular interpretation of the model is that the markets are relatively efficient with respect to the relationship between trading volume and volatility, which are typical inputs of the model. Any reduction in impact that results from more trading volume would be offset by an increase in impact due to increased volatility. The lowest absolute rate of trading can be realized by distributing one's orders evenly over time. This is called a time-weighted average price (TWAP) execution.