Abstract
Portfolio algorithms have captured renewed attention in the financial industry due to increased program trading and quantitative money management. By understanding how implementation decisions affect market impact, portfolio risk and correlations, traders are better prepared to determine optimal execution strategies that are consistent with overall investment objectives, resulting in lower cost or lower risk exposure. Ultimately, this leads to better managed investment portfolios. Unfortunately traditional optimization techniques appropriate for portfolio construction have not proven adequate in the algorithmic space due to many factors including the non-linearity of the market impact function, the large number of decision variables, and the length of time to solve the problem. In this chapter we present various different approaches to trade schedule optimization and provide formulations that will provide accurate solutions in amounts of time that can be useful for traders. We expand our optimization to real-time situations and provide guidelines for investors to determine how and when to best take advantage of market conditions, namely price movement and liquidity.
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