Improvement of Mean-Variance Framework for Securities Trading

摘要

In a mean-variance framework, an optimal execution strategy minimizes variance for a specified maximum level of expected cost, or conversely. In this setup, trade-schedules in some path-independent (static) execution algorithms are deterministic and do not modify the execution speed in response to price motions during trading. In this paper, we consider the execution of portfolio transactions in a trading model with market impact and present an adaptive trading strategy. We show that the static execution strategies can be significantly improved by adaptive trading. We first illustrate this by constructing strategies that update exactly once during trading, i.e., at some intermediary time they may readjust in response to the stock price movement up to that moment. We show that such single-update strategies yield lower expected cost for the same level of variance than the trajectories of static algorithms, or lower variance for the same expected cost.