Optimal order execution for algorithmic trading: A CVaR approach

Order execution for algorithmic trading has been studied in the literature as a means of determine the optimal strategy by minimizing a trade-off between expected execution cost and risk. Usually, the variance of the execution cost is taken as a proxy of risk. The problem of this approach is that variance being a symmetric measure of risk disregard the fact that investors only considered as risky cost realizations that are higher than an expected target value. This fact becomes even more sensitive when the return distribution is nonnormal, negatively skewed, or leptokurtic. In this paper, we propose the use of the conditional value-at-risk of the execution cost as risk measure, which allows for taking only the unfavorable part of the return distribution, or equivalently unwanted high cost, into consideration.