Fairness and Efficiency in Multiportfolio Optimization

We deal with the problem faced by a portfolio manager in charge of multiple accounts. We argue that because of market impact costs, this setting differs in several subtle ways from the classical (single account) case, with the key distinction being that the performance of each individual account typically depends on the trading strategies of other accounts, as well. We propose a novel, tractable approach for jointly optimizing the trading activities of all accounts and also splitting the associated market impact costs between the accounts. Our approach allows the manager to balance the conflicting objectives of maximizing the aggregate gains from joint optimization and distributing them across the accounts in an equitable way. We perform numerical studies that suggest that our approach outperforms existing methods employed in the industry or discussed in the literature.