Optimal portfolio deleveraging under market impact and margin restrictions

Abstract

We consider the problem of optimally deleveraging a high net-worth long-short portfolio in a short time period to position the fund favorably with respect to leverage and margin risks, in the face of an adverse outlook on future uncertainty. We develop a generalized mean-variance deleveraging optimization model that accounts for market impact costs in portfolio trading under market illiquidity. Due to asset price impact stemming from both volume and intensity of trading, the model has significant non-convexities. For portfolios with a large number of assets, the model is not solvable using standard software, and thus, we employ an efficient solution scheme based on dual optimization, along with a sequence of progressively-improving feasible portfolios computed under convex approximation. Our computational analysis using real data on ETF assets provides new insights on performance sensitivity. In particular, ignoring market impact severely downgrades portfolio performance depending on leverage and margin policies, as well as market liquidity conditions. Such insights can guide portfolio managers in setting deleveraging policy parameters ex-ante when faced with potential market turbulence. We also test the solution algorithm using random problem instances under thousands of assets to demonstrate the scalability and solvability of the deleveraging model.