Theory of Leveraged Portfolio Selection Under Liquidity Risk

We study the impact of liquidity in optimal portfolio choice under leveraging to improve risk-adjusted and absolute returns. We consider a quasi-elastic market with continuous trading where temporary liquidity costs are sufficiently large relative to permanent impact. We show analytically that the Sharpe-maximizing unlevered portfolio is no longer a tangency portfolio. As target mean increases, required portfolio-leverage increases at an increasing-rate, while Sharpe-Leverage frontiers are progressively-dominated. Moreover, security-market relationships are no-longer linear and the usual proportionate-leveraging is not an optimal strategy. We develop insights for choosing return targets for leverage-constrained investors, and provide computational analyses to highlight the analytical findings