Optimal Leveraged Portfolio Selection Under Quasi-Elastic Market Impact

We study optimal portfolio choice under leveraging to improve portfolio performance when trade execution faces market impact. We consider a quasi-elastic market with continuous trading in which temporary liquidity costs are sufficiently large relative to permanent impact. The resulting convex optimization model is used to show analytically that an unlevered portfolio maximizing the Sharpe ratio is no longer a tangency portfolio, and increasing the portfolio target mean leads to severely undermining the risk-adjusted returns and requiring increased portfolio leverage. This paper develops theoretical properties underlying the relationships among target mean, leverage, and Sharpe ratio in optimal portfolio selection under market impact. The Sharpe-leverage efficient frontiers under market impact are consistently dominated when setting higher return targets. Moreover, leverage-constrained and less risk-averse investors ignoring liquidity costs ex ante suffer the most losses in expected utility. Detailed computational analyses are provided using real-world data to support and highlight our analytical findings.