Mean–Variance Portfolio Efficiency under Leverage Aversion and Trading Impact

Abstract

This paper addresses the optimal rebalancing problem of a long–short portfolio with high net asset value under trading impact losses. The fund manager may employ leveraging as a tool to increase portfolio returns. However, to mitigate potential leverage risks, frequent rebalancing may become necessary, which leads to significant slippage losses that dampen portfolio performance ex post. We consider the problem in an integrated framework by incorporating trading impact and leverage restrictions ex ante within a mean–variance framework, where leverage control is imposed using a chance constraint. The resulting mean–variance–leverage optimization model (MVL) is non-convex, and we develop an efficient scheme to obtain the optimal portfolio. We investigate how portfolio leverage modifies the MV efficient frontier in the presence of trading impact, and highlight the significant outperformance of the proposed model relative to the standard mean–variance model. Increased target means require less restrictions on leverage, which result in higher rates of slippage losses. Our analysis supports the notion that leverage restrictions contribute to choosing high beta assets, even in the presence of trading impact.