IT'S 11 PM—DO YOU KNOW WHERE YOUR LIQUIDITY IS?: THE MEAN–VARIANCE–LIQUIDITY FRONTIER

AbstractWe introduce liquidity into the standard mean–variance portfolio optimization framework by defining several measures of liquidity and then constructing three-dimensional mean–variance–liquidity frontiers in three ways: liquidity filtering, liquidity constraints, and a mean–variance–liquidity objective function. We show that portfolios close to each other on the traditional mean–variance efficient frontier can differ substantially in their liquidity characteristics. In a simple empirical example, the liquidity exposure of mean–variance efficient portfolios changes dramatically from month to month, and even simple forms of liquidity optimization can yield significant benefits in reducing a portfolio's liquidity-risk exposure without sacrificing a great deal of expected return per unit risk.