IT’S 11 PM—DO YOU KNOW WHERE YOUR LIQUIDITY IS? THE MEAN-VARIANCE-LIQUIDITY FRONTIER

Andrew W. Lo, Constantin Petrov, and Martin Wierzbicki

We 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.