It's 11pm - Do You Know Where Your Liquidity is? The Mean-Variance Liquidity Frontier

We introduce liquidity into a 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 change 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