Testing liquidity: A statistical theory based on asset staleness

Using asset staleness as liquidity proxy, two novel test statistics that allow to make inference on the level of liquidity of an asset and on the difference in liquidity between two assets are proposed. The (in-fill) asymptotic properties of the tests are established, and correct procedures to use the tests in multiple testing are provided. A simulation study confirms that the newly defined tests show desirable finite sample properties. Two applications show how the tests can be used for the investor’s asset allocation problem in a high-dimensional setting.