A Robust Test for Monotonicity in Asset Returns

Abstract

In this paper, we propose a robust test of monotonicity in asset returns that is valid under a general setting. We develop a test that allows for dependent data and is robust to conditional heteroskedasticity or heavy-tailed distributions of return differentials. Many postulated theories in economics and finance assume monotonic relationships between expected asset returns and certain underlying characteristics of an asset. Existing tests in literature fail to control the probability of a type 1 error or have low power under heavy-tailed distributions of return differentials. Monte Carlo simulations illustrate that our test statistic has a correct empirical size under all data-generating processes together with a similar power to other tests. Conversely, alternative tests are nonconservative under conditional heteroskedasticity or heavy-tailed distributions of return differentials. We also present an empirical application on the monotonicity of returns on various portfolios sorts that highlights the usefulness of our approach.