Many postulated relations in finance imply that expected asset returns should monotonically increase in a certain characteristic. To examine the validity of such a claim, one
typically considers a finite number of return categories, ordered according to the underlying characteristic. A standard approach is to simply test for a difference in expected returns between the highest and the lowest return category. However, such an approach can be misleading, since the relation of expected returns could be flat, or even decreasing, in the range of intermediate categories. A new test, taking the entire range of categories into
account, has been proposed by Patton and Timmermann (2010). Unfortunately, the test is based on an additional assumption that can be violated in many applications of practical interest. As a consequence, it can be quite likely for the test to ‘establish’ strict monotonicity of expected asset returns when such a relation actually does not exist. We offer some alternative tests which do not share this problem. The behavior of the various tests is illustrated via Monte Carlo studies. We also present empirical applications to real data.