Alternative Tests for Monotonicity in Expected Asset Returns

Many postulated relations in finance imply that expected asset returns should monotonicallyincrease in a certain characteristic. To examine the validity of such a claim, onetypically considers a finite number of return categories, ordered according to the underlyingcharacteristic. A standard approach is to simply test for a difference in expected returnsbetween the highest and the lowest return category. However, such an approach can bemisleading, since the relation of expected returns could be flat, or even decreasing, in therange of intermediate categories. A new test, taking the entire range of categories intoaccount, has been proposed by Patton and Timmermann (2010). Unfortunately, the test isbased on an additional assumption that can be violated in many applications of practicalinterest. As a consequence, it can be quite likely for the test to ‘establish’ strict monotonicityof expected asset returns when such a relation actually does not exist. We offersome alternative tests which do not share this problem. The behavior of the various testsis illustrated via Monte Carlo studies. We also present empirical applications to real data.[...]