| Summary: | Portfolio sorts are used extensively in finance to explore the relation between firm characteristics and expected returns. Existing empirical tests have largely been limited, however, to comparing expected returns of the top and bottom ranked portfolios. We propose a new and general approach to test for a monotonic relationship between expected returns and variables used to sort stocks and form portfolios, such as firm characteristics or past returns. Empirical evidence suggests that inference from standard t-tests can be overturned by our monotonicity tests. In particular, the short-term reversal and momentum effects and the declining relation between firm size and average returns are shown not to hold monotonically in post-1963 data. Conversely, the evidence in favor of other patterns, such as the value effect, is strengthened by our tests.
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