{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,14]],"date-time":"2026-10-14T13:45:10Z","timestamp":1791985510032,"version":"4.4.0"},"posted":{"date-parts":[[2026]]},"group-title":"SSRN","reference-count":25,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,1,1]],"date-time":"2026-01-01T00:00:00Z","timestamp":1767225600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.uspto.gov\/ip-policy\/copyright-policy\/copyright-basics"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Cross-sectional asset-pricing research typically summarizes a signal with the high-minus-low spread: the average return on the highest-ranked portfolio minus that on the lowest-ranked one. As a general default, both investment practice and statistical theory argue against discarding the interior portfolios. I propose the Abelson-Tukey (AT) spread as an alternative default summary statistic: a prespecified long-short portfolio built from all of the sorted portfolios, with weights that maximize the test's minimum power across monotone expected-return profiles. Under the classical equal-variance, zerocovariance sampling benchmark, the AT spread's worst-case floor for decile sorts is 47.8% of the information available to an infeasible test tailored to the true shape of the return relation, against 20.0% for high-minus-low. I illustrate the method using 170 published signals in value-weighted deciles. The exercise reorganizes the evidence contained in the full sorts: the median t-statistic rises from 1.80 to 1.94, while nine signals are promoted and three are demoted at the 1.96 threshold. Tailoring the weights to each signal's estimated covariance adds almost nothing.<\/jats:p>","DOI":"10.2139\/ssrn.7149560","type":"posted-content","created":{"date-parts":[[2026,7,29]],"date-time":"2026-07-29T14:12:35Z","timestamp":1785334355000},"source":"Crossref","is-referenced-by-count":0,"title":["The Other Eight Deciles: A Maximin Summary Statistic for Portfolio Sorts"],"prefix":"10.2139","author":[{"given":"Sandro C.","family":"Andrade","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"ref1","doi-asserted-by":"crossref","first-page":"1347","DOI":"10.1214\/aoms\/1177703869","article-title":"Efficient utilization of non-numerical information in quantitative analysis: General theory and the case of simple order","volume":"34","author":"R Abelson","year":"1963","journal-title":"Annals of Mathematical 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