  We decompose returns for portfolios of bottom-ranked, lower-priced assets
relative to the market into rank crossovers and changes in the relative price
of those bottom-ranked assets. This decomposition is general and consistent
with virtually any asset pricing model. Crossovers measure changes in rank and
are smoothly increasing over time, while return fluctuations are driven by
volatile relative price changes. Our results imply that in a closed,
dividend-free market in which the relative price of bottom-ranked assets is
approximately constant, a portfolio of those bottom-ranked assets will
outperform the market portfolio over time. We show that bottom-ranked relative
commodity futures prices have increased only slightly, and confirm the
existence of substantial excess returns predicted by our theory. If these
excess returns did not exist, then top-ranked relative prices would have had to
be much higher in 2018 than those actually observed -- this would imply a
radically different commodity price distribution.
