  A market portfolio is a portfolio in which each asset is held at a weight
proportional to its market value. Functionally generated portfolios are
portfolios for which the logarithmic return relative to the market portfolio
can be decomposed into a function of the market weights and a process of
locally finite variation, and this decomposition is convenient for
characterizing the long-term behavior of the portfolio. A permutation-weighted
portfolio is a portfolio in which the assets are held at weights proportional
to a permutation of their market values, and such a portfolio is functionally
generated only for markets with two assets (except for the identity
permutation). A reverse-weighted portfolio is a portfolio in which the asset
with the greatest market weight is assigned the smallest market weight, the
asset with the second-largest weight is assigned the second-smallest, and so
forth. Although the reverse-weighted portfolio in a market with four or more
assets is not functionally generated, it is still possible to characterize its
long-term behavior using rank-based methods. This result is applied to a market
of commodity futures, where we show that the reverse price-weighted portfolio
substantially outperforms the price-weighted portfolio from 1977-2018.
