# The Rank Effect

## TL;DR

This paper decomposes portfolio returns based on asset ranks into rank crossovers and relative price changes, showing that bottom-ranked assets can outperform the market under certain conditions, with empirical evidence from commodity futures.

## Contribution

It introduces a general decomposition method for asset returns based on rank dynamics and demonstrates its implications for asset pricing and market performance.

## Key findings

- Bottom-ranked assets can outperform the market in certain markets.
- Substantial excess returns are observed in commodity futures.
- Relative prices of bottom-ranked assets have increased slightly over time.

## Abstract

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.