Investing Is Compression: A Three-Term Decomposition of the Kelly Objective
ORIGINAL / Investing Is Compression
Borrowing a trick from the universal portfolio algorithm, the author decomposes the Kelly objective into a money term, an entropy term, and a divergence term, showing that maximizing growth is equivalent to minimizing the divergence (in bits) between the predicted distribution and the true distribution. This offers a theoretical view of investing as a compression problem and yields two practical byproducts: in backtests, the difference in log growth between two strategies mea
01 ABSTRACT
Fact: the author shows that the Kelly objective can be decomposed into a money term, an entropy term, and a divergence term, and that maximizing growth is equivalent to minimizing divergence. Author's view: investing is fundamentally a compression problem, and on this basis proposes a winner fraction heuristic and an entropy bound, claimed as original contributions.
02 KEY FINDINGS
- The Kelly objective decomposes into money, entropy, and divergence terms; maximizing growth is equivalent to minimizing the divergence (in bits) between predicted and true distributions.
- In backtests, the difference in log growth between two strategies measures their relative divergence because money and entropy terms are constant across strategies.
- A winner fraction heuristic is introduced that allocates capital in proportion to each asset's probability of dominating the candidate set, with its growth shortfall bounded by the entropy of the winner fraction distribution.
AI GENERATED SUMMARY / DISCOVERED BY ARXIV Q-FIN