Objective and subjective entropy measures of portfolio suboptimality

Battle Count: 69

Highly relevant to portfolio construction and performance evaluation in quantitative trading. The paper provides an information-theoretic interpretation of the cost of deviating from the Kelly-optimal portfolio, which is foundational in growth-optimal investing. The dual objective/subjective perspective (Theorems 3 and 4) offers a novel way to understand why suboptimal portfolios can appear to outperform under their own implied measure. However, it is purely theoretical with no direct algorithmic implementation or backtesting, limiting immediate practical applicability for trading systems.

The paper is theoretical and does not propose an algorithm or model to implement. The mathematical framework (Itô calculus, Girsanov theorem, KL divergence computation) is standard in quantitative finance. If one were to compute the growth gap via the entropy representation, it would require estimating the market price of risk θ_t and the portfolio-implied θ_t^π, which involves standard stochastic calculus operations. The main complexity lies in the theoretical derivation rather than computational implementation.

As a purely theoretical paper with complete proofs (Theorems 1-4, Lemma 2), the results are fully reproducible by verifying the mathematical derivations. All assumptions (Novikov condition, full row rank of σ_t, usual conditions on filtration) are explicitly stated. No code or data is needed; verification requires only stochastic calculus and measure theory.