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arxiv: 2606.19175 · v1 · pith:3GSUOCEUnew · submitted 2026-06-17 · 💰 econ.TH

To Gamble, Perchance to Grow

Mark Whitmeyer This is my paper

Pith reviewed 2026-06-26 18:46 UTC · model grok-4.3

classification 💰 econ.TH
keywords Kelly criterionreturn transformsportfolio choicerisk aversionrational inattentiongrowth-optimal portfoliosPratt measurecomparative statics
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The pith

A return transform produces more conservative Kelly portfolios if and only if it is concave, strictly increasing, and r/f is convex.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper studies how changes to asset returns affect choices in the growth-optimal Kelly portfolio problem. In the standard one-safe-one-risky-asset case, it derives an if-and-only-if condition on a return transform f that makes the optimal portfolio strictly more conservative for every possible risky return distribution. The same condition yields a characterization of comparative risk aversion between rationally inattentive agents that builds on the classic Pratt criterion. A reader would care because the result supplies a simple functional test for when any modification of returns—such as a tax, fee, or perception adjustment—induces safer long-run betting behavior without reference to a specific utility function.

Core claim

In the one-safe-one-risky-asset problem, a return transform f universally produces a more conservative portfolio if and only if f is concave and strictly increasing and r/f is convex. As a corollary, the paper characterizes comparative risk aversion for a rationally-inattentive agent: a more risk-averse agent is one who is sufficiently more risk averse in the Pratt sense.

What carries the argument

The return transform f, required to be concave and strictly increasing with convex r/f; this triple condition is necessary and sufficient to guarantee a smaller optimal stake in the risky asset for every distribution.

If this is right

  • Any return transform satisfying the three conditions can be applied to produce more conservative Kelly portfolios without further assumptions on the return distribution.
  • The characterization directly identifies the boundary between transforms that always increase conservatism and those that do not.
  • Comparative risk aversion between two rationally inattentive agents reduces to whether one agent's effective transform satisfies the condition relative to the other's.
  • The result supplies a functional test that extends Pratt's measure to the growth-optimal setting under inattention.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The condition could be used to design return modifications such as fees that reliably induce safer Kelly behavior across environments.
  • Similar convexity requirements might govern conservatism in multi-asset or dynamic Kelly problems.
  • Empirical tests could check whether observed changes in perceived returns satisfy the concavity and r/f convexity properties and predict corresponding shifts in bet sizes.
  • The link to rational inattention suggests the framework may apply to other attention-constrained decision problems in finance.

Load-bearing premise

The analysis assumes the standard one-safe-one-risky-asset Kelly setup together with rational inattention by the agent.

What would settle it

A concrete counterexample return transform that fails to be concave or to make r/f convex yet still produces a strictly smaller optimal risky position in the Kelly problem for all distributions would falsify the claim.

read the original abstract

I study transformations of returns in the growth-optimal (Kelly) portfolio problem. In the one-safe-one-risky-asset problem, a return transform f universally produces a more conservative portfolio if and only if f is concave and strictly increasing and r/f is convex. As a corollary, I characterize comparative risk aversion for a rationally-inattentive agent: a more risk-averse agent is one who is sufficiently more risk averse in the Pratt (1964) sense.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The paper studies transformations of returns in the growth-optimal (Kelly) portfolio problem. In the one-safe-one-risky-asset problem, a return transform f universally produces a more conservative portfolio if and only if f is concave and strictly increasing and r/f is convex. As a corollary, it characterizes comparative risk aversion for a rationally-inattentive agent: a more risk-averse agent is one who is sufficiently more risk averse in the Pratt (1964) sense.

Significance. If the result holds, the paper delivers a clean if-and-only-if characterization of return transforms that induce more conservative Kelly portfolios for all return distributions in the standard one-safe-one-risky setup. The direct mapping to Pratt (1964) comparative risk aversion for rationally inattentive agents is a natural and useful extension. The universal (distribution-free) nature of the conditions and the absence of free parameters or ad-hoc axioms are strengths of the derivation.

minor comments (2)
  1. [Abstract] The abstract states the main iff claim cleanly but does not indicate where in the manuscript the full proof appears; adding a brief pointer (e.g., “see §3”) would improve readability.
  2. Notation for the return transform f and the ratio r/f is introduced without an explicit reminder of the domain (positive returns, I assume); a short definitional sentence at first use would prevent any ambiguity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript and the recommendation of minor revision. The report contains no specific major comments.

Circularity Check

0 steps flagged

No circularity; mathematical if-and-only-if characterization stands independently

full rationale

The central result is an if-and-only-if characterization of return transforms f that produce more conservative Kelly portfolios in the one-safe-one-risky-asset setting. It relies on the standard Kelly setup plus an external reference to Pratt (1964) for the risk-aversion corollary. No quoted step reduces a prediction or uniqueness claim to a fitted parameter, self-definition, or self-citation chain. The derivation is self-contained against external benchmarks and does not invoke any of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on standard domain assumptions from portfolio theory and rational inattention models; no free parameters or invented entities are evident from the abstract.

axioms (2)
  • domain assumption Agents solve the growth-optimal (Kelly) portfolio problem in a one-safe-one-risky-asset setting.
    This is the core setup invoked for the main result.
  • domain assumption Comparative risk aversion is defined via Pratt (1964) sense for rationally inattentive agents.
    Invoked in the corollary characterizing risk aversion.

pith-pipeline@v0.9.1-grok · 5581 in / 1151 out tokens · 13208 ms · 2026-06-26T18:46:57.587494+00:00 · methodology

discussion (0)

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