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To Gamble, Perchance to Grow

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  • Mark Whitmeyer

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.

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  • Mark Whitmeyer, 2026. "To Gamble, Perchance to Grow," Papers 2606.19175, arXiv.org.
    • Handle: RePEc:arx:papers:2606.19175
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    References listed on IDEAS

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    1. Christian Gollier, 1997. "A Note on Portfolio Dominance," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 64(1), pages 147-150.
    2. Gregorio Curello & Ludvig Sinander & Mark Whitmeyer, 2025. "Outside options and risk attitude," Papers 2509.14732, arXiv.org.
    3. Ross, Stephen A, 1981. "Some Stronger Measures of Risk Aversion in the Small and the Large with Applications," Econometrica, Econometric Society, vol. 49(3), pages 621-638, May.
    4. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    5. Thomas M. Cover, 1991. "Universal Portfolios," Mathematical Finance, Wiley Blackwell, vol. 1(1), pages 1-29, January.
    6. Gollier Christian, 1995. "The Comparative Statics of Changes in Risk Revisited," Journal of Economic Theory, Elsevier, vol. 66(2), pages 522-535, August.
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