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Single-Period Portfolio Selection via Information Projection

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  • Bo-Yu Yang
  • Michael Gastpar

Abstract

We study the single-period portfolio selection problem under Constant Relative Risk-Aversion (CRRA) utility through the information-theoretic lens. Assuming only that the market payoff vector has finite support, we show that the Certainty-Equivalent (CE) growth rate under CRRA utility can be exactly decomposed into a portfolio-induced R\'enyi divergence term, a R\'enyi entropy term of the risk-tilted market law, and a log-partition term. In this setting, the R\'enyi order has a clear operational meaning: it exactly coincides with the investor's coefficient of relative risk aversion. We further show that CRRA portfolio selection is equivalent to a R\'enyi information-projection problem. Using a variational representation of R\'enyi divergence, we obtain a Blahut-Arimoto-style alternating optimization with a closed-form auxiliary update and a KL-type portfolio step. In the low risk-aversion regime, this method empirically requires fewer iterations than both direct CRRA utility optimization and Cover's method.

Suggested Citation

  • Bo-Yu Yang & Michael Gastpar, 2026. "Single-Period Portfolio Selection via Information Projection," Papers 2605.03184, arXiv.org.
    • Handle: RePEc:arx:papers:2605.03184
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    File URL: http://arxiv.org/pdf/2605.03184
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