Brown Bag Seminar - Ulf von Lilienfeld-Toal (University of Luxembourg), Monotone Comparative Statics in Multi-Asset Portfolio Choice: Wealth and Risk Aversion

Abstract

Arrow (1965) and Pratt (1964) laid the bedrock of portfolio theory by characterizing how risk aversion governs portfolio choice with one risky and one safe asset. Extending these insights beyond the one-risky-asset benchmark proved elusive: Cass and Stiglitz (1972) and Hart (1975) show that risk aversion alone has essentially no predictive content for portfolio rebalancing across risky assets. This paper closes that gap: once returns satisfy a single-crossing riskiness property, sharp monotone predictions reemerge in portfolio choice with n risky assets. This property arises from nonlinear factor models and distributional conditions such as directional log-supermodularity. More risk-averse investors tilt their risky portfolios, in relative terms, toward less single-crossing-risky assets. The framework resolves the asset-allocation puzzle, helps explain empirically observed underdiversification and individualized portfolios, reconciles professional guidance with utility-maximizing portfolio choice, and nests mean-variance analysis and two-fund separation as linear limiting cases.