Equilibrium in Securities Markets with Heterogeneous Investors and Unspanned Income Risk

Peter Ove Christensen, Kasper Larsen, Claus Munk

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In a finite time horizon, incomplete market, continuous-time setting with dividends and investor incomes governed by arithmetic Brownian motions, we derive closed-form solutions for the equilibrium risk-free rate and stock price for an economy with finitely many heterogeneous CARA investors and unspanned income risk. In equilibrium, the Sharpe ratio is the same as in an otherwise identical complete market economy, whereas the risk-free rate is lower and, consequently, the stock price is higher. The reduction in the risk-free rate is highest when the more risk-averse investors face the largest unspanned income risk.
Original languageEnglish
JournalJournal of Economic Theory
Issue number3
Pages (from-to)1035-1063
Number of pages29
Publication statusPublished - 2012
Externally publishedYes

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