Equilibrium in Securities Markets with Heterogeneous Investors and Unspanned Income Risk

38 Pages Posted: 23 Mar 2009 Last revised: 24 Dec 2016

See all articles by Peter O. Christensen

Peter O. Christensen

Copenhagen Business School - Department of Finance

Kasper Larsen

Rutgers, The State University of New Jersey

Claus Munk

Copenhagen Business School

Date Written: May 2, 2011

Abstract

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 a finite set of 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. In numerical examples with reasonable parameters, the risk-free rate is reduced by several percentage points.

Keywords: Unspanned income, heterogeneous preferences, continuous-time equilibrium, risk-free rate puzzle, equity premium, incomplete markets, Brownian motion

JEL Classification: G12, G11, D53

Suggested Citation

Christensen, Peter Ove and Larsen, Kasper and Munk, Claus, Equilibrium in Securities Markets with Heterogeneous Investors and Unspanned Income Risk (May 2, 2011). Available at SSRN: https://ssrn.com/abstract=1364237 or http://dx.doi.org/10.2139/ssrn.1364237

Peter Ove Christensen

Copenhagen Business School - Department of Finance ( email )

Solbjerg Plads 3
Frederiksberg, DK-2000
Denmark
+45 6140 3237 (Phone)

Kasper Larsen

Rutgers, The State University of New Jersey ( email )

311 North 5th Street
New Brunswick, NJ 08854
United States

Claus Munk (Contact Author)

Copenhagen Business School ( email )

Department of Finance
Solbjerg Plads 3
Frederiksberg, DK-2000
Denmark

HOME PAGE: http://sites.google.com/view/clausmunk/home

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