Equilibrium in Securities Markets with Heterogeneous Investors and Unspanned Income Risk

Peter Ove Christensen, Kasper Larsen, Claus Munk

Research output: Working paperResearch

Abstract

We provide the first closed-form solution for the equilibrium risk-free rate and the
equilibrium stock price in a continuous-time economy with heterogeneous investor preferences
and unspanned income risk. We show that lowering the fraction of income risk spanned by
the market produces a lower equilibrium risk-free rate and a lower stock market Sharpe
ratio, partly due to changes in the aggregate consumption dynamics. If we fix the aggregate
consumption dynamics, the Sharpe ratio is the same as in an otherwise identical representative
agent economy in which all risks are spanned, whereas the risk-free rate (and the expected
stock return) is lower in the economy with unspanned income risk due to an increased demand
for precautionary savings. 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.
Original languageEnglish
PublisherSSRN: Social Science Research Network
Number of pages35
Publication statusPublished - 2009
Externally publishedYes

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