## 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.

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 language | English |
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Publisher | SSRN: Social Science Research Network |

Number of pages | 35 |

Publication status | Published - 2009 |

Externally published | Yes |