### Abstract

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 |
---|---|

Publisher | SSRN: Social Science Research Network |

Number of pages | 35 |

Publication status | Published - 2009 |

Externally published | Yes |

### Cite this

*Equilibrium in Securities Markets with Heterogeneous Investors and Unspanned Income Risk*. SSRN: Social Science Research Network.

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**Equilibrium in Securities Markets with Heterogeneous Investors and Unspanned Income Risk.** / Christensen, Peter Ove; Larsen, Kasper; Munk, Claus.

Research output: Working paper › Research

TY - UNPB

T1 - Equilibrium in Securities Markets with Heterogeneous Investors and Unspanned Income Risk

AU - Christensen, Peter Ove

AU - Larsen, Kasper

AU - Munk, Claus

PY - 2009

Y1 - 2009

N2 - We provide the first closed-form solution for the equilibrium risk-free rate and theequilibrium stock price in a continuous-time economy with heterogeneous investor preferencesand unspanned income risk. We show that lowering the fraction of income risk spanned bythe market produces a lower equilibrium risk-free rate and a lower stock market Sharperatio, partly due to changes in the aggregate consumption dynamics. If we fix the aggregateconsumption dynamics, the Sharpe ratio is the same as in an otherwise identical representativeagent economy in which all risks are spanned, whereas the risk-free rate (and the expectedstock return) is lower in the economy with unspanned income risk due to an increased demandfor precautionary savings. The reduction in the risk-free rate is highest when the morerisk-averse investors face the largest unspanned income risk. In numerical examples withreasonable parameters, the risk-free rate is reduced by several percentage points.

AB - We provide the first closed-form solution for the equilibrium risk-free rate and theequilibrium stock price in a continuous-time economy with heterogeneous investor preferencesand unspanned income risk. We show that lowering the fraction of income risk spanned bythe market produces a lower equilibrium risk-free rate and a lower stock market Sharperatio, partly due to changes in the aggregate consumption dynamics. If we fix the aggregateconsumption dynamics, the Sharpe ratio is the same as in an otherwise identical representativeagent economy in which all risks are spanned, whereas the risk-free rate (and the expectedstock return) is lower in the economy with unspanned income risk due to an increased demandfor precautionary savings. The reduction in the risk-free rate is highest when the morerisk-averse investors face the largest unspanned income risk. In numerical examples withreasonable parameters, the risk-free rate is reduced by several percentage points.

M3 - Working paper

BT - Equilibrium in Securities Markets with Heterogeneous Investors and Unspanned Income Risk

PB - SSRN: Social Science Research Network

ER -