Increased Risk-Bearing with Background Risk

Analyses of risk-bearing often assume that agents face only one risk when deciding how much risk to bear. Agents however usually face several risks at the same time and the interaction between risks can affect the willingness to bear any particular one of them. We consider how the introduction of uninsurable background risk affects the comparative statics predictions of distribution changes in the standard two-asset portfolio model. We show that such predictions are fairly robust, no matter what the correlation between the background risk and the risky asset's return distribution. We consider changes in the conditional distributions of the risky asset's return (holding the marginal distribution of the background risk fixed); and changes in the marginal distribution of the asset's return (holding the conditional distributions of the background risk fixed). For the first question, a version of Gollier's (1995) Central Riskiness order is sufficient and necessary to increase risk-bearing. For the second question, Monotone Likelihood Ratio improvements are sufficient and necessary.