Why do household portfolio shares rise in wealth?

We develop a life-cycle consumption and portfolio choice model in which households have nonhomothetic utility over two types of goods, basic and luxury. We calibrate the model to match the cross-sectional and life-cycle variation in the basic expenditure share in the Consumer Expenditure Survey. The model explains the degree to which the portfolio share in risky assets rises in wealth in the cross-section of households in the Survey of Consumer Finances. For a given household, the portfolio share can fall in response to an increase in wealth, even though the model implies decreasing relative risk aversion.