Several targeted welfare programs across the world have made owner-occupied housing exempt from the means test, such as the Supplementary Social Income (SSI) in the US and the age pension scheme in Australia. Relatively little is known about the impact of such exemption on household portfolio choice. We study the case of the Australian age pension scheme, and argue that current uncapped exemption may lead to distortionary incentives for very high levels of housing wealth to be sheltered from the means test. We set up a quantitative lifecycle framework, with business and housing investment, borrowing constraints, and wealth inequality, that is able to match a number of key features in the Australian economy. We find that abolishing the current exemption of owner-occupied housing in the assets test increases aggregate output, capital accumulation, and welfare, while lowering housing investment and homeownership. However, removing such distortions, however, does not necessarily imply that all households would be better off. The lowering of other taxes to maintain fiscal balance would result in households at the top of the wealth distribution experiencing a large welfare loss, however the majority of the population would benefit.