Optimal annuitisation, housing and reverse mortgage in retirement in the presence of means-tested public pension

Abstract

In this paper we develop a retirement model under the expected utility stochastic control framework to find optimal decisions with respect to the consumption, risky asset allocation, access to annuities, reverse mortgage and the option to scale housing. The model is solved numerically using Least-Squares Monte Carlo method adapted to handle optimal stochastic control problems in the expected utility models. To demonstrate the applicability of the framework, the model is applied in the context of the Australian retirement system. Few retirees in Australia utilise financial products in retirement, such as annuities or reverse mortgages. Since the government-provided means-tested Age Pension in Australia is an indirect annuity stream which is typically higher than the average consumption floor, it is argued that this is the reason why Australians do not annuitise. In addition, in Australia where assets allocated to the family home are not included in the means tests of Age Pension, the incentive to over allocate wealth into housing assets is high. This raises the question whether a retiree is really better off over allocating into the family home, while accessing home equity later on either via downsizing housing or by taking out a reverse mortgage. Our findings confirm that means-tested pension crowds out voluntary annuitisation in retirement, and that annuitisation is optimal sooner rather than later once retired. We find that it is never optimal to downscale housing with the means-tested Age Pension when a reverse mortgage is available; only when there is no other way to access equity then downsizing is the only option.

Keywords: Dynamic Programming, Stochastic Control, Optimal Policy, Retirement, Means-Tested Age Pension, Defined Contribution Pension

JEL Classification: D14, D91, G11, C61