Lifetime consumption and investment with housing, deferred annuities and home equity release

Abstract

We develop a life-cycle optimal investment and consumption model with deferred annuities, housing, mortgages and home equity release. The investor can hold cash, bonds, stocks, annuities and can invest in housing, through renting, purchasing, or a mix of both, with access to variable-rate mortgages. In retirement, the investor can access his housing equity through a form of home equity release called a home reversion contract. Transaction costs, taxes and management fees are explicitly included. The investor’s risk preferences are represented by standard power utility derived from housing and non-housing consumption, both before and after retirement, and from bequest. We use multi-stage stochastic programming to solve the optimization problem numerically. Our results show that both non-housing and housing consumption may be higher in retirement when deferred annuities and home reversion are available than when they are absent. The bequest motive has little effecton home reversion and results in a small reduction in overall annuitization.