Optimal investment for a retirement plan with deferred annuities allowing for inflation and labour income risk

Abstract

We construct an optimal investment portfolio model for an individual investor saving in a retirement plan. The investor earns stochastic labour income with both permanent and temporary shocks, and has access to equity, conventional bond, inflation-indexed bond and cash, as well as two types of deferred annuities: nominal and inflation-protected. The objective function consists of power utility in terms of real retirement income from the annuities as well as bequest from remaining wealth in tradable securities. Asset returns are represented by a vector autoregressive model underpinned by Nelson–Siegel real and nominal yield curves. The optimization problem is solved numerically using multi-stage stochastic programming with a hybrid scenario structure combining a scenario tree with scenario fans. Our numerical results show that deferred annuities are bought early and in increasing amounts during the working lifetime of the investor, with portfolio risk declining with age. Welfare is diminished by 40% if deferred annuities are not available. Inflation-protected deferred annuities are marginally more important in the presence of real labour income risk, but nominal deferred annuities are bought as a cheaper alternative if real yields are low or negative. Portfolio composition and annuity allocation vary depending on financial market expectations, but our central result about the importance of deferred annuities is robust to a variety of financial market conditions.