Optimal annuity portfolio under inflation risk

Abstract

The paper investigates the importance of inflation-linked annuities in retirement planning. Given nominal, inflation-linked, and variable annuities, as well as bonds and stocks, we search for optimal consumption and investment decisions under two different objective functions: (1) maximization of expected utility of real consumption, and (2) minimization of expected deviations from an inflation-adjusted target. When optimizing the objective, we allow for rebalancing the portfolio during retirement by buying additional annuities and by trading bonds and stocks. To find the optimal solution, we apply a multi-stage stochastic programming approach. Our findings indicate that independently of the considered objective function, real annuities are a crucial asset in every portfolio. In addition, without investing in real annuities, the retiree has to rebalance the portfolio more frequently, and still obtains a lower and more volatile real consumption.