Floor and Upside Investing in Retirement with Nominal SPIAs

Abstract

I investigate optimal stock/bond asset allocation, gradual SPIA purchase decisions, and consumption decisions in retirement. I use a utility function that is intended to be representative of a retired individual's need for an income floor and desire for upside potential. The optimal strategy is similar in terms of asset allocation to the optimal strategy for stocks and bonds alone, but with annuitization occurring. Bond and stock annuitization appear to largely occur independently. Annuitization is both portfolio size and age dependent. Portfolio size dependent annuitization may start to occur prior to age 50. Unlike traditional floor and upside recommendations no SPIAs should be purchased if the portfolio is too small or too large. Turning to age dependence, the annuitization of bonds occurs earlier than the annuitization of stocks. For a male, bonds are fully annuitized by about age 62, and stocks are annuitized from about age 72 to 81. The results for a female are delayed by about 3 years. Nominal SPIAs are purchased even once annuitization reaches a maximum to counter the loss of purchasing power of nominal SPIAs due to inflation. The observed improvement in consumption from the availability of nominal SPIAs ranges from 11 to 53% depending upon age and portfolio size.

Keywords: single premium immediate annuity, SPIA, gradual annuitization, asset allocation, consumption, stochastic dynamic programming