Saving to Decumulate: a Lifetime Journey, Introducing the Perfect Contribution Rate and its Relation to the Perfect Withdrawal Rate 

Abstract

This paper examines the relationship between the accumulation (the contribution) and decumulation (withdrawal) phases of pension saving across one's economic life. These are concepts which are usually considered 'independent' but for which we find a surprisingly strong empirical relationship generated most likely by the long-run mean reversion of returns. Using evidence from a long run of US data since 1870 we introduce the idea of a Perfect Contribution Rate which is the annual contribution required over one's savings' life which will allow the individual to achieve a real wealth target prior to the start of decumulation assuming perfect foresight of asset returns. In particular, there is an interesting positive relation between PCR and subsequent PWR which we believe reflects mean reversion in asset returns over long time periods. In other words, if an agent has to save larger amounts to achieve their target wealth since investment returns are poor, then typically the subsequent (possible) withdrawal rates may also be large.

Keywords: Pension accumulation, Decumulation, Sequence Risk, Withdrawal Risk, Mean Reversion