The Implied Longevity Yield: A Note on Developing an Index for Life Annuities

The Implied Longevity Yield: A Note on Developing an Index for Life Annuities We develop an index for tracking the dynamic behavior of life (pension) annuity payouts over time, based on the concept of self-annuitization. Our implied longevity yield (ILY) value is de…ned equal to the internal rate of return (IRR) over a …xed deferral period that an individual would have to earn on their investable wealth if they decided to self-annuitize using a systematic withdrawal plan. A larger ILY number indicates a greater relative bene…t from immediate annuitization. We suggest age 65 –with a ten year period certain –compared against the same annuity at age 75 as the standard benchmark for the index, and calibrate to a comprehensive time-series of weekly (Canadian) life annuity quotes for the years 2000 to 2004. We …nd that during this period the ILY varied from 5.45% to 6.90% for males and 5.00% to 6.42% for females and was highly correlated with a duration-weighted average yield of 10-year and long-term Government of Canada bonds. We believe our ILY metric can help promote and explain the bene…ts of acquiring lifetime payout annuities by translating the abstract-sounding longevity insurance into more concrete and measurable …nancial rates of return. JEL Classi…cation: H55, G12, G22, Keywords: Pensions, Financial Index, Insurance, Investments, Self-Annuitization, Mortality Credits 1 BACKGROUND AND MOTIVATION In this paper we develop a …nancial metric and index for tracking the time series behavior of life annuity payouts. Indeed, as North American baby boomers approach age 65 and their so-called retirement years there is a growing interest in pension and annuity issues, especially given the apparent liability crises in de…ned bene…t (DB) pension plans. Most retirees lack the actuarial intuition needed to understand the longevity insurance bene…ts of annuitization compared with traditional alternatives in the market. It is also di¢ cult to position the rate of return from life annuities within a portfolio’s risk and return context. We therefore believe that a properly designed annuity payout annuity index might contribute to a greater appreciation and intuition for these products. Against this demographic backdrop, a number of recent papers in the pensions, insurance and actuarial literature1 have explored the properties of self-annuitization. This retirement strategy is a consumption and investment plan that attempts to closely mimic the payout from a generic life annuity while allocating investable assets to minimize or limit the probability of lifetime ruin. This plan is not necessarily optimal within a classical life-cycle model with no bequest motives – in which continuously renegotiated tontine annuities are available –as originally demonstrated by Yaari (1965) and recently extended by Brown, Davido¤ and Diamond (2003). However, as pointed out by Yagi and Nishigaki (1993) and others, incomplete annuity markets is just one of the many theoretical justi…cations for consumers who shun annuitization. In practice, the popularity and interest in ‘drawdown’and ‘annuity alternative’continues to grow amongst practitioners. Our proposed index goes beyond a (trivial) cross-sectional average of life annuity payouts o¤ered by di¤erent insurance companies. Rather, our contemporaneous index value is de…ned equal to the internal rate of return (IRR) that an individual would have to earn on their …nancial portfolio during a deferral period, if they choose to self-annuitize, instead of purchasing a life annuity. We de…ne this IRR –which is based on the current term structure of annuity payouts – as the implied longevity yield (ILY) at a given age and for a given 1See Khorasanee (1996), Milevsky (1998), Kapur and Orszag (1999), Milevsky and Robinson (2000), Albrecht and Maurer (2002), Blake, Cairns and Dowd (2003), Gerrard, Haberman and Vigna (2003) as well as recent work by Huang, Milevsky and Wang (2004), Dushi and Webb (2004), Young (2004) and Reichenstein (2003)