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

I 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 defined equal to the internal rate of return (IRR) over a fixed 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 benefit from immediate annuitization. I use age 65-with a 10-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 from 2000 through 2004. I find that during this period the ILY varied from 5.45 percent to 6.90 percent for males and from 5.00 percent to 6.42 percent for females and was highly correlated with a duration-weighted average yield of 10-year and long-term Government of Canada bonds. I believe our ILY metric can help promote and explain the benefits of acquiring lifetime payout annuities by translating the abstract-sounding longevity insurance into more concrete and measurable financial rates of return. Copyright The Journal of Risk and Insurance.