Annuity Duration

Duration is a measure of the time associated with cash flows or payments from a bond. Duration measures the amount of time (in years from the purchase date) required for a bond owner to receive interest and principal payments that are equal to the cost of the bond.

Long duration bonds have payments that are spread-out over a relatively long period of time (e.g. 10-20 years). Shorter duration bonds have payments that might span over five years or less.

Duration provides an indication of how much a bond’s price will change when interest rates change. The prices of long duration bonds are more sensitive than short duration bonds to changes in interest rates. As a result, long duration bond prices increase the most when interest rates fall and decrease the most when interest rates rise.

Annuities also provide fixed payments and have prices that are sensitive to changes in interest rates.

Similar to bonds, annuity prices move in the opposite direction of interest rates:

  • When interest rates increase, a higher annuity payout can be obtained for a given amount of money so the annuity can be seen as “less expensive.”
  • When interest rates decrease, the same pile of money that would be converted into an annuity results in a lower payout.

Consider the following example where $100,000 is used by a single 65 year old male to purchase a single premium immediate annuity when interest rates are 2 percent:

  • This $100,000 premium results in an annual annuity payout of $7,400.
  • Another way of looking at this is that the cost of buying $7,400 in annual pension income is $100,000.

Next, consider the same 65 year old single male using $100,000 to purchase a single premium immediate annuity when interest rate are 4 percent:

  • This $100,000 premium results in an annual annuity payout of $8,846.
  • Securing $8,846 in annual pension income costs $100,000.

The concept of duration does apply to annuities. Professor Moshe Milevsky and two colleagues examine annuity duration in a recently published research paper titled The Annuity Duration Puzzle

Professor Milevsky’s paper looks at duration in the context of a life-contingent single premium immediate annuity where cash flows begin right away and are fixed over the life of the annuity owner. The authors’ analysis produces several interesting results and conclusions regarding annuity duration:

  • Unlike bond prices, annuity prices to not adjust rapidly in response to changes in interest rates.
  • Annuity prices adjust in response to changes in interest rates over a period of weeks or even months.
  • The 30 year U.S. mortgage rate provides is a better indicator of future annuity payouts than conventional “risk-free” interest rate benchmarks such as the 10 year swap rate.
  • Annuity duration is asymmetric--annuity prices adjust faster in reaction to increases in interest rates than decreases in interest rates.

As Prof Milevsky acknowledges, the research results have broad implications--not the least of which is the whole issue of when is the best time to buy an annuity.

What would also be interesting is to compare SPIA to longevity annuity in the context of duration. Since longevity annuities are deeply deferred income annuities their payments are pushed-out many years (potentially multiple decades) into the future.

Are longevity annuities analogous to very long duration bonds with the weighted average of future cash flows pushed so far into the future?

If so, longevity insurance prices would presumably be very sensitive to interest rate changes (especially increases), and potential buyers of longevity insurance might have reason to consider waiting or delaying their irrevocable decision to buy. After all, the value of monetizing one’s mortality only increases with age and interest rates are currently at the zero bound. 

That said, mortality credits are a relatively large component of longevity annuity coupons since those payments begin late in life. The mortality yield component is presumably affected entirely by mortality trends rather than changes in interest rates. An income annuity amortization schedule that shows the ebb and flow of the various components of the annuity coupon (interest payments, mortality credits, etc) over time would be interesting.

Maybe the single premium immediate annuity represents longer duration than the longevity annuity since the mortality credits--if the product is purchased at a younger age--are a relatively small portion of the coupon and the interest component is relatively large.



Professor Milevsky just published a shorter piece on annuity duration.

It presents the actual formula for annuity duration.

Also interesting to note that Prof Milevsky's piece confirms that:

  • Annuity duration is inversely related to age (shorter duration at older ages).
  • This means that those who might be waiting to annuitize at older ages will not get the bang for the buck if and when interest rates do increase.
  • Single premium immediate annuities that are purchased at older ages are much more sensitive to changes in mortality rates than changes in interest rates.  The isssue, though, is that the mortality rates are not nearly as volatile/dynamic as interest rates.