Annuities and Random Interest Rates

Just buzzed through this paper (Dynamic Portfolio Choice with Annuities When the Interest Rate Is Stochastic Yannick Dillschneider, Raimond Maurer, and Peter Schober August 29, 2019). It was analytically a little dense for me. I can maybe 20% follow Americans and Canadians in their notation. For Germans writing in English, that drops off to about a 1% follow…on a good day. They lost me pretty quickly. Here are some excerpts, though:

· Economically, the mortality credit reflects the monetary value of the deallocation of wealth from states in which the annuitant is dead.

· In the presence of annuity risk, unconstrained optimal annuitization decisions are expected to be spread over the complete life cycle, opportunistically exploiting favorable market conditions and mortality credit constellations if they sufficiently outweigh the illiquidity costs due to irreversibility (see also Milevsky and Young 2007). By spreading annuity purchases over the whole life cycle instead of concentrating them to a single date, a significant temporal diversification of annuity risk may potentially be achieved.

· Therefore, imposing the restriction that annuitization can only occur at retirement could imply significant welfare losses. Our numerical model results support this conjecture. We find that one-time annuitization at retirement is economically costly relative to gradual annuitization over the whole life cycle, with the magnitude of the associated welfare losses being positively related to the prevailing level of interest rate risk. For example, the welfare loss over the whole life cycle amounts to −2.76 % of certainty equivalent consumption for our base case level of interest rate risk, while the welfare loss in retirement even totals −8.88 %

· We find that one-time annuitization at retirement leaves the annuitant with a significant welfare loss compared to gradual annuitization. This loss increases with the level of interest rate risk and nearly diminishes when there is no interest rate risk.

· This means, the optimal annuitization demand is spread over the life cycle, and the individual is opportunistically exploiting favorable interest rate states.

· Looking at preferences for early and late resolution of uncertainty, we find that average cumulated annuity claims are higher for higher EIS [elasticity of inter-temporal substitution], and interpret this result as long term precautionary savings of the to-be annuitant. All in all, our results underline the importance of allowing for temporal diversification of annuity risk, which contributes significantly to the welfare of the household.

-------

The caveats are as interesting as the conclusions and of which the last is the most:

· we did not include any actuarial loadings on annuity prices

· we assume that annuity prices promptly respond to changes in interest rates—which might not hold true in reality (Charupat, Kamstra, and Milevsky 2015) [ there is a lag ]

· we neglect inflation risk, which is as substantial as the interest rate risk for choosing optimal retirement policies (Koijen, Nijman, and Werker 2011)

· our interest rate model does not allow for the currently observed persistent low level of interest rates.