# AN ANNUITY THAT PEOPLE MIGHT ACTUALLY BUY

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3 Issue in Brief 3 Table 3 compares the value of longevity insurance provided by an with that provided by a traditional annuity, as reported in Table 2. 8 Assuming a coefficient of risk aversion of five, an commencing at 85 provides 62.4 percent of the longevity insurance of an annuity. And achieving this protection through an can be done at the cost of only a small loss of liquidity (an issue that will be examined in more detail below). Table 3. Percent of Longevity Insurance Provided by an Purchased at Age 60 type Commencement Risk aversion Immediate % % Note: For assumptions, see Table 2. s and Annuities in Practice In practice, annuities are actuarially unfair, reflecting both adverse selection and expense loads. 9 Previous research has shown that the money s worth, the expected present value of the payments, discounted by an interest rate and annual survival probabilities, of a traditional immediate annuity is only 75 to 85 cents on the dollar to a household with population aver mortality. The precise result depends on whether the corporate or Treasury bond interest rate is used. 10 Calculations made for this brief indicate that the money s worth of inflation-protected annuities to someone with aver mortality is slightly less than 80 cents on the dollar, when payments are discounted at the Treasury Inflation Protected Securities interest rate. Multiplying the annuity equivalent wealth in Table 2 by 0.8 to adjust for actuarial unfairness results in figures close to one. These results imply that full annuitization at retirement is of only marginal benefit to the aver household. s are likely to be even more actuarially unfair than traditional annuities to the aver house- hold. s only start to pay benefits at advanced s, and people who purchase s are likely to have a much higher than aver probability of surviving to such s. But actuarial unfairness is a poor indication of the relative attractiveness of s. As shown earlier, households will have to spend only a small portion of their wealth to purchase an, so they will experience a relatively small amount of actuarial unfairness in dollar terms. Table 4 takes account of actuarial unfairness and compares strategies using annuities and s relative to a base case of undertaking an optimal decumulation of unannuitized wealth. The table shows the ratio of equivalent wealth of a household undertaking an optimal decumulation strategy relative to the alternative. When the factor is greater than one, the household is better off choosing the alternative. Purchasing a traditional annuity is of marginal benefit to the household. For example, the household is 2.6 percent better off at a coefficient of risk aversion of five. But when the household purchases an commencing at 85 and consumes the Table 4. and Equivalent Wealth Purchase Age 60 Incorporating Actuarial Unfairness Equivalent wealth Commencement Immediate Risk aversion Optimal strategy Naïve strategy Note: The assumptions are those used in Table 2 and authors estimates of the actuarial unfairness of s based on calculations of the -related variation in the actuarial unfairness of inflation-protected annuities currently on the market.

4 4 optimal amount every year from 60 to 84, it is 10.3 percent better off. (The result that the household is better off choosing the than either an immediate annuity or an optimal decumulation of unannuitized wealth is robust to alternative assumptions about mortality, interest rates, and expense loads.) 11 The above calculations assume that households undertake an optimal decumulation strategy with respect to unannuitized wealth. That is, they carefully trade off the risk of outliving their wealth against the cost, in terms of foregone consumption, of decumulating their wealth too conservatively. But determining an optimal consumption plan is a complex task. Most households, to the extent that they plan at all, probably adopt a rule of thumb, such as setting annual consumption equal to some percent of initial wealth. Such rules of thumb are likely to be far from optimal unless withdrawal rates are set at a very low level, households are at significant risk of outliving their wealth. Once a household purchases an, however, a naïve strategy of consuming an equal amount each period performs almost as well as the optimal strategy. A household would be only 0.8 ( ) percent worse off following the naïve strategy than following the optimal strategy. The transforms the difficult task of managing wealth decumulation over an uncertain period ending on the date of death to the much simpler task of managing decumulation over a certain period ending on the date on which the payments start. Finally, Table 5 shows the percent of initial wealth that a household would spend to purchase an, taking account of actuarial unfairness. A household purchasing an with benefits starting at 85 would optimally spend between 13.2 and 15.8 percent of its wealth on the product. As noted above, this would allow the household to undertake a naïve decumulation strategy between the time of purchase and the start of payments and be assured of an income for life. Table 5. Percent of the Household s Initial Wealth at Age 60 Spent on and type Conclusion Commencement Immediate Note: For assumptions, see Table 2. Risk aversion 100 % 100% Optimal strategy Naïve strategy The s attractiveness is that it provides a lot of longevity insurance at a relatively low cost. It also makes decumulation much simpler during the period before the payments kick in. It remains to be seen whether such a product would overcome annuity aversion. One possible solution might be to make the purchase of an the default in 401(k) plans. In a forthcoming paper, the authors of this brief investigate the distributional consequences of such a policy.

6 6 References Brown, Jeffrey R. and Mark J. Warshawsky Longevity-Insured Retirement Distributions from Pension Plans: Market and Regulatory Issues. Working Paper Cambridge, MA: National Bureau of Economic Research. Milevsky, Moshe Real Longevity Insurance with a Deductible: Introduction to Advanced-Life Delayed Annuities (). North American Actuarial Journal 9(4): Mitchell, Olivia S., James Poterba, Mark J.Warshawsky, and Jeffrey Brown. New Evidence on the Money s Worth of Individual Annuities. American Economic Review. 89(5):

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