Estimating internal rates of return on income annuities

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1 Estimating internal rates of return on income annuities Vanguard research March 212 Executive summary. This paper presents computations of internal rates of return that would accrue to purchasers of fixed immediate annuity contracts based on recent prices from Income Solutions 1 and updated data on mortality patterns. These computations may be relevant to investors considering the relative value of the insurance provided by an annuity. We emphasize that annuities are a form of insurance, and that if they are evaluated solely on the basis of expected value, it is reasonable to expect a higher cost relative to an investment involving similar levels of risk that lacks the insurance feature. The point of our analysis is to estimate this cost differential. We conclude that annuities continue to be most appropriate for the population subset in good health, with substantial concern about expenses associated with living a long time, the ability to sacrifice liquidity on a fraction of their resources, and familiarity and comfort with the costs of annuitization. Authors Nathan Zahm John Ameriks, Ph.D. 1 Income Solutions is Vanguard s online annuity purchase program, in partnerhip with Hueler Investment Services; for more information, see vanguard.com/us/whatweoffer/annuities/income. Connect with Vanguard > vanguard.com

2 The desire to mitigate retirement income volatility and investment risk has led many individuals entering or in retirement to regard fixed immediate annuities (henceforth referred to in this paper as annuities ) as a potential source of income stability. For many investors making this decision, having some knowledge of the effective rate of return an annuity can generate is vital. In interpreting this data, it is critical that investors understand annuities are a form of insurance that, like other forms of insurance, will have low or even negative expected rates of return but this does not mean they are a bad deal. We expect to pay regular premiums and to lose money on insurance for our homes, autos, and health care in exchange for the substantial benefits it provides if needed. The same holds true for annuities: On average, an annuity should not be expected to generate a high return, but if life is unexpectedly long, it will have a higher payoff. We begin our discussion by examining estimates of the mortality/longevity patterns of potential annuity purchasers at different ages. We then compute internal rates of return (IRR) based on this data and recent real-world annuity quotations to provide insight on the returns that both average-lived and long-lived annuity purchasers would obtain from an annuity. Finally, we compare current annuity prices with those available when we sampled annuity data in April 211. Key terms Immediate annuity. An insurance product in which the purchaser pays an insurance company a set amount of money up front in exchange for a fixed monthly payment until death. Consumer Price Index (CPI) adjusted annuity. Similar to an immediate annuity, except the monthly payment is updated annually to reflect inflation based on the CPI. Internal rate of return (IRR). The rate at which future payments are discounted to equate them to a present value. In this case, the IRR is the rate the annuity payments are discounted to equate them to the annuity purchase price. 2

3 Figure 1. Median future length of life at various starting ages Number of future years Age 65 Age 7 Age 75 Age 8 Current age Longest lived of a male/female couple Note: Results reflect mortality assumptions from the Society of Actuaries RP-2 gender-distinct annuitant mortality tables, projected generationally using Scale AA. Estimating future life expectancy When determining the IRR for an annuity, the expected future lifetime of the annuity purchaser needs to be estimated. Throughout this paper, we use the RP-2 gender-distinct annuitant mortality tables projected generationally with Scale AA. These data were assembled by the Society of Actuaries based on the experience of a large set of healthy annuitants (that is, people without disabilities) who were eligible for lifetime pension benefits. We believe these mortality assumptions provide a good baseline estimate of the mortality for those contemplating purchasing an annuity. Using these mortality assumptions, Figure 1 shows the median number of future years that potential annuity purchasers can expect to live at different starting ages. 3

4 Figure 2. Pre-tax annual annuity payments per $1, annuitized amount: fixed annuity $12, 1, 8, 6, $6,771 $6,32 $5,66 $7,734 $7,135 $6,26 $9,164 $8,433 $7,187 $1,966 $1,123 $8,42 4, 2, Age 65 Age 7 Age 75 Age 8 Age of annuity purchase/commencement 1% joint Source: Vanguard, Income Solutions. Current annuity pricing Figures 2 and 3 present recent annual annuity payouts based on the average of quotations obtained from the Vanguard Income Solutions annuity tool. All payments continue for life only. Joint annuity assumes a male-female couple with a 1% benefit to a survivor of the same age. Quotations were obtained on October 27, 211, based on a $1, total purchase for annuitants born on December 1, 211, minus the indicated age, for payments commencing December 1, 211. Annual payments are the sum of 12 monthly installments. For a 65-year-old couple potentially facing 3 or more years in retirement, a typical initial withdrawal recommendation is 3.5% 4.% of their portfolio balance at age 65, with that dollar amount adjusted for inflation thereafter. Figure 3 shows that a CPIadjusted income annuity would roughly be 3.85% of the $1, purchase price ($3,849 annually) for a 65-year-old couple, adjusted for inflation thereafter. At the cost of relinquishing control and liquidity of a lump sum, joint annuitants are therefore able to stay in the range that they could safely spend, while eliminating the risk that poor performance of their portfolio will force them to reduce withdrawals in the future. It is important to note that only the CPI-adjusted payments actually provide an income flow directly comparable to an inflation-adjusted withdrawal strategy. Although the fixed annuity option in Figure 2 provides even higher payments initially, this option leaves the retiree more exposed to substantial inflation risk over time. 4

5 Figure 3. Pre-tax annual annuity payments per $1, annuitized amount: CPI-adjusted annuity $1, $9,294 $8,56 8, 6, 4, $4,964 $4,481 $3,849 $6,22 $5,388 $4,593 $7,62 $6,832 $5,684 $6,975 2, Age 65 Age 7 Age 75 Age 8 Age of annuity purchase/commencement 1% joint Source: Vanguard, Income Solutions. Annuitant returns, on average Annuitants pay a price or load for annuitizing, reflecting the fact that insurers must: Price conservatively, because people who voluntarily buy income annuities live longer than others. Maintain a reserve against the risk that the entire population may live longer than actuaries currently anticipate. Pay for administrative costs. Make a profit. Typically these costs are not separately identified in the disclosures that insurers provide to annuity purchasers. Purchasers simply see an all-in annuity quote as a single net yield offering and must assess the attractiveness of the annuity arrangement on that all-in basis (much like an all-in interest rate quote on a certificate of deposit [CD] from a bank). The ultimate payoff for owning an annuity (or any other individual insurance policy) relates to individual specific characteristics and risks. Thus, it is difficult to assess expected returns for any particular individual without knowing specific facts and circumstances. However, the typical risk faced by potential annuitants can be estimated and then used to estimate the IRR on an annuity contract for customers whose characteristics are close to the median in the mortality table. One important characteristic used to derive the mortality estimates discussed here is that the annuitants are healthy individuals at the time of purchase. For potential annuitants with chronic medical conditions that could affect their length of life, analyzing such data is not an appropriate way to estimate potential rates of return. 5

6 Figure 4. Nominal median internal rates of return: fixed annuity 4% % 3.27% 3.18% 3.2% 3.2% 2.69% 2.74% 2.37% 2.28% 2.4% 1.81% 2.28% %.55%.45% % Age 65 Age 7 Age 75 Age 8 Age of annuity purchase/commencement 1% joint 2-/1-year U.S. Treasury Notes: Treasury rates are based upon average yields for the week of Monday, October 24, 211. Results reflect mortality assumptions from the Society of Actuaries RP-2 gender-distinct annuitant mortality tables, projected generationally using Scale AA. For advanced-age purchasers, the mortality assumption we are using may not reflect the typical individual contemplating an annuity purchase. Specifically, the RP-2 table represents the mortality patterns of those who generally make annuitization decisions at significantly younger ages. Those seeking to purchase life annuities at advanced ages may well be a significantly healthier group. Figures 4 and 5 show the IRR on annuities at different ages of purchase for annuitants surviving to their median life expectancy, under the RP-2 projected annuitant mortality tables (see the appendix for IRRs for alternative ages of survival). We compare the median IRR for the fixed annuities with a corresponding risk-free investment (in this case, either the 2- or 1-year U.S. Treasury Inflation-Protected Securities [TIPS] are used for comparison with CPI-adjusted annuities). The 2-year Treasury is used for comparison for the 65- and 7-year-old annuity purchaser, while the 1-year Treasury is used for the 75- and 8-year-old purchaser, to adjust for the shorter life expectancy. According to these estimates, the annuity provides insurance at a cost, which is substantial at later purchase ages, to the typical purchaser. In general, the IRR estimates for inflation-linked annuities are relatively further beneath comparable Treasury yields than are nominal fixed annuities. The IRRs in Figure 5 for CPI-adjusted payments are returns above inflation, similar to TIPS yields. The median IRR on a single life CPI-adjusted annuity for a 65-year-old man is 79 basis points lower than the real yield of the 2-year TIPS (which is.74%). In the case of the nominal fixed annuity, the median IRR for a 65-year-old male is slightly ahead of the comparable 2-year Treasury note. For all payout options, median IRRs fall with the increasing age at which purchase occurs, most likely as a result of increased adverse selection/conservative pricing (see Walliser, 2). For most commencement ages, IRRs are higher for women and joint annuitants, meaning that estimated costs are generally lower. For males considering the purchase of an inflation-adjusted annuity, we estimate that the median real IRRs are negative, becoming substantially so at advanced ages. 6

7 Figure 5. Real median internal rates of return: CPI-adjusted annuity 2% %.8%.7%.74%.63%.38%.95%.74% 1.36%.88%.19%.19% % 2.54% % % Age 65 Age 7 Age 75 Age 8 Age of annuity purchase/commencement 1% joint 2-/1-year TIPS Notes: Treasury rates are based upon average yields for the week of Monday, October 24, 211. CPI-adjusted IRRs are real rates of return (i.e., above inflation), similar in concept to TIPS returns. Results reflect mortality assumptions from the Society of Actuaries RP-2 gender-distinct annuitant mortality tables, projected generationally using Scale AA. For advanced-age purchasers, the mortality assumption we are using may not reflect the typical individual contemplating an annuity purchase. Specifically, the RP-2 table represents the mortality patterns of those who generally make annuitization decisions at significantly younger ages. Those seeking to purchase life annuities at advanced ages may well be a significantly healthier group. As stated earlier, substantial costs do not necessarily mean that annuities are not worth the expense. They simply mean that those who buy annuities are obtaining insurance, not superior returns. As with many other forms of insurance such as health, auto, or life insurance, the expected unconditional return on owning an annuity is generally less than that for investments with similar investment risks. However, returns conditional on the realization of the insured risk are generally higher than comparable investments. The same is true of annuities. Individuals must decide whether the benefits promised in the case of long life are worth the typical costs. This is a case of trade-offs, not right or wrong answers. Returns for long-lived annuitants As noted earlier, income annuities can potentially provide a valuable benefit to retirees worried about the possibility of living longer than the typical life expectancy. Not everyone will have a typical life span. Figures 6 and 7, on page 8, show the internal rates of return that would be received by the longestlived 25% of the population that may be considering purchasing an annuity (given the same payouts cited earlier, as well as the earlier mortality estimates). Thus, for an individual who ends up living longer than 75% of the population, the payoff for having owned the life annuity can be substantial. The internal rates of return for this group are all above current yields 7

8 Figure 6. Nominal internal rates of return for 75th percentile length of life: fixed annuity 7% % 4.64% 5.7% 4.86% 5.25% 5.34% 4.69% 5.59% % 3.99% 4.8% 3.95% 3 3.2% 3.2% 2.28% 2.28% 2 1 Age 65 Age 7 Age 75 Age 8 Age of annuity purchase/commencement 1% joint 2-/1-year Treasury Note: Seventy-fifth percentile life expectancy was calculated by determining the age at which the mortality table indicated a 25% chance of survival from the annuity purchase age. Figure 7. Real internal rates of return for 75th percentile length of life: CPI-adjusted annuity 4% % 2.65% 2.77% % 1.68%.99%.74% 2.22% 1.98% 1.17%.74% 1.48% 1.62% 1.34% 1% joint 2-/1-year TIPS.19% Age 65 Age 7 Age 75 Age 8 Age of annuity purchase/commencement.19% Note: Seventy-fifth percentile life expectancy was calculated by determining the age at which the mortality table indicated a 25% chance of survival from the annuity purchase age. 8

9 available on investments with comparable investment risk over similar horizons. These rates are the lowest that would be ultimately received by this long-lived group; and the longest-lived of those within this group will receive even higher rates of return. These facts are not intended to minimize annuitization costs to those that do not live a long time. The data simply demonstrate that income annuities can provide effective insurance against longevity risk by providing higher returns if life is long. (See the appendix for the number of future years of expected life by those with life spans at the 75th percentile.) Historical comparison Current interest rates significantly affect the annuity payout, and lower interest rate environments will drive up annuity quotes in terms of the price per dollar of income and drive down IRRs. Figure 8 shows the change in annuity income for a $1, purchase from April 2, 211 to October 27, 211. Figure 8 s comparison shows that purchasing an annuity today is less rewarding than it was six months ago. The reduction in payouts from an annuity purchase arises primarily from changes in interest rates but is also affected by mortality improvement, any changes in the degree of adverse selection that insurers face, and, for CPI-adjusted annuities, higher inflationary expectations (or, equivalently, lower real rates of return). Conclusion This paper s findings are consistent with patterns observed in earlier estimates of annuity costs (see Brown et al., 21; and Ameriks, 25). When considering annuities, it s important to remember that the annuity is an insurance product first, and thus comes with costs. Costs arising from adverse selection in the insurance market and from administering the annuities are substantial. Other trade-offs in lost liquidity and potentially lower bequests to heirs must also be considered. Alternatively, annuities can help provide a base level of income stability in conjunction with Social Security for retirees. In addition, as noted earlier, for those living beyond their median life expectancy, the returns from an annuity can be substantial. Figure 8. Fixed CPI-adjusted Male Single life Age % 6.7% Age Age Age Female Single life Age % 6.48% Age Age Age Joint and 1% survivor Age % 7.53% Age Age Age Annuities continue to be most appropriate for the population subset in good health, who have substantial concerns about costs involved in living a long time, who have the ability to sacrifice liquidity on a fraction of their resources, and who are familiar and comfortable with the costs that annuitization involves. References Percentage change in annual annuity payments per $1, annuitized amount: 4/2/211 through 1/27/211 Ameriks, John, 25. The Basics of Income Annuities. Valley Forge, Pa.: The Vanguard Group. Brown, Jeffrey R., Olivia S. Mitchell, James M. Poterba, and Mark J. Warshawsky, 21. The Role of Annuity Markets in Financing Retirement. Cambridge, Mass.: MIT Press. Walliser, Jan, 2. Adverse Selection in the Annuities Market and the Impact of Privatizing Social Security. Scandinavian Journal of Economics 12(3):

10 Appendix. Background data Figure A-1. 75th percentile future length of life Age 65 Age 7 Age 75 Age 8 Current age Longest lived of a male/female couple Note: Results reflect mortality assumptions from the Society of Actuaries RP-2 gender-distinct annuitant mortality tables, projected generationally using Scale AA. Figure A-2. Nominal internal rates of return based on survival age Age of death Purchase age a. Male fixed annuity % 7.8%.21% 3.25% 4.76% 5.6% 6.9% b. Female fixed annuity % 8.21%.7% 2.47% 4.6% 4.95% 5.49% c. Joint and survivor fixed annuity* % 9.94% 2.1% 1.27% 3.% 3.98% 4.58% *Last survivor age of death. Note: Internal rates of return based on the annuity payouts as shown in Figure 2, on page 4. 1

11 Figure A-3. Real internal rates of return based on survival age Age of death Purchase age a. Male CPI-adjusted annuity % 11.91% 3.68%.7% 1.81% 2.9% 3.57% b. Female CPI-adjusted annuity % 13.38% 4.86% 1.7%.93% 2.1% 2.83% c. Joint and survivor CPI-adjusted annuity* % 15.46% 6.53% 2.48%.31%.99% 1.81% *Last survivor age of death. Note: Internal rates of return based on the annuity payouts as shown in Figure 3, on page 5. 11

12 P.O. Box 26 Valley Forge, PA Connect with Vanguard > vanguard.com Vanguard research > Vanguard Center for Retirement Research Vanguard Investment Counseling & Research Vanguard Investment Strategy Group > Vanguard Annuity Access is offered in collaboration with Hueler Investment Services, Inc., through the Income Solutions platform. Income Solutions is a registered trademark of Hueler Investment Services, Inc., and used under license. United States Patent No. 7,653,56. Vanguard Annuity Access is provided by Vanguard Marketing Corporation, d/b/a VMC Insurance Services in California. 212 The Vanguard Group, Inc. All rights reserved. Vanguard Marketing Corporation, Distributor. ICREIR 3212

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