My previous article in this series introduced protected lifetime income benefits (PLIBs), and was based on a larger research paper. PLIBs are similar to products that offer a guaranteed lifetime withdrawal benefit (GLWB), but I created a separate category since the income calculation process can be different, and income can decline with a PLIB. PLIBs are not new; similar strategies such as tontines have been available for centuries.
The article explores the efficacy of PLIBs against a retirement income strategy that does not include an annuity, as well as strategies which allocate to either a single-premium immediate annuity (SPIA), a deferred-income annuity (DIA, which could be a qualified longevity annuity contract, or QLAC, if purchased in a qualified account assuming certain provisions are met), or a GLWB. I used a utility framework for this analysis.
Overall, the potential benefits of the approaches vary depending on the specific client situation. One important determinant of efficacy is the portfolio withdrawal rate; there is relatively little difference among strategies for well-funded retirees (i.e., with lower withdrawal rates), while PLIBs were superior for more aggressive withdrawal rates and outperformed GLWBs.
PLIB strategies are an exciting evolution of GLWBs and should be considered as part of a holistic income strategy for retirees. In the next article in the series, I will explore some of the drivers of the efficiency of PLIBs and provide context on optimal risk levels.
The optimal strategy
The optimal retirement income strategy is determined using an approach based on the constant relative risk aversion (CRRA) utility function, shown in equation 1, where the amount of utility received varies depending on level of consumption and level of investor risk aversion
I used a utility-based approach, versus other more commonly used metrics among financial advisors such as the probability of success, since it better captures the economic implications of shortfall in retirement. The CRRA utility function incorporates the law of diminishing marginal utility, whereby negative outcomes (especially extreme negative outcomes) are weighted more heavily than positive outcomes. The specific utility approach used in this research is a modified version of the approach introduced by Blanchett and Kaplan (2013). Please refer to the main paper (appendix 1) for additional information on the particular model.
My analysis assumes the household is a male and female couple, both age 65, retiring immediately with $500,000 in savings. The savings amount assumed for the analysis is not important compared to the saving relative to other sources of retirement income. Taxes are ignored for the analysis.
I considered four different types of annuities: a SPIA, a DIA, a GLWB, and a PLIB. I varied the allocations by product to have approximately the same level of income for the products, which generates income immediately (SPIA, GLWB, and PLIB) while the DIA generates roughly double the income of the immediate-income products.
I determined the payout rate for the SPIA by averaging the five highest available quotes obtained from CANNEX on April 27, 2022 for a 65-year old couple, male and female, with a 100% continuation benefit and a 20-year period-certain rider. The average payout was 5.45%. While researchers commonly assume retirees purchase life-only annuities, only a minority of annuities quoted are life-only (and likely even a lower percentage of sales). For example, only 12.87% of the 669,574 annuities quoted by CANNEX (2021) in the calendar year 2020 were life-only. The SPIA allocation is assumed to be 30% of the initial balance.
The payout rate for the DIA is determined by averaging the five highest available quotes obtained from CANNEX on April 27, 2022, for a 65-year-old couple, male and female, with a 100% continuation benefit with a cash-refund provision where payments commence at age 80. The average payout was 14.92%. The DIA allocation is assumed to be 20% of the initial balance.
The GLWB is assumed to have a 4.5% payout rate[1] with a 60% equity allocation and 1.5% total annual fee, which is assessed against the contract value. This is consistent with institutionally priced products, especially those available in the fee-only advisor space or in defined-contribution plans. The GLWB allocation is assumed to be 35% of the initial balance and the benefit base is assumed to step-up annually if the contract value exceeds the previous year’s benefit base.
The PLIB is assumed to have a 4.0% initial payout rate with a 1.5% total annual fee. Income from the PLIB changes based on account performance, which is reduced by the total contract fee (i.e., 1.5%). In other words, if the PLIB achieves a return of 0% per year, the income amount would decline by 1.5% (the fee). The assumed equity allocation for the PLIB is 40%, to reflect the higher risk implications of lower returns (i.e., the subsequent reductions in lifetime income), although the equity allocation is varied as part of the analysis to determine optimal equity levels across scenarios. The income from the PLIB is assumed to remain constant once the account value is depleted. The PLIB allocation is assumed to be 35% of the initial balance.
Rather than testing a single set of household attributes, I considered a variety of scenarios by varying four key parameters:
1. Portfolio equity allocation: This is the equity allocation for the investment portfolio (i.e., the monies that are not annuitized) and is assumed to remain constant for the duration of retirement. The low, mid, and high equity allocations tested were 10%, 40%, and 70%, respectively. The total assumed expense ratio of the portfolio was assumed to be .50%.
2. Social Security retirement benefits: The household is assumed to have Social Security retirement benefits of either $10,000, $30,000, or $50,000, resulting in low, mid, and high levels, respectively. The absolute value of the Social Security retirement benefits is not important; rather it’s the relative amount of the guaranteed income to total savings (which is held constant at $500,000).
3. Shortfall risk aversion: This variable captures how an income shortfall would affect a retiree household based on the utility model.
4. Initial portfolio withdrawal rate: Since I am opposed to assuming the retiree household follows an “optimal” withdrawal strategy, a variety of initial withdrawal rates are tested to determine how the strategies vary across different funding levels. Households with lower withdrawal rates would be considered better funded for retirement, since the required withdrawal rate will be lower.
Three separate types of returns were generated for the analysis: inflation, bonds, and stocks. Annual returns for the three asset classes were assumed to be 2.5%, 3.5%, and 8.5%, respectively, with standard deviations of 1.5%, 7.0%, and 18.0%, respectively. Returns were assumed to be normally distributed. While the actual historical annual returns of these assets have not been perfectly normally distributed, they have been approximately so, especially at the frequency considered (annual). The correlation between these asset classes was assumed to be zero, which is also roughly consistent with historical values.
The return assumptions for the analysis reflect the bond yield environment, since the rate environment plays an important role in annuity pricing (especially for SPIAs and DIAs). While it’s certainly possible bond yields (and the respective payouts for annuities) could increase and return closer to long-term averages, assuming interest rates would rise in the forecast would bias the results (in particular against SPIAs and DIAs, since they are priced based on the current rate environment).
Mortality rates for the analysis were based on the Society of Actuaries Individual Annuity Mortality (2012 IAM) table with improvement to year 2022. Mortality rates for the couple were assumed to be independent and the retirement goal is assumed to be the same whether either or both members of the couple are alive.
Using the utility model to select the optimal strategy
While utility models are incredibly common in academic literature, they are rarely used (or available) in financial planning programs, especially those commonly used by financial advisors, where probability of success-type metrics is most common.
Utility models quantify satisfaction, where the higher the resulting utility, the “better” the respective strategy. When selecting among a variety of potential options, the strategy with the highest utility would be considered optimal. A utility model can be used to compare the efficacy of different retirement-income strategies, providing insights into not only whether a household should annuitize, but if so, which type of product would be optimal.
The exhibit below includes the utility values for various real initial withdrawal rates from 2% to 8% for the five strategies included in the analysis. The results are based off the moderate base set of assumptions, where the portfolio equity allocation equals 40% (mid value), Social Security retirement benefits equal $30,000 (mid value), and the risk aversion level is moderate.
The utility levels are virtually identical at lower initial withdrawal rates (e.g., up to a ~3% real initial withdrawal rate). This is because the retiree household is unlikely to deplete savings when spending rates from assets are relatively low, which means the specific strategy selected will not materially affect the outcome. This suggests, for example, that retirees with relatively low portfolio withdrawal rates do not need to annuitize. This is consistent with expectations, since annuities are effectively a form of lifetime income insurance, guaranteeing some minimum level of support for spending, which is going to be less of a concern if the household has high relative wealth.[2]
The higher the initial withdrawal rate, the higher the probability of portfolio depletion and therefore the more likely the household would benefit from an annuity, and the differences in utility across annuities increase as withdrawal rates increase. Other factors also impact the resulting utility estimates, such as the existing guaranteed income sources (i.e., Social Security retirement benefits), income risk aversion levels, etc., which we will discuss more next.
Certain strategies in the previous exhibit clearly result in more utility (i.e., are better) than others, a point which becomes clearer at higher withdrawal rates (e.g., a 7% withdrawal rate). To rank the strategies based on their utility (from high to low), the results would be: PLIB, SPIA, DIA, GLWB, and no annuity. In other words, the PLIB strategy is best among the five, while the no-annuity strategy is the worst (compared to not annuitizing).
Scenario analysis
For the scenario analysis, I list the optimal strategy for each scenario among the five possible options. I imposed a constraint where the utility values from the strategies that include an annuity must be at least 1% higher than the non-annuity option for the respective scenario. If they do not exceed that threshold, the non-annuity strategy was assumed optimal. This “hurdle” was imposed to reflect the fact that if strategies result in utility values that are substantially similar, a household would be more likely to select the one that does not include an annuity.
While I was primarily focused on the relative efficiency of the strategies tested, in most instances each of the strategies that includes an allocation to an annuity was better than the one that did not. In other words, any of the four strategies was generally better than not annuitizing. Therefore, while I effectively assume a household would be indifferent between GLWBs, PLIB, SPIAs, and DIAs, if the household is only willing to entertain certain strategies (e.g., a DIA) doing so would likely be better than not annuitizing, consistent with decades of research on this topic.
Since I was opposed to selecting a potential single representative set of attributes, I varied the assumed attributes to approximate different households for robustness purposes. My analysis considered 135 different potential scenarios with the key attributes varying by risk aversion level, Social Security retirement benefits, portfolio allocations, and the initial real withdrawal rate.
The exhibit below includes the optimal strategy for real withdrawal rate for the five strategies considered. The average optimal safe initial withdrawal rate (considering all strategies and potential withdrawal levels) was 4.4%, which is why the 4% is the middle initial real withdrawal rate was selected.
There are several notable takeaways. The optimal initial real withdrawal rates differed significantly by scenario. For example, a household that does not purchase an annuity with a very high level of risk aversion, with $10,000 in assumed Social Security benefits, and a 10% portfolio equity allocation would have a 2.00% initial real withdrawal rate. In contrast, another household that also does not wish to annuitize, but has a very low level of risk aversion, with $50,000 in assumed Social Security benefits, with a 70% portfolio equity allocation should have an initial real withdrawal rate of 5.84%. This is a staggering difference, especially since the assumed portfolio value is the same for both scenarios. This highlights a key weakness of using metrics like the probability of success to determine initial safe withdrawal rates because they generally cannot appropriately consider things like the magnitude of failure during retirement.
Optimal initial withdrawal rates increased when considering an annuity, from 3.65% to 4.40% on average, but to varying degrees across household scenarios. The benefits of allocating to an annuity tended to be higher for households with higher risk aversion levels with lower levels of existing guaranteed income (i.e., Social Security retirement benefits). The impact of these is intuitive since a household that is more risk averse with respect to an income shortfall would benefit more from transferring the longevity risk income component versus one that is more risk tolerant. The impact of guaranteed income level relates to the potential impact to consumption if the portfolio is depleted. Households with relatively higher levels of guaranteed income level rely less on income from the portfolio to fund consumption and therefore are less affected should the portfolio become depleted.
The general optimal annuitization strategy differed notably by withdrawal rate. For the lowest initial withdrawal rates (e.g., 3% nominal) not annuitizing or considering a SPIA or DIA was optimal, assuming the household was comfortable with the irrevocable nature of the products. As the withdrawal rate increased, the PLIB became the most attractive while the GLWB was never optimal for any of the scenarios considered.
The optimality of the PLIB compared to the SPIA and DIA seems like a “free lunch” to some extent, since PLIBs generate similar levels of certainty-equivalent income and do not require an irrevocable election. I will provide some context around the drivers of this effect in a future article, but the differences are likely due to a variety of factors, such as lapsation, mortality experience differences, differences in return expectations (in particular the ability of the PLIB to access the positive assumed equity risk premium), and the marginal role of an annuity when it comes to funding retirement income.
Conclusions
The “annuity puzzle” is still alive and well in America. But a new guaranteed income product strategy that is gaining adoption in the market, that holds significant promise, an approach I refer to as a “protected lifetime income strategy” or PLIB.
PLIBs are structurally similar to GLWBs, but there are notable differences in how the benefits evolve during retirement. The increased risk “sharing” approach of a PLIB benefits retirees, especially those targeting higher initial withdrawal rates (who are therefore more likely to benefit from annuitization).
PLIBs exist in a variety of structures, such as overlaying a regular portfolio (e.g., as CDA) or within an annuity, and be combined with a variety of investment strategies, such as FIAs, VAs, RILAs, etc.
However, the most important objective is to get retirees to increase their allocations to guaranteed income. While PLIBs may be more efficient than other approaches (e.g., GLWBs), any one of the annuity strategies considered is better than not annuitizing, and therefore retirees and financial advisors should determine the optimal strategy in light of the unique preferences of the client.
David Blanchett, PhD, CFA, CFP®, is managing director and head of retirement research at PGIM. PGIM is the global investment management business of Prudential Financial, Inc. He is also an Adjunct Professor of Wealth Management at The American College of Financial Services and a Research Fellow for the Retirement Income Institute.
[1] While 5% is a common GLWB payout at age 65 for a single annuitant, as a reminder, this analysis is for a joint couple, which is why the payout is lower (4.5%).
[2] This focused on the potential economic benefits of annuities and ignores the potential behavioral benefits associated with annuitization, such as higher spending levels.
My previous article in this series introduced protected lifetime income benefits (PLIBs), and was based on a larger research paper. PLIBs are similar to products that offer a guaranteed lifetime withdrawal benefit (GLWB), but I created a separate category since the income calculation process can be different, and income can decline with a PLIB. PLIBs are not new; similar strategies such as tontines have been available for centuries.
received varies depending on level of consumption 
and level of investor risk aversion 
