Jean-Michel Maeso, Senior Quantitative Researcher, EDHEC-Risk Institute; Lionel Martellini, Professor of Finance, EDHEC Business School, Director, EDHEC-Risk Institute; Vincent Milhau, Research Director, EDHEC-Risk Institute; Anil Suri, Head of Investment Analytics, Merrill Lynch Global Wealth Management Group, Bank of America; Nevenka Vrdoljak, Director of Retirement Strategies, Merrill Lynch Wealth Management, Bank of America
A major crisis is threatening the sustainability of pension systems across the globe. The first pillar of pension systems, which is made up of public social security benefits and aims to provide a universal core of pension coverage to address basic consumption needs in retirement, is strongly impacted by rising demographic imbalances. Life expectancy at age 65 in OECD countries is expected to grow by 4.2 years for women and 4.6 years for men between 2020 and 2065. As a result, the number of individuals aged 65 and over for every 100 individuals aged between 20 and 64 rose from 13.9 in 1950 to 27.9 in 2015, and is expected to grow to 58.6 by 2075. In parallel a massive shift from defined benefit pension schemes to defined contribution pension schemes is taking place across the world, implying a transfer of retirement risks from corporations to individuals.
As an almost universal rule, pillar I and pillar II pension arrangements deliver replacement income that is inferior to the needs of individuals in retirement, and the resulting inadequacy risk is sometimes severe. According to the aforementioned OECD report, an individual earning the average income in the US can expect to enjoy a mere 49.1% replacement rate upon retirement, a number that falls to 29.0% in the UK. With the need to supplement public and private retirement benefits via voluntary contributions, the so-called third pillar of pension systems, individuals are becoming increasingly responsible for their own retirement savings and investment decisions. This global trend poses substantial challenges, as people often lack the expertise required to make such complex financial decisions.
In principle, annuity products, designed as contracts by which the beneficiary pays a premium today in exchange for receiving lifetime income, can be used to generate a target level of replacement income throughout retirement.
In practice, however, the demand for such products is extremely low, despite their risk-free nature in a retirement investment context. Using the RAND Health and Retirement Study dataset for the cohort aged 65–75 in 1998, Pashchenko (2013), for example, reports that only 5% of individuals receive income from annuities, with a peak at 12.2% among the highest income quintile and a low at 0.4% for the lowest quintile. Common explanations of this so-called ‘annuity puzzle’ are related to the fact that annuities involve counterparty risk and high levels of fees, and also that they do not contribute to bequest objectives. One additional key drawback of annuity products is their severe lack of flexibility. Indeed, annuitisation is an almost irreversible decision, unless one is willing to bear the costs of extremely high surrender charges, which can amount to several percentage points of the invested capital. This lack of flexibility is a major shortcoming in the presence of life event uncertainties such as marriage and children, changing jobs, changing locations to lower or higher cost cities or countries, decisions about retirement dates, and also, perhaps most notably, long-term care needs driven by health-related issues in the later stage of retirement. These uncertainties require changes to retirement plans on a regular basis, annually or when life events occur, which is simply not possible with annuities.
In Maeso et al (2020) we propose a comprehensive simulation framework that contains notably:
We consider the framework developed in Maeso et al (2020) applied to a 65-yearold woman who is already retired (and assumed to have just retired) in a two-asset base case universe, where retirement wealth is allocated to a 50%/50% stock/bond balanced fund and a single premium immediate annuity (SPIA) with a 2% cost-of-living adjustment and a death benefit. In terms of retirement needs, we test withdrawal rates of 3%, 4% and 5% of the initial wealth, and a 2% annual cost-of-living adjustment.
We systematically report the results obtained in both the absence and presence of life events to check for the impact of long-term care needs on the optimal demand for annuities. We assume that if and when the individual experiences long-term care needs, she will need additional retirement income to secure a semi-private room at a cost of $90,155 per year, and an annual cost increase of 3.10%.
The performance and risks associated with any given allocation between the two available assets (SPIA and balanced fund) will be measured with a number of key indicators, which can be broadly sorted into figures of merit (to be maximised) and figures of risk (to be minimised). In terms of figures of merit, we first report the median discounted income shortfall, which is defined for a given scenario as the discounted sum of the differences between actual withdrawals and target withdrawals (which are defined as 3%, 4% or 5% of initial wealth subject to a 2% cost-of-living adjustment (COLA), plus cost of long-term care needs, if and when they are incurred). By definition, this quantity is equal to zero at best, when the individual has enough wealth to finance all target withdrawals. As a related indicator we also report the median discounted percentage of lifetime income (PLI) achieved, which is defined as the median value across all scenarios of the ratio between the sum of the individual’s discounted actual withdrawals and the sum of the discounted target withdrawals until death. We finally report the median discounted bequest value, which is unbounded. In terms of figures of risk, we first report a short-term risk indicator defined as the median (over the scenarios) maximum (over time) annual loss (MAL) on the liquid portion of the portfolio (invested in the balanced fund). We also report several long-term risk indicators, including:
An optimisation exercise requires the identification of a proper optimisation objective (and possibly some constraints). This raises two main questions: the integration of potentially conflicting goals and aggregation of risk and return dimensions for a given goal. Meaningful goals include expected lifetime income needs, unexpected lifetime income needs (long-term care), a bequest and capital preservation. The first challenge is to aggregate these four goals, which can conflict with each other in the framework developed above. Expected and unexpected lifetime income needs can naturally be aggregated so that when the probability of a shortfall or expected shortfall is reported, it includes both the expected and unexpected components as part of the target. The bequest objective must then be aggregated with the total (expected plus unexpected) income objective. We propose an integrated approach where we treat the bequest as a final income cash flow, which is equivalent to treating it as a residual quantity.
Formally we define the discounted surplus on a given scenario as the discounted bequest plus the sum of discounted income shortfalls (note that this quantity can be positive or negative, and it is a deficit and not a surplus when it is negative). We then use the average (across scenarios) discounted surplus (AS) as a performance indicator in the optimisation objective, and the 5% VaR, or 5% percentile (VS) as a risk indicator in the optimisation objective. Defining as a risk-aversion parameter that characterises the risk appetite of the individual, we can finally write the objective function as:
where represents the percentage of initial wealth invested in each asset, encompassing financial liquid assets, annuities and insurance. In the analysis that follows, as indicated before, we consider only two assets (n = 2), namely the balanced fund and an SPIA, and we take five values for , which we interpret as defining the aggressive, moderately aggressive, moderate, moderately conservative and conservative investor, respectively. We also report results for two limit cases, namely , which captures a pure focus on performance, and , which represents a strong focus on risk.
Overall the main inputs of our framework are:
We now define and analyse a base case situation, where we assume that the individual (a 65-year-old female) is endowed with a $500,000 initial wealth level at retirement date. As indicated before, we assume that she has access to a simple investment universe that contains a balanced fund (BF) with an annually rebalanced 50%/50% stock/bond mix, and an immediate annuity with a 2% cost-of-living adjustment and a death benefit (SPIA-COLA). In this base case analysis, we systematically test three levels of initial target withdrawal rates, namely 3%, 4% and 5%, and we let target withdrawals grow by 2% per year to account for expected growth in the cost of living. Reading in figure 1 that the initial pay-out rate of the SPIA-COLA annuity for a 65-year-old female is 3.79%, we can define the individual funding ratio as the percentage of her replacement income needs that she can secure with certainty (and in the absence of a life event) by investing her assets in an SPIA-COLA annuity. These funding ratios for initial target withdrawals of 3%, 4% and 5% are respectively 3.79/3 = 126.3%, 3.79/4 = 94.8% and 3.79/5 = 75.8%. These results suggest that someone with an aggressive target withdrawal rate (5%) is initially underfunded (by a bit less than 25%, with a funding ratio at 75.8%) while someone with a conservative target withdrawal rate (3%) is initially overfunded (by a bit more than 25%, with a funding ratio at 126.3%).
Figure 2 displays selected charts representing the various indicators introduced in the previous section as a function of the initial percentage allocation to the SPIA-COLA, with values ranging from 0% to 100%, with a grid step of 1%. We observe that for a given initial target withdrawal rate, short-term risk decreases as a function of the allocation to annuities, as expected. We also note that for initial target withdrawal rates of 4% and 5%, the shortfall probability increases with the allocation to the SPIA. This is because investing a large fraction of the portfolio in annuities does not generate the amount of upside potential needed to finance a higher target level of consumption in retirement. On the other hand, in the case of a 3% withdrawal rate, the individual is sufficiently funded (with a funding ratio at 126.3%) to be able to meet target levels of withdrawals without substantial upside potential, that is without a significant investment in the balanced fund. Similarly, we find that the extreme shortfall durations increase with the allocation to the SPIA-COLA, except in the case where the initial target withdrawal rate is equal to 3%. The median percentage of lifetime income decreases as the allocation to annuities increases when the initial withdrawal rates are 4% or 5% and when life events are not taken into account. When accounting for life events and when the initial withdrawal rates are 4% or 5% respectively, the median percentage of lifetime income first decreases as the allocation to annuities increases, then it reaches a minimum for annuity allocations of 92% and 84% respectively, and finally starts to slightly increase for even higher annuity allocations. We also note that the median discounted bequest is a decreasing function of the allocation to annuities, as expected. In the same spirit, we find that in most cases (except for a 3% initial withdrawal rate case in the presence of life events), the extreme discounted shortfall, which is measured as the fifth percentile of the shortfall, decreases in absolute value when the SPIA allocation increases, again in line with the intuition that the SPIA is the natural safe asset in a retirement context. On the other hand, the median discounted shortfall is not a monotonous function of the allocation to annuities. We confirm in particular that the presence of long-term care needs has a strong impact on the distribution of discounted shortfall with a median value that is significantly lower (more negative), especially in the case of a 3% withdrawal rate, which is the situation where the unexpected component of replacement income needs is particularly sizable with respect to the expected component.
Turning to the two key ingredients in the optimisation problem, namely the average discounted surplus AS and the value-at-risk of the discounted surplus VS, we confirm from figure 2 the presence of a typical risk-return trade-off. On the one hand, an increase in the allocation to annuities leads to a decrease in AS, which is not desirable since AS is a measure of merit. We also confirm that the surplus decreases with the target withdrawal rate, as expected since it is more difficult to maintain a surplus starting from a given wealth level (here $500,000) when replacement income needs are higher. We also confirm, as expected, that the presence of the life event (solid lines) leads to a smaller surplus compared to a situation without the life event (dotted lines), and this is true for all values of the initial withdrawal rate. On the other hand, an increase in the allocation to annuities tends to lead to a higher (less negative) value for VS, which is desirable since VS is a measure of risk. This is actually always the case in the absence of the life event (dotted lines), for all values of the initial withdrawal rate. When life events are introduced, the monotonic relationship between VS and the allocation to annuities no longer holds. In particular, the fifth percentile of the discounted surplus distribution ceases to increase beyond a certain allocation to annuities.
In other words, an allocation to annuities beyond the 22%, 30% and 49% levels in the 3%, 4% and 5% withdrawal rate cases, respectively, not only implies a decrease in performance (measured by AS) but also an increase in risk. Intuitively, this is because a minimum amount of upside potential, which is generated by a non-zero allocation to the balanced fund, is needed in the 5% worst scenarios to ensure that replacement income needs (including both the expected and unexpected components) are met.
Figure 3 shows the optimal strategies for the base case universe in both the absence and presence of life events for various risk aversion levels. As expected given the analysis of the risk-return trade-offs involved in an increase in the allocation to annuities, we find that investors with low risk aversion ( = 0, 0.5, 1) will find it optimal not to purchase annuities, and this is true for all initial withdrawal rates and in both the absence and presence of life events. As risk aversion increases, the optimal demand for annuities increases when risk aversion becomes higher than 1. One important finding in this analysis, which is robust to changes in withdrawal rates, is that the presence of long-term care risk strongly reduces the optimal demand for annuities for most individuals, at least those that are sufficiently risk-averse to show some appetite for annuities in the first place. Focusing for example on the case of a 3% withdrawal rate, we find that the demand for annuities from the moderately conservative individual decreases from 78% to 18% when long-term care needs are accounted for. This impact is even more dramatic for the conservative investor , for whom we find that the introduction of long-term care needs reduces the demand for annuities from 88% to 18%. Overall, these results suggest that the costly reversibility of annuitisation decisions can help explain the annuity puzzle for individuals facing life event uncertainty.
In this section we conduct the following robustness check for a base case with a 4% initial target withdrawal rate: we test for the impact of changes in initial wealth on risk and return indicators and on the optimal demand for annuities. Specifically, we test two additional initial wealth values, namely $250,000 and $1m. For given values of the initial target withdrawal rate and the risk aversion parameter, in the absence of life events, the optimal allocation is independent of initial wealth since the replacement income needs of the individual represents the same deterministic percentage of her initial wealth. However, when life events are taken into account, their relative costs have a stronger impact on individuals with a lower initial wealth. The charts in figure 4 confirm this intuition. In particular, we find that the location and shape of the risk indicator (VS) are strongly impacted by changes in the individual’s initial wealth, with a maximum value corresponding to SPIA-COLA allocations of 1%, 30% and 67% for initial wealth levels of $250,000, $500,000 and $1m, respectively.
Figure 5 shows the weight for the optimal strategies in the base case universe in the absence and presence of life events for these three different initial wealth levels. We again find that the introduction of long-term care needs has a strong impact on the demand for annuities for sufficiently risk-averse individuals , an impact that decreases in the initial wealth level. For example, when the initial wealth is $250,000, the optimal demand for annuities decreases from 100% to 1% when the life event is introduced for the moderately conservative investor , while it decreases from 100% to 19% when initial wealth is $500,000 (our base case value) and only from 100% to 58% for initial wealth of $1m. Overall these results suggest that the impact of life events should be stronger for individuals with lower initial endowment, as expected.
Maeso et al (2020) present a flexible framework developed to provide personalised advice on retirement investment decisions in the presence of life event risk. This article shows an application of this framework in a simple setting with two assets, a 50%/50% stock/bond balanced fund and an immediate annuity with a 2% COLA indexation. The analysis presented here can be extended in a number of directions involving the use of alternative welfare functions or the introduction of additional assets such as target date funds or variable annuities. We refer the interested reader to Maeso et al (2020) for more details on these extensions.
The research from which this article was drawn was supported by Bank of America.
This article was originally published in the Spring 2021 edition of the EDHEC-Risk Institute special issue of the EDHEC Research Insights supplement to Investment & Pensions Europe.
 Figures cited here are from the OECD report, Pensions at a Glance 2017.
2 The death benefit is defined as follows: if the total income paid by the annuity to the individual until her death is lower than the premium she paid, then her heirs will receive the difference between the premium paid and the income collected.
These figures are borrowed from the Genworth Cost of Care Survey 2019.
The initial withdrawal rate is expressed as a percentage of the initial wealth.
Maeso, J.M., and L. Martellini (2020). A Holistic Goals-Based Investing Framework for Analyzing Efficient Retirement Investment Decisions in the Presence of Long-Term Care Risk. Working Paper.
Pashchenko, S. (2013). Accounting for Non-Annuitization. Journal of Public Economics 98: 53–67.