by David M. Blanchett, CFP®, CLU, AIFA®, QPA, CFA
Executive Summary
- The majority of past research on variable annuities with guaranteed minimum withdrawal benefit riders (GMWB annuities) has noted a “cost” associated with investing in a GMWB annuity versus a non-annuity portfolio with the same equity allocation in which the cash flows are equalized, to varying degrees. This is somewhat of an unfair comparison, though, given the unique nature of a GMWB annuity and its potential benefits.
- A GMWB annuity compares much more favorably against an immediate fixed annuity, which is a more relevant proxy for generating guaranteed income for life.
- When viewed from a total portfolio framework in which the goal is to maximize a utility function based on income replacement, the appeal of a GMWB annuity increases considerably, especially for retirees with lower levels of pension income, more conservative withdrawal rates, and more conservative equity allocations during retirement.
- Therefore, while GMWB annuities may appear to be relatively “inefficient” at an individual product level, a GMWB annuity can improve the overall efficiency of a retirement portfolio and better help a retiree generate sustainable income for life for the right situations.
David M. Blanchett, CFP®, CLU, AIFA®, QPA, CFA, is the head of retirement research for Morningstar Investment Management in Chicago, Illinois. Blanchett has published over 30 papers in various industry journals and has an M.B.A. from the University of Chicago, Booth School of Business. (david.blanchett@morningstar.com)
The debate surrounding the potential benefits of variable annuities with guaranteed minimum withdrawal benefit riders (GMWB annuities) is alive and well. At the surface, there appears to be a great deal of disagreement about whether or not these products are viable approaches to generating retirement income or are simply a “money illusion”1 created by “actuaries gone wild.”2 This author would contend that the varied opinions regarding the product stem primarily from the different frameworks used to quantify the benefits, and that most research to date that has focused solely on the relative comparative costs have taken an incomplete view of the potential benefit of the products.
This paper will explore the potential benefit of a GMWB annuity from a total portfolio perspective, both at retirement for income generation as well as before retirement as an accumulation vehicle. The expected net cost of GMWB annuities will be reviewed, and a utility function assuming constant relative risk aversion (CRRA) based on total income replacement during retirement is employed to determine the optimal combination of a GMWB within a portfolio based on varying levels of pension income (for example, Social Security) and target withdrawal initial rates.
Do You Feel Lucky?
An important point to clarify when discussing the potential benefit of purchasing an annuity is that the average person will not make more money.3 Buying insurance is similar to going to the casino: while a few folks may beat the house, the majority will leave the casino losers.4 With respect to annuities, because benefits must be paid over long periods, the fact that insurance companies do not lose money on each annuity sold is probably a good thing; this implies the insurance company is correctly pricing the risk and the company should have the ability to pay future claims. It is certainly possible for an individual to profit from an annuity purchase based on that individual’s actual life expectancy (for example), but the purchase should result in a negative sum game in the aggregate. While it is possible for a group of annuitants to profit if the insurance company underprices the true risk of an event occurring (which appears to have been the case with initial GMWB rider premiums), insurance companies generally have the right to “change the rules” if the odds move against them.
Most research on GMWB annuities has taken the “casino” perspective with respect to the potential benefits, and has found after a rigorous analysis that the “house” (insurance company) wins, on average, and the annuitant loses, on average. This should be expected. If one assumes the same equity allocation between the GMWB annuity and an outside portfolio and equalizes the payments from the two portfolios, the non-annuity portfolio should “outperform” the GMWB annuity portfolio based on fees alone.5 However, a number of attributes associated with GMWB annuities make this type of comparison overly simplistic. For example, the income guarantee within a GMWB annuity allows the annuitant to take on more market risk than he or she may have taken had the guarantee not been available. Milevsky (2007) notes this attribute, and that annuitants who are 65 and older with income guarantees have equity allocations that are approximately 20 percent higher than those without.
One key premise of this paper is that the “risk contribution” of a GMWB annuity is more conservative than its actual asset allocation. This “effective allocation” can often be a better starting place when thinking about the risks associated with a GMWB annuity, and is a concept introduced by Xiong, Idzorek, and Chen (2010), from which this paper can be viewed as somewhat of an extension. The potential ability of a GMWB annuity to add value to a portfolio, therefore, is similar to the diversification premise of modern portfolio theory, whereby an asset may be “inefficient” on an individual basis but can nevertheless reduce the risk of a portfolio when viewed within a total portfolio framework.
An Introduction to GMWB Annuities
GMWB annuity riders guarantee a minimum level of income for life and allow the annuitant to pass on his or her contract account balance to a beneficiary if there is any remaining policy value at the time of death. GMWB riders are also sometimes known as guaranteed lifetime withdrawal benefits (GLWBs). The guaranteed percentage, also known as the lifetime distribution factor (referred to as GMWB rates herein), is based on the age of the annuitant at the time of the first withdrawal, and usually increases the older the annuitant is at first withdrawal. The GMWB rate is applied to what’s known as the “benefit base,” which is usually the greater of the current policy total dollar value or the maximum value at each of the previous policy anniversary dates. Some GMWB products have additional valuation methods, such as guaranteed crediting rates, which guarantee minimum increases in the benefit base through time.
The annuitant receives a fixed percentage of the benefit base, the lifetime distribution factor (GMWB rate), based on the age of the retiree/annuitant at the time of the first withdrawal. For example, if a male retiree age 65 invested $1 million in a GMWB annuity and received a lifetime distribution factor of 5 percent, he would be guaranteed income of at least $50,000 per year for life from the annuity. If the annuity portfolio value were to increase to $1.1 million on the second anniversary date, the benefit base would “step up” to $1.1 million and the guaranteed lifetime income amount would increase to $55,000. If the portfolio value were to fall to $900,000 the following year and were to never again exceed $1.1 million in value, the guaranteed withdrawal amount would still be based on the high-water mark value for the annuity, which was $1.1 million. Therefore, the annual income generated from the GMWB annuity would be $50,000 in year one and $55,000 for year two and until the annuitant passes away. Alternatively, if the portfolio value increased to an amount greater than $1.1 million at some point in the future, the guaranteed lifetime income would increase to 5 percent times that amount (in this example). At death, any remaining contract value in the GMWB annuity would be paid to the designated beneficiary. Even if the value of the GMWB annuity portfolio drops to $0 during the annuitant’s lifetime, the annuitant is still guaranteed lifetime income.
Lifetime distribution factors (GMWB rates) tend to increase for older annuitants, and like fees and other annuity provisions, are going to vary by provider. Because the GMWB rider is essentially a lifetime put option, if the fee associated with the GMWB rider doesn’t vary by equity allocation (which is common), investors are best served investing in the most aggressive portfolio possible inside the annuity. In response to this, though, many providers have maximum allowable equity allocations in GMWB policies (for example, 60 percent–70 percent). Just because a provider offers a higher (or lower) equity allocation maximum rate, though, does not mean the annuity is better (or worse), because the higher equity allocation benefit may be offset by some other benefit (such as a lower distribution rate); therefore, the features of each product need to be reviewed in their entirety to determine the overall quality of a given product.
Quantifying the Payoff
There is an increasing body of literature addressing the “costs” associated with purchasing a GMWB annuity. This paper takes a similar approach to Blanchett (2011), in which the “net value” of the GMWB annuity is determined by subtracting the net present value of the balance in the GMWB annuity at death from the outside account value at death and adding the net present value of the income generated by the GMWB annuity that the outside account was unable to fund during the lifetime of the retiree (or for this analysis, the retirees). Most other research quantifying the benefit of a GMWB annuity has employed a relatively similar approach.
When compared against a non-annuity (an “outside account/portfolio”) with the same equity allocation, a guaranteed minimum withdrawal benefit (GMWB) annuity rider is only going to “pay off” if two things happen: first, if the outside portfolio can no longer sustain the guaranteed withdrawal rate, and second, if the annuitant is still alive. Assuming equivalent cash flows from the two products/portfolios, the “cost” is going to be the difference in the balance at death between the GMWB annuity and the outside account, while the “benefit” is going to be the cash flows generated by the GMWB annuity when/if the outside portfolio were to fail for a given run.6
Given the additional fees associated with a GMWB annuity, if the equity allocation is assumed to be the same for both the GMWB annuity and the outside account (using the same return series for both simulations), the outside account should have a larger balance at death (unless both are $0). This can generally be attributed to fees alone, because the fees involved with the GMWB annuity are usually higher than the assumed fees in a non-annuity portfolio analysis. While it is possible for the GMWB annuity to have a positive net present value for an individual run (the lifetime of a single annuitant), given the nature of insurance products, a GMWB annuity should not be expected to pay off on average, because this would imply the insurance company is losing money.
To determine the net value associated with a GMWB annuity, two portfolios are compared: the first is an annuity that includes a GMWB rider and the second is an “outside” portfolio. The assumed cash flows from the two portfolios are the same and are based on the income generated from the GMWB annuity. If the benefit base and subsequent cash flows increase from the GMWB annuity, the same cash flow is assumed to be withdrawn from the outside portfolio. The net value (or cost) of the GMWB annuity is the difference between the net present value of the outside account and annuity contract value at death, plus the net present value of the unfunded cash flows by the outside portfolio if the outside portfolio should “fail” during a given simulation.
The total cost of the GMWB annuity is assumed to be 260 basis points (bps) and the cost of the outside account is assumed to be 60 bps. The total GMWB annuity cost could be viewed as the GMWB rider fee (approximately 110 bps for the joint couple), the annuity administration and M&E fees (approximately 75 bps), and the investment management fees in the annuity (approximately 75 bps). The GMWB annuity is loosely modeled off the cheaper GMWB products available (for example, Ameritas or Vanguard), but has slightly higher fees to better reflect more attractive benefits (for example, higher available equity allocation and crediting rate). For simplicity purposes taxes are ignored for the analysis.
The analysis is based on a couple, male and female, both age 65. All mortality calculations are based on the Annuity 2000 Table, and life expectancies for members of the joint couple are assumed to be independent. The joint couple is considered to be “alive”—receiving benefits from the GMWB annuity—if either member of the couple is still alive for the year. All returns are based on a normal distribution, with equities having an average nominal return of 10 percent and standard deviation of 20 percent, and bonds having an annual nominal return of 5 percent and a standard deviation of 7 percent. The correlation between stocks and bonds is assumed to be zero. The equity allocation for the GMWB annuity is 70 percent for all scenarios, which is assumed to be the maximum equity allocation available within the product. The assumed distribution factor is 5.5 percent, which is that of a comparative low cost GMWB annuity (Ameritas’s no-load annuity). The discount rate for all net present value calculations is the return on bonds (5 percent).
Table 1 includes the net value of the GMWB annuity for the base scenario (65-year-old joint couple, male and female) for various equity allocations based on the probability of the GMWB annuity having a positive value, the average net value, and various percentile net values. A negative value implies the investor would be worse off purchasing the annuity versus investing in an outside portfolio in the respective equity allocation, by some percentage of the initial purchase price. For example, if the median net value were –7 percent and the average annuity purchased $100,000, the “average” annuitant would be expected to lose $7,000 from the total future benefits from the GMWB versus the outside portfolio. If the total expected holding period is 30 years, this loss could be roughly amortized at 30 bps per year.
The net value estimates are relatively similar to those determined by Blanchett (2011), which noted the median “cost” for a 50 percent equity portfolio against a 5.5 percent GMWB rate for a 65-year-old couple is –5.1 percent, versus –9 percent in Table 1 (this methodology suggests a slightly higher “cost” for the GMWB annuity). The results in Table 1 suggest that someone who is an aggressive investor and is concerned with “average” outcomes is likely better off not investing in a GMWB annuity when the two are viewed as mutually exclusive investment options. For example, there is only roughly a 20 percent probability that a GMWB annuity will generate the same income that could be generated from an “outside” portfolio with the same equity allocation (70 percent in this example). However, the GMWB annuity could be very attractive if it allows the annuitant to take more risk than he or she was going to in the outside portfolio (for example, a 25 percent equity allocation) as well as when viewed in a total portfolio framework based on its effective asset allocation (more on this later).
An equity allocation of 37 percent creates a median net value that is approximately 0 percent (the average net value would yield an equity allocation of 42 percent). This means a married couple targeting a 37 percent equity allocation and focused on the average outcome should be indifferent between the two choices (ignoring things like subjective life expectancy, liquidity preferences, etc). Just because the net value is 0 percent, though, does not mean the expected value is constant (0 percent) regardless of the holding period. Figure 1 demonstrates how the “cost” changes through time for the purchaser of an annuity. Figure 1 is based on the difference of account value of the GMWB annuity and the outside account at death plus the net present value of future unfunded cash flows by the outside portfolio for each year. Figure 1 demonstrates that the true benefit of the GMWB annuity increases the longer the annuitant survives. This is intuitive, because the longer the survival period the higher the probability the GMWB rider would actually need to be activated (because the outside portfolio was unable to sustain the desired cash flow).
An additional way to determine the relative cost (or benefit, depending on one’s perspective) of a GMWB annuity would be to compare it to another guaranteed lifetime income option, such as an immediate fixed annuity. An immediate fixed annuity is likely a better proxy for the “cost” of lifetime income because both products guarantee income for life and materially simplify the retirement income decision making process for a retiree. According to immediateannuities.com, the current income rate for an immediate fixed annuity for a joint couple—male and female, both age 65, from Illinois, with an installment refund paid to beneficiaries—is 5.81 percent of the initial premium. Therefore, if the couple were to purchase this annuity for $100,000 it would generate $5,810 per year (or $484 per month) for the life of either annuitant for a minimum of 17.2 years.
When comparing this immediate fixed annuity to the GMWB annuity outlined previously, the GMWB annuity has a positive average net value of 9.0 percent (someone is better off purchasing a GMWB annuity, on average), but a negative median net value of –1.5. The rather significant difference between the average and median is a function of the distribution of the potential outcomes, which is displayed in Figure 2. Note how the distribution has a significant right tail (positive skewness), indicating the potential “upside” associated with purchasing a GMWB annuity (versus an immediate fixed annuity) should the markets, and the corresponding contract account value, do well. Therefore, while the GMWB annuity may be viewed as “expensive” when compared against a traditional portfolio, the cost is on par with an immediate fixed annuity. 
Utility Function
Because it is difficult, if not impossible, to model the exact risk preferences of retirees, one approach is to introduce the notion of “utility,” where the satisfaction achieved from some given event or action is quantified. The objective is to maximize the utility (or satisfaction) based on the different options available. One common theory of risk preference, constant relative risk aversion (CRRA), is depicted in Equation 1:
In order for a utility function to be valid, though, it must effectively convey the actual preferences of the individuals it’s reflecting. For this analysis, the utility maximizing value is the percentage of the total income goal replaced during retirement. This is calculated by dividing the net present value of all payments achieved over the lifetime of the retirees plus the total balance of assets at death by the net present value of the total income need. Based on this methodology it is possible to have a replacement amount greater than 100 percent if there are assets remaining upon the death of both retirees.
Including the total assets at death factors incorporates the “trade-off” a retiree would potentially make by purchasing an annuity with retirement assets. The lack of a guarantee (income stability), therefore, must be worth the potential upside of having more assets at death to warrant not making the trade. While bequest versus maximizing lifetime income motives may differ, focusing on the income component alone would overly penalize strategies that have a potential balance at death. While one approach would be to use a subject weight measure to gauge the investor’s preference for income versus bequest, the analysis assumes the investor has a high bequest preference, therefore penalizing the GMWB annuity in the scheme of things most possible.
The annual income need is assumed to be a constant real value, increasing by 3 percent per year for inflation. The discount rate for all net present value calculations is 5 percent, which is the return on bonds. While it would potentially make sense to use a lower discount rate for income sources that are guaranteed (for example, GMWB income and pension income) versus those that are not (for example, portfolio income), a constant discount rate is used so as not to favor the GMWB annuity. The income need is assumed to exist as long as either member of a couple is still living.
For the equation, the risk aversion level (gamma or γ) is set at 4, which indicates a moderate level of risk aversion. This creates the utility function for replacement levels 50 percent to 200 percent as depicted in Figure 3. The key idea behind the utility approach is that only being able to replace a smaller percentage of the total need becomes increasingly costly at lower replacement levels. While it is certainly good to build a large surplus, the utility maximizing portfolio will be the combination of assets that maximizes retirement income and minimizes the downside variability associated with generating the income.
Determining the Optimal Equity Allocation in a Two-Asset Portfolio
The goal of this paper is to explore the optimal allocation to a GMWB annuity within the context of a total portfolio. This portfolio is assumed to consist of two assets: pension income and an “outside” portfolio. The pension income is assumed to be a nontransferable asset that generates constant inflation-adjusted income for life. The outside portfolio is assumed to consist of liquid assets that can either be invested in the market or some portion used to purchase a GMWB annuity.7 The utility function introduced in the previous section (Equation 1) will be used to determine the relative appeal of different combinations among the available assets for various target income withdrawal rates.
For the purposes of this analysis, pension income could be broadly defined as any source of income that will be received for life that increases annually with inflation. For most Americans this will be a Social Security benefit, although it could also include other fixed payments the retiree may receive such as a defined benefit plan payment. To reflect the reduced benefit impact that occurs when one spouse dies under the Social Security program, the pension benefit is reduced by one-third if either member of a couple dies during a simulation. Therefore, the pension benefit has a 66.67 percent survivor benefit, not a 100 percent survivor benefit.
While pension income is usually expressed as some annual or monthly amount (indexed for inflation), for the purposes of the analysis the pension income will be expressed as a percentage of total assets available to fund retirement based on the mortality weighted net present value8 of the payments (at the beginning of retirement). Viewing pension income as a lump sum asset helps demonstrate how the optimal allocation changes for different total amounts of pension income. A general rule for the analysis is that the mortality weighted net present value is roughly 19 times the annual income. Therefore, if total pension income were expected to be $30,000 per year, the mortality weighted net present value of these benefits would be roughly $570,000 using the return on bonds as the interest rate (5 percent). If the retiree had an additional $700,000 in savings, the pension income would represent 45 percent of the total assets available to fund retirement.
For this section, the potential existence of a GMWB annuity is ignored and the utility function is used to determine the optimal equity allocation for various levels of Social Security income and initial withdrawal rates. While the withdrawal rates are called “initial,” for calculation purposes the withdrawal is actually a constant dollar amount based on the initial balance, assumed to increase annually for inflation (fixed 3 percent per year). Therefore, a 4 percent withdrawal from a $500,000 portfolio would result in $20,000 in income for year one, $20,600 in year two, etc.
The optimal equity allocation is determined for various levels of total pension assets (0 percent to 100 percent in 10 percent increments) and withdrawal rates (3 percent, 4 percent, 5 percent, and 6 percent) for equity allocations ranging from 0 percent to 100 percent in 10 percent increments (11 possible portfolios). For each scenario the total beginning assets are assumed to be the same ($1 million), so a higher initial withdrawal rate represents a more aggressive withdrawal strategy. Table 2 includes the optimal equity allocation to the outside portfolio for varying levels of pension income and target initial withdrawal rates.
The optimal equity allocation is not constant across the levels of pension income or withdrawal rates, whereby the equity allocation tends to be higher for more aggressive withdrawal rates (for example, 6 percent versus 3 percent) and higher levels of pension income (for example, 70 percent versus 10 percent). The equity allocations are included for the 100 percent pension scenarios because for those scenarios where there is initial excess monies (for example, the 5 percent and 6 percent withdrawal rate) any excess income over the target is assumed to be saved to fund a future potential shortfall if one member were to die within the simulation (because the survivor pension benefit is only two-thirds of the initial benefit). The 10 percent allocation for the 100 percent pension, 6 percent initial withdrawal is not an error, the allocation is so conservative because the pension income is not enough to cover the need and the 10 percent allocation is approximately the minimum variance portfolio, therefore it leads to the most consistent income per run.
The results in Table 2 are actually quite intuitive from a risk-aversion perspective, whereby the equity allocations are minimized for the more conservative (over-funded) scenarios and more aggressive for the higher withdrawal rates. This follows the premise that a retiree should take as little risk as necessary to achieve a goal. Just because an equity allocation is utility maximizing (given the assumed utility function), though, does not mean a retiree would (or should) actually invest accordingly. For example, while a 90 percent equity allocation may be the utility maximizing equity allocation for an investor with 90 percent of total assets as pension assets, few retirees are likely to be interested incurring that level of market volatility, especially at older ages. Therefore, while these results provide a useful starting point for determining the equity allocation for the outside portfolio, as when running a mean variance optimization, it can be helpful to incorporate constraints on the maximum equity allocation to ensure the results are reasonable. Constraints will be incorporated into the three-choice framework (next section) to ensure reasonable results, where the equity allocation for the outside portfolio is limited to 60 percent and the allocation to the GMWB annuity is limited to 50 percent of the total available investible assets.
GMWB Modeling: Moving to a Three-Choice Framework
A utility framework was used in the previous section to determine the optimal equity allocation for a distribution portfolio for various withdrawal rates and levels of pension income. In this section the selection framework will be extended to include an additional asset, where some portion of the non-pension assets (the outside account or “investible assets”) can either be invested in a GMWB annuity or remain invested in the outside portfolio.
Two primary tests are performed to determine the optimal allocation to a GMWB annuity. For the first test the equity allocation for the outside portfolio is held constant at 40 percent, while for the second test the optimal combination of GMWB annuity and outside portfolio allocation is determined jointly. For both tests any income that is not funded by pension or the GMWB annuity is assumed to be deducted from the outside portfolio first until the balance is drawn to zero. At this point the unfunded income versus the annual target income represents the shortfall for that run/strategy.
For both tests, if multiple scenarios for the same test have the same utility (100 percent success for all runs) the scenario with the lowest allocation to the GMWB annuity is selected first, and then is followed by a lower equity allocation (for the second test). The allocation to the GMWB annuity is limited to 50 percent of the remaining investible assets as a reasonable assumption for the analysis. While some retirees may in fact be better served with a higher than 50 percent allocation to a GMWB annuity, this author is concerned that the results could be taken too literally by some readers, and therefore a constraint is imposed.
The first test held the equity allocation of the outside account constant at 40 percent. The reader may question the fairness of comparing a GMWB annuity with a higher sub-account equity allocation (70 percent) versus the outside account (40 percent); however, this serves as both a reasonable and simplifying assumption for a variety of reasons. First, 40 percent is probably a relatively good estimate of the appropriate equity allocation for most retirees. Second, GMWB riders serve fundamentally as put options for the equity allocation within the variable annuity because they guarantee an income stream that is fixed and “bond-like” in nature. This creates an “effective” asset allocation that is more conservative than the underlying equity allocation. Third, individuals purchasing variable annuity contracts with lifetime income guarantees tend to be more aggressive than those purchasing variable annuity contracts without an income guarantee. This has been noted by Milevsky (2007), who finds annuitants who are age 65 and older with income guarantees have equity allocations that are approximately 20 percent higher than those without. Finally, a GMWB annuity allows a retiree to take on market risk when he or she may not normally be willing to do so, given the nature of the income guarantee.
For the second test, in which the allocation to the GMWB annuity and optimal portfolio equity allocation are determined jointly, a total of 3,080 scenarios are considered, based on 10 different pension levels (0 percent to 90 percent in 10 percent increments; no need to test 100 percent because all assets would be pension assets and the equity allocations can be extracted from Table 2), 11 GMWB holding levels (0 percent to 50 percent of non-pension assets in 10 percent increments of investible assets), 7 different equity allocations (0 percent to 60 percent in 10 percent increments), and 4 different withdrawal rates (3 percent, 4 percent, 5 percent, and 6 percent). The first test (40 percent fixed equity allocation) really represents a smaller sub-sample of the second test, whereby the non-40 percent equity allocation results are excluded from consideration.
Table 3 includes the optimal allocation to a GMWB annuity for various levels of pension income and initial withdrawal rates for the two test scenarios. The equity allocations for the variable equity allocation test (Test 2) were 60 percent for all but four scenarios, two of which were the 0 percent pension runs where the equity allocation was 50 percent. The high allocations to the GMWB annuity in Table 3 may surprise the reader to some extent, given the fact that the GMWB annuity had a negative net value against those portfolios with higher equity allocations (60 percent) yet was still featured in the variable equity allocation test.
The results in Table 3 clearly suggest the GMWB annuity is more attractive for scenarios when the retiree is planning to have a more conservative asset allocation during retirement (40 percent in the example). As a reminder, the equity allocations for the variable equity allocation test were 60 percent for virtually every scenario (the maximum allowable number). While 60 percent is a common equity allocation for defined benefit plans and pensions, it is likely more aggressive than most retirees are going to choose to invest their accounts.
The allocation to the GMWB annuity is not constant across initial withdrawal rates, as depicted in Figure 4. The 3 percent initial withdrawal had the highest GMWB allocation. As a reminder, the allocation to the GMWB annuity was constrained to 50 percent of the total outside investible assets, so there are scenarios (for example, the 3 percent withdrawal rate) where the actual allocation would be higher if the constraint were removed. The allocation to the GMWB annuity was also not constant at different levels of pension income—as the level of pension income increases, the allocation to the GMWB annuity decreases, as depicted in Figure 5. This suggests the GMWB annuity can be an important “floor” allocation for retirees with minimal pension or Social Security benefits.
If the GMWB annuity did not add value from a utility maximizing perspective, it would not be included in any of the optimal portfolio combinations, which would include only the outside portfolio with an equity allocation of 60 percent. However, because the GMWB annuity is featured in a number of withdrawal scenarios (especially those with more conservative assumptions) there definitely appears to be some potential benefit of a GMWB annuity within a total portfolio framework for a retiree.
Effective Equity Allocation
Table 1 can be used to determine the “indifference level” for a retiree considering a GMWB annuity based entirely on the average expected costs. For example, because the median net value of the GMWB annuity is equivalent to an approximately 37 percent equity allocation, a retiree should be indifferent between the two investments from a pure income-generation perspective. This creates the “effective” asset allocation when viewed in conjunction with other investments.
Under the effective asset allocation theory, assuming the GMWB annuity has an effective asset allocation of 37 percent (which we will assume is 40 percent for simplicity purposes for the next example), the lifetime net value of the income generated from a portfolio valued at $500,000 with a target equity allocation of 60 percent equities should be equivalent whether the money were invested $300,000 in equities and $200,000 in bonds in an outside account, or $250,000 in equities, $125,000 in bonds, and $125,000 in a GMWB annuity (which creates the same effective equity allocation). However, the utility from the blended approach, in which the GMWB annuity is included as part of the allocation, is superior to the non-GMWB portfolio for each of the four withdrawal rates considered. Therefore, just because a retiree is targeting a more aggressive equity allocation during retirement (for example, 70 percent) does not mean a GMWB annuity should not be considered.
Investing in a GMWB Annuity Before Retirement
Up to this point, the potential benefits of a GMWB annuity have been viewed entirely from an income perspective—the decision is made upon retirement to create immediate retirement income and funded from available savings. This section will provide a brief analysis of the potential benefits of holding a GMWB annuity in accumulation, primarily as it relates to the guaranteed benefit base “step-up” provision that is common in GMWB annuities.
One common feature with GMWB annuities is the annual step-up benefit, in which the benefit base is guaranteed to increase by some fixed percentage (usually 5 percent) regardless of the change in contract account value while the GMWB annuity is still in accumulation (not in payout mode). In order to realize this benefit, though, the GMWB rider must be activated, which increases the annuity fees by the cost of the GMWB rider (approximately 100 bps), reducing the future compounded growth of the annuity. Note, though, that the benefit base increases by the 5 percent, and is generally compounded on an annual basis, and is not assumed to be reduced by the fee.
The annuitant will only realize any actual value from the 5 percent step-up rate if the contract account value is less than the guaranteed step-up value at annuitization (other than peace of mind). If we assume a 10-year accumulation period in which the “greater of” comparison only takes place at the end of the 10th year (just before annuitization) we can determine the likelihood of this even occurring. Based on the same primary assumptions as the previous analysis (70 percent equity allocation and 2.60 percent total contract fee) there is only a 48 percent chance the 5 percent step up will be greater than the actual contract value after 10 years. The fact that the probability is only about 50 percent is not surprising given the compounded return of the GMWB is approximately 5 percent. Regardless, a guaranteed “floor” return creates a more favorable eventual benefit base for income, as exhibited in Figure 6. 
The annual guaranteed benefit base growth rate (5 percent) is clearly attractive, especially for risk-averse retirees who are most attracted to the guaranteed income feature of a GMWB annuity. The guaranteed 5 percent growth rate effectively creates a floor guarantee for the benefit base while allowing the benefit base to potentially be higher, depending on the performance of the underlying contract value. This potential benefit, though, must be weighed against the cost associated with paying the higher fees.
There are two components in the net value calculation when comparing the value of the GMWB annuity to the outside account: the present value of the contract value at death and the net present value of the cash flows the outside account is able to fund during the lifetimes of the retirees. Purchasing an annuity early reduces the expected account value at death relative to the outside account because of the effect of higher fees through time, but potentially increases the amount of cash flows available from the annuity given the higher potential benefit base at retirement. Figure 7 includes the probability of the contract value or the benefit base (which is the greater of the account value or the guaranteed step-up rate) being greater than the outside account for various equity allocations based on a 10-year accumulation period.
While the probability of the contract value being greater than the outside account value for a 70 percent equity allocation is 0 percent (because the returns are the same but the fees are higher in the GMWB annuity) there is still a 32 percent chance the benefit base will be higher than the outside account value. The key determination, therefore, is whether the potential distribution of benefit bases and contract values is more attractive. Using the same utility function introduced previously (Equation 1), but testing the account balance at the end of the 10-year period versus the income replacement level, regardless of the equity allocation for the outside account, assuming the equity allocation in the GMWB annuity is 70 percent, the utility is always the highest for the benefit base value, followed by the outside account balance, followed by the annuity contract value. This holds regardless of the level of risk aversion (gamma) or the equity allocation for the outside account (between 10 percent and 100 percent9).
Additional simulations involving the long-term utility asset allocation from a three-choice perspective suggest an investor would likely be better off in most circumstances investing outside an annuity if he or she were planning to invest more than half (50 percent) of the account in equities. These findings are relatively consistent with Table 1, where the median/average “cost” associated with owning a GMWB annuity increases against higher outside account equity allocations. Therefore, the considerations regarding whether or not to purchase an annuity and activate the GMWB rider for the step-up feature are the same ones used when assessing the net value.
Solving the “Annuity Puzzle”
In his 1985 Nobel acceptance speech, Franco Modigliani (1986) drew attention to the “annuitization puzzle.” He said: “It is a well-known fact that annuity contracts, other than in the form of group insurance through pension systems, are extremely rare. Why this should be so is a subject of considerable current interest. It is still ill-understood.” This annuity puzzle is addressed at length in a recent paper by Benartzi, Previtero, and Thaler (2011). The authors note that rational choice theory predicts that at the onset of retirement, households will find annuities attractive because they address the risk of outliving one’s income, but relatively few of those facing retirement choose to annuitize a substantial portion of their wealth. Annuities clearly are not a “one size fits all” investment, but they can definitely be a valuable addition to a portfolio under the right circumstances.
Conclusion
The majority of past research on variable annuities with guaranteed minimum withdrawal benefit riders has noted a “cost,” to varying degrees, associated with investing in a GMWB annuity versus a non-annuity portfolio with the same equity allocation and cash flows. This is somewhat of an unfair comparison, though, given the unique nature of a GMWB annuity and its potential benefits. A GMWB annuity compares much more favorably against an immediate fixed annuity, which is a more relevant proxy for generating guaranteed income for life. When viewed from a total portfolio framework, where the goal is to maximize a utility function based on income replacement, the appeal of a GMWB annuity increases considerably, especially for retirees with lower levels of pension income, more conservative withdrawal rates, and more conservative equity allocations during retirement. Therefore, while GMWB annuities may appear to be relatively “inefficient” at an individual product level, a GMWB annuity can improve the overall efficiency of a retirement portfolio and better help a retiree generate sustainable income for life.
Endnotes
- Pfau, Wade. 2011. “GLWBs: Retiree Protection or Money Illusion?” Advisor Perspectives (December 13).
- Tomlinson, Joseph A. “Thoughts on the Future of Retirement Income Products.” www.josephtomlinson.com/Thoughts_on_the_Future_of_Retirement_Income_Products.pdf.
- This statement is purely based on dollar gains and does not seek to incorporate any type of utility framework, more on this later in the paper.
- Despite this relatively well-known fact, people still go to casinos.
- This is because fees are generally going to be higher in an annuity versus in some type of non-annuity/outside portfolio.
- It is possible for the account balance of the GMWB annuity to be greater than the outside account if the portfolios have different equity allocations.
- That portion is limited to 50 percent of the outside assets for this analysis.
- Five percent is the discount rate for the NPV calculation.
- At 0 percent, the GMWB annuity has higher utility than the outside account.
References
Benartzi, Shlomo, Alesssandro Previtero, and Richard H. Thaler. 2011. “Annuity Puzzles.” Journal of Economic Perspectives 25 (Fall): 143–164.
Blanchett, David M. 2011. “The Expected Value of a Guaranteed Minimum Withdrawal Benefit (GMWB) Annuity Rider.” Journal of Financial Planning (July): 52–61.
Milevsky, Moshe A., and Vladyslav Kyrychenko. 2007. “Asset Allocation Within Variable Annuities:
The Impact of Guarantees.” Working paper. www.ifid.ca/pdf_workingpapers/WP2007JUNE28_AAVA.pdf.
Modigliani, Franco. 1986. “Life Cycle, Individual Thrift, and the Wealth of Nations.” American Economic Review 76, 3: 297–313.
Xiong, James X., Thomas Idzorek, and Peng Chen. 2010. “Allocation to Deferred Variable Annuities with GMWB for Life.” Journal of Financial Planning (February): 42–50.
