Abstract
Even though they have only existed since 1981, some analysts have concluded that 401(k) plans are a failure. For example, some argue that 401(k) plans are “coming up short” due to, among other factors, the low contribution rates of participants. A recent government report concluded that “low defined contribution plan savings may pose challenges to retirement security.” There are also proposals to replace 401(k) plans with mandated savings. This article illustrates that moderate 401(k) contribution rates can lead to adequate retirement income for many workers; that adequate asset accumulation can be achieved using only a 401(k) plan; and that these results do not rely on earning an investment premium on risky assets. Using Monte Carlo simulation techniques, this study also illustrates the investment risk faced by participants who choose to invest in risky assets, or who choose to make systematic withdrawals in retirement rather than annuitize their account balance.
When introduced in 1981, 401(k) plans were expected to be supplemental plans used in conjunction with a defined benefit (DB) pension or a traditional defined contribution (DC) pension. 1 Increasingly, employees are provided pension benefits solely through a 401(k) plan. This development has raised concerns that 401(k) plans alone will not provide future retirees with adequate financial resources. This article illustrates that moderate 401(k) contribution rates can lead to adequate income replacement rates in retirement for many workers, that adequate asset accumulation can be achieved using only a 401(k) plan, and that these results do not rely on earning an investment premium on risky assets. Using Monte Carlo simulation techniques, this study also illustrates the investment risk faced by participants who choose to invest their 401(k) contributions in risky assets.
Despite only having been in existence for thirty years and despite the fact that most workers approaching retirement have had access to a plan for only a portion of their career, some analysts appear to have concluded that 401(k) plans are a failure (see Tergesen 2008). For example, Munnell and Sundén (2004, 2006) argue that 401(k) plans are “coming up short” due to low participation rates, inadequate contributions, poor investment decisions, and individuals withdrawing money from their 401(k) when changing jobs. The US Government Accountability Office (GAO) echoes many of these sentiments by noting, “ . . . workers may receive limited or no contributions from their employers, spend accumulated savings prior to retirement, or choose not to participate in a pension plan at all, ultimately arriving at retirement with insufficient savings to support themselves” (GAO 2007, 1). In testimony before Congress, Ghilarducci (2008a) proposed replacing 401(k) plans with Guaranteed Retirement Accounts, in part due to belief that 401(k) plan participants will not be adequately prepared for retirement.
This article focuses on the question of whether or not 401(k) plans can provide adequately for retirement, given the modest contribution rates of many participants. 2 Munnell and Sundén (2006) points to two facts to support the conclusion that contributions to 401(k) plans are inadequate: (1) few 401(k) participants contribute the legal maximum to a 401(k) plan ($15,000 in 2006) and (2) the modal contribution rate is a 6 percent employee deferral plus a 3 percent employer match. The proposition that 401(k)s are inadequate in Ghilarducci (2008a) is based in part on the fact that a riskless portfolio has historically yielded a real return of 3 percent or less and that such a low rate of return would require too high a level of savings to achieve adequacy (Ghilarducci 2008b, 126–27). To assess the validity of these arguments, this study simulates realistic savings behavior combined with both riskless and risky investments. In addition, Social Security benefits are fully integrated into the assessment of adequacy. Despite noting the importance of Social Security and that “… evaluations of income security should consider total retirement income from all sources, not just DC plans” (GAO 2007, 4), GAO largely ignores Social Security when evaluating the adequacy of retirement savings in DC plans.
This study constructs representative earnings paths that roughly represent median earnings for full-time, full-year workers with a high school degree, a bachelor’s degree, and a graduate degree. For a given earnings path and marital status, individuals are assumed to follow a particular savings path. There is no attempt to derive the optimal path for retirement savings or to define the exact amount of resources needed to adequately fund retirement. Instead, this article assumes saving behaviors that a priori seem reasonable to the author and which are consistent with the observed behavior of 401(k) plan participants. Income in retirement is assumed to consist of Social Security benefits and income derived from financial assets accumulated in a 401(k) plan. Replacement rates are calculated under two investment scenarios: (1) contributions are invested in a portfolio of treasury inflation-protected securities (TIPS) and retirees purchase an annuity at retirement, and (2) contributions are invested in a portfolio of corporate stocks and bonds and retirees make systematic withdrawals from the account in retirement.
Assumptions Used in the Simulations
The representative individuals in the simulations 3 are assumed to be born on January 1, 1966. These individuals are forty years of age in 2006 and reach their Social Security normal retirement age of sixty-seven in 2033. Earnings paths are constructed that roughly represent median earnings for workers with different levels of education. For a given earnings path, individuals or married couples follow an assumed savings path. Married individuals are assumed to be the same age as their spouse. Retirement income is assumed to be derived from two sources: Social Security benefits and payments derived from assets accumulated in a 401(k) plan. Retirement adequacy is assessed using a replacement rate that compares potential consumption after retirement to potential consumption prior to retirement. The relevant measures of preretirement potential consumption are calculated separately for renters and homeowners.
Earnings Paths
The representative earnings paths are anchored at the approximate median earnings of full-time, full-year workers of age forty with a high school degree, a bachelor’s degree, and a graduate degree. In addition, a fourth earnings path is created that is one-third higher than the median earnings of a worker with a graduate degree. The series are plotted in Figure 1 . The names of the series reflect their origin: (1) HS-35K (high school graduate earning $35,000 at age forty in 2006 dollars), (2) Col-55K (college graduate earning $55,000), (3) Grad-75K (graduate degree worker earning $75,000), and (4) Scaled Grad-100K (scaled graduate degree worker earning $100,000).
Representative earnings paths
Savings
All savings accumulate within—and receive the tax treatment of—a 401(k) plan. The contribution rate assumptions are behavior that a priori seemed reasonable to the author and which are consistent with pension plan participation as documented in Brady and Bogdan (2011) and with employee deferrals and employer contribution rates as reported in Profit Sharing/401(k) Council of America (PSCA; 2008).
Those with higher earnings contribute a higher percentage of earnings to the 401(k) plan and start contributing at an earlier age. Similarly, because they have more earnings on a per-person basis, single individuals are assumed to begin contributing at an earlier age than do married couples with the same total household earnings. For single individuals, participation in 401(k) plans is assumed to begin at age forty-two for workers with HS-35K and Col-55K earnings, and at age thirty-two for workers with Grad-75K and Scaled Grad-100K earnings. For married couples, participation is assumed to begin at age fifty-two for workers with HS-35K earnings, at age forty-seven for workers with Col-55K earnings, and at age thirty-seven for workers with higher earnings. Including employer matching contributions, single HS-35K workers are assumed to contribute 6 percent of earnings to the 401(k) plan each year they participate and Col-55K workers 9 percent. Married workers with the same level of total earnings contribute 4 percent and 6 percent, respectively. Including employer contributions, both single and married Grad-75K workers are assumed to contribute 9 percent of earnings and Scaled Grad-100K workers 10 percent. Once begun, savings continue until retirement with no withdrawals taken until retirement.
Social Security Benefits
Workers are assumed to work until their Social Security normal retirement age, which is sixty-seven years of age in 2033. Parameters for the calculation of Social Security benefits either use historic values (for 2006 and years prior) or are consistent with the Social Security Administration's (SSA's) intermediate projection as reported in SSA (2006). Most parameters used in the calculation are indexed to wage growth, using the Average Wage Index (AWI). The SSA’s intermediate projection has average real wages growing by a steady 1.1 percent a year after 2015, with nominal wage growth of 3.9 percent and inflation of 2.8 percent. The initial benefit is indexed to inflation in the years after retirement. For each earnings path, I calculate three Social Security benefit levels: assuming the earnings are for a single individual; assuming the earnings are for a single-earner married couple; and assuming the earnings are for a married couple with each spouse earning one-half of total earnings (hereafter, dual-earner married couple).
Owner-Occupied Housing and Mortgage Payments
For homeowners, it is assumed that all individuals and couples (1) purchase a home at age thirty-five, (2) finance 100 percent of the purchase price using a 30-year fixed-rate mortgage charging a 7.0 percent rate of interest, and (3) pay off the mortgage at age sixty-five. 4 The purchase price of the home is assumed to vary by earnings path and is set (approximately) equal to the observed median purchase price in the second quarter of 2006, as reported by the National Association of Realtors (2006), in specific geographic regions. In 2006 dollars, the purchase prices are assumed to be $300,000 for the Scaled Grad-100K earnings path (equal to the median purchase price of a home in the Northeast region), $230,000 for the Grad-75K earnings path (median, all of the United States), $190 for the Col-55K earnings path (median, southern region), and $100,000 for the HS-35K earnings path (median, Buffalo, NY). The real price of the house is assumed to stay constant.
Taxes
Payroll taxes are the sum of two taxes: the Social Security or Old Age, Survivor, and Disability Insurance (OASDI) tax of 6.2 percent of earnings up to the annual earnings base ($94,200 in 2006) and the Medicare or Hospital Insurance (HI) tax of 1.45 percent on total earnings.
For federal income taxes, 2006 tax laws are applied in all periods, and the parameters of the tax code that are indexed are adjusted for inflation (without regard to rounding rules) in periods both before and after 2006. Without loss of generality, state income taxes are calculated using the Virginia income tax. Adjusted gross income (AGI) while working is assumed to be equal to earnings less employee 401(k) contributions. In retirement, AGI is set equal to distributions from the 401(k) account plus includable Social Security benefits.
Baseline Simulations: TIPS Portfolio Annuitized at Retirement
For the baseline case, contributions to a 401(k) are invested in inflation-indexed Treasury bonds, also known as Treasury inflation-protected securities (TIPS). Net of investment expenses of 20 basis points, real yields are assumed to be 2.2 percent real, 5 which, through most of the projection period, yields a nominal rate of 5.0 percent.
Upon retirement, the entire 401(k) balance is used to purchase an immediate life annuity that provides annual payments until death and adjusts the payments annually to account for changes in the cost of living. Because the SSA’s intermediate projection assumes life expectancy at age sixty-five will increase 1.9 years for males and 1.5 years for females between 2005 and 2035, annuity prices for individuals aged sixty-seven in 2033 are assumed to be equal to annuity prices for individuals aged sixty-five in 2006. Married workers purchase joint and 50 percent survivor annuities; that is, a surviving spouse would continue to receive one-half of the original annuity payment.
Accumulations and Distributions
Table 1 reports the amount of assets accumulated at retirement and the amount of annuity income generated by the accumulated assets. Controlling for marital status, higher-earning households accumulate more because they have higher earnings, contribute a higher percentage of pay, and begin contributing earlier. Controlling for household earnings, single individuals accumulate more because they begin contributing to their 401(k) at an earlier age and, for HS-35K and Col-55K earners, contribute a higher percentage of pay. For single individuals, assets at retirement (in 2006 dollars) range from $75,751 for HS-35K earners to $539,687 for Scaled Grad-100K earners. For married couples, assets range from $27,825 to $450,252.
401(k) Asset Accumulation and Annuity Income in Baseline Simulation: Certain Investment Returns a
Source: Author’s calculations.
aAssumes savings are invested in inflation-indexed bond earning 2.2 percent real, net of investment expenses. Inflation rates are taken from history and Social Security Administration’s Intermediate Projection. At retirement, an inflation-indexed annuity—that is, one that pays an amount that increases with inflation—is purchased. Annuity does not have guaranteed minimum payment amounts or death benefits. Single individuals buy a single life annuity and married couples buy a joint and 50 percent survivor annuity. Pricing for annuities taken from Vanguard’s annuity website on October 31, 2006.
With their accumulated 401(k) assets, single males could purchase inflation-indexed immediate annuities providing income ranging from $4,472 per year for those with the HS-35K earnings path to $31,859 per year for those with the Scaled Grad-100K earnings path. Because women typically live longer, annual annuity payments for single women are 12 percent lower than for single men. With less money to invest—both absolutely and on a per-person basis—married couples can purchase annuities providing income ranging from $1,433 per year for HS-35K workers to $23,190 per year for Scaled Grad-100K workers.
Replacement Rates 6
Preretirement potential consumption is calculated as average (from age thirty to age sixty-six) real net earnings. Net earnings are gross earnings less taxes and savings for renters and gross earnings less taxes, savings, and mortgage payments for homeowners. For both renters and homeowners, net income in retirement is Social Security benefits and 401(k) distributions less any taxes, as it is assumed retirees no longer save and homeowners pay off their mortgage prior to retirement.
Results from the baseline simulations are presented in Table 2 . All dollar amounts are reported in 2006 dollars. Because real earnings increase over time, average real earnings for each earnings path are higher than real earnings at age forty. For example, for the Col-55K earnings path, average real earnings after age thirty are $58,306.
Results from Baseline Simulation: Certain Investment Returns
Source: Author’s calculation.
aSee note in Table 1.
Prior to retirement, the percentage of gross earnings accounted for by savings and taxes for single individuals ranges from 26 percent for HS-35K workers to 36 percent for Scaled Grad-100K workers. Holding total earnings fixed, married individuals have a lower reduction in income from savings and taxes, ranging from 18 percent to 30 percent. For homeowners, mortgage payments, net of tax benefits, represent an additional 10 percent to 15 percent of average preretirement earnings. All told, savings, taxes, and mortgage payments reduce preretirement gross earnings, on average, from 30 percent to 46 percent.
In retirement, annual Social Security benefits for single individuals range from $18,814 for the HS-35K earnings path to $33,315 for the Scaled Grad-100K earnings path, and range from $24,754 to $49,973 for married couples. In the case of single-earner married couples, benefits are higher than for single individuals because the nonworking spouse is eligible for benefits equal to 50 percent of the working spouse’s benefit. In the case of dual-earner married couples, benefits are higher because each spouse earns half the amount of the single individual, and the progressive benefit formula results in benefits that replace a higher proportion of earnings. For example, for the Col-55K earnings path, single-earner married couples would receive $39,187 annually and dual-earner married couples would receive $32,547 annually, compared to $26,124 for single individuals.
Adding in the annuity income derived from 401(k) accumulations, annual gross income ranges from $22,970 for single females with HS-35K earnings to $73,163 for single-earner married couples with Scaled Grad-100K earnings.
For single individuals with HS-35K earnings, taxes in retirement are negligible, while for those that have Scaled Grad-100K earnings, taxes represent about 15 percent of gross income. For married couples, taxes are negligible for those with HS-35K and Col-55K earnings, and only reduce income by 6 percent for those with Scaled Grad-100K earnings. Differences between gross income and net income decline in retirement because (1) retirees do not save, (2) retirees do not pay payroll taxes, (3) income taxes decline, and (4) homeowners are assumed to have paid off their mortgage. Income taxes are lower because (1) gross income is lower, (2) Social Security income is at least partially excludable from taxable income, and (3) the availability of age-related deductions and credits.
Replacement rates for single renters range from 82 percent to 90 percent. For married renters, replacement rates range from 83 percent to 102 percent of net income. Replacement rates for single homeowners range from 96 percent to 107 percent. For married homeowners, replacement rates range from 102 percent to 122 percent.
Judging Retirement Resource Adequacy
A starting point for judging retirement resource adequacy is to assume that a retiree would want to replace 100 percent of average real net earnings. The results presented above suggest that most workers can achieve, or come close to achieving, this goal by supplementing Social Security benefits with income from a 401(k) plan, with moderate 401(k) contribution rates, conservative investments, and starting contributions at some point after reaching age thirty. However, 100 percent potential consumption replacement may not be the correct standard for adequacy.
The adequacy standard may be below 100 percent for several reasons. First, work-related expenses may be eliminated or reduced in retirement. Second, with more leisure time, retirees may substitute home production for market purchases. 7 Further, the result that individuals will optimally smooth consumption over time is derived from models where period utility is a function of consumption. If both consumption and leisure separately enter the period utility function, lower consumption in retirement could be optimal, as retirees substitute leisure for consumption. 8 Third, consumer durables purchased prior to retirement may continue to provide services well into retirement or need to be replaced less often in retirement. Last, but perhaps most importantly, if workers raised children while working, household expenses presumably would be lower if they are no longer supporting minor children in retirement. 9
The adequacy standard may also be above 100 percent. The primary argument in favor of a higher adequacy standard is that health care expenses increase in retirement. Properly accounting for the costs of medical care requires not only information about the current cost of medical care and an accurate projection of future cost growth, but also the proper characterization of medical expenditures. If medical care is assumed to enter an individual’s utility function the same as any other type of consumption, then no adjustments need be made to the replacement rate measures. At the other end of the spectrum, medical expenditures could be treated as a necessary expense that impacts an individual’s budget constraint but does not enter an individual’s utility function. In this case, all medical expenditures—insurance premiums and out-of-pocket expenses—would be deducted from income both before and after retirement.
However, even if medical expenditures are characterized as a pure expense, it is not clear that the proper measure of 401(k) adequacy should be the extent to which it can fund both living expenses and health care costs, particularly if the estimate of the resources needed to fund health care expenses in retirement are a multiple of what would otherwise be needed to fund living expenses. 10 If, for example, the adequacy of 401(k) plans is judged relative to the traditional DB pension plans, 401(k) plans do no better or worse than traditional DB plans in hedging medical expenses. In addition, if rising retiree medical costs are a public policy concern, encouraging individuals to accumulate enough financial assets to self-insure against these risks may not be the optimal public policy response.
On balance, a consumption replacement rate at or below 100 percent is likely to provide adequate retirement resources, particularly for individuals who have raised children. Escalating health care costs could justify a higher standard of adequacy, but it is unlikely that health care costs would justify a much higher standard for lower-income individuals unless the Medicare and Medicaid programs were substantially changed.
Sensitivity of Baseline Results to Changes in Assumptions
The simulations above require many assumptions. An effort was made by the author to make reasonable and defensible assumptions. Nonetheless, the results are sensitive to the assumptions. 11 Three generalizations can be made regarding the sensitivity of the results, all related to the structure of Social Security benefits. First, because Social Security benefits are the primary source of retirement income for all of the households simulated, the results are more sensitive to changes in assumptions that impact Social Security benefits—such as assuming benefits will be reduced relative to current law—than they are to changes in assumptions that primarily impact 401(k) accumulations. Second, changing assumptions that primarily impact 401(k) accumulations has the largest effect on those households that rely most on 401(k) income in retirement: households with higher earnings (controlling for marital status) and single individuals (controlling for household earnings). Third, controlling for savings as a percentage of pay, negative shocks to earnings—such as unemployment spells—increase, rather than decrease, measured replacement rates. Such shocks reduce well-being in retirement on an absolute scale. However, replacement rates are a relative measure, and—because Social Security benefits are progressive—negative shocks reduce net earnings more than they reduce net retirement income.
Stochastic Simulations
In this section stochastic simulations are used to illustrate the range of potential outcomes if 401(k) plan contributions are invested in risky assets. Specifically, Monte Carlo simulation techniques are used which assume that, in any given year, investment returns are a random draw from all possible investment returns. Assets are assumed to be invested in a portfolio that is one-half large corporate stocks and one-half corporate bonds, with the portfolio rebalanced annually.
Data on investment returns for large company stocks and corporate bonds from 1926 to 2004 were taken from Ibbotson Associates (2005). Investments are assumed to be in mutual funds, with mutual fund expenses plus transaction costs equal to 120 basis points for stock funds and 70 basis points for bond funds. 12 Annual real returns are calculated as nominal returns less concurrent inflation. Over the 1926–2004 period, the geometric mean real annual return for a portfolio with 50 percent large company stocks and 50 percent corporate bonds was 4.4 percent; the arithmetic mean real annual return was 5.2 percent; and the standard deviation of annual returns was 12.8 percent.
For ease in exposition, the simulations presented above—which assume that 401(k) assets are invested in TIPs and that an inflation-indexed immediate annuity is purchased upon retirement—will be referred to as the “baseline case.” Simulations that assume 401(k) assets are invested in a portfolio that is 50 percent large company stocks and 50 percent corporate bonds, rebalanced annually, with systematic withdrawals taken from the account during retirement, will be referred to as the “investment account.”
Accumulation of Assets
For a single simulation of investment returns, random real rates of return are generated for each year over a forty-seven-year period corresponding to the time simulated individuals or couples are twenty to sixty-six years of age. Nominal returns are calculated as the sum of real returns plus inflation. Inflation is either historical inflation (before 2006) or as projected in the SSA’s intermediate projection (2006 and after). Assumptions regarding savings behavior are the same as used in the baseline case. A single simulation produces eight account balances at retirement, one for each possible combination of marital status and earnings path. This process is then repeated 5,000 times to get a range of possible outcomes.
Results from these simulations are presented in Table 3 . On average, over all 5,000 simulations, the investment account outperforms the baseline case. Retirees who began saving at age fifty-two could expect to have 26 percent more in accumulated assets compared to the baseline case, and retirees who began saving at age thirty-two and would be expected to have 79 percent more in accumulated assets compared to the baseline case. However, higher average returns are associated with higher risk. In the highest 10 percent of simulations, returns were substantially higher for the investment account than for the baseline case—with accumulated assets slightly more than twice as high for those starting contributions at age fifty-two and nearly four times as high for those starting contributions at age thirty-two. In the lowest 10 percent of simulations, the investment account substantially underperformed the baseline case, with accumulated assets 26 percent lower for those starting contributions at age fifty-two and 28 percent lower for those starting contributions at age thirty-two. An alternative measure of the risk is the percentage of cases in which the baseline case outperformed the investment account. This ranged from 26 percent of the time for investors with the shortest investment horizon to 15 percent of the time for investors with the longest investment horizon.
Accumulation Results from Stochastic Simulations
Source: Author’s calculation.
aAssumes savings are invested in portfolio that is 50 percent stocks and 50 percent bonds, with returns drawn from a distribution of returns with mean and standard deviation equal to historical experience (5.2 percent mean, 12.8 percent standard deviation).
bSee note in table 1.
Distribution of Assets
In the baseline case, all accumulated 401(k) assets are used to purchase an inflation-indexed annuity at retirement. In contrast, the investment account remains invested with annual distributions taken from the account after retirement. For married couples, it is assumed distributions continue until the surviving spouse dies.
Annual withdrawals from the investment account are based on remaining life expectancy. This assumption is made for two reasons. First, Utkus and Young (2010) find that, among participants over age sixty, who terminated employment in 2004 and preserved their 401(k) assets, 80 percent had rolled the assets to an individual retirement account (IRA) within five years; and, among households making withdrawals from a traditional IRA in 2008, 64 percent used required minimum distribution rules—which are based on life expectancy—to calculate the amount they withdrew (Holden and Schrass, 2010). Second, Dus, Maurer, and Mitchell (2005) compare multiple methods of distributing funds from a retirement account, and this withdrawal method rates highly by several criteria. Choice of this payout method to illustrate the potential risks faced by participants is not meant to imply that this particular method is somehow optimal. To the extent that superior payout methods exist, the simulations will understate the rewards and/or overstate the risks faced by participants who choose to take systematic withdrawals from their retirement account.
Conditional on survival to age t, withdrawals from the account are equal to
13
Account balances evolve in the following manner:
Replacement Rates in Retirement: Combining Accumulation and Distribution
This section combines the simulation results from the accumulation phase and the distribution phase to generate net income streams in retirement. As was the case with the simulation through age sixty-six, 5,000 simulations are run, assuming a portfolio that is 50 percent stocks and 50 percent bonds, rebalanced annually. Simulations are run from age twenty to age one hundred. Ranking payment streams is more difficult than ranking accumulations, as both the timing and the total amount of payments are important. To rank and evaluate payout streams, this article borrows a measure of present discounted value (PDV) of withdrawals used by Dus, Maurer, and Mitchell (2005), which takes into account life expectancy as well as the time value of money and is calculated as
Net Income Streams
For workers with HS-35K earnings, Figure 2 plots the net retirement income conditional on survival for the baseline case and for the top, middle, and bottom deciles of simulations for the investment account. The area between the top and bottom deciles represents an approximate 90 percent confidence area for net income with an investment account. Results are plotted for single men, single-earner married couples with both spouses surviving, and single-earner married couples with one surviving spouse.
Net retirement income, conditional on survival, by deciles for single men and dual-earner married couples with HS-35K earnings
For single males with HS-35K earnings, the average net income for the middle decile of investment account simulations is higher than the baseline case until age ninety-two, when the likelihood of survival is 13 percent. Average net income for the top decile of simulations is considerably higher, with net income 128 percent of the baseline case at age sixty-seven, increasing to 157 percent at age eighty-one, and not falling below the baseline case until age ninety-eight. Conversely, average net income for the bottom decile of simulations is 97 percent of the baseline case at age sixty-seven, falling to 83 percent by age one hundred. The simulation results for single females (not shown) are very similar. These simulations show that there can be considerable variance in the amount of income generated from the investment account. However, the overall risk is fairly low, as Social Security benefits provide a floor beneath which net income cannot fall.
Because Social Security benefits make up an even larger proportion of retirement income, the overall risk associated with the investment account is much less for married couples with both spouses surviving than for single individuals. For married couples with HS-35K earnings—both single-earner couples (shown) and dual-earner couples (not shown)—average net income for the middle decile of investment account simulations is higher than the baseline case until age ninety-three, when there is a 2 percent chance that both spouses are alive. As a percentage of net income in the baseline case, the range of possible results from the investment account is much lower than is the case for single individuals, ranging as high as 117 percent but no lower than 95 percent.
When a spouse dies, the surviving spouse has less net income than the couple. In the baseline case, net income for the surviving spouse is lower for two reasons. First, Social Security benefits are reduced by one-third for single-earner couples (from 150 percent of calculated benefits of the working spouse to 100 percent) and reduced by one-half for dual earner couples (the surviving spouse continues to get his or her own benefit, but does not get the spouse’s benefit). Second, payments from the annuity are cut in half because it is assumed that the annuity is a joint and 50 percent survivor annuity. In the investment account simulations, Social Security benefits are exactly the same as the baseline case, but payments from the investment account continue unchanged until both spouses die. 15
In the case of married couples with HS-35K earnings where only one spouse survives, the investment account performs even better relative to the baseline case than for either single individuals or married couples with both spouses surviving. For survivors of both single-earner couples (shown) and dual-earner couples (not shown), average net income from the investment account for the middle decile of simulations is higher than the baseline case until age ninety-eight, when the chance of one spouse surviving is 8 percent. However, in contrast to other cases, the average net income of the lowest decile of simulations is higher than the baseline case from age sixty-seven to age ninety, and never falls below 96 percent of the baseline case.
The results are similar for Col-55K earners, Grad-75K earners, and Scaled Grad-100K earners. As with HS-35K earners, (1) average net income from the investment account for the middle decile of simulations is higher than the baseline case until retirees are in their mid-to-late 90s; (2) married couples with an investment account have less overall risk than single individuals because more of their income is from Social Security benefits; (3) the ratio of net income from the investment account to net income from the baseline case is higher for married couples with one surviving spouse than for all other cases.
As lifetime earnings increase, the main difference in the investment account simulations relative to the baseline case is that, as a percentage of net income, both the rewards and the risks of the investment account are increased. This is because Social Security benefits become a smaller portion of income and distributions from 401(k) accounts become a larger portion of income as lifetime earnings increase. For a single male with Col-55K earnings, the average net income for the middle decile of simulations peaks at 118 percent of the baseline case, and for the top decile peaks at 176 percent of the baseline case. For a single male with Scaled Grad-100K earnings, the same ratios peak at 131 percent and 273 percent, respectively. The risk of shortfall also increases with earnings. Average net income for the bottom decile of simulations falls to 77 percent at age 100 for a single male with Col-55K earnings, compared to 63 percent at age 100 for a single male with Scaled Grad-100K earnings. With all the simulations, married couples face lower risks. Even for the bottom decile of simulations, the ratio of average net income from the investment account to net income from the baseline case never falls below 85 percent for the surviving spouse of a one-earner married couple, regardless of lifetime earnings.
Replacement Rate Measures
The replacement rate measures average real net income in retirement as a percentage of average real net income prior to retirement (from age thirty to age sixty-six). The measure of average real net income in retirement takes into account survival probabilities and thus places greater weight on income received in the early years of retirement.
Table 4 reports replacement rate measures for the baseline case and the investment account for single males and for dual-earner married couples. The investment account produces higher expected replacement rates than the baseline case. For example, the expected replacement rate for single male renters with HS-35K earnings is 98 percent for the investment account, compared to 87 percent in the baseline case. However, the investment account involves risk and, for the bottom decile of simulations, the expected replacement rate for this individual is 81 percent. Higher earners are subject to more risk with the investment account. Over all 5,000 simulations, the average replacement rate for a single male with Scaled Grad-100K earnings is 118 percent, but the average replacement rate for the bottom decile of simulations is 79 percent.
Source: Author’s calculation.
aSee note in Table 1.
bAssumes savings are invested in portfolio that is 50 percent stocks and 50 percent bonds (see note on Table 3). Assumes investment account that annually pays out 1/E[T] of the account balance, where E[T] is life expectancy conditional on age; upon death, account balance is left to heirs. Life expectancy in 2033 at age sixty-seven expected to equal life expectancy in 2006 at age sixty-five.
Because distributions from 401(k) plans are a smaller portion of their total retirement income, the investment account generates less variance in replacement rates for married couples. For example, even in the lowest decile of simulations, the investment account averages a replacement rate of 87 percent for dual-earner married renters with HS-35K earnings with both spouses surviving, compared to an 88 percent replacement rate in the baseline case. For dual-earner married renters with Scaled Grad-100K earnings, the lowest decile of investment account simulations averages a replacement rate of 91 percent, compared to 93 percent for the baseline case. Relative to the baseline case, the investment account offers surviving spouses much higher average replacement rates and less risk than for either single individuals or married couples with when both survive. For survivors, even the worst 10 percent of investment account simulations produce a higher average replacement than does the baseline case.
Discussion of the Stochastic Simulation Results
The stochastic simulations illustrate investment risk by showing a range of potential outcomes; they should not be used to assess the adequacy of retirement savings. The amount of savings deemed adequate ex ante should not vary with the type of investment chosen. When choosing a contribution rate, 401(k) participants should assume investments will earn the risk-free rate of return. The portfolio allocation of the 401(k) account is a separate decision and should be based on the individual’s assessment of the trade-off between risk and return. Ex ante a dollar invested in corporate stocks or corporate bonds is worth the same as a dollar invested in TIPS. Ex post a dollar invested in corporate stocks or corporate bonds could be worth more or less than a dollar invested in TIPS. The actual returns realized will cause individuals invested in risky assets to adjust future behavior—that is, consume more and/or work less, or consume less and/or work more.
The higher expected rate of return should not cause those invested in risky assets to save less than those investing in TIPS. The popular financial press often treats investment risk as the solution to an equation relating savings and the amount of resources “needed” in retirement. That is, it is often implied that an investor should first determine the rate of return needed and then pick investments with that average return (and associated level of risk). For example, Richard needs average gains of 8 percent over 10-1/2 years on his Roth IRA, 401(k) and other investments to [finance his retirement goals. . . . [A financial planner] thinks he should be willing to take on more risk in hopes of boosting his returns. (Marantos, 2002)
Assessing the savings needs of a 401(k) plan participant is analogous to determining the PDV of liabilities for a defined benefit (DB) pension plan. Traditional methods of pension accounting allowed the discount rate used in calculating liabilities to be based on the average historical returns of the assets held to fund the liabilities, with no adjustment for risk. Thus, for any given stream of future liabilities, pensions with risky portfolios were required to hold fewer assets. Financial economists objected to this method, arguing that the risk-free rate should be used to discount liabilities, as to do otherwise would imply that a dollar's worth of stocks was worth more than a dollar's worth of bonds. Similarly, a 401(k) participant should not assume that they can reduce the amount they need to save for retirement by investing in risky assets.
However, just as a dollar invested in a risky asset should not be valued more than can a dollar invested in a safe asset, neither should it be valued less. Ex ante, a voluntary rational decision to invest in risky assets cannot make an investor worse off than investing in the safe asset. Willingly taking on risk implies that an investor prefers adjusting planned future consumption and/or planned future leisure to having the (certain) consumption path and leisure time associated with the risk-free investment.
Although not explicit, some recent studies seem to suggest that investors who choose riskier portfolios require more savings. For example, VanDerhei (2006) concludes that investment in equities and a lack of annuitization can lead to higher required “initial retirement wealth,” or a higher “necessary replacement rate.” Ernst and Young (2008) illustrates that those without guaranteed lifetime income need to reduce their standard of living to ensure that they have only a 5 percent probability of outliving their assets. These studies imply that, ex ante, a dollar invested in risky assets is worth less than a dollar invested in the risk-free asset.
In addition to providing no additional insight regarding adequate savings rates, the stochastic simulation results cannot, by themselves, indicate whether an individual “should” invest in the riskless asset or “should” invest in risky assets. To make that determination requires information on the individuals' preferences, including tolerance for risk and desire to leave bequests, and the individual’s beliefs regarding life expectancy and future market returns. Nonetheless, the results suggest some insights into which individuals would be more or less likely to take on investment risk.
First, perhaps counterintuitively, the simulations in this article suggest that workers with lower lifetime earnings would be the most inclined to invest in risky assets and the least likely to voluntarily purchase an annuity in retirement, all else equal. This is because most of their wealth is in the form of future Social Security benefits, making 401(k) assets a smaller portion of wealth and making risks incurred in 401(k) investments smaller as a percentage of retirement income.
Second, the simulation results also show that married couples face a different trade-off than single individuals when choosing to annuitize their wealth. 16 Married couples—and surviving spouses in particular—face a much lower risk that the investment account will underperform the baseline case. Most individuals approaching retirement are married, which may help explain why so few individuals choose to annuitize their wealth at retirement. 17
An important caveat regarding the simulations is that the variance modeled is across time periods rather than across individuals. That is, the simulations do not illustrate that some individuals will experience better investment returns than others. The simulations assume all individuals are invested in the same investment portfolio. The extent to which individuals investing over the same period experience different returns would represent an additional source of variation that is not modeled.
Conclusion
Some analysts have concluded that, with typical contribution rates and without investments in risky assets, 401(k) plans cannot provide retirees with adequate resources. To assess these claims, this article uses simulations to calculate the amount of retirement income that could be generated by 401(k) participants with different levels of earnings using realistic assumptions of participant behavior. The results suggest that most workers can achieve adequacy by supplementing Social Security benefits with income from a 401(k) plan funded with moderate contributions and invested conservatively.
The conclusions reached in this study differ from previous analysis due, at least in part, to the method of analysis. First, the simulations used in this study account for owner-occupied housing and fully specify income taxes, payroll taxes, and the Social Security benefit formula. Second, the replacement rate used in the analysis measures the ratio of retirement to preretirement potential consumption rather than the ratio of retirement to preretirement gross income. Modeling the benefit formula and simulating benefits not only illustrates that, for any standard of adequacy, the portion of earnings which 401(k) distributions need to replace varies significantly with lifetime earnings, but also illustrates the social insurance aspect of the system: all else equal, negative earnings shocks tend to increase replacement rates because of the progressive Social Security benefit formula. Explicitly modeling income and payroll taxes show that taxes not only vary with earnings but that they also will typically decline in retirement. In addition, typical replacement rate analysis ignores equity in owner-occupied housing, which represents a large portion of net worth for many households.
This study constructs representative earnings paths for individuals and married couples that roughly represent median earnings for full-time, full-year workers with a high school degree, a bachelor’s degree, and a graduate degree; and a fourth earnings path is created that is one-third higher than median graduate degree earnings. All workers are assumed to have access to a 401(k) plan, but participation, employee contributions, and employer matching contributions vary by household earnings and marital status. Total contributions rates, including employer contributions, range from 4 percent to 10 percent of earnings. Contributions to the account begin at age thirty-two for the highest earners and at age fifty-two for the lowest earners. Once begun, savings continue until retirement with no withdrawals taken until retirement at age sixty-seven. Separate replacement rates are reported for renters and homeowners. Homeowners are assumed to purchase a house at age thirty-five and to pay off the mortgage prior to retirement.
In the baseline case, it is assumed that 401(k) participants invest in TIPS that provide a real yield of 2.2 percent, net of investment expenses, and, at the time of retirement, use accumulated assets to purchase an annuity in the private market. For single individuals who rent, net income in retirement replaces 82 percent to 90 percent of net preretirement income. For single individuals who are homeowners, net income in retirement replaces 96 percent to 107 percent of net preretirement income. Because they get higher Social Security benefits, controlling for total earnings, married couples achieve even higher replacement rates. For married renters, replacement rates range from 83 percent to 102 percent, and for married homeowners, from 102 percent to 122 percent.
Investment in risky assets increases the expected return of investments. For example, with baseline assumptions, a single female with earnings comparable to median earnings for workers with a bachelor’s degree would replace 87 percent of preretirement net income in retirement. If she instead invested in risky assets and did not annuitize those assets at retirement, she would expect to increase her net income in retirement by nearly 20 percent. Associated with the higher average returns, these investments subject the participant to risks. However, because Social Security provides the bulk of most individual’s retirement income and represents a floor beneath which retirement income cannot fall, the risk as a percentage of total retirement assets is not as large as would be suggested by examining the 401(k) plan distributions separately. For example, even if this individual experienced the investment returns of the bottom decile of simulations, her net income in retirement would be 95 percent of the baseline case at age sixty-seven, not fall below 90 percent of the baseline case until age ninety-two (when the probability of survival would be 20 percent) and would be 85 percent at age one hundred (when the probability of survival would be 3 percent). Further, because of the presence of Social Security, all else equal, lower-earning households (controlling for marital status) and married couples (controlling for household earnings) would be more likely to choose to take on risk in their 401(k) portfolio.
Footnotes
The views presented in this article are those of the author and do not necessarially reflect the views of the Investment Company Institute or its members. I thank Curtis Carlson for providing assistance in programming the stochastic simulations used in this article and Sean Collins, Sarah Holden, Brian Reid, John Sabelhaus, and two anonymous referees for helpful comments, as well as the participants at the National Tax Association Annual Meetings and the Tax Economist Forum. Any errors are the responsibility of the author.
The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.
The author(s) received no financial support for the research, authorship, and/or publication of this article.