Saving for retirement

Saving for retirement

The biggest question facing anyone considering retirement is financial: are my savings sufficient to provide for my lifestyle for the rest of my life? For the fortunate among us, the answer is yes. But for a large fraction of the population, the answer is likely no.

The typical U.S. household has few retirement savings. The National Institute on Retirement Security reports that the median for near-retirement households is $12,000, while that for all households is only $3,000. Most people are relying on government social security to meet their retirement needs.

There are many reasons for this. One is the reduction in the fraction of employers offering any retirement plan at all, and another is the shift away from defined-benefit (DB) and toward defined-contribution (DC) pension plans. The result is that many individuals face risks that they are not equipped to bear, and many households need to save substantially more than they would have had these changes not occurred.

Let’s start with a description of the difference between DB and DC plans. In a DB plan, a beneficiary receives a lifetime retirement income based on their years of service and their final salary. In most plans, the benefit is indexed to inflation. By contrast, a DC plan is one in which the beneficiary makes payments into an investment account, and then receives the accumulation, plus the investment income, on retirement.

Before going into the details, it is worth saying a few words about Social Security. For workers with the requisite contribution history, Social Security functions much like a DB plan, but with two exceptions. First, it is more generous to those with low incomes and to beneficiaries in certain age cohorts. Second, it is funded by a combination of current contributions and future tax revenue. (The trust fund holds a special form of U.S. government securities that, when redeemed, will lead to either additional Treasury borrowing, or reduced expenditure.) In theory, this pay-as-you-go structure leads to a reduction in private savings, which could influence overall economic growth.

Returning to the topic at hand, a fully-funded DB structure has three attractive features. First, it compels savings, with the contribution rate set at a level that ensures the promised benefits can be paid. Second, DB plans provide insurance against long life (longevity risk), so participants need not fear exhausting their savings. And third, if the provider is very long-lived, these plans reduce “market-timing risk” that arises from the possibility that someone will be very unlucky and happen to live during a period of poor investment returns.

So, what does participation in U.S. pensions plans look like today? The Center for Retirement Research at Boston College reports that roughly 45% of people are engaged in a plan, a share that has been stable in recent decades. However, the shift from DB to DC plans has been dramatic: in 1983, fully 88% of workers with pension coverage had DB plans; by 2013, the latest data currently available, this share had dwindled to 30% (see chart).

Workers with Pension Coverage by Type of Plan, various years

To appreciate the consequences of this enormous shift, we developed a crude simulation for a person in a DC pension system who is paid $50,000 at retirement age (close to the median). Here’s what we did: start with a worker who works from age 23 to age 68 and then retires. Each year, the person’s wage rises by 2½%—similar to the slope of the age earnings profile (see here). At retirement, their goal is to replace 80% of their income. With 40% coming from social security (close to the replacement rate for someone with an income at retirement of about $50,000), retirement savings need to provide 40% of final working income. Our baseline investment strategy is to start with 90% equity (the S&P 500) and 10% bonds (10-year Treasuries), and slowly shift to one-third/two-thirds at retirement. (We use the weights in the Vanguard target retirement funds.)

So what is the probability that this worker will run out of retirement savings at various ages? That is, following this saving, investment and withdrawal plan, what is the likelihood of running out of money before turning 75, 80, 85, etc.?

To examine this longevity risk, we conducted a “Monte Carlo experiment:” using historical data on the S&P 500 and 10-year Treasury bonds from 1928 to 2016, we constructed 1,000 sequences of equity and bond investment returns. For each sequence, we then looked at the worker’s age when the savings accumulation was exhausted, assuming that they spent funds equivalent to an inflation-adjusted $20,000 annually (that is, 40% of $50,000). (The reliance on historical returns probably makes our results optimistic, because forward-looking inflation-adjusted equity returns probably have declined by 2 percentage points or more from the sample average of more than 6%.)

The following chart displays the results. To understand them, take the example of the thick black line labeled “Age 85.” Let’s start with the 5% saving rate case, since that’s the national average. The results show that someone who starts work at age 23, gets a steady 2½% inflation-adjusted salary raise, saves 5% of their pre-tax income, invests it in a target-date retirement mutual fund, retires at age 68 and then withdraws 40% of their final salary every year, has a probability exceeding 50% of running out of money before reaching age 85. If, instead, this worker were to save 10% per year, the probability of exhausting her or his savings by age 85 falls to 14%. Driving the probability down below 5% requires saving 13½% of income each year, more than double the national average.

Probability of Exhausting Retirement Savings at Various Ages, by Saving Rate

Source: Authors’ calculations based on data from the website of NYU Stern Professor Aswath Damodaran.

Source: Authors’ calculations based on data from the website of NYU Stern Professor Aswath Damodaran.

You might wonder how the results differ if the worker had invested 100% in equity for their entire life, including during retirement. At low saving rates, the equity-only strategy substantially reduces the probability of exhaustion, but at higher saving rates, the results are very similar (see below).

Probability of Exhausting Retirement Savings at Various Ages with 100% Equity Investment, by Saving Rate

Source: Authors’ calculations based on data from the website of NYU Stern Professor Aswath Damodaran.

Source: Authors’ calculations based on data from the website of NYU Stern Professor Aswath Damodaran.

Now, at the outset we noted that retirees face two potential risks: longevity risk and market-timing risk. We can use our calculations to get some sense of how important these are.

Starting with longevity risk, the actuarial life tables for the United States tell us that at age 68, a man has a life expectancy of 17 additional years and a woman has life expectancy of 19 years. That is, a 68-year-old man is expected to live to 85 and a similarly aged woman to 87. Furthermore, the man of 68 years has a roughly 5% chance of living to 96, and the woman has the same chance of making it to age 99.

Let’s suppose that people are quite risk averse when it comes to being impoverished in old age. Say that a typical person who would like to be prepared to live to age 100 would be willing to take a 5% chance of outliving their savings, but not much more. If so, in our shifting portfolio scenario, that person would wish to save around 21% of their income in a DC plan (consistent with the green line in the first simulation chart).

However, a DB arrangement pools longevity risk, so that avoiding the threat of old-age penury doesn’t require such high savings. A DB system can promise to pay everyone a life-long benefit, knowing that some people will live beyond the mean and some will not. With a large pool that is representative of the population, at retirement, each person need only have savings equal to the amount they would need if they exhausted it at age 85 or 87 (depending on gender). That rate is about 13½% (consistent with the black line in the first simulation chart). In other words, lacking protection against longevity risk means having a saving rate that is 7½ percentage points higher every year. Put differently, the cost of insuring against longevity risk in a DC plan means that your consumption has to be 7½% lower throughout your working life.

What about market-timing risk? Suppose that you are unfortunate and accumulated your savings during a period of relatively low investment returns? Again, DB plans provide a benefit that is absent from DC plans. While longevity risk is reduced by pooling within an age cohort, market-timing risk is reduced by pooling across age cohorts. That is, people of different ages can insure each other because some will experience better investment returns than others. Importantly, though, this can only happen with a fund that exists for a long time and has participants that vary across generations.

How big are the benefits of reducing market-timing risk? To see this, we can compare the saving rate from our experiment in which investment returns vary with the saving rate that would be needed if our worker could assume lifetime investment returns are equal to the average rate every year. That is, if real equity returns were a stable 6% per year, every year, what savings rate would be required to replace 40% of income for 17 years of retirement? The answer is just over 5%!  If forward-looking equity returns average only 4%, which seems entirely possible, then the required savings rate rises to about 8%. That is, the market-timing risk could be worth an addition 5 to 8 percentage points of consumption!

Putting this all together, if people have to prepare for both longevity and market-timing risk, then they will have to save much more for retirement. But since this risk can be avoided by pooling both within and between age cohorts, there is a sense in which these high-saving levels would be inefficient. People could have permanently higher consumption if they could insure against these risks in ways that DB plans do. (To be sure, this conclusion does not take account of the impact of reduced aggregate savings on long-term economic growth.)

This leads us to ask two questions. First, why have DB plans disappeared? And second, why haven’t other privately supplied financial products taken their place as insurance mechanisms?  On the first, the standard answer is cost. In one system that is currently operating, the State Teachers’ Retirement System of Ohio (STRS Ohio), qualifying employees accrue income benefits equal to 2.2% of final salary per year of service in exchange for a contribution of roughly 25% of current income. (The Ohio plan includes health benefits and covers a population with longer-than-average life expectancy, so its cost almost surely exceeds that of a broad DB-only plan.)

As for the dearth of annuities, this puzzle has been lurking for a very long time. Economists generally agree that—in a fair market—people should annuitize a portion of their savings at retirement. So why is this practice not the norm? One possibility is that straight-vanilla annuity prices are high. A comparison of numbers used to construct our charts with commercial quotes available here suggests that the cost of a life annuity is equal to the amount you would need to save to assure yourself of the same income should you live to be 100 years old. That is, to the extent that the longevity risk is being pooled, the benefits are going to the provider. Another possibility is a demand-limiting combination of inertia and lack of financial sophistication. The latter may be particularly important in light of the complex characteristics of many annuities. Regardless of the ultimate cause, so long as the pool is small, the provider bears residual risk, helping to sustain high prices (for discussions, see here and here).

So what are the takeaways? First, the current retirement savings shortfall needs to be addressed. Second, creating a system that allows people to manage both longevity and market-timing risk would limit the sacrifice of consumption and the macroeconomic impact. By addressing longevity risk, standard annuities go part way, but may need to be re-framed and “nudged.” Addressing market-timing risk would require large systems that enroll people of all ages and are highly creditworthy. Perhaps this can also be done in the private sector, but one obvious alternative would be to enhance the Social Security system.