Hopefully this section can illustrate the impressive power of compounding growth that makes comfortable retirement possible. We'll also discuss the evidence on how to invest after retiring. Let's start with a broad overview of how to think about long-run investing and financial independence.
Factors over which you exercise some control include:
- Income during your working years and changes in income over time;
- Allocation and timing of investments;
- Use of tax-advantaged accounts;
- Use of insurance;
- Where you live;
- At what age you may merge finances with a long-term partner;
- At what age you may have children;
- Support you expect to provide to and receive from your family;
- How much you will spend, save, and invest during working years;
- How much you will change your spending during retirement;
- How you will change your investment approach during retirement;
- Age of retirement;
- Whether you retire suddenly or continue earning a smaller income for some time;
- Personal goals such as charitable donations or leaving money for your children.
Factors over which you exercise little or no control include:
- Asset class returns for stocks and bonds;
- Inflation rates;
- Interest rates;
- Federal tax rates;
- Government benefits like Social Security and Medicare, which may change by the time you retire.
The daunting scope of retirement planning may provoke some people who haven't thought much about the arc of their life plan to start to consider some important questions. What do you value about money and what do you want to do with it? How much is enough? How much time and how many years do you want to spend working for pay? After approaching financial independence, is there something you would enjoy doing that pays less or nothing at all?
Although there are variables you cannot control, like federal tax rates, you can adjust variables which are under your control, like savings rates, to make it more likely that you’ll be prepared for an uncertain future. There are also factors which are under your control to a great degree, except in rare situations. Health is a perfect example: most people have the opportunity to reduce expected health care costs by keeping themselves healthy, but it is always possible to be dealt an unavoidable illness or injury. As discussed in the previous section, this falls in the category of potentially catastrophic risks you can insure yourself against.
Many of these variables can be entered into an online retirement calculator like this one. Basic calculators give you an idea of how your saving and investing will add up in the long run, and whether they can sustain you during retirement. There are factors that can't be explicitly included in these calculators, but working out imprecise numbers is far better than the vague assumptions that would take their place. Planning your future will also demonstrate how useful it is to keep track of your spending. Exactly how much do you spend on food? How much does car maintenance cost? You will be able to project future spending far more accurately if you record and categorize your current spending. You may also be able to target areas in which you’re spending more than you thought.
I don't recommend relying on calculators like the one above. Nor would I propose using misleading rules of thumb like this one. It suggests that I should have the equivalent of my salary saved by 30, and three times my salary saved by 40. Perhaps this could be sensible for someone who started working at 22. For a boarded physician with a negative net worth at 30 but very high earning potential, it is nonsense that has the potential to promote confusion and financial anxiety. Some of the math needed for retirement planning is more advanced than many people are used to, but it's important to understand the assumptions behind the numbers that guide your saving and investing. So we'll review the calculations needed for retirement planning in detail.
It's essential to understand compounding growth, so watch this video if you aren't sure you completely understand it. Let's walk through a few math problems based on compounding growth that everyone should know how to do.
If a $500 investment earns an average annual return of 7.5% for 30 years, how much is that investment worth at the end of the period? To indicate 7.5% growth in one year, we would multiply the initial amount by 1.075. To indicate an average 7.5% annual return over 30 years, we multiply by 1.075 30 times: 1.075^30 = 8.75496. Now we know that 7.5% average annual growth over 30 years is equivalent to multiplying by 8.75496, so we calculate the final balance as $500 × 8.75496 = $4,377.48.
If a $300 investment grew to $9,083.15 over 40 years, what was the average annual return? We reverse the process above. First we must find the factor by which the investment grew: 9,083.15/300 = 30.2772. Now we can ask, what average return is needed to multiply an investment by 30.2772 over 40 years? We want the number which solves the equation x^40 = 30.2772. So we calculate x = 30.2772^(1/40) = 1.089. This indicates an average annual return of 8.9%.
If over three years our investments provide annual returns of 7%, 15.5%, and -2%, what is the average annual return? We must convert these percentage changes to multipliers: 1.07, 1.155, and .98. The geometric mean is calculated as (1.07×1.155×.98)^(1/3) = 1.0659, a 6.59% average annual return. The geometric mean of annual returns is often called the compound annual growth rate (CAGR). If it's unclear, see this footnote[1] for why the calculation must be done this way.
Next, how does inflation work when calculating returns? Let's say we project an 8% average annual return over 40 years, so the asset will be multiplied by 1.08^40 = 21.7. This is our nominal return, which is distinguished from the real return — that which remains after accounting for inflation. With average 2.5% inflation, the real return is calculated as 1.08/1.025 = 1.0537, or 5.37%. This gives us a real multiplier over 40 years of 1.0537^40 = 8.1. So instead of imagining that your money will multiply by 21.7, remember that your dollars will be worth less in 40 years, and the multiplier will feel much more like 8.1 (under these assumptions). If this shrinking multiplier is discouraging, imagine how your dollars would decay if you didn't invest at all: (1/1.025)^40 = .37. They would lose 63% of their purchasing power over 40 years! An 8% nominal return converts that multiplier of .37 to 8.1.
Finally, how can we find the savings needed to spend a given amount during retirement, while accounting for inflation and investment earnings? First we need to decide how much we'd like to be able to spend in terms of today's dollars. It's not easy to predict spending desires decades in advance, let alone the funds you'll need to set aside for health care and potentially for beneficiaries. One reminder may be comforting. Because you no longer need to save money once you've retired, the "income" you require from investments and Social Security for a particular standard of living is inherently lower than the income needed during working years. If a 68-year-old retires and was making $75K/year while saving $25K/year, they need only $50K/year to support the same lifestyle (in fact, even less due to reduced taxes). Many retirement experts find that overall retirement spending tends to be around 70-80% of pre-retirement spending.
Let's imagine that we want a comfortable annual "income" of $60,000 in today's dollars by drawing from our investments and receiving Social Security old age benefits. This is well above what the average American needs during retirement! Most people don't need to save and invest as much as we will in our example.
It's difficult to estimate your Social Security benefits if you're young, because benefits depend on your income throughout life as well as whether benefits will be fully funded. Both of these variables are uncertain. Let's say we've used the government's website to estimate that someone with our income would receive about $20K per year from Social Security if they retired today and applied for benefits at full retirement age (currently 67 for everyone born in 1960 or later). But the latest official report expects that, if neither tax rates nor benefit policies are adjusted, old age benefits will be reduced by roughly 23% around 2034. (Any alarmist predictions about future retirees receiving nothing need to contend with the fact that new money is added to the trust funds every year. Benefit payouts can never be zero unless Congress abolishes the program.) Congress will certainly make some changes to taxes and benefits, but we can't predict what those will be. So for the sake of this example we'll anticipate three-quarters of the payments we're supposed to receive (around $15K). We'll rely on our investments for the remaining $45K.
These amounts are expressed in today's dollars, because that's what we can relate to — $161K of inflated dollars 40 years in the future is not intuitive. We decide that our initial withdrawal rate will be 4% of the nest egg per year (withdrawal strategies are addressed below). A 4% withdrawal of $45K translates to a nest egg of 45,000×(100/4) = 1,125,000 at the beginning of retirement. Assuming 2.5% average inflation for 40 years, cumulative inflation would be a factor of 1.025^40 = 2.685. The cumulative inflation factor multiplied by $1.125M is $3.02M. That's the actual dollar amount we're aiming for in 40 years to provide a standard of living similar to $45K/year today. How can we reach it?
There are many ways of doing so. We'll describe the simplest first. We save and invest $8,080 the first year, and every year we increase that amount by our anticipated average inflation rate, 2.5%. So in the second year we save $8,080×1.025 = $8,241, and so on until we save $21,165 in the 40th year. We'll have saved $544,588 and, if our nominal returns are 8%, built a nest egg of $3.02M by the end of the 40th year. See this footnote[2] for how to calculate the first year's target using this approach as well as the next one. You can do so easily by changing the variables in a formula I typed into WolframAlpha.
The figure below illustrates this process. It shows our cumulative contributions to retirement savings (black) as well as the value of our nest egg as it grows over time with various rates of return (colors). Notice how the value of the nest egg explodes near the end, increasing more in the last 10 years than in the first 30 years. This is how any exponential process looks, but it underlines the importance of beginning as early as possible. All else equal, every year delayed is one year less of that ever-accelerating explosion at the end. Of course, there will be a great deal of volatility in the colorful lines — stock market returns are not smooth.
A variation on the first approach is to increase savings each year by last year's inflation, rather than an assumed long-term average inflation rate like 2.5%. This is a good idea, but of course when planning you will find yourself doing the same calculations because you cannot know what each year's inflation will be.
This first approach could be called time-invariant or flat: you contribute the same inflation-adjusted amount every year. This is advantageous because the more you frontload your retirement savings, the less you need to save overall. In the example above, we contributed only 18% of the final nest egg and investment took care of the rest. In other words, more than four out of every five dollars were the fruits of investing! If you could put away even more in your early life than this approach would suggest, that would be great. But many people need to do the opposite: they cannot save much until later in life. So we could design an approach in which we increase savings each year in addition to inflation, to acknowledge the growth in ability to save.
Imagine the same conditions as described above, but we increase savings each year by 2% on top of 2.5% for inflation. Our target savings in the first year will be only $6,109, a 24% reduction from the flat approach above. In the second year we save $6,109×1.02×1.025 = $6,387. In the 40th year we need to save $34,642, a 64% increase compared to the first example. Investment still does most of the work for us: we save about 22% of the $3.02M. But it turns out to be a lot more in absolute terms: we had to put away $661,735 using this approach, an increase of about $117,000 or 21.5%. We saved more to build the same wealth in this example, but it is a more realistic model for many people. An interesting twist for people who can frontload their savings would be to decrease inflation-adjusted savings each year. For example, someone who frontloads so that they make the same contribution every year would need to save only $10,797 each year, for all 40 years! Although they would be saving the same dollar amount each year, they're frontloading because they're saving less each year in real terms. The total savings needed to reach the $3.02M goal would be only $431,864 (14% of the total).
You may find it useful to reverse this process and convert certain savings patterns into retirement income. This footnote[3] explains how to use the WolframAlpha calculator linked here. Anyone interested in how the equation is derived can click here.
First: the earlier in life a financial sacrifice is made to save money for retirement, the more potent that act will be. $1,000 invested at an average 5.37% real return (8% nominal with 2.5% inflation) until age 75 becomes:
- $2,840 if saved at age 55
- $4,800 if saved at age 45
- $8,090 if saved at age 35
- $13,650 if saved at age 25
Because these dollar values are in real terms, they reflect how much more valuable the investment becomes after accounting for inflation.
We can also use the flat method of saving to illustrate how important it is to start early. In our example, the first year savings target is $8,080 with a 40-year horizon. But with 30 years the figure is $15,088; with 20 years it is $31,062; and with 10 years it is $83,449. When you start late, you give your capital less time to appreciate. In addition, allowing yourself more time implies that your average return will tend to revert to long-term expected returns. The average return of someone with a timeline of only 10 or 15 years will be strongly influenced by idiosyncratic trends and events; their results may be fantastic or underwhelming. For example, someone investing in the cap-weighted US market only from 2000-2009 would have been disappointed, whereas someone investing only from 2010-2019 would have experienced a dazzling run-up. The average return of someone with a timeline of 30 or 40 years is more predictable, in the neighborhood of 8% for the stock market. We will discuss in the next section how to increase expected returns above 8% through diversification beyond the cap-weighted total market.
Of course, it is many people's financial reality that they cannot save large amounts of money at a young age. The point here is not to wag a finger at them, but to emphasize the importance of saving and investing as early as possible within the constraints of your situation.
A high savings rate in your early career has another benefit: it helps tame hedonic adaptation. The initial years of your career will likely see the most drastic improvements in the living standards you can afford. You'll (hopefully) be able to buy more of everything you want, and some people respond by spending every raise. Living well below your income forces you to consider what you value spending money on, and lets you load up on savings (or quickly pay off debt) while you're young.
Second: the plot shows that a difference of even one percentage point in average returns makes an enormous difference to lifetime wealth. Even half a percentage point can easily amount to hundreds of thousands of dollars! And, of course, investing doesn't end at retirement age. I don't say this to encourage extreme risk-taking, but there are three free lunches that will increase your expected return: minimizing tax, minimizing fees, and increasing diversification. You also don't want to hinder your expected return by choosing low-risk investments for assets with long time horizons.
Third: if your spending closely matches your income, you will appear to be living within your means. But failing to save for an eventual goal of financial independence means that the appearance of spending responsibly is superficial. An ever-deepening well of savings is not only necessary for retirement: it also gives you the freedom to not rely on the next paycheck to sustain your lifestyle. The ability to make decisions without the pressure of imminent financial need is one of the great rewards of building wealth. There is a lot more to saving than maximizing your wealth at age 70.
During retirement, investments are vulnerable to sequence risk. When withdrawing from a portfolio, poor returns are more harmful if they occur early rather than after some period of positive returns. If a retired person's portfolio experiences a large, protracted drawdown, then they need to withdraw a larger fraction of their portfolio to maintain the same spending. Although the portfolio recovers, the parts that were withdrawn never get a chance to recover.[4] If depleting your assets is a concern, then flexible spending during retirement is important. Your portfolio's longevity will be extended if you're able to reduce withdrawals during large drawdowns. Another safeguard against sequence risk is to continue earning income for some time. Even 10% of your pre-retirement income made doing something you enjoy augments the compounding of your investments by reducing your need to withdraw from them. Working part-time for a while can also help with the transition into retirement. Not everyone thrives after a sudden switch from full-time work to 100% free time.
Pfau and Kitces (2014) argued that the best portfolio approach to contend with sequence risk is a large allocation to bonds early in retirement, followed by a gradual increase in stock allocation. This is known as a rising equity glide path (where a glide path describes how asset allocation is deliberately shifted over time). Michael Kitces advocated for this approach in his Rational Reminder interview, and this recommendation has reached many people. However, they found this result through Monte Carlo simulation — randomly sampling market returns in a way that doesn't retain all the qualities of real market returns, such as mean reversion. They didn't backtest in historical data until a later paper. That analysis compared a limited selection of portfolios — static allocations had either 45% or 60% equities — and they still focused on US data only. They commented that in their data, rising equity glide paths were safer than static allocations mainly when a retirement period started at high stock valuations (making poor stock performance more likely).
Javier Estrada (2015) conducted a much more thorough study of the issue. He compared the performance of rising equity, declining equity, and static glide paths in the US and many other countries since 1900. The bonds in the database he used are long-term government bonds. Estrada found that certain static allocations had the lowest failure rates as well as the most wealth remaining at the end of 30 years in the mean and median historical periods, most favorable periods (90th, 95th, 99th percentiles), and most unfavorable periods (10th, 5th, and 1st percentiles). Static, high-equity allocations were the top performers. Shockingly, a 100% equity allocation had the lowest failure rates, best downside protection, highest upside potential, and best average outcomes in US and international markets. A static 60/40 portfolio also outperformed all rising equity glide paths (but not all declining equity glide paths) in the US and international samples. Estrada found that in real historical data, rising equity glide paths consistently had worse outcomes than declining equity or static glide paths.
A popular approach to retirement spending is the bucket approach. The first bucket holds one to five years of expenses, and is held in very safe investments. One or more other buckets hold riskier investments, and are hopefully protected from being accessed while in a downturn by the safer buckets. I could hold three years of expenses in short-term US Treasury bonds in one bucket and a 100% stock portfolio in my second bucket. I would replenish my safe bucket only if my stocks had positive returns in the last year; otherwise, I would wait to replenish until stocks had positive returns or my safe bucket was depleted. This is the simplest version of a bucket strategy. Other versions could split my portfolio into more buckets, or replenish my safe bucket only if stocks had above-average returns (rather than positive returns) over the past year or five years. A bucket approach is touted by some financial advisors because they say clients feel comfortable knowing they have a safe bucket that is insulated from harrowing market drops. They also praise the simplicity of a bucket approach.
The problem is that all bucket strategies perform worse in retirement than another simple approach: one portfolio of stocks and bonds that is periodically rebalanced. Javier Estrada (2019) used US and international data since 1900 to test different bucket and single-portfolio strategies. In contrast to his paper discussed above, the government bonds used in this paper were bills (short-term bonds). Single portfolios with equity allocations between 50% and 100% tended to be most successful. All of the bucket variations underperformed a simple 70/30 allocation (recall that this means 30% bills). Bucket strategies undermine one of the keys to a diversified portfolio: buying what recently underperformed and selling what recently outperformed. This explains why bucket strategies with smaller safe buckets perform better than those with larger safe buckets — the less bucket-y, the better! If only a small part of the portfolio is set aside from rebalancing, it hurts performance less. Some bucket approaches do engage in consistent rebalancing. If they do, then those aren't buckets in any meaningful sense, they're just parts of the portfolio that are being labeled buckets.
For some resources on safe withdrawal rates, check out this video covering the basics and this post, which is part of a detailed discussion of withdrawal strategies. In the running example above, we used a 4% initial withdrawal rate. So we withdraw 4% in the first year, but what do we do next? Following the famous "4% rule", we would adjust the withdrawal amount each year by last year's inflation, and would continue doing this every year regardless of portfolio performance. The rule is straightforward, but lacks flexibility. One sign of its weakness is that it backtests well only in historically successful markets. New Zealand and Canada are the only countries where a domestic investor could've retired and followed the 4% rule without running out of money in every 30-year period since 1900. With the right allocations, a few other countries have failure rates below 5%. So if your unknowable future returns aren't as good, your portfolio could struggle to hold up under the 4% rule. It could also fail if your retirement extends beyond 30 years. This is longevity risk: the risk that you could live a long time and run out of money! So maybe the withdrawal rate should be less than 4%?
A major issue with debating whether a safe initial withdrawal rate is 3% or 3.5% or 4% is that static withdrawal amounts adjusted only for inflation are very suboptimal. What we need is not an ultra-conservative initial withdrawal rate, but the flexibility to reduce withdrawals when our portfolio shrinks. At the same time, we don't want withdrawals permitted by the rule to swing drastically with the size of our portfolio. Say we took 4% of the portfolio value each year (or one-third of 1% each month). A constant percentage rule would be very safe if we could follow it, but our withdrawals would be more volatile than most people would like. Ideally, we could seek a middle ground that doesn't completely ignore market conditions but limits withdrawal volatility.
One method is to truncate any large fluctuation in withdrawals that a constant percentage rule would indicate. Vanguard and others call this a dynamic spending rule. A withdrawal of (say) 4% would be the starting point, but the rule wouldn't allow our withdrawal amounts to rise by more than 5% or fall by more than 2.5% compared to the prior year. So if we took 4% at the beginning of Year 1 and the portfolio fell by 30% during Year 1, we would reduce our withdrawal amount by only 2.5%. With a $1M initial portfolio, that would mean withdrawing $40K for Year 1 and $39K for Year 2 (instead of dropping all the way to a $26,880 withdrawal under a constant percentage rule). $39K would be 5.8% of the portfolio at the beginning of Year 2. Not only does a dynamic spending approach help us curb withdrawals while the portfolio is down, but it keeps withdrawals from springing upward too quickly and gives the portfolio more opportunity to recover. You could enhance the approach's safety by modifying the volatility limits (e.g., maximium 4% rise and 3% fall). Dynamic spending rules tend to be safer than "dollar plus inflation" rules like the famous 4% rule, so in exchange for more volatile spending, you can take a larger initial withdrawal for a given level of safety.
Based on all this, I would suggest a simple approach for the typical retiree. A static allocation is the easiest to maintain, especially if you use an all-in-one fund like AVMA, AOR, or VSMGX. The best allocation is 100% stocks, but most people would experience behavioral issues if they attempted that. By the time someone retires, they hopefully should have a sense of their stomach for volatility. If you include bonds, arguably the best bonds to complement stocks are long-duration US Treasury bonds. Estrada found that the best declining equity glide paths migrated from 80% to 20% and 70% to 30% — they even beat a 60/40 portfolio! See this section for info on different types of bonds, this section for how to build a stock portfolio, and the advanced topics for asset classes beyond stocks and bonds. If depletion of assets is on the table — which is the case if your desired spending is initially greater than perhaps 3% of your portfolio, or you expect a retirement much longer than 30 years — then spending should be regulated by a flexible approach with an initial withdrawal rate of 4-5%. Of course, all this should be adapted to each individual's risk tolerance, life expectancy, Social Security and pension income, anticipated changes in desired spending over the retirement period, wishes to bequest money to children or charity, and other unique factors.
The website ficalc.app (where FI is financial independence) beautifully illustrates portfolio values and spending based on a given length of retirement, portfolio, spending strategy, and more. It draws on US data only, so don't take it as a final word, but it is a great tool to see how different approaches would've developed in the past. You can see how a portfolio would've been depleted if someone began retirement in 1965-1969 and strictly followed the 4% rule (and no static allocation could've avoided depletion in all cases).
(1) Annual savings targets like $8,080 don't all come from your paycheck. Employer contributions in your work retirement plan might account for several hundred to some thousands of dollars, depending on your income and their matching policy. Once you add your own contributions, this minimum 401(k) activity can put a large dent in the savings you need. Some employers also contribute to your HSA.
(2) The risky, long-term portfolio I suggest is made up of 100% stocks. Many people cannot psychologically tolerate the volatility associated with that portfolio, even in a retirement account they won't touch for 20 years. So they allocate partly to less risky assets like aggregate bond funds. If you do this, projections for your portfolio's long-term growth must be lowered accordingly. Of course, as you approach within eight or ten years of retirement, you may want to begin adding some lower-risk bonds to your portfolio. The lower expected returns due to this transition were not considered in the simple examples above, but they could be accounted for by doing calculations for multiple periods.
(3) If you're decades from retirement, you can't anticipate the precise age at which you'll stop working full-time. That's okay: retirement is a financial status, not an age. You don't have to know when you'll retire, but you should form an approximate goal for the age at which you'll have the option to retire. This could be 40, 60, or 75. The older your target retirement age, the more likely it becomes that unexpected obstacles will make it harder to keep earning. Retiring earlier than 65 carries the challenge of paying for health insurance during the gap between group health insurance with an employer and enrolling in Medicare at 65. You can't collect Social Security until age 62, and every month you wait to enroll until age 70 will augment your monthly payments for the rest of your life.[5]
(4) Your retirement plan should be robust: it shouldn't collapse if stock returns are only 7% nominal (or 4% real) during your working years. If returns fall short, you may have to be prepared to work longer, increase your withdrawal rate, or decrease your spending. "Plan B" actions can include part-time work; reducing large expense categories like restaurants and certain kinds of travel; leaving less to children or charity; moving into a smaller home or to an area with lower cost of living; and forgoing major luxuries like a boat, a second residence, or expensive vehicles. The best way to avoid making financial compromises like these is to save to a degree that you hope is excessive, and invest with modest expectations. Give yourself the capacity to be flexible: don't fixate on a precise retirement date, or rely on above-average investment returns to meet your basic goals.
(5) Taxes are an essential part of retirement planning. The section on taxes discusses various techniques for tax-efficient investing. Your expected return could be 8% before taxes but, if you're investing in a taxable account, gains are undercut whenever they're realized. So the most important factor is how much you contribute to tax-advantaged accounts. Moreover, remember that money in your traditional IRA is pre-tax, so using withdrawals from a traditional IRA to generate a $45K "income" is very different than doing the same with a Roth IRA. The best approach is to use a combination of Roth and traditional accounts.
I recommend this interview with Michael Kitces on a variety of retirement topics. Despite the disagreement with Kitces stated above, I think it's a great watch. Larry Swedroe and Kevin Grogan's book on retirement provides good coverage of the major retirement considerations.
Uncertainty dominates the processes of investing for retirement and drawing partly on your investments to spend during retirement. Unfortunately, even Social Security benefits are a source of uncertainty, given the imminent funding shortfall for those benefits. We can prepare for retirement by saving at a high rate, saving as early in life as we can, investing in a diversified portfolio with high expected return, and minimizing tax — mainly by using tax-advantaged accounts. These practices reduce the impact of uncertainty about investment returns, tax rates, future income, future spending, marital status, and more. During retirement, uncertainty about your lifespan expands into a dominant variable, and combines with uncertainty about the lifespan of your partner (if you have one). Since an individual's lifespan can't be reliably predicted, a retirement nest egg needs to be spent carefully, and we reviewed guidelines for how to sustainably withdraw from your portfolio.
Click here for the next section — Guidelines for personal finance
All sections:
- Cover page
- Introduction to index funds
- Thinking about risk
- Tax-advantaged accounts
- Your psychology
- Investing for retirement
- Guidelines for personal finance
- Building a stock portfolio
- Fund proposals
- Advice
- Practical information for execution
- Taxes
- Vocabulary and further resources
- Advanced topics
Footnotes:
1 For some people it may not be obvious why the more common arithmetic mean is unsuitable. Perhaps we could have found the average return like this: (7+15.5-2)/3 = 6.83 or (1.07+1.155+.98)/3 = 1.0683. To consider this, we can imagine an unlikely sequence of returns, in which we double our money the first year and halve it the following year. Multiplying an asset by 2 and then .5 returns it to its original value. We can calculate the geometric mean of these multipliers, which we know intuitively should be 1: (2×.5)^(1/2) = 1. That's right, but the arithmetic mean gives us an incorrect answer, (2+.5)/2 = 1.25. Another way of checking this is finding that the average return matches the actual return. 1.07×1.155×.98 = 1.21, which equals 1.0659^3. The arithmetic mean of 1.0683 does not satisfy this test. Because we are averaging multiplicative factors, the geometric mean must be applied. ↩
2 You can click here to use a formula I set up in WolframAlpha. There are six variables. Five were already discussed: R for annual real return, T for years until retirement, D for desired retirement income in today's dollars, W for withdrawal rate, and G for inflation-adjusted annual growth of savings. G is introduced in the second approach to saving; to use the flat approach, set G equal to 1. The sixth variable is A, savings which already exist. The examples above assume no savings are set aside for retirement yet, but we can easily add this to the equation. R is the nominal return rate divided by inflation rate, 1.08/1.025 in the example above. To see how the equation is derived, click here. ↩
3 The WolframAlpha calculator for calculating retirement income based on savings is here. If a flat approach is desired, set G equal to 1 to effectively remove it. The variable S is the savings target in the first year. ↩
4 An attentive reader might wonder if a similar concern about volatility applies to building the nest egg during working years. One of the assumptions used in my calculations was not only that the average annual nominal return was 8%, but that the nominal return every year was 8%. Yet there are unlimited combinations of annual returns whose average is 8%. Couldn't some of those combinations result in a nest egg that is significantly smaller or larger than the one I calculated? The short answer is that as long as the average ends up close to 8%, it's not a concern. Any plausible sequence of returns that has the same average annual return will produce a similar outcome during the accumulation phase. All else equal, worse returns earlier (when you’ve contributed a smaller fraction of your total) and better returns later are desirable. This is exactly the sequence you don't want once you retire! ↩
5 Although waiting to apply for Social Security benefits increases the monthly benefit for the rest of your life, this doesn't imply that everyone should wait until 70 to begin taking them. We need to consider (a) the time value of money and (b) that we may die too soon for the larger, delayed payments to catch up in cumulative value. We also need to consider tax, but we can't do that for everyone in a single calculation.
How long do we need to live for it to be worth waiting to enroll in benefits at the full retirement age (67) instead of at the first opportunity (62)? Let's consider point (b) first, just the cumulative amounts of cash. Monthly benefits at 62 would be 70% of the benefits received at 67, so we'll define the benefit amounts as 0.7 and 1 for the sake of general calculations. You can use a spreadsheet with equations or some math to find that the age 67 path will catch up to the age 62 path in terms of dollars received at 77 and 8 months. If we wait even longer to take benefits at age 70, our monthly benefits will be 24% larger than in the age 67 path (so our benefit amount is 1.24). It takes the age 70 path until 79 and 5 months to catch up to the age 62 path, and until 81 and 6 months to catch up to the age 67 path. Lots of people die before they turn 81! To wait until 67 or older to take benefits, we're already betting that we'll live pretty long. Now let's consider the additional value of receiving benefits earlier.
It's better to receive money sooner than later, because we can invest the money in the intervening time. Let's say the bulk of our liquid net worth is in a portfolio with an expected return of 6%. This refers to the after-tax return, but many retirees have significant assets in tax-advantaged accounts, so tax may not be a major issue. What if taking benefits sooner allowed us to avoid withdrawing those amounts from our portfolio, so we could continue investing them? How much more appealing do earlier benefits become when we recognize the time value of money? Using our 6% expected return, the age 67 path now catches up with the age 62 path at 92 and 9 months! The age 70 path takes until 94 and 3 months to catch up to the age 62 path, and until 96 and 4 months to catch up to the age 67 path. Does it make sense to place a bet that you'll live well past 90 when you're 62? In my mind, it usually does not. However, we haven't covered taxation of benefits.
| 67 catches 62 | 70 catches 62 | 70 catches 67 | |
|---|---|---|---|
| No return | 77y 8m | 79y 5m | 81y 6m |
| 4% return | 84y 0m | 85y 7m | 87y 9m |
| 5% return | 87y 3m | 88y 10m | 91y 0m |
| 6% return | 92y 9m | 94y 3m | 96y 4m |
| 7% return | 107y 5m | 108y 7m | 110y 1m |
If Social Security old age benefits are an individual's or married couple's only income, that income is generally not taxed at the federal level. Even a person or couple with the highest possible monthly benefit would have an adjusted gross income lower than the standard deduction, so they wouldn't owe federal income tax. (These concepts are covered in the tax section.) Benefits may be taxed if someone has other income, which could be from employment, investments, a pension, or withdrawals from a tax-deferred account. This video explains the complex taxation of Social Security benefits.
We showed above why applying for benefits at age 62 could be a wise choice. So the crucial question is: are there any situations in which the effects of tax should cause us to delay applying for benefits? Yes: the main exception is if we’ve reached 62 but expect our income to fall significantly in the future. If we're still working at age 62, then it probably wouldn't make sense to apply for benefits yet. If we reach 62 but our spouse is still working, that would also probably justify waiting. Every situation is different. There's no substitute for sitting down and estimating the effects of applying for benefits now and later, with your own tax situation.
You may have reasons that don't immediately show up in a spreadsheet for why you want to delay applying for benefits. You may be so terrified of risky assets that the expected return of your portfolio is very low. Or you may find it easier to regulate your spending with a larger monthly deposit that allows you to avoid frequently withdrawing from your investments. Or if there's no one you'd trust to manage your money at the end of your life when you could be suffering from cognitive decline, you may want to be able to rely on a simple benefit payment instead of managing a portfolio. ↩
The WolframAlpha formula to calculate savings from desired retirement income is:
ReplaceAll[(D/(W*R^T)-A) / Sum[(G/R)^Y, {Y, 0, T-1}], {R -> 1.08/1.025, G -> 1, T -> 40, D -> 45000, W -> .04, A -> 0}]
And to calculate retirement income from savings:
ReplaceAll[W*R^T*(A+S*Sum[(G/R)^Y, {Y, 0, T-1}]), {S -> 6108.87, G -> 1.02, R -> 1.08/1.025, T -> 40, W -> .04, A -> 0}]