In this post, we examine the incentives, assumptions, and calculations around retirement planning.
Retirement in the Abstract
Increasingly, people are outliving their potential for productive labor. Nihilistic as that may sound, it isn’t a bad thing. Indeed, it’s the byproduct of some incredibly good things: advanced medicine and improved quality of life. Yet such a state of affairs creates a need for people to possess income that likewise goes beyond their working years. The prudent example therefore is the biblical story of Joseph in the Old Testament: save a surplus during the seven good years to survive the seven lean years.
Retirement planning applies the same concept: save a piece of your income every year, invested in some financial asset (usually stocks/bonds) and collect the returns several years hence once you’ve stopped working. This makes sense: you’re essentially letting the power of compound interest work for you over long periods of time. It also enables savers to benefit from long-term economic growth during their lifetimes in a way other than their incomes—incomes which may be unaffected or adversely affected by economic changes over such a long period.
One could make the argument that mass participation in the financial markets makes ordinary people vulnerable to unscrupulous behavior by Wall Street professionals. This is a complex question that includes a lot of factors: emotional mistrust toward city slickers and financial sharks, market dynamics of passive vs. active investment approaches, and (most importantly) alignment of incentives between finance professionals/services and their clients.
Call me a shark if you like, but I see institutionalized, tax-incentivized retirement investing as bringing America the most democratic financial markets in the world. Keynes recognized this a century ago in his General Theory: “To the average Englishman, Throgmorton Street [location of the London Stock Exchange] is, compared with Wall Street to the average American, inaccessible and very expensive.” This is, of course, a mixed blessing, as it exposes these retirement savings to higher levels of volatility in the stock market (as opposed to lower risk, lower return instruments like bonds). That said, some financial planning advice is still more expensive than the value it offers.
Determining Retirement Outcomes
There are a handful of ways to structure or display a retirement calculator. There are plenty of online calculators that take different approaches, like this one. However, for our purposes I’m going to use an Excel model that captures the variables in a way that makes sense to me.
Our model will need to capture the following factors:
- Income. This should be obvious, as you cannot save money unless you come by it in the first place.
- Savings rates; what percentage of income you save
- Investment returns: higher returns have to be weighed against more volatility (for instance, stocks return more than bonds but can be riskier). During retirement, I assume a much lower rate of return as it’s likely savings would only be invested in conservative asset classes at that point.
- Tax impacts: these will differ depending on what type of account your saving is done in. We’ll cover this in more detail later.
- Cost of living: I separate this into housing and other (and use percentage of income as a cross-check for each
- Age you start work, as well as retirement age
- Expected growth in income and costs of living (based on career progression and life events). I ignore inflation in this analysis & try to keep everything in today’s dollars.
- How much of your savings you want to retain at your death. This can be to give a bequest to family or to provide a margin for error in case of longevity risk (living longer than expected in the financial plan).
The output of this is how many dollars a retiree would receive per month upon retirement. Here’s a basic example to show what the output would look like. Note that for readability, I won’t show every year.
If you like, you can download the model I built below to change assumptions yourself.
In fairness, the above is not necessarily the most realistic. It assumes someone starts working at a minimum-wage job (roughly $15/hr, or $30k/year) and begins contributing at a 12% rate immediately into a pre-tax account. However, costs of living are low—unreasonably so, in fact. Yet the summary in the upper right shows that such an individual would withdraw $24,000 a month in retirement—partly due to the early and consistent saving, partly due to the high rate of return on investments.
About that return: in the above example, I use 10% as a pre-tax return on investments. I compare this with the S&P 500 index, which has done a little better than that in the long run. However, in the examples below I’ll use 7% for the S&P to approximate a real return (that is, a return less inflation). When we consider different investment strategies, the returns will look different. And, of course, after-tax return will be lower all else equal.
A Realistic Base
To serve as a baseline for our analysis, we’ll try to approximate a median/average profile. To do this, we’ll use the following assumptions:
- Graduate from college at age 22 with $30k in student debt (treated as a negative starting balance in the after-tax savings account)
- Starting salary of $60k, close to the average for a new bachelor’s degree grad
- Making six figures by age 35, make ~$200k by age 55. These may be slightly conservative, but remember, we’re ignoring future inflation here, and assuming a typical white-collar professional career arc.
- Will save 10% of income until around age 40, at which point will start saving 4% of income. These savings will be evenly split between pre-tax and after-tax accounts (we’ll get into these more later). Savings will be 100% invested in a major stock index like the S&P, which is assumed to have a real return of 7% pre-tax.
- After retirement (age 65), investments will earn only a 4% return to represent a safer portfolio. Expected to live until 85, and will spend 90% of retirement savings over the 20-year retirement horizon (the 10% is a margin for longevity risk and any future bequests).
- Has two kids: one at age 33, one at age 35.
- Buys two houses: a starter home at age 37, and a family home at age 44.
- Pays for children’s college as a one-time payment at age 51.
Here’s a snapshot of our base case.
In the base case, we find a retirement withdrawal rate of $11.3k per month, or 69% of prior income. This is slightly below the 70-80% threshold often cited as a rule of thumb. However, it’s still more than the going lifestyle rate—26% more than this individual was spending on expenses before retirement—so it appears to be a reasonably safe retirement outcome.
It’s important that this is very simplified example, and may depart from a typical case in a few ways. While we try assume a fairly standard middle-class case in terms of income and lifestyle (albeit probably biased toward a big city, where both income and expenses will be higher), there’s one factor we assume that may not be accurate: financial prudence. Our base case includes saving early and often, avoiding high-interest debt on credit cards and car payments.
There is No Law but Murphy’s
If anything can go wrong, it certainly will: not necessarily wrong, but just “not according to plan”. We’ll take a look now at a few different cases to bear in mind—both to illustrate the sensitivities of the model and provide some practical comments.
Returns Matter—a Lot
Compound interest calculations are very sensitive to the compounding rate assumed, especially for long time periods. We can illustrate this in a handful of ways through our model.
Say you pay a 1% annual fee to some financial service provider for allocating your portfolio. Compared to our base case, this would approximate to a net 6% return on retirement assets (pre-tax) compared with the original 7%. This may not feel particularly expensive, especially at first—on the first $1000 you invest, your annual fee will only be $10 in your first year. But in the long run, this erosion of returns wipes out a huge amount of post-retirement purchasing power.
In this case, a 6% net return yields a retirement withdrawal of $1.8k per month less than our base case. It’s a good reminder to make sure to understand the long-term cost of any financial service you agree to pay for.
Returns also depend on the asset mix—most commonly between stocks and bonds. So far we’ve just used stocks in our analysis. This gives a higher long-run return, but also runs the risk of market downturns at the exact wrong time—a 10% drop in the stock market is survivable at age 25, but not so much at age 65. Because of this, many investors diversify between stocks and bonds. We’ll examine two commons ways of doing this.
The most basic way of diversifying between stocks and bonds is a 60/40 portfolio: 60% stocks, 40% bonds. For our purposes, we’ll keep the 7% real rate of return for stocks, and assume a 1% real return for bonds.
This lower rate of return does reduce risk, but it also reduces the quality of expected outcomes. In this case, an individual has only $7.5k per month in retirement, less than half their pre-retirement income. This may be a more “certain” return, but it appears inadequate.
As an aside: this line of analysis may suggest some of the problems with the U.S. Social Security System, which invests exclusively in U.S. Treasury securities. While these are incredibly safe assets, their returns are often low, meaning that Social Security is doing a poor job of compounding present contributions for future consumption. I understand aversion to a large government fund owning large swaths of the stock market. But the current system is tantamount to the government borrowing from its own citizens without their consent to fund current spending. At any rate, it’s worth questioning whether a more balanced return-seeking portfolio may have served Social Security better.
Leaving aside such a complex issue, let’s examine a more dynamic stock/bond mix, assuming that the percentage allocated to stocks equals 120 minus the person’s age—so starting out at 98% and phasing down each year.
This approach still does a decent job of hedging risks, but doesn’t do much better on expected outcomes, at $8k per month or less than half of prior income. Early in career, the return profile is better but the asset base is too small. Approaching retirement, the asset base is larger but the returns just aren’t high enough.
We can even revisit our base case to determine that it would have done better than a dynamic diversification strategy even if the stock market fell by 25% the year before retirement. This suggests that risk can be worth taking in some moderate cases.
Again, we only scratch the surface of complex issues here. But let’s move on to everyone’s favorite subject.
How to Pay Taxes
So far, we’ve treated our investments three different ways in terms of taxation:
- Pre-tax saving: These contributions are tax deductible (helping reduce total income taxes paid) and compound tax-free each year, but are taxed on distribution (essentially taxing the entire investment value at retirement).
- After-tax saving: After-tax saving is taken from after-tax income, meaning it’s already been taxed once and won’t be again. It compounds tax-free and can be withdrawn tax-free at retirement.
- Taxable/discretionary saving: This comes from after-tax income, and is taxed each year (essentially reducing the rate of return for taxation), but is not taxed at distribution. This is easily the least tax-efficient of the three alternatives.
In our base case, we assume a 50/50 split of contributions between the pre-tax and after-tax methods, and any leftover income in excess of spending is allocated to the taxable account. But what if compare each approach on its own?
For this, we’ll just show the output summaries for easy comparability.
It’s worth noting that the taxable account produces easily the worst outcome—not surprising, since these investments have to compound at after-tax returns after being taxed as income. The pre-tax and after-tax strategies end up being pretty similar in this case. Pre-tax will receive a slight edge as the tax deduction makes it possible to contribute a higher percentage of income. To offset, after-tax offers the benefit of taxing income today at a lower rate than future withdrawals will likely be taxed at (since as someone gets older, their marginal tax rates tend to rise with their income).
Of course, this analysis is not sufficient to prove that either pre-tax or after-tax savings methods are superior or inferior—to do this would require much more thoroughness. But we can illustrate that the two are roughly comparable given our assumptions, and that they offer competing and offsetting tax benefits.
But In Practice?
The goal I had in mind for this piece was to simply provide some mathematical framework for thinking about retirement planning in general, particularly regarding the power of compound interest to affect outcomes. But I also had another fundamental question: is such a straightforward path actually achievable? Can an average young college graduate in the U.S. expect to be able to retire at 65 given a certain set of reasonable assumptions? Or does “something have to give”, either in later retirement age or a more modest lifestyle?
Answering this, unfortunately, requires a definition of what’s reasonable. Should we take reasonable to mean a typical case of financial behavior, or a typical example of financial literacy? These are two very different answers. There are plenty of available statistics on credit card debt, student loans, and general financial imprudence on the part of Americans, regardless of age. Given our investigation of compound interest, we should be able to understand that a double-digit rate on a car loan or a 30%+ rate on a credit card balance will bring major drag on saving for retirement. Compound interest is a powerful tool, and we should make sure it works for us, not against us.
I’ll happily acknowledge my biases as someone who leans heavily toward financial caution and has a pathological dislike for leverage, so take my harangue with a grain of salt. Further, I don’t want to advocate for some Dave Ramsey-esque rejection of all things debt—or, at least, I won’t go quite that far. What I will suggest is simply an awareness that when viewed with a long time horizon, consumption today has a higher opportunity cost than we realize, and this is doubly so when consumption is financed by debt. Saving is difficult often because we can see right in front of us what we’re giving up by saving: a new phone, trying a new restaurant, or buying a nicer car. To keep us in balance, we need to know what we’re forsaking when we don’t save.
So: does something have to give? Does the standard retirement model still seem to work? If individuals who underspend their means and invest early and consistently in return-seeking assets, the answer appears to be an emphatic no. But the operative word here is “if”. Poor financial decisions today will result in poor financial outcomes tomorrow. The world is full of voices urging us to spend, spend, spend, with a few financial coaches suggesting the exact opposite (some to the point of extremes). Neither extreme is necessary—but we must understand the cost of either decision & keep things in balance.
The best approach is that of Thanos: “perfectly balanced, as all things should be.”