A heuristic for retirement savings

Most persons should save at least a quarter, perhaps as much as half, of their post-tax (i.e., "take-home") income.

Saving for retirement feels complicated, because there are so many decisions to make. The purpose of this essay is to enumerate a few rules of thumb I shall use for simplifying these decisions. I think there may be some social benefit in promulgating these heuristics if they produce more-sustainable retirement outcomes.

Thaler and Sunstein (Nudge, 2008) make several useful points in this area:

• Economists disagree on exactly how much people should save for retirement.
• Humans are lazy.
• Default choices or settings are extremely powerful.
• Many people, when surveyed, say that they would like to save more for retirement; and then fail to do so.
• Tversky and Kahneman demonstrated how associations and references affect our judgement.

References and Reality

What is retirement? Television commercials portray bliss with vacations and Viagara. I suspect the average reality is quite different. A few years ago, at a hotel in Clearwater, FL, an old woman said, "Retirement isn't all roses." Indeed, retirement is just permanent unemployment. And when you are unemployed, the key drivers that determine whether you will remain solvent are:

1. How much money you have, and
2. How quickly, and for how long, you'll deplete that money.

The first rule-of-thumbs I shall offer will be for part (2). Part (1) is left as an exercise to the reader.

Companies selling financial products offer (but do not guarantee) to help you realize your dreams. Many provide some sort of calculator to help you estimate how much to save. While these calculators range from simplistic to sophisticated (some even with Monte Carlo simulations to obtain a distribution on investment returns), the biggest problem is that they offer no transparency or guidance on assumptions --- and the assumptions are critical. The default settings on several calculators imply that income needed in retirement can be less than current income, and your investment growth rate exceeds inflation by several percentage points. Both can be dangerous assumptions.

On the income point, if you can hardly afford to take vacations now, there is no way that all the senior-citizen discounts will accrue to allow you to take any vacations on less income. If you maintain a car to commute to work, are you going to wait for the bus to visit the public library and supermarket? If you expect to finish paying a mortgage on your home, you should not forget to plan for increasing house-repair expenses, such as a new roof or water heater; if you rent, your housing costs are not going to decrease. If you are not one of the few C-suite executives, tenured professors, or government- or union-pensioners eligible for subsidized health insurance for life, you should start studying Medicare-related issues now. Otherwise, consider that private health-insurance quotes for a 60-year-old couple today range from $5,000 to $28,000 per year; and, in the past ten years, health-insurance premiums have increased at double the rate of inflation. There goes the prescription for Viagara. In summary, I think you should plan to spend about the same amount of money each year in retirement as now. (Moshe Milevsky: Your Money Milestones (2010) cites Modigliani for this idea of smoothing consumption.)

• Source: http://www.ehealthinsurance.com/, quotes for family health insurance for male born 1/1/1950 and female born 1/1/1952 in zip code 10022, retrieved 2/15/2010, ranged $400-2,300 per month
• Source: http://money.cnn.com/2009/09/15/news/economy/health_insurance_costs/index.htm

On the investment growth assumption, most persons should not expect to realize inflation-adjusted returns over 30 years in excess of the +6% (net of inflation but not taxes) annualized historical S&P 500 rate. And what of taxes? The historical inflation-adjusted rate may be appropriate for estimating pre-tax-with-tax-deferral (401(k) and traditional IRA) dollars, or post-tax-with-tax-free-growth (Roth 401(k) and Roth IRA) dollars, but may be as low as +3% or +4% in a taxable account. I shall provide an example in a postscript. I am not going to discuss the suitability or the moral implications of owning stock.

Savings Pipeline

Now, how many years should you plan for? For Generation-Xers and Generation-Yers, life expectancy at birth was about 70-75 years; and there is a significant chance that you'll outlive the typical lifetime. I am roughly 35 now, and I think it's safe to estimate that I'll work 30 years and then live 30 years more.

In this case, my savings in year 1 of my career will grow (or lay dormant) for 30 years, to be spent in year 1 of retirement. My savings during year 2 of my career will grow (or lay dormant) for 30 years, to be spent in year 2 of retirement. And so on. With this pipeline, I calculated the below table to estimate the amount I need to save, given various inflation-and-tax-adjusted investment returns.

If you expect your savings to grow, compounded, by this percent each year after subtracting inflation and taxes,	then, to have the same annual budget in retirement as now, assuming a schedule (years of work/years of retirement) of
	30/30	40/20	45/15	48/12	50/10
	your savings rate should be:
-4%	77%	72-53%	68-38%	64-29%	61-23%
-2%	65%	52-43%	45-31%	40-24%	35-20%
0%	50%	33%	25%	20%	17%
+2%	36%	18-25%	12-20%	9-16%	7-14%
+4%	24%	9-19%	5-16%	4-14%	3-12%
+6%	15%	5-13%	2-12%	2-11%	1-10%

To read this table, let's imagine you can invest in a 30-year certificate of deposit (CD) that returns 0% above inflation and taxes. (This product doesn't exist, but you may be able to simulate it with I bonds or TIPS. I am not going to discuss the suitability or the moral implications of owning government debt.) Then, for every $1.00 you put into the CD, you can withdraw $1.00 (today's dollars) 30 years from now. If your current post-tax income is X, you can simulate a future budget now by saving 50% of X (leaving 50% of X). If you are comfortable with the 50% you can spend today, then your lifestyle will not need to suffer much adjustment when limited to the saved 50% available in 30 years. If you save less of your income now, you are leaving yourself less to spend in retirement. You can vary your assumptions by considering:

• Perhaps you will plan to work for 40 years and retire for 20 years. Then you can use two years of savings for each year of retirement, and (based on the same 0% tax-free, inflation-adjusted growth assumption) you could start by saving 33%. Why not 25% --- half of 50%? If you save 25%, then you are giving yourself a budget of 75% during your work years, but only 2 * 25% = 50% for each year of retirement, which violates the rule-of-thumb I suggested above. The other columns of the table show the needed savings rates for two, three, four, and five years of savings per year of retirement. Where there are percentage ranges, they indicate the saving rates needed in the first and last years of the non-retirement period. If you are saving 15% now, you are on a frontier hoping for a +6% annualized return on the 30/30 (years of work/years of retirement) schedule, or planning for the 50/10 schedule and with a 0% annualized return.
• Perhaps you will have access to investments that return more than 0% after inflation and taxes. Good luck with that.
• Perhaps you will receive Social Security payments or a pension. Good luck with that.

Changes in these assumptions can modify the savings fraction by perhaps a factor of two or three, but the conclusion is still robust: you should save a substantial fraction of your income.

To summarize, I am using two heuristics to estimate retirement savings:

1. Retirement income requirements are the same as now.
2. Using the savings pipeline and a conservative investment returns assumption, I must save a quarter to a half of post-tax income.

Pre-tax or post-tax?

In the above discussion, I've tried to use all post-tax, inflation-adjusted numbers. This is partly because it would be difficult for many persons to save 50% of their pre-tax income.

When it comes to retirement investing under United States laws, one often has three choices: (1) pre-tax funds with tax-deferral (401(k) or traditional IRAs), (2) post-tax funds with tax-free returns (Roth 401(k) or Roth IRAs), and (3) post-tax funds with taxable returns (depending on choice of investment vehicle). The benefits of (1) and (2) are that taxes are a one-time cut, either (1) at the time of withdrawal or (2) before investment; while in case (3), taxes not only take the the same one-time cut, but also reduce the realized return each year. For example, if over 30 years, your investment returns 4% each year with 3% inflation, the inflation-adjusted return will be 1% = 4% - 3%; if taxable each year with a 25% tax rate (on the 4% earned), your real return would be zero, but if taxed only at the end with the same 25% tax rate, your real return would total 26%, or about 0.77% per year. The disadvantages of (1) and (2) are that they come with restrictions on the amounts you can save and the conditions under which you can take a penalty-free withdrawal. The only difference between (1) and (2) is whether you expect your future tax rates to be higher or lower than now, and if you aren't sure, you can hedge by dividing your saving between them.