8. Spending Your Retirement in a Risky World
“...I am getting older, closer to retirement and can’t afford to take financial chances, so I am going to invest my money in bonds....”
—Myth #8
America is in the midst of a retirement crisis. A 2011 Gallup poll confirmed this with some shocking results—66% of Americans stated that not having enough money for retirement was their top financial concern. This was 53% higher than a similar poll conducted more than a decade ago.
However, it is no surprise Americans feel this way. The financial crisis saw retirement assets significantly drop (see Chapter 1, “You, Inc.”) and more Americans are delaying retirement as a result. In 2010, according to an Employee Benefit Research Institute (EBRI) report, 31.5% of Americans between the ages 65–69 and 18% between the ages of 70–74 were still working. This is up from 21% and 11%, respectively in 1990. In fact, over the last 20 years, the number of Americans over 65 in the workforce has doubled, reaching 6.7 million in 2010.
Putting the aforementioned crisis into more formal words, we see that Americans are concerned about the sustainability of their retirement portfolios. They are worried about whether or not their nest eggs are large enough to see them through a successful retirement. The remainder of this chapter focuses on the sustainability of your retirement plan.
I’ve already mentioned one of the most widely cited general rules in the field of retirement investment planning: that the percentage of your portfolio that should be invested in the stock market is 100 minus your age. So, if you are 70 years old, you should only have 30% in the stock market, by 80 you should only have 20%, and so on. Some recent variants of this rule have upped the number 100 to 110 or even 115, but the same idea applies. According to this thinking, your age is the most important determinant. Indeed, I have spent a good amount of time and effort in this book trying to dispel this idea on various levels. Yet, at retirement, the impact of age on asset allocation becomes a very controversial issue.
The debate on this issue is divided. On the one hand, retirees supposedly have a shorter investment horizon and, therefore, incur the risk of not being able to recover from losses in the early stage of retirement by owning a portfolio heavily weighted in equities. On the other hand, by shifting the retirees’ investment assets to fixed-income products, especially with current interest rates at historically low levels, the resulting lower income stream could potentially jeopardize their standard of living.
In this chapter, I use some ideas and concepts from recent advances in statistics that fall under the general label of Monte Carlo techniques to provide yet another perspective on the problem of generating a sustainable retirement income.
Conducting a Needs Analysis
Obviously, before I begin any discussion of retirement investment strategies, you must determine the extent to which you are dependent on your financial assets to sustain a standard of living. In other words, you must conduct a “needs analysis.” Pertinent questions would include: What standard of living would you like to maintain during your retirement years? Do you want to travel the world? Will you stay at home? These questions might not be as easy to answer as they seem. They certainly involve making important assumptions about lifestyle preferences and market conditions. But the bottom line is that you—possibly with the help of a financial adviser—must estimate how much you will require on an annual basis to maintain a desired standard of living in retirement. Ideally, this “needs analysis” should be conducted many years prior to retirement while you are still in the process of converting your human capital into financial capital.
The objective is to get a desired number—an annual income level—that can be funded by the total financial assets that you have “mined” from your human capital over your working years (and possibly beyond). Without a good feel for what you’ll need, talking about appropriate investments to finance those needs is meaningless.
When the needs analysis is completed, you can move on to stage two. There you and your financial adviser can discuss an appropriate asset allocation during the retirement years.
Now, at the risk of sounding simplistic, I want to start this analysis by stating the obvious. If, at age 65, you have liquid financial assets that are 100 times greater than your annual consumption requirements, then no matter how you invest during your retirement years, you will never run out of money. Of course, very few Americans are fortunate enough to be in this category. But presumably, those who are have no reason to change their investment philosophy at retirement.
Furthermore, if at age 65 you have liquid financial assets that are only five times greater than your desired annual income level, then you are, quite frankly, doomed. You certainly won’t be able to invest or gamble your way out of this conundrum.
With these polar opposites out of the way, I am ready to address the question of an appropriate asset mix to support a desired annual consumption requirement. In other words, given a desired standard of living, what asset allocation—or mix between stocks, bonds, and short-term reserves, such as money market funds—will minimize the probability that you will run out of money during your retirement years?
Let’s look at some hypothetical numbers. You have just retired at age 65 with a fairly decent Social Security and company pension, which should provide a large portion of consumption needs on an annual basis. In addition, after many years of contributing financial capital to a 401(k), IRA, or 403(b) plan, you have managed to build a nest egg of approximately $200,000, which is currently sitting in an assortment of mutual funds, term deposits, and other minor investments. The house, fortunately, is fully paid for, and you have no other major liabilities.
After conducting a needs analysis, taking full account of lifestyle choices and retirement plans, you have determined that you require, in addition to your pension, approximately $10,000 every year for the rest of your life. Let’s call this the income gap. Naturally, the hope is that the nest egg will be able to provide this additional amount.
Before continuing, I should clarify what I mean by $10,000 per year. This estimate assumes that today’s prices on which you based your needs will remain the same throughout retirement. In other words, it assumes that the inflation rate for goods and services will be zero for the next 30 years. Rather unrealistic, I’m sure you would agree. True, inflation has averaged less than 3% almost every year since 1991. But there is no guarantee that the rate will not increase.
Indeed, economic history teaches us that price inflation can resurface suddenly and dramatically. And of course, as I discussed in Chapter 5, “Personal Inflation and the Retirement Cost of Living,” the projected inflation rate for retirees might be higher than the general inflation rate for the population at large. Think of the cost of geriatric medical care over the years.
Therefore, a better way to deal with long-term planning (given inflation uncertainty) is to budget and state your needs in real, after-inflation terms. At the same time, you must also project your investment returns in real, after-inflation terms. Let me explain.
As I said earlier, you essentially want to consume $10,000 of today’s dollars for the rest of your life. By real consumption, I mean that you will consume $10,000 in your 65th year, $10,000 adjusted by the first year’s inflation rate in your 66th year, $10,000 adjusted by the first and second years’ inflation rate in your 67th year, and so on. So for example, if the inflation rate for these three years was 2%, 3%, and 4%, respectively, then you would consume $10,000 in your 65th year, $10,000×(1+0.02) in your 66th year, and $10,000×(1+0.02)×(1+0.03) in your 67th year.
However, to keep things in balance, when I talk about what invested money can earn, I look at returns in after-inflation terms as well, to account for the fact that your needs were expressed in the same framework.
Ideally, the pension payments come with some form of inflation protection—or indexing—as well. The indexing can be implicitly tied to the consumer price index (CPI) or implicitly tied to the performance of some investment fund.
Practically speaking, the easiest way to get at the $10,000 that you will need each year (about $833 per month) is to set up a systematic withdrawal plan that sells an appropriate number of stocks, mutual funds, or bonds each month to create the desired cash flow. This is like a reverse dollar-cost averaging strategy. Instead of buying an arbitrary number of units with a fixed amount of cash each month, you are selling an arbitrary number of units to create a fixed amount of revenue each month. Then, to account for any price inflation in your consumption needs, you increase the amount withdrawn under the systematic plan on a yearly basis.
Now, before proceeding, we must deal with one other unpleasant aspect of financial budgeting for retirement—income taxes. Your estimate of $10,000 per year probably does not account for income taxes. If this is the case, then the $10,000 that you plan to consume is really an after-tax amount. The pre-tax withdrawal will, therefore, be higher. Everything you pull out of your tax-sheltered plan will be taxed at your marginal tax bracket because you have never actually paid income tax on that money (for the most part). Now, of course, there are also Roth versions of an IRA in which taxes have been paid upfront; the investments then grow tax sheltered but you are exempt from paying income taxes when you withdraw the funds. I won’t get into this.
What this all boils down to is that if you require $10,000 to live on—and you are in a 33.33% marginal income tax bracket, for example—then you will really have to withdraw $15,000 from the nest egg, two-thirds of which you will be able to consume yourself. (Just to err on the conservative side, I’m not factoring in certain expenses—for example, medical expenses—that might be tax-deductible.)
Now, a Pandora’s box that I would certainly like to avoid is the whole question of what marginal tax brackets will be 10 or 20 years from now. Today, we know that the highest marginal tax bracket is in the 30% to 40% range. But who’s to say that federal and state authorities won’t raise that number, especially as it applies to funds withdrawn from a tax-sheltered savings plan? In fact, on a professional level, I feel much more confident predicting the long-term expected rate of return from various asset classes than I do predicting what the income tax structure will look like in 15 years. We might move toward a flatter tax system, in which all income is taxed at roughly the same rate, or we might see an increase in progressivism, which would raise tax rates on the top income bracket above the current 30% to 40% region. Unfortunately, it’s probably one of the biggest question marks in the financial planning equation. Nevertheless, we must play the game of life based on the current rules, and we must, therefore, make plans based on the current tax system.
By this point, you should have a good sense of your needs, and those needs should be specified on a pretax basis. In the example we’ve been using, you have $200,000 in a tax-sheltered plan and will need to withdraw $16,000 annually, in after-inflation, pretax terms.
Roughly speaking, therefore, your Needs-to-Wealth (abbreviated as NtW) ratio is $16,000/$200,000 = 8%. Another way of looking at it is to say that your annual income needs represent 8% of the initial wealth available to support those needs. Thus, if you had $400,000 and your needs were $32,000, you would also have an 8% Needs-to-Wealth ratio. This ratio is important because it gives you a general sense of what kind of investment returns you will require to support your annual needs. I would argue that all people—at age 65—with an 8% NtW ratio are more or less in the same boat. That’s because whether they have $1,000,000 or a mere $100,000 at retirement, they all have the same relative needs.
We are now ready to revisit the main question. Is $200,000 enough to support $16,000 in annual needs? The answer, of course, really depends on how you invest the $200,000. Another way of asking the question is, can you sustain a NtW ratio of 8%? The answer to this question clearly depends on the holy grail of asset allocation. In other words, it depends on what your investment portfolio looks like during your retirement years.
First of all, let’s examine the scenario in which you, as a retiree, will live on the interest and dividends alone. In this case, the $200,000 will have to generate exactly 8% annually to create $16,000—after inflation and before taxes. Unfortunately, money market instruments will earn nowhere near that amount. So, you have a clear choice: 1) invest in these relatively safe investments, knowing that you eventually will have to liquidate your capital and might run out of money or 2) invest a bit more aggressively, and hopefully build your capital instead. Or, of course, you can always decide to reduce consumption.
The math is relatively simple. If your money earns a fixed 5% in real terms, and you consume $16,000 in real terms every year, you will run out of money in about 20 years. That’s because the present value of $16,000, discounted at the rate of 5%, is exactly equal to $200,000. Stated differently, a $200,000 mortgage, amortized at a rate of 5% will be paid off in exactly 20 years, when the annual payments add up to $16,000.
Okay, you say to yourself, if you can earn a consistent 5% every year in real terms, your money will last for exactly 20 years. That’s plenty of time, right?
Well, maybe, or maybe not. Remember, statistics tell us that, using moderate estimates, a 65-year-old man has a 46% chance of living for 20 more years; a 65-year-old woman has a 56% chance of living for 20 more years. So let’s put two and two together and see what happens. If they earn 5%, they will run out of money in 20 years. That much is clear. But there’s a 46% chance (56% for women) of living for 20 more years. In other words, there is a 46% (56%) chance of outliving your money, if you earn 5% each and every year. Why? Well, the odds of outliving your money are the odds of being alive when the money runs out. If you know exactly when the money will run out, and you know the odds of living to that point, put them together and you have the odds of outliving your money.
Similarly, if your $200,000 nest egg earns a fixed 4% in real terms, you will run out of money even sooner—in about 18 years—because you are earning less. And the odds of living for 18 more years are, not surprisingly, higher than the odds of living for 20 more years. The chances are 54% for men and 63% for women. So if you earn 4% every year, the odds of running out of money are 54% and 63%, respectively.
Another way of saying this is that slightly less than one of every two men (and six of every ten women) will outlive $200,000 invested at 4%, if your annual pretax needs are $16,000.
Again, here’s the procedure: Simply compute when the money will run out and then look at the probability of being alive at that time. The higher the number, the more likely it is that your standard of living is simply not sustainable.
The same formula applies in the other direction. If your capital base can earn 6% in real terms, you won’t run out of money for 24 years. For a 65-year-old, 24 years might seem far out in the future. Indeed, men at that age have only a 28% chance of living that much longer (and running out of money); women have a 39% chance. These probabilities are lower, but not entirely comforting, especially for women.
Finally, if you are lucky or smart enough to have your capital earn 8% each year—you’ll notice it works out to $16,000 each year—you will never run out of money.
Another way to think of this is that a $200,000 mortgage, amortized at 8%, with annual payments of $15,000, will never be paid off. You will barely manage to pay the interest, let alone pay down the principal.
So what are the odds of running out of money when your capital earns 8% every year? Well, I hope you see that they are zero for both men and women. In fact, even if you earned slightly less—7.75% each year—you would run out of money in about 46 years. And the odds of being alive then are virtually zero for both genders.
No great secrets here: The less you earn, the sooner your money will run out, assuming that you’ll need $16,000 in real terms each year.
Incidentally, all of these calculations can be easily performed with the aid of a calculator or spreadsheet, and then you can examine the odds from a mortality table. This calculation is essentially a mortgage amortization schedule that tells you when the money will run out, as opposed to when the mortgage will be paid off.
Now, at some point, of course, you would realize that you are about to run out of money and would consequently lower your annual consumption. In fact, as you might have been thinking, social support payments would have kicked in long before disaster struck. Or your children might lend financial support. Nobody, in other words, really faces the prospect of starvation.
I would definitely have to agree that in reality this would never happen. Certainly, nobody would withdraw that final year’s sum of $16,000 and then say, “Oops, what do I do next year?” But the idea is to plan ahead and to realize the consequences of your actions in their most drastic, worst-case scenarios. To avoid a potential crisis, you must do one of two things, at this point:
• Reassess your asset allocation to determine whether your total capital allocation would permit you to invest more aggressively so that you earn more return on your nest egg
• Cut down on your consumption—in other words, reduce your needs
But here is the $200,000 question. What if you don’t know exactly what your rate of return will be? In an ideal world, everyone would know the rate of return for every asset class and the exact rate of inflation during retirement; therefore, you could figure out precisely when your money would run out.
So how can we perform this exercise in the real world, where market returns fluctuate on a daily basis and the length of a human lifespan is so uncertain?
Well, here is where a different set of probabilities come in. We are now ready for the full-fledged model. I call it the “Dual Uncertainty Model” because two sources of uncertainty must be dealt with here: future investment returns and mortality rates.
Table 8.1 averages male and female mortality for simplicity and examines the probability that a given needs-to-wealth ratio is sustainable when market returns and life spans are random.
Table 8.1. What Is the Probability That Spending Is Sustainable?
Simulation assumptions: Moderate mortality assumptions; Equity: expected returns =7%, volatility = 20% Source: Moshe Milevsky and the IFID Centre, 2012.
Your question at this point, of course, is how and where did I come up with these numbers? I’m glad you asked. I borrowed a technique developed by scientists over the last few decades to deal with complicated questions in nuclear physics. These days, it’s used in everything from traffic control to designing better soap. It’s called the Monte Carlo simulation method. We used this method in earlier chapters; now let me explain how it works in more detail.
Together with some colleagues at the Individual Finance and Insurance Decisions (IFID) Centre in Toronto, Canada, we constructed a computer program that generates millions of different scenarios for the financial markets and human mortality. It is, if you like, the ultimate imagination machine. In one scenario you live to the ripe old age of 97; in another scenario you live to age 86. Some scenarios show the stock market booming for the next 20 years; others indicate a 10-year bear market.
As you might know, simulations of future market behavior have been employed quite successfully in corporate risk management, when a company wants to compute the probability of losing a specific amount of money over a particular time horizon. Government regulators also use the Monte Carlo method to estimate and measure the stability of financial systems.
As you might have guessed, the name Monte Carlo itself comes from the underlying roulette wheel in the computer that generates the different scenarios. Letting a computer determine what the future will look like might sound a bit removed. But in fact, with its exhaustive computing capability, it does cover all possible contingencies, every possible scenario of what could happen over the next 40 years.
True, no computer could have predicted the financial crisis a few years ago, or the dot-com bubble. The point is not to identify or predict specific events; rather, it is to compute all possibilities for the evolution of the financial markets in conjunction with human mortality.
In one scenario, the computer predicted that the U.S. stock market would fall by 15% in one month. The computer certainly didn’t give a reason. It didn’t explain why that would happen. It simply said that it was within the realm of possibility. And lo and behold, during October of 2008, the height of the financial crisis, the S&P 500 index fell by slightly more than that amount. Quite uncanny!
Obviously, this doesn’t mean that the computer actually predicted the future. It simply means that, using the Monte Carlo simulation, it computed a remote possibility of the market’s declining by 15% in one month—and, implicitly, recommended that we should plan for such a possibility. I don’t want to alarm you unnecessarily, but in a few scenarios it generated drops even scarier than 25%. The financial crisis demonstrated that such drops are within the realm of possibility. Fortunately, the computer estimated the odds of such events to be very small.
Now comes the fun part. After leaving the computer on all night, running millions of these future scenarios, we returned in the morning and started counting.
Specifically, for every possible asset allocation, we counted the number of times that the 65-year-old who starts out with $200,000 and consumes $16,000 per year will run out of money before she dies. These are the people who (theoretically) run out of money. The remaining people, who die with wealth, have managed to avoid outliving their money. The ratio of the former to total number of trials provides us with the probability of outliving your money. We then sift through the cases to locate the asset allocation that minimizes the probability of outliving wealth.
Let’s look at an example. In one simulation, a 65-year-old who invested all of his capital in the stock market—consuming $16,000 real dollars each year—ran out of money in roughly five years because he had the uncanny bad luck of investing right before a horrendous (computer-generated) bear market. Again, however, the computer assigned a very low probability to this event.
In another scenario, we found that a 55-year-old was able to take very early retirement, with only $200,000 in wealth, and still manage to consume $16,000 per year for life, by investing completely in equities. But this is because the computer killed him off at age 68, long before his full life expectancy. The computer also assigned this event—a robust stock market combined with early death—a very low probability. Overall, the chance that a 55-year-old man who retires at age 45 with only $200,000 will be able to support a spending habit of $16,000 per year is not great.
Before I go further, I must emphasize the assumptions that go into such a Monte Carlo simulation study. First, I made a moderate assumption about human longevity patterns. If you believe that you are healthier than the average American, then your probabilities of sustainability or success are even lower than the preceding estimates. Remember, if you are healthier than average, then a different mortality table (representing a selected healthy population group) might apply to you. In this case you might be more likely to live much longer and consume longer. All else being equal, this reduces the chances of sustainability.
Second, I assumed in the simulation that the real, after-inflation rate of return from equity markets would be 7% with a volatility of 20%. These numbers correspond with the behavior of American equity markets during the last 50 years. Please note: I am not assuming that you will earn 7% in real terms each year. Rather, I’m assuming that in the long term, you’ll earn an average of 7% per annum, with a volatility of 20%. (Remember that volatility is a measure of how wide the spectrum of investment returns is expected to be. Again, a volatility number of 20% means that 95% of the time, the returns will be within 2 × 20% = 40% of the expected value.) Admittedly, 7% might be a bit aggressive; a variety of financial commentators believe that the equity risk premium, as it is called, will be much less than observed in the past.
Another approach and technique for obtaining these values can be attributed to the famous Russian mathematician, Andrei N. Kolmogorov, who studied, among other things, the mathematics of these sorts of probability questions. Kolmogorov came up with a partial differential equation that combined 1) the random movements of stocks and bonds within your retirement portfolio, and 2) your withdrawals from this portfolio. With this equation, you could predict the probability of retirement ruin. In other words, you could find the chance of your nest egg running out while still alive.
Additional details behind this equation are beyond the scope of this book. However, interested readers can check out my book, The 7 Most Important Equations for Your Retirement (2012), for further information on Kolmogorov’s partial differential equation and how to apply it to your own retirement portfolio.
What is the key takeaway of this chapter? Once your human capital runs out, the management of your financial capital becomes very important. Your goal should be to create a sustainable retirement plan by effectively converting your human capital into financial capital throughout your lifetime. The more financial capital you are able to stockpile, the greater your chance will be of generating sufficient income to meet your desired retirement consumption level. If you find that your retirement plan is unsustainable, then you might have to reduce your standard of living or spend less.
Using Monte Carlo analysis can help you play around with different scenarios to guide some key decisions. For example, should you delay retirement by two additional years because your nest egg isn’t as large as you wanted it to be? Simulating different possible outcomes might better allow you to make a decision. My general rule is that you should strive for sustainability numbers above 90%. To assist you with these calculations, I have created a tool in Excel that calculates the probability you will run out of money before you die. To obtain this spreadsheet, visit http://www.qwema.ca/index.php/our-calculators/ and download “The 7 Most Important Equations for Your Retirement” Excel file. The worksheet in the file titled “#7 Kolmogorov” is the one of interest.
Summary
• There is nothing magical about retirement that should force a more conservative portfolio allocation, especially when you consider longevity risk.
• The method of Monte Carlo simulations is being widely used in the financial services industry to compute and illustrate the impact of various retirement income strategies. Get used to it, and ask your financial or investment advisor to generate a Monte Carlo illustration of your financial future.
• After your human capital runs out, you must manage your financial capital so that it can sustain you throughout retirement. The more human capital you convert into financial capital throughout your lifetime, the greater the chances of sustainability. Striking a fine balance between these two elements of your personal balance sheet is at the heart of retirement planning.
• Retirees are obviously still exposed to the risk of a poor sequence of returns, which brings us full circle to the next chapter about annuities.
Endnotes
The article by Bengen (2001) is worth reading because Bengen was one of the first people to conduct Monte Carlo simulations to compute retirement income sustainability in the early 1990s. Ho, Milevsky, and Robinson (1994) likely wrote the earliest published paper to combine uncertain lifetime and longevity risk with uncertain investment returns to generate a combined probability of retirement ruin. In my opinion, the article by Markowitz (1991) is the intellectual precursor to retirement income simulations and, more recently, Taleb (2001) provides an excellent critique of the simulations and risk management methodologies, which should remind us to accept all these numbers with the proverbial grain of salt. I also recommend The 7 Most Important Equations for Your Retirement (2012), which has an entire chapter dedicated to the sustainability of retirement plans.