About Fidelity's Health Care Cost Estimate for Retirees

When I recently posted about a highly-circulated report from Fidelity Investments estimating the expected lifetime cost of health care for a 65-year old couple today at $245,000, some readers were skeptical. Fair enough. We should question the motives of the authors of any study, and one assumes Fidelity generally has a profit motive. There were also complaints that Fidelity published only the expected value of $245,000, so we don’t know the distribution of those expected costs.

Fidelity's estimated $245,000 includes the cost of deductibles and co-pays, premiums for optional coverage for doctor visits and prescription drugs, and out-of-pocket expenses for prescription drugs. It does not include long-term care or most dental care.

I queried Fidelity regarding the distribution of those expected costs, but they informed me that the information is considered proprietary. That’s OK. There are multiple sources for this kind of data, so I pulled a few of them together for a comparison.

One of my favorite sources, the Center for Retirement Research at Boston College, had this to say in 2009 about expected health care costs in retirement (download PDF):

". . . the mean and 95^th percentile of remaining lifetime health care costs, including the cost of nursing home care including . . . Medicare, Medigap, and retiree health insurance premiums. . . are $260,000 and $570,000, respectively."

". . . the results of the same simulation, but excluding the cost of
nursing home care. . . including insurance premiums. . . the age 65 mean and 95^th percentile amount to $197,000 and $311,000 ."

(The four studies mentioned in this post were conducted at different times. For a fair comparison, I adjust the expected expenses to 2014 dollars. Hover over the expenses above to see the 2014 dollar value assuming medical cost inflation from 2009 through 2014 of 3.8, 3.8, 3.6, 3.7, 2.0 and 3.6%, respectively. Values in the table and graph below are shown in 2014 dollars. For example, the CRR reported a cost of $260,000 in 2009. Hovering over that figure above will show the 2014 dollar value of $318,029, which will also appear in the table and graph below.)

A 2013 study sponsored by the Society of Actuaries (download PDF) found the following:

“The future health care needs for a retiree vary by the retiree’s current age and their expected lifetime, but are estimated to be about $146,400 for someone currently age 65 with an average expected lifetime of 20 years ($292,800 for a couple of the same age). That amount includes health care costs not paid for by the federal government through the Medicare program (including Medicare Parts B and C premiums). If they think they will live until age 90 (25 years instead of 20 years) they will need $220,600 (or $441,200 for a couple). These amounts are for the “average” retiree and do not include long term care costs that some retirees may incur.”

Another analysis is provided by HealthView Services (download PDF):

“The average lifetime retirement health care premium costs for a 65-year-old healthy couple retiring this year and covered by Medicare Parts B, D, and a supplemental insurance policy will be $266,589. (It is assumed in this report that Medicare subscribers paid Medicare taxes while employed, and therefore, will not be responsible for Medicare Part A premiums.) If we were to include the couple’s total health care (dental, vision, co-pays, and all out-of-pockets), their costs would rise to $394,954.

Lastly, the Employee Benefit Research Institute (download PDF) provides expected health care costs for 65-year old couples broken down by the need for prescription medicines. Their estimate ranges from $150,000 for median prescription drug usage to $220,000 for high usage. Their 90^th percentile estimate (not 95^th!) is $255,000 to $360,000.

Here is the more-precise data in tabular format.

	Fidelity Investments	Boston College CRR	Society of Actuaries	HealthView	EBRI	Average
Publication Date	2014	2009	2010	2014	2013
Mean Lifetime Health Care Costs for a 65-year Old Couple
Excluding LTC Costs	$245,000	$240,968	$309,408	$394,954	$155,400 to $227,920	$261,442
Including LTC Costs		$318,029				$318,029
90th/95th Percentile Lifetime Health Care Costs for a 65-year Old Couple
Excluding LTC Costs		$380,411			$269,464 to $372,960	$328,824
Including LTC Costs		$697,217				$697,217

Although Fidelity Investments took it on the chin from some readers for an expected cost appearing too low and for not publishing a standard deviation or 95^th percentile estimate, their expected value is almost identical to that from the Center for Retirement Research and only 6% below the average of all studies. EBRI's expected cost was even lower.  Furthermore, among the five studies listed, only two provided a 95^th percentile expected value.

Why would studies exclude long-term care costs? Medical expenses excluding long-term care are significantly easier to predict than long-term care expenses, so it makes sense to think of them separately. You may have retirement-threatening long-term care expenses or none, at all, but you will undoubtedly have substantial "other" medical care expenses.

The two are insured differently, as well. Medicare covers medical expenses (though, not all) but not most long-term care costs. Long-term care is covered by LTC insurance or Medicaid. So, there's another reason to think of them separately. They are different and distinct risks.

It’s important to note that, according to this AARP Bulletin, health care costs will consume most of the future Social Security benefits for some households. And as HealthView puts it,

“With health care cost inflation rate likely tripling COLAs for the foreseeable future, retirees will eventually use more of their Social Security income to pay for health care. Over time, the compounding effect of this differential will place incredible stress on the average retirement budget.”

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According to AARP, health care costs will consume most of the future Social Security benefits for some households.

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According to Fidelity Investments, their 2015 Couples Retirement Study showed that "nearly three-fourths of couples surveyed said being able to afford unexpected health care costs in retirement was their top concern. However, only 22 percent of couples had factored it into their financial planning." It should be near the top of every retiree's list of concerns and factored into everyone's retirement plan.

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Nearly three-fourths surveyed by Fidelity said affording health care costs in retirement was top concern, but only 22% planned for it.

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The range of potential lifetime health care expenses for retirees is huge and there is no way to predict where an individual household will fall within the spectrum, so how does a retiree best use this data for planning purposes? Consider the following:

• Even the best-case predictions for lifetime health care costs in retirement will threaten the budgets and sustainability of many households. Health care costs should play an important role in retirement budget planning. 

• Estimate them as accurately as you can for your individual circumstances. Consider the averages a starting point and Google costs for health care and long-term care in your geographic area, and consider your own health.

• Assume a higher rate of inflation for medical expenses than for other costs. The cited HealthView paper reports medical cost inflation of around 3.7% for the past few years, but that is historically low. (The Economist provides a chart of historical rates of health care cost inflation here.)

• Because this key budget item is so unpredictable, especially the long-term care component, consider reducing your overall spending a bit to provide some safety margin.

• Plan for expected (mean) annual health care costs excluding long-term care, but be aware that your own costs may be a lot lower or several times higher than you "expect." (Don't plan on expected lifetime costs as these assume median life expectancy. Your retirement plan should anticipate a long life.)

• Look at long-term care costs separately. They can break the bank.

• When we combine elder bankruptcies caused by medical expenses with those caused by credit card debt spawned by medical expenses, health care costs are the greatest bankruptcy threat to retirees. Protect your retirement assets from creditors as best you can.

Retirement Plan or Investment Plan?

My last few posts have explained that outliving retirement savings as a result of sequence of returns risk isn’t the worst thing that can happen to a retiree. Becoming insolvent as the result of unexpected and uncontrollable expenses is significantly worse, though less likely – less than half a percent of Americans over age 65 declare bankruptcy.

I also recommended that a comprehensive retirement plan address all known financial risks and not simply the risk of outliving our savings due to market volatility and overspending. In this post, I want to suggest what those other risks might be (by reviewing reasons that people over age 65 typically file for bankruptcy and adding a couple of risks of my own), and some potential ways in which planning might mitigate (lessen the severity) or even insure against them.

Becoming insolvent (unable to pay your debts) and declaring bankruptcy are not the same thing. Declaring bankruptcy is a legal action that might help deal with insolvency, depending on the specifics of your situation. Whether or not it is the best alternative is something you would want to discuss with a bankruptcy attorney, should you ever need to consider it.

(In this post, I am discussing the risk of insolvency. In previous posts, I used bankruptcy statistics from the U.S. Court system. It's important to distinguish between the two.)

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Far too many retirement planning discussions focus primarily on market risk.

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Given that I described spending crises as chaotic, synergistic (in a bad way – they combine to have a greater negative impact that the sum of their parts), unpredictable, and difficult to stop once they begin to spiral downward, it might seem that there would be little to be gained from planning, but that isn't the case.

Certainly, there are some spending crises that would completely overwhelm nearly anyone's personal finances (a spinal cord injury, for example, could cost millions), but there are many crises that can be mitigated with the right planning. Let's start by recalling the 10 most common causes of elder bankruptcies:

• Credit Card Interest and Fees (67%)
• Illness and Injury (65%)
• Income Problems (41%)
• Aggressive Debt Collection (35%)
• Housing Problems (27%)
• Divorce (15.1%)
• Birth or adoption of child (9.7%)
• Death of family member (7.5%)
• Retirement (6.7%)
• Identity Theft (1.9%)

Recall that the major causes were self-reported and that most respondents to the survey reported multiple causes, so the percentages total more than 100%.

In Retirement and Chaos Theory, I suggested that insolvency behaves like a fixed point attractor. Our finances can develop a positive feedback loop and spiral downward to that point if they enter into insolvency's “gravitational field.” Sometimes, it's nearly impossible to avoid ruin once that process begins.

One way to mitigate that risk would be to stay as far away from insolvency's region of influence as possible, avoiding the risk of going broke like avoiding the gravitational field of a black hole. Consumer credit, inadequate insurance, and financial dependence on a spouse, for example, move you closer to insolvency's gravitational pull.

Let's look at those risks, chaotic though they may be, and show that there are ways we can plan for them.

Credit card interest can be deadly and research shows that typical credit balances continue to increase throughout retirement. Retirees can plan to pay off all consumer (non-mortgage) debt before they stop working and to control credit use after retiring by sticking to a solid retirement spending plan.

Most retirees will be eligible for Medicare when they turn 65, but Medicare doesn’t pay all of our medical costs. Fidelity Investments has been tracking retiree health care costs since 2005 and estimates that a 65-year-old couple retiring in 2015 will need $245,000 to cover future medical costs, not including the cost of long-term care.

That's more than most households save for retirement. It will devour a large portion of Social Security benefits for many. Retirement plans shouldn't ignore this risk.

We might consider planning to retire to a state with low health insurance costs, lower long-term care costs, and lower medical costs, but we should also consider the quality of care available.

Income problems cited in the studies were primarily the result of either age discrimination leading to unplanned early retirement or medical problems leading to unplanned early retirement. In some cases, unplanned early retirement was necessary to take care of a family member with a medical problem.

A retirement plan can assess the risk of unplanned retirement in our profession. Optometrists can work longer than oil field roughnecks. We can also assess our own health risks and the health risks of others who might need our care. These observations might lead us to the conclusion that we need to plan to find a job where we are more likely to be able to work to an older age, even if it pays less, or that we need to increase our savings, or lower our retirement income expectations.

Foreclosures soared in 2007 and they are particularly damaging to seniors. Foreclosure risk can be reduced by relocating to an area with less expensive housing, for example, or by planning to pay off (or pay down) a mortgage before retirement.

Believe it or not, one can purchase divorce insurance, though that doesn’t seem like a great way to deal with the devastating risk of elder divorce. A comprehensive retirement plan will model our financial risk of a divorce at various ages and can show the impact that a break-up would have on each spouse. E$Planner software can provide such contingency plans, for example. This analysis may provide insight into ways our retirement plan might be adjusted to improve outcomes for both spouses.

As with elder divorce, the impact of the death of a spouse at various ages can be modeled in a retirement plan. Life insurance, however, works much better than divorce insurance and software like E$Planner can calculate the amount of life insurance that will be needed at various ages. It can also model the impact of that death on Social Security benefits.

The final cause for bankruptcy cited by the Institute for Financial Literacy is identity theft (1.9%). I have previously recommended placing a freeze on your credit report.

Although lawsuits don’t appear to be major contributors to elder bankruptcy, I’m still fond of umbrella liability insurance.

Do you have a child or parent with health issues? Legal or medical costs could break your retirement plan and need to be considered.

Lastly, if you can’t avoid bankruptcy, there are steps you can take to protect assets. Holding assets in a retirement account will usually protect them from creditors. Future Social Security benefits are also protected. Even Social Security benefits that you have already received can be protected in bankruptcy if you hold them in a separate account that is only funded by those benefits. Commingling them with other funds can expose them to creditors.

The following list of insolvency risks is not comprehensive (though all but the last two risks were identified in a study as the top causes cited for elder bankruptcy). Nor is my list of possible strategies to mitigate them by any means complete. The key point is that it is important to identify the major financial risks in your retirement plan, to quantify them, and to identify ways to mitigate them, if possible. If mitigation is not possible, it is important to understand the risks if for no other reason than to avoid overconfidence in your plan. Far too many retirement discussions focus primarily on market risk.

Risk	Potential Mitigation or Insurance
Credit Card Interest and Fees	Pay off consumer debt before retiring
Illness and Injury	Relocate for lower medical costs, Medicare, Health Insurance
Income Problems	Change to a more sustainable job, evaluate your household's health risks
Aggressive Debt Collection	Understand your rights
Housing Problems	Pay off mortgage before retiring, relocate
Divorce	Develop retirement financial contingency plans for divorce
Birth or adoption of child
Death of family member	Develop financial contingency plans, life insurance
Retirement	Evaluate your prospects for continued employment
Identity Theft	Educate yourself, keep current on identity theft scams and freeze your credit report
Fraud	Educate yourself and keep current on elder fraud
Financial needs of parents and children
Legal liability	Umbrella liability insurance

A good place to start would be to list the risks to which you have significant exposure from the table above, add any other risks that might apply specifically to you, and then check to see if they are considered in your current retirement plan. If not, then you (or your advisor) have more work to do.

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A plan that only addresses asset allocation and withdrawals isn't a retirement plan – it's an investment plan.

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Does your retirement plan consider these common causes of insolvency and plan for them? If it mostly tells you how to invest your savings and how much of your portfolio you can safely spend each year then you don’t really have a retirement plan.

You have an investment plan.

A Dozen Ways to Get More from the Retirement Cafe´

Thanks for reading The Retirement Cafe´. There are a number of ways you might get more value from the blog. Here are a few suggestions.

1.) Images can be small and difficult to read in the blog. Click on an image to increase its size in a new window. Or, to zoom in on text or images, type “CTRL +” or “CMD +”. Change the + to a - to make the font smaller, or change it to a 0 (zero) to change the zoom back to normal. Whether to use the Control button or the Command button varies by browser and operating system, so just try both to see what works.

2.) Text that appears in yellow will provide an explanation of the highlighted text if you hover the cursor over it and wait a few seconds (this is sometimes called a “mouse-over”). Hover your cursor over the yellow text and try it out. If that isn’t enough information, clicking on the link will often open another browser window with even more information. Closing the new window will take you right back to the one you were reading.

3.) Clicking orange text opens another website in a new window without closing the one you've been reading. Again, closing the new window will take you right back to the one you were reading.

4.) I tweet as @Retirement_Cafe. You can follow me on Twitter by clicking on the little bluebird on the right side of the page here:

I tweet a lot of links to posts you may not have noticed from great retirement writers like Wade Pfau, Michael Kitces and Moshe Milevsky. If you don’t use Twitter, you can see the tweets here on my blog.

5.) I try to keep a recent retirement news story at the bottom of the right column that I think might interest you. It won’t always be about finance, but it will almost always be about retirement.

6.) Want to find my post about chaos theory? You can use Google to search my blog. Use the window at the top left of the blog with the little magnifying glass (or maybe it's a capital “Q”). It looks like this:

There is another “Search this Blog” box at the bottom of the post.

7.) Click the G+1 button to recommend the post on Google Plus.

8.) I place key points in a “Tweet This” box like the following. If you are a Twitter user, you can click on the orange [Tweet This] link and retweet the information in the box with a link back to my post.

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Spending a sustainable amount of your portfolio is retirement savings insurance, not bankruptcy insurance.

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9.) I try to point out the key take-aways of each post in the summary paragraphs at the end.

10.) Links to my other recent posts appear in the right column just below my bio.

11.) I post roughly once a week, but not always on the same day. The best way to be notified that I have published a new post is to enter your email address in the Follow by Email box, also in the right column and just below Recent Posts. The entire post will appear in your inbox. Clicking the title of the post within the email will take you to the post on my website, where it might be easier to read, and you will have access to the other features mentioned above, but you can also just read the post in your email.

12.) Often, the best part of a post will be readers' comments at the bottom. They have great ideas, great opinions and they give me an opportunity to explain parts of the post that perhaps were less than totally clear. I encourage you to read them, but also to post your own comments and questions.

A permanent copy of this information is available at the page link in the right column of the blog. You will find the link under "Resources" and "Reading Tips".

I hope these tips make Retirement Cafe´ even more valuable for you. Thanks for reading!

Expense Risk in Retirement

I have recently posted about bankruptcy risk, positive feedback loops, chaos theory and Kaplan-Meier estimators and now I'll try to tie all of those posts together. They're mostly about the unpredictability of spending in retirement compared to sequence of returns risk, the probability of outliving your retirement savings due to market volatility. A retiree can enjoy a favorable sequence of market returns, limit spending to a sustainable amount, and still suffer insolvency as a result of huge medical bills, divorce or identity fraud.

Much of retirement writing focuses on the unpredictability of market returns, but unpredictable spending is a greater risk. The most you can lose of your savings is 100% of your portfolio, but you can have unexpected expenses far greater than your savings – a medical catastrophe, for example. Retirees typically plan for a 5% to 10% probability of outliving their retirement savings, but about a half-percent of Americans 65 and older file for bankruptcy, and that number appears to be growing.

First, the big picture. Your retirement finances will likely include some combination of Social Security benefits (in the U.S., or a similar program where you live), private pensions, personal retirement savings, and more and more, working longer. Sadly, private pensions, known as defined-benefit (DB) plans, are disappearing and a sizable majority of Americans don’t have a significant amount of retirement savings to invest. The GAO recently found that older households typically have retirement savings only “equivalent to an inflation-protected annuity of $310 [to] $649 per month.”

Your retirement finances will also include expenses and that spending side of the equation is significantly less predictable than market returns. Most retirement research assumes that you will only spend a "sustainable" amount of your savings portfolio ( a "spherical cow") but in reality, you will spend whatever life costs. Spending a sustainable amount of your portfolio is "retirement savings insurance", not bankruptcy insurance.

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Spending a sustainable amount of your portfolio is retirement savings insurance, not bankruptcy insurance.

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David Blanchett and Sudipto Banerjee showed that retirement spending typically declines about 2% annually for retirees spending appropriately for their wealth and that even when there are large end-of-life expenses these are usually less in real dollars than spending was at the beginning of retirement. Spending crises, however, are not typical. They develop from unpredictable and uncontrollable expenses like large medical bills, housing problems, debt problems, and fraud.

Much retirement research focuses on how to make your personal retirement savings last your entire lifetime, by spending only 3% or 4% annually, for example. This does not, however, consider what happens when life costs more than your sustainable withdrawal plus your Social Security benefits. If it costs a lot more, you could end up insolvent.

You can manage your savings portfolio's longevity risk by reducing spending, but elder bankruptcies are most often the result of spending crises. By definition, you can’t reduce spending in a spending crisis. Controlling spending is the problem, not the solution.

When a household’s finances crash and lead to bankruptcy, it is most often the result of a positive feedback loop of two or three problems. Not only is the household subjected to multiple problems, but these problems feed off one another and act in synergy, “the interaction of two or more agents to produce a combined effect greater than the sum of their separate effects.”

The key point of the Positive Feedback Loops: The Other Roads to Ruin post is that a financial crisis in retirement is often the result of a spending problem that causes another problem that causes a third problem, the problems become synergistic, and then the downward spiral is nearly impossible to stop. These failures can begin without warning and can bankrupt a family in a year or less.

Your retirement plan should consider all risks to your financial well-being, not just sequence of returns risk, and you should not be overconfident even if you have a low annual withdrawal rate. The four households I discussed in that post were all flying high a year before insolvency.

Positive feedback loops in retirement finance suggest the presence of chaos. In Retirement Income and Chaos Theory, I investigated that possibility and found that there are good reasons to believe that retirement finances are chaotic. If they are, then we will never have enough empirical data to understand the underlying mechanisms. Predicting your financial future using probabilities based on past data will always be suspect and can also lead to overconfidence.

The key point of that post is not that our financial future is totally unpredictable and planning is useless, or to measure how much more random market returns are than we believe. The take-away is that, while simulations and forecasts are useful when our finances are in equilibrium (which is most of the time), there will be times when our finances can behave wildly outside expectations. We need to plan for that.

We should plan for the most likely outcomes but try to create backup plans for “worst-case” scenarios. Like a floor, for instance, made up of assets that are not exposed to the equity markets and are protected from creditors.

In the post entitled, “Why Retirees Go Broke”, I combined the findings of an outstanding paper from Dr. Deborah Thorne with a paper my son and I recently co-authored analyzing the timing of portfolio ruin to show that, while sequence of returns risk might eventually deplete your savings, it is unlikely to be a major contributor to bankruptcy.

Outliving your savings and going bankrupt are two different risks. You can outlive your savings without going bankrupt. You may not spend all of your savings if you declare bankruptcy because Social Security benefits are protected from creditors and so are some retirement account assets, especially in bankruptcy. But, poor market returns aren’t the only way to deplete your savings. A spending crisis can deplete savings even faster than market losses and can lead to bankruptcy.

(ERISA-qualified retirement accounts – 401(k)s, are a typical example – are typically protected from judgments even when bankruptcy is not declared, but protection of non-ERISA-qualified retirement accounts like IRAs is complicated. You should discuss both with an estate attorney, but you can find good explanations at Nolo.com and at the Strictly Business Law Blog.)

You can become insolvent even if you invest all of your savings in Treasuries and annuities because expenses will still be uncertain – owning stocks isn’t a prerequisite for financial disaster. The culprit is unpredictable expenses.

The point of the bankruptcy post is that you should not confuse mitigating portfolio ruin with mitigating insolvency. Most elder bankruptcies result from spending crises, not poor market returns. Plan for both.

Most retirement research calculates a lifetime probability of portfolio ruin, the probability that you will deplete your retirement savings sometime during your life. Spend 3% of your portfolio annually, for example, and you have only a 5% probability of outliving your savings. In reality, that probability of portfolio survival ranges from near zero in the first decade of retirement to 5% after three decades or so. Kaplan-Meier curves, as I described in Death and Ruin, show how your probability of portfolio survival changes with age.

That post also explains that unless you live past your median life expectancy, you probably won’t outlive your savings with a reasonable withdrawal rate. The biggest risk of portfolio ruin, assuming you select a reasonable annual spending rate, is longevity, not market risk.

Retirement finance may be quite different than what you’ve read. Losing your savings due to market volatility is only one risk of retirement and it isn’t the worst outcome. You aren’t likely to go broke because you spend 4% of your savings annually instead of 3%, or even to completely deplete your savings. You’re more likely to see your savings decline, then to reduce spending to avoid going broke, and finally to suffer a decline in your standard of living as a result. About half of us won’t live long enough to be exposed to sequence of returns risk, at all.

In the unlikely event that you do spend all your savings, that doesn’t mean you’ll be bankrupt. Bankruptcy is far worse. It means you have more debt than you can repay and your debts need to be reorganized. You may lose all your assets that are not protected from creditors, but you will still receive Social Security benefits and you will keep assets in retirement accounts, although traditional and Roth IRA's are only protected to an inflation-adjusted $1,000,000 (currently about $1,200,000) and this applies to all your plans combined. You won't have credit and you will probably have trouble using banks for a long time.

Sequence of returns risk will rarely be a big contributor to bankruptcy and it takes decades to erode savings. Bankruptcy will strike like a bolt out of the blue as a result of spending shocks and may cost much more than just your savings. (All four of the families I wrote about in Positive Feedback Loops lost their homes, too.) The crisis will be difficult to stop once it starts.

Some shocks are impossible to avoid, but we should plan for the ones we can. We should be aware of the ones we can’t, if for no other reason than to avoid overconfidence in our retirement planning.

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Retirees should focus on a bigger picture than just spending sustainable amounts of savings and the right asset allocation.

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The expense side of the retirement finance equation is at least as important as the income side and it's probably riskier. Retirees should focus on a bigger picture than just spending sustainable amounts of their savings and getting their asset allocations right.

Retirement research should, too.

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In my next post, I'll review the major expense risks of retirement and suggest a few ways to deal with them.

Moshe Milevsky just published a piece entitled, "It’s Time to Retire Ruin (Probabilities)". Regular readers of this blog will recall a similar post, "Time to Retire the Probability of Ruin?", from last April, though Dr. Milevsky makes a much better argument.

Death and Ruin

An MBA and a med student walk into a bar.

(Stop me if you’ve heard this one.)

My son and I had just shot a round of sporting clays (“catch-and-release hunting”) on a hot summer day and we stopped into City Tap in Pittsboro on the drive home for a couple of ice cold, locally brewed adult beverages and a lunch of disgusting chili dogs, and by “disgusting” I mean “outstanding”.

Here in the South we often have a couple of beers after shooting because several generations of experience have taught most of us that having the beers before shooting is sub-optimal in so many ways.

I soon began complaining about the quality of much of the retirement finance research dealing with portfolio survival, as clay shooters often do (OK, not really). My son is on a “Physician-Scientist” track and spends much of his time researching patient survival. He immediately noticed that portfolio survival research isn’t terribly different than patient survival research and that medical research has better tools to study this than we have in financial research.

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Portfolio survival is a lot like patient survival but medical researchers have better tools to study it.

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We had a “you-got-peanut-butter-in-my-chocolate” moment and decided to co-author a paper studying portfolio survival by using two medical research survival study tools, Kaplan-Meier analysis and Competing Risks analysis. Our paper hasn’t been published, yet, but here’s a sneak preview.

In clinical trials, information on some patients will be incomplete. Some patients will drop out of the trial, move away, or the trial will end without discovering the patient’s eventual outcome. Kaplan-Meier analysis is a statistical technique that makes as much use as possible from the incomplete data available for these patients. Kaplan-Meier analysis also removes patients who are no longer at risk from the calculated probabilities.

Kaplan-Meier analysis divides time into intervals and for each interval survival probability is calculated as the number of patients surviving (or portfolios, or whatever is being studied) divided by the number of patients still at risk. In portfolio survival studies, simulated retirees who die or go broke are no longer at risk of going broke before they die. They should be removed from the denominator of the probabilities. (This is referred to as “right-censoring.”)

The probability of a patient or portfolio surviving to any point in time (or age, in our study) is estimated from the cumulative probability of surviving each of the preceding time intervals. This all no doubt sounds very complicated, and it is, but it is easier to see if we look at a Kaplan-Meier curve.

The following graph is the result of a portfolio survival study assuming annual withdrawal rates of 3%, 4% and 5%. The analysis used actuarial tables to generate random lifetimes for a retired couple of the same age retiring at age 65. (Double-clicking any Retirement Cafe´ graphic will enlarge it in a separate window.)

To read the curves, for example, a retiree who withdraws 5% annually from her retirement savings portfolio (blue curve) has about an 80% probability of portfolio survival if she survives to age 90. With 4% withdrawals (green curve), she has about a 93% probability of portfolio survival if she lives to age 90.

Reading the curves more generally, retirees don't outlive their savings before about age 80 to 85 assuming any reasonable (say, 5% or less) annual withdrawal rate. Then, the percentage of outlived portfolios heads south, the higher the withdrawal rate, the steeper the fall.

Portfolio survival studies typically calculate a single lifetime probability of survival, commonly quantified around 95%, that doesn’t show how that probability decreases with age, or the effects of random lifetimes. Kaplan-Meier curves do.

Most portfolio survival studies calculate absolute "lifetime" probabilities, or the percentage of all retirees in the study whose portfolios can be expected to fail at some point in their lifetimes. Kaplan-Meier analysis calculates conditional probabilities, meaning the percentage of failed portfolios expected among retirees who are still alive and haven't already depleted their savings.

There is a big difference between losing most or all of your retirement savings, thereby losing some standard of living, and experiencing financial setbacks so dire as to lead to bankruptcy. In my previous post, Why Retirees Go Broke, I suggested that very few retirees will go broke due to sequence of returns risk though there is a possibility of losing standard of living for that reason. Our portfolio survival research, combined with bankruptcy rates by age, is part of that argument.

As the following graph shows, few simulated portfolios are outlived before age 80 to age 85 (blue curve) but most bankruptcies (red curve) are filed before that age – portfolio ruin accelerates about the same time that new bankruptcy filings become negligible. By about age 83, nearly everyone who is going to go bankrupt has, while portfolio ruin has just begun. Thus, the probability that a retiree filed bankruptcy due to sequence of returns risk is quite small – retirees go broke for several reasons, but sequence of returns risk doesn't appear to be a major contributor.

(Note the vastly different scales of the y-axes. Portfolio survival probabilities range from about 80% to 100% in this scenario while bankruptcy probabilities are always less than half a percent. I present the graph this way to emphasize the timing of the two events.)

We applied Kaplan-Meier analysis to a portfolio survival model that included random lifetimes to provide greater insight into the portfolio ruin process. This should help you understand how your risk of outliving your savings – as a function of market volatility – will change as you age. (There are other "non-market" reasons that you might deplete your savings, like devastating medical expenses. Portfolio survival studies typically only look at ruin due to poor market returns.)

We also considered another statistical method from the medical research field, competing risks analysis.

I’ll discuss that in the near future.

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Special thanks to my son, Cary, of whom I am obviously ridiculously proud, for collaborating on this research and for helping me explain it in a blog post.

What I Do When the Market Tumbles

When stocks take a dive, investors call their financial advisors and ask them what they should do. I received a few of those calls this week. Most advisors respond with some version of “Don’t panic.”

Here’s what I do when the market crashes: nothing.

To be completely honest, I wasn’t aware that the market had fallen 8% so far in January until my wife told me late this week. I don't watch business news – life is too short. She picked it up on CNN while she was watching election news. (I don’t follow that, either.)

Here’s my theory. If you have such a high allocation to equities that market declines make you anxious, you own too much stock. Find the allocation at which severe bear market losses won’t keep you up at night.

In the 2007-2009 bear market, the S&P 500 fell over 50%. My portfolio fell just 15% because I had a 40% equity allocation. As one of my favorite baristas, Mandy, would say, “It didn’t feel totally awesome.” On the other hand, I didn’t lose sleep.

William Bernstein addressed this in a couple of his early books, including The Four Pillars of Investing (page 268). He suggests that the initial pass at the correct asset allocation for you be based on how much you can tolerate losing in a bear market. He provided the following table:

I can tolerate losing  this percent  in a bear market	Invest this  much in stocks
35%	80%
30%	70%
25%	60%
20%	50%
15%	40%
10%	30%
5%	20%
0%	10%

Every December I evaluate my finances and plan for the coming year. I calculate my desired asset allocation, which might not be the same as last year’s. If my current allocation is within an absolute 5% or so of my desired allocation, I do nothing. Otherwise, I may trade a few funds or ETF’s to implement my new allocation. In reality, this rarely happens because my allocation doesn't often stray very far.

Because I am willing to lose 15% in a severe bear market, I don’t labor over my portfolio value daily. I probably check it four times a year, at most. I retired to enjoy the remainder of my life, not to fret over the stock market.

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6 Tips for Investors When the Stock Market Tumbles –NY Times via @Retirement_Cafe

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Here’s some advice from other advisors I trust. Wade Pfau suggests reading this piece in the New York Times entitled, “6 Tips for Investors When the Stock Market Tumbles.” It’s a good one.

Dana Anspach suggests that if you feel that you must do something, instead of selling stocks, enroll in her free online class on retirement – another great idea.

Joe Tomlinson and I provided suggestions in Robert Powell’s USA Today column, “Advice for investors during crazy stock market volatility.”

If you’re retired or plan to be soon, set your asset allocation to a level of equities that you can tolerate. By definition, that means you won’t feel the need to do anything at all when stocks tumble. For young people still accumulating savings for retirement, invest most of your portfolio in stocks and don’t you do anything, either. In fact, do less than nothing. Time will fix this for you. As I recall, the 22% loss on a single day on Black Monday in 1987 didn’t feel totally awesome, either, but now it is barely a blip on the history of the S&P 500.

So, here’s my advice: pick an allocation you can stomach and ignore the noise. If you owned too much equity this time, gradually adjust it downward.

You'll know you're at the right allocation when the market takes a dive and you don't feel a need to call me.

Oh, and don’t panic.

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While you're ignoring current market volatility, read about the changing nature of sequence risk as we age in my next post, Death and Ruin. Or, follow me on Twitter by clicking the FOLLOW button on the right side of this page and I'll link you to the best web sources of retirement information. Or, heck, do both!

Why Retirees Go Broke

According to the American Bankruptcy Institute, the number of personal bankruptcy filings by Americans of all ages peaked at 1.5 million in 2010, the highest level since 2005, when the Bankruptcy Abuse Prevention and Consumer Protection Act made it more difficult to have debt forgiven. Filings declined to about 935,000 by 2014.

The Institute for Financial Literacy reports that older people are making up an increasing proportion of bankruptcy filers. The over-65 group made up 8.3 percent of all filers in 2009, or about 99,600, a rise from 7.8 percent in 2006.

Most bankruptcy filers were employed when they filed, but about 10% were retired.

Retirement research suggests that retirees can set up their spending and asset allocation to limit their “probability of ruin” to about 5% or so, but that is only the probability that he or she will deplete a savings portfolio as a result of market volatility and sequence of returns risk. Actually, there are several reasons a retiree might go broke.

The top five reasons for filing bankruptcy, according to a study entitled, “The (Interconnected) Reasons Elder Americans File Consumer Bankruptcy”, conducted by Dr. Deborah Thorne in 2010, are shown in the following chart recreated from her paper:

Other reasons for bankruptcies that were cited by filers and reported by the Institute for Financial Literacy included:

• Divorce (15.1%)
• Birth or adoption of child (9.7%)
• Death of family member (7.5%)
• Retirement (6.7%)
• Identity theft (1.9%)

Respondents could choose more than one reason, so the total exceeds 100%.

The “retirement” reason includes both unplanned and unwanted retirement (another form of unemployment), and bankrupt retirees who believed they had adequate financial resources to retire but discovered they did not.

It is conceivable that some number of the filers who cited “retirement” as a cause for their bankruptcy succumbed to sequence of returns risk, though that data is not directly available. However, probability of ruin models show that portfolios are rarely depleted in less than 15 to 20 years for reasonable withdrawal rates, or until a 65-year old retiree is 80 to 85 years old. Research shows that bankruptcy filings decline significantly beginning at age 65 and the bankruptcy filing rate for age 85 and older is negligible. About 40% of elder bankruptcies are filed between ages 65 and 74. The fact that portfolio ruin is much more likely at older ages after bankruptcy rates actually decline suggests that sequence risk is probably not a large portion of this 6.7% of bankruptcy filings.

In other words, most bankruptcy filers in the study were too young to have depleted their portfolios as a result of a poor sequence of market returns.

Note that there is no category of reports of bankruptcies due to market losses or sequence of returns risk, so if this reason for bankruptcy were cited by any filers it wasn't in the top ten. One might reasonably expect “Income Problems (41%)” to include loss of income from assets, but a closer read of Thorne (2010) shows this category refers to unemployment issues and not loss of income generated from savings.

According to Thorne (2010), the probability of an American over age 65 filing bankruptcy is less than half a percent (about 0.43%), an order of magnitude less than the probability of ruin studies predict for premature portfolio depletion. The causes of bankruptcy are predominantly an unexpected increase in expenses, an unexpected loss of income or, more often, a combination of the two.

I will refer to the risk of bankruptcy from either lost income or unexpected expenses as spending risk, combining the two because the net result is the same whether we have too much expense or too little income, and a crises will often include both. Most retirement income research doesn’t address either disruptions due to large unexpected expenses or those due to loss of income, focusing primarily instead on the risk of outliving one’s savings resulting from disappointing market returns and poor sequences of returns. I will refer to the latter as earnings risk, or the risk that portfolio returns don't ultimately support the chosen spending rate.

Dr. Thorne goes out of her way to note that the reasons elder Americans file consumer bankruptcy are interconnected, including the term parenthetically in the study’s title. As I argued in two recent blog posts, Positive Feedback Loops: The Other Roads to Ruin and Retirement Income and Chaos Theory, I believe the causes are more than simply interconnected.

“I agree,” Dr. Thorne responded in an e-mail. “It's a cascade effect of really unfortunate events.”

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Five top causes of elder bankruptcy: credit cards, illness, income problems, aggressive debt collection, housing problems.

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Thorne notes in her study that “it appears that there is seldom a single reason for their bankruptcies; instead, elder debtors often file because of the cascading effects of multiple interrelated life crises, each as consequential as the last.” The percentage of respondents reporting the number of the five leading reasons for bankruptcy were:

• None of the five reasons (8%)
• One of the five reasons (22%)
• Two of the five reasons (23%)
• Three of the five reasons (27%)
• Four of the five reasons (18%)
• All five reasons (3%)

This is consistent with my theory that bankruptcies primarily result from positive feedback loops that initially develop from an income or expense shock, then form a positive feedback loop and spiral out of control. In other words, I believe that retirement income/expense systems, especially when spending crises are included in the model, are chaotic.

When credit cards are mentioned as a reason for bankruptcy, some assume that these households used consumer credit to live beyond their means. This is surely true of some households, but in many instances credit cards are the last resort for households whose finances are spiraling downward for other reasons, such as unemployment, medical expenses, or the death of a spouse or divorce.

For example, I helped a household with their finances in 2008 when bankruptcy was imminent. They owed more than $60,000 in credit card debt but the charges had been made for living expenses such as feeding and clothing three teenagers, not for shopping at Neiman Marcus. The reason for their bankruptcy was a prolonged period of unemployment.

We may have created the impression that retirees who invest in stocks and bonds and spend from a volatile portfolio have about a 5% probability of going broke, but retirees don’t go broke as a result of sequence of returns risk. They go broke as a result of illness, injury, unemployment, housing problems, divorce, birth or adoption, death or illness of a family member, forced retirement, identity theft, consumer debt and aggressive debt collection and the interconnected, cascading effects of all of the above.

Retirees can, however, lose their standard of living due to sequence of returns risk. This might or might not contribute to bankruptcy.

Are there actual retirees who go broke due to a sequence of poor returns? I’m not convinced. I’ve never met one. Or, read about one by name. I would think that if 5% of retirees were going broke for that reason, we would spot one or two occasionally and the elder bankruptcy rate would be much higher than half a percent. I have not found data describing the number of retirees whose standard of living was significantly lowered by sequence of returns risk, but I have seen anecdotal evidence from retirees who experienced this.

On the other hand, there were nearly 150,000 Americans over age 65 who filed for bankruptcy for other reasons in 2010.

Retirees who invest in equities are exposed to earnings risk, often referred to as sequence of returns risk or probability of ruin. All retirees are exposed to the risk of a spending crisis, whether or not they invest in a volatile portfolio. These are two very different risks.

Sequence of returns risk develops slowly and allows time for mitigation through spending reductions, requiring at least one to two decades to deplete savings. It might contribute to bankruptcy, but it is more likely to reduce the retiree's standard of living at worst. (Rational retirees will reduce spending when their savings decline in an effort to avoid ruin.)

Sequence of returns risk can be mitigated by reducing spending and, to a lesser degree, by managing portfolio allocation. This risk, which appears to be roughly 5% to 10% with reasonable withdrawal rates, is an order of magnitude more likely than the risk of bankruptcy from spending crises, but the magnitude of the risk is smaller, entailing reduced standard of living but probably not bankruptcy. This is the risk that attracts the most retirement research and planner attention.

Earnings risk can also be mitigated by a floor of safe, income-generating assets like TIPS bond ladders, annuities and Social Security benefits.

Spending risk, on the other hand, is a bolt of lightning that can reduce an apparently stable household to bankruptcy in a year or less. (I provided examples in Positive Feedback Loops: The Other Roads to Ruin.) Retirees who invest in stocks and those who don't appear about equally at risk of a spending crisis.

Once the downward spiral begins, it often cannot be stopped. Reducing spending is, by definition of the crisis, not an option – if we had the ability to adequately reduce spending, we wouldn’t be in a spending crisis. The magnitude of this risk is greater than that of earnings risk, entailing both loss of standard of living and bankruptcy.

Retirees with a volatile portfolio and a low, “safe” spending rate are not immune from spending risk. The low spending rate mitigates only the risk of portfolio depletion resulting from market volatility. It does not mitigate the risk of portfolio depletion resulting from say, a huge medical bill.

Spending risk can also be mitigated by a "floor" of protected assets, such as Social Security benefits held in a separate account or assets held in a retirement account. Delayed Social Security benefits would also be protected until received (the creditor risk is to benefits already received and commingled).

Spending risk is seldom considered in retirement studies. The closest relevant research is bankruptcy studies that allow us to separate data for older bankruptcy filers, though age is not an exact proxy for retirement status.

When we ignore expense and income shocks in our retirement models and simply assume that we will always be able to reduce spending whenever our portfolio balance declines, we ignore the risk of unacceptable outcomes from spending crises. Retirement plans should anticipate and plan for both risks. As Michael Kitces recently pointed out, a projection of future asset values is not a plan.

Our goal isn’t to avoid going broke due to market volatility and sequence risk.

It’s to avoid going broke.

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Our goal isn’t to avoid going broke in retirement due to market volatility and sequence risk. It’s to avoid going broke.

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A version of this post was recently published at Advisor Perspectives.

What I Learned in 2015: Old Guys Rule

My blog posts are largely a mechanism for me to think aloud about retirement finance and to receive helpful feedback from my readers. I’m learning, not teaching, and I learned a lot in 2015.

I published 44 posts on this blog over the past year averaging about 958 words per post, or a little more than 42,000 words. I also co-authored a paper on portfolio ruin with my son and daughter, which I expect to publish early in 2016, that adds another 4,000 words (many of which I didn’t know before we wrote the paper), plus a few posts at Advisor Perspectives. I don’t even want to estimate the number of lines of R code and Mathematica code I wrote this year and there were a few presentations at conferences. Let's just ballpark it at 50,000 words.

(A classic novel is typically 80 to 100 thousand words; Fahrenheit 451 is a little over 46,000.)

That’s a lot of words for a hobby, a lot of lattes and a lot of learning.

My audience is diverse and knowledgeable and teaches me a lot, often by simply asking the right questions. Nearly 86% of them log on from the US, 4% log on in the UK and 1.8% from Canada. The surprise, however, is that 3% of my readers log on from Ukraine and nearly 2% from Russia. I extend a heartfelt Дякую! to the former and Спасибо! to the latter.

(I really hope I got that right. A Russian-speaking friend confirmed one, but my only Ukrainian friend moved to South Carolina last summer.)

Here are a few of the important things I learned in 2015.

There is no dispute between Jeremy Siegel and Zvi Bodie about stocks becoming safer the longer you hold them. They don’t.

I also learned that people have a difficult time giving up beliefs about finance. I still have planners argue that stocks become safer. Spending only dividends is not a valuable retirement income strategy and risk of ruin is primarily useful only as a research tool. A bond ladder held to maturity and a bond fund are not the same thing. A ladder of TIPS bonds held to maturity is essentially cash.

My son’s potato casserole is outstanding, but should be baked in a disposable dish. (I wash the dishes at our house.)

I learned that time segmentation (“bucket”) strategies can’t be depended upon to avoid a bad sequence of returns. They might, but it isn’t a sure thing.

I received an award for a paper in Indianapolis this summer. I had not visited the city for decades and I learned that it is still incredibly flat. I also learned that a small replica of Rodin’s “The Thinker” in your carry-on looks like a bunny rabbit on the x-ray screen of a TSA employee. ("Are you sure it's not a bunny rabbit? It really looks like a bunny rabbit.")

Game theory can be a useful way to think about retirement strategies.

I learned that even decaffeinated coffee after 3 pm can impact my evening’s sleep. My wife insisted that I test this theory and, much to my chagrin, she was proven correct. This dramatically altered my afternoon writing strategy at Caffe Driade.

Retirement income systems may be chaotic and virtually impossible to predict except in equilibrium, so chaos theory is another useful way to view retirement finance.

I learned that co-authoring a research paper with a son you taught to play basketball and who taught you how to play Super Mario World, and a daughter you taught to fish and who danced with you at her wedding is one of the coolest things that you will ever do.

Even with a basic assumption that our portfolio will return 5% with a standard deviation of 12%, the range of reasonable likely outcomes is too broad to effectively choose among spending rates and asset allocations.

Retirement income models probably involve a lot more uncertainty than most people assume.

I learned that academic papers on retirement finance are often misinterpreted, not just by retirees, but by financial planners, as well. Examples include "retirement spending looks like a smile" (the rate of annual spending change looks like a smile, but actual spending typically declines throughout retirement) and “retirees should increase their asset allocation as they age” (it depends – a custom asset allocation plan is always preferable).

I took the GMAT 30 years ago to get my MBA and again this past year. Perhaps most fun of all, I learned in 2015 that I can still outperform 4 out of 5 young whippersnappers taking the exam.

Old guys rule.

Here’s to an educational 2016.

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In my next post, I'll explain Why Retirees Go Broke.

Retirement Income and Chaos Theory

Are retirement spending models chaotic? In my last post, Positive Feedback Loops: The Other Roads to Ruin, I pointed out the exposure to the risk of these loops in at least three aspects of typical retirement income models: market returns, spending from a volatile portfolio, and the total and rapid collapse of a large real estate portfolio. I noticed these loops because I have an amateur interest in chaos theory, and as I mentioned at the end of that post, positive feedback loops are characteristic of chaotic systems.

Whether or not retirement income systems are chaotic is an important issue because chaotic systems are riskier than stochastic (probabilistic) systems. We tend to study retirement income systems with probabilities. If the systems are chaotic, they're riskier than inferential statistics (probabilities) suggests. Bear with me through some background and I will explain the relevance to your retirement plan.

According to the website, FractalFoundation.org, “chaos is the science of surprises, of the nonlinear and the unpredictable. It teaches us to expect the unexpected.” Most retirement income research uses the science of probabilities and statistics that reveal what is unlikely, but not necessarily what is unexpected. 

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Are retirement spending models chaotic?

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As early as 1887, Henri Poincaré showed that while Newtonian physics could perfectly predict the orbit of two planetary bodies, adding a third body to the mix turned a straightforward problem into one that is virtually unsolvable. A system as simple as the double pendulum simulated below can exhibit chaotic behavior. Its trajectory varies dramatically with small changes in its initial position. Probabilities won't predict the trajectory of the double pendulum because we can't know precisely enough where it will start. As the three body problem and the double pendulum show, systems don't have to be complex to behave chaotically.



When I study the models of retirement income studies, I see a number of characteristics of the models that are also characteristics of chaotic, not probabilistic, systems.

Let’s look at those characteristics as suggested by FractalFoundation.org.

Sensitive dependence on initial conditions. Often colorfully illustrated by "the butterfly effect", this is the characteristic of chaotic systems such that small changes in initial conditions can lead to drastic changes in the outcome. In retirement income studies, someone who retired in 1966 might have exhausted their savings in 30 years while someone retiring in 1967 with identical resources might not have, as a result of unpredictable market returns and unpredictable sequence of returns risk.

Unpredictability. “Because we can never know all the initial conditions of a complex system in sufficient detail, we cannot hope to predict the ultimate fate of a complex system.” Like the starting point of the double pendulum, we can’t predict precisely enough where we are in the cycle of future market returns at the outset of retirement. Is the market overvalued? Undervalued? Did we pick a fortuitous retirement date for the sequence of future returns? Only time will tell.

The Transition between Order and Disorder. “Chaos is not simply disorder. Chaos explores the transitions between order and disorder, which often occur in surprising ways.” Chaotic systems, such as the stock market may be, can remain in a stable state for long periods of time before inexplicably becoming unstable. The 2010 Flash Crash is an example that is still not well-explained. In the example I provided in my previous post, two households went from well-to-do to bankrupt in less than a year when the U.S. economy crashed in late 2007. Everything looked fine for both families just months earlier.

Mixing. “Turbulence ensures that two adjacent points in a complex system will eventually end up in very different positions after some time has elapsed. Two neighboring water molecules may end up in different parts of the ocean or even in different oceans." Look at the range of outcomes for a retirement portfolio balance simulation in the chart below. One scenario depleted the portfolio in just 19 years while another grew to more than $6M. Each scenario started at the same point (a $1M portfolio balance) under the same initial conditions.



Positive Feedback Loops. “Systems often become chaotic when there is feedback present. A good example is the behavior of the stock market. As the value of a stock rises or falls, people are inclined to buy or sell that stock. This in turn further affects the price of the stock, causing it to rise or fall chaotically.” See my previous post on positive feedback loops for retirement examples.

Here are more characteristics of chaotic systems not included in the Fractal Foundation's list.

Attractors. An attractor is a state toward which a system tends to evolve from a wide variety of starting conditions. System values that get close enough to the attractor tend to remain close to it. A type called a "fixed point attractor", which attracts trajectories to a single point, describes portfolio ruin.

Here's a graphical depiction of a point attractor from Young Scientists Journal. Imagine this as two portfolio balance trajectories that enter a positive feedback loop and spiral downward to ruin.

(Want to see something really cool? Google "images of strange attractors" and you will find some amazing graphics, like this.)

Prediction Horizons. Another characteristic of chaotic systems is a prediction horizon, explained by Professor Jonathan Borwein.

“What at first glance appears to be random behavior is completely deterministic – it only seems random because imperceptible changes are making all the difference. The rate at which these tiny differences stack up provides each chaotic system with a prediction horizon – a length of time beyond which we can no longer accurately forecast its behavior. In the case of the weather, the prediction horizon is nowadays about one week.”

As the Terminal Wealth chart above shows, the prediction horizon for retirement portfolio balances is a less than a year, beyond which the outcomes diverge dramatically and become much more uncertain.

Experts disagree on an exact definition of chaotic systems. They tend to describe their characteristics, instead, much in the way Supreme Court Justice, Potter Stewart once described obscenity – “I know it when I see it.” I'm not an expert in chaos theory, but when I consider the characteristics in common with retirement income models, I think I see it.

My interest in chaos theory is limited to popular books on the subject because the math, differential equations and fractal geometry, is pretty demanding. So, I posed several questions to chaos theory expert, Tom Konrad, who has a doctorate in complex analysis and chaos theory and edits AltEnergyStocks.com. I described spending from a volatile portfolio to Dr. Konrad and asked if he thought it might be a chaotic system.

“It's impossible to ‘prove' that a system is chaotic or is not when we don't completely understand the underlying mechanisms,” he explained.

“It certainly displays chaotic characteristics”, he continued, “but other than acknowledging that, I'm not sure if anything would be accomplished by quantifying them.”

In my interpretation, if it quacks like a duck and tastes like a duck, dinner probably won’t suffer if mathematicians can’t agree to the precise extent of its duck-ness. If the retirement income system displays chaotic characteristics, there may be limited practical negative consequences to treating it as chaotic and it is safer to assume that it is.

Now, why is it important to understand if retirement income systems are chaotic or simply probabilistic? Because stochastic systems are unpredictable but statistically quantifiable, while complex and chaotic systems are even more unpredictable. It was on this point that Dr. Konrad provided my favorite explanation.

“Chaotic systems are less predictable than stochastic systems. Sufficient historical data will eventually allow you to quantify a stochastic system; this is not true for a chaotic system. The stock market seems to be un-quantifiable based on the historic record. That does not necessarily mean that it is chaotic (although there are other reasons, such as positive feedback loops, to believe that it is) but it is clearly harder to quantify than a stochastic system would be.”

We debate whether 200 years of stock market returns are enough to characterize the returns of the market's internal processes, or its impact on retirement plans. If the system is chaotic, we will never have enough historical data to make it predictable.

Retirement income studies tend to use probabilities to focus on long-term sustainability of savings as a function of market volatility alone. This approach won't catch many quickly developing expense-related crises, especially since the studies tend to ignore expense uncertainty altogether. When we say a retiree has a 5% risk of outliving her savings, we mean a 5% risk of outliving savings due solely to market volatility. But, there are other risks to those savings that should also be considered.

These studies explain long, slow declines in standard of living, not catastrophic failures, in a world where market returns are normally distributed and mean-reverting and no one ever needs to spend more than their "sustainable withdrawal." Their recommendations – diversification and spending adjustments – provide little help in a spending crisis.

Chaos theory helps explain household finances that veer suddenly from normal equilibrium into a crisis. Debt, divorce or some other expense shock shoves the portfolio balance trajectory into a positive feedback loop and toward the point attractor that is portfolio ruin.

Take another look at the green trajectories in the spiral above and consider the households from my previous post that went from equilibrium to bankruptcy and, in one case divorce, in less than a year. This is not the stuff of 30-year Monte Carlo simulations of normally distributed market returns.

Probabilities and equilibrium are important parts of the story, but they aren't the entire story.

I admit this post is a bit dense, particularly if you have no interest in chaos theory. But, if you take away the following, I think you'll be fine. When a planner tells you that you have a 5% probability of depleting your savings, she typically means a 5% probability of going broke as a result of market volatility. Alas, there are other ways to go broke. If spending systems are chaotic, which I suspect but can't prove mathematically, there are conditions under which their outcomes are unpredictable and probabilities don't help. And lastly, as Dr. Konrad suggests, if they behave chaotically, we might not gain much by proving how chaotic they are.

Unless and until we know that these systems are not chaotic, the safest path for a retiree would be to assume that they are and that the probability of ruin is greater than studies have indicated.

Once again, I note that my posts about market risk shouldn't be taken as an argument against investing in stocks. Retirement income without equities is terribly expensive. But it's important to understand the risks and to be prepared to deal with them. There's more to worry about than a bad sequence of returns and living too long.

Next time, I'll sum up what I learned about retirement finance in 2015.

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Looking for some good popular books on chaos theory without the differential equations? Try The Black Swan, Fooled by Randomness, Chaos: Making a New Science, or Dr. Konrad's column in Forbes.