Wednesday, July 26, 2017

Katrina, Fukushima and Retirement Risk: When Risks Create Risk

What is a retiree's greatest risk of financial ruin? Long-term care costs? Longevity risk? Market risk? Inflation?

The answer is none of these individual risks but a combination of interrelated or "dependent" risks.

The empirical argument to support this is research published by Dr. Deborah Thorne entitled, "The (Interconnected) Reasons Elder Americans File Consumer Bankruptcy"[1] that I reviewed in Why Retirees Go Broke. Dr. Thorne concludes:
"The data also suggest that the majority of elder bankruptcies result from multiple interrelated crises, rather than a single unfortunate event."
Note that I am talking about financial ruin or bankruptcy here and not the loss of a retiree's standard of living. I generally consider two classes of retirement plan failure: loss of standard of living and the more-severe bankruptcy or "ruin." Retirees rightfully worry about inflation, market losses, and spending too much from their retirement savings portfolio and a single "unfortunate event" may be all that is needed to suffer a loss of one's standard of living.

But, ruin appears to result most often from multiple dependent risks according to Dr. Thorne's research, such as an illness that results in job loss and large medical bills that, in turn, generate unserviceable credit card debt that ultimately forces the household into bankruptcy. Dependent risk losses can fall like dominoes.

In my last post, Retirement is Risky Business, I listed 26 potential financial risks of retirement. I'll probably add a few in the near future, so let's call it thirty-ish.

Not all of the risks on that list will apply to every household. For example, if you don't have a spouse then you obviously don't have a risk of your spouse dying. So, let's say that you are exposed to only twenty of the risks on the list.

If you calculate your exposure to each of those twenty risks and total them the sum will provide an underestimate of your overall risk and perhaps even a false sense of security.

Not only are risks difficult to quantify but they are even difficult to identify and they are often inter-dependent (not independent). Here are three major reasons it is misleading to merely check off the list of risks:
  • Unknown unknowns,
  • Hidden risk exposures, and
  • Dependent risks.
Financial risks are uncertainties by definition but there are some uncertainties that we aren't even yet aware of — unknown unknowns.

Not long ago we weren't aware that identity theft would one day be an issue for retirees or that credit default swaps could imperil our personal finances. There are undoubtedly risks in our retirement future that we don't yet foresee.

An example of hidden risk that will be closer to home for most retirees can be found in broadly held mutual funds. A retiree who holds a half dozen large cap funds may feel well diversified. She will likely find, however, that most of the funds own Microsoft, Alphabet and other broadly-held company stocks[3] and that her exposure to the risk of these individual stocks is greater than expected. ( has a feature called X-Ray that will help you find these overlapping stocks but another solution is to hold fewer mutual funds.)

In other words, some risks may not be on your list simply because you overlook them.

The far more complicated and potentially much greater risk that will not be addressed by checking off a list of individual risks is what the risk management field refers to as "dependent risks."

Dealing with Dependent Risk”, published by Claudia Klüppelberg and Robert Stelzer[4] in 2012, defines dependent risk and demonstrates its complexity. The paper begins with this paragraph:
In most real life situations we are not only confronted with one single source of risk or one single risk, but with several sources of risk or combinations of risks. An important question is whether individual risks influence each other or not. This may concern the time of their occurrence and/or their severity. In other words, we need to understand how to model and describe the dependence structure of risks. Clearly, if risks influence each other in such a way that they tend to occur together and increase the severity of the overall risk, then the situation may be much more dangerous than otherwise.
Here’s an analogy. Maybe you recall the classic Microsoft game Minesweeper[5]. Imagine a similar game except that it's played on a large field with different kinds of mines scattered around to represent individual retirement risks. Let's call it Risksweeper. Each mine has a different probability of exploding, representing risk probability, and each has a different potential “blast radius” range representing risk magnitude.

Classic Microsoft Minesweeper game winner and loser.
The goal of Minesweeper is to figure out where the mines are and to avoid "stepping on" one and ending the game. Notice that when you step on one mine (the red one on the right) they all explode. In the Risksweeper game, stepping on a single mine can end the game or only leave the player weakened but stepping on a mine that causes other mines to explode is likely to mean "game over."

The Risksweeper mine that I'll call “Medical Expense Risk” can make a small bang with a small blast radius (a $5,000 doctor bill). If we get the small bang, it is unlikely to set off other nearby mines and result in financial ruin.

On the other hand, the Medical Expense Risk mine can sometimes make a big bang (a $250,000 doctor bill) with a blast radius large enough to set off other mines. If the second mine is also a big one, like job loss, for instance, its blast radius may set off still other mines. If the third mine is large enough, the field starts to look like one of those mouse-trap-and-ping-pong-ball demonstrations of a nuclear chain reaction[6] or like Dr. Thorne’s description of interconnected losses leading to elder bankruptcy.

The biggest risk on the playing board is not medical expense risk, consumer debt risk or longevity risk; it's a chain reaction of multiple dependent risks.

In the following diagram, the solid circle represents the radius of a "typical" blast (a $5,000 doctor bill, for example) and the dotted line surrounding it represents the radius of an "extreme" blast from the same risk (a $250,000 doctor bill).

Risk management literature refers to the amount of connectedness, or dependency, between two risks as probabilistic distance. The less wealth, or “safety margin”, a household has the closer together the mines are situated on the field. Less probabilistic distance between the mines means that smaller bangs are more likely to set off a chain reaction that can lead to ruin.

Very wealthy retirees have very sparse “minefields” and have to be pretty unlucky for an explosion to be “extreme” enough to set off a chain reaction. A $5,000 medical expense might be easily paid by a wealthy retiree but represent an "extreme" loss to a marginally-funded household.

As you imagine this Risksweeper game (or view the mouse traps) it should become obvious that figuring out how closely all of the various risks are linked and the probability that explosions of various sizes will cause other explosions is incredibly complicated when you need to consider twenty or thirty dependent risks and even a few levels of inter-dependency. (This is, after all, a small scale version of the problem nuclear scientists had to solve at Los Alamos in the 1940's except they were trying to cause a chain reaction.)

You should also see that the retiree’s risk is not fully represented by the individual mines alone but includes the risk that one large bang can set off another and possibly even start a chain reaction of cascading financial losses leading to ruin.

Katrina, Fukushima and Retirement Risk: When Risks Create Risk.
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A simple list of retirement risks does not take this connectedness into consideration, although I did include “Interconnected Loss Risk” in that list. (I'm going to refer to it as "Dependent Risk" going forward.)

Dependent risk analysis is a staple of many fields from nuclear power plant design to insurance to aerospace engineering but it appears to be rarely referenced in retirement literature. A Google search of "dependent risk and retirement" turned up a single reference including both terms and it's from the field of political science research[7] referring to retiring from an election. Dr. Thorne's analysis of elder bankruptcy data tells us that retirees should also be should be concerned about it.

Modeling these dependent risks can be done using a statistical construct referred to as a “copula” [8], but as Klüppelberg and Stelzer note, “copulae provide a way to characterize the dependence structure completely, but are rather complex objects.” The complexity seems to make them unrealistic for typical retirement planning processes, not so much because the math is complicated (it is) but because we don't have a good understanding of the probability distributions of the risks to model.

It seems likely, however, that if one did undertake a detailed analysis of the dependence risk structure of retirement using a copula the results would be the same as Dr. Thorne discovered with empirical bankruptcy evidence – the biggest risk is a sequence of dependent risks.

The scenario above describes a series of three dependent risks, healthcare expense risk, job loss risk and credit risk. A retiree might, however, succumb to the interdependence of even more individual risks.

Let's go back to the assumption that a retiree is exposed to 20 risks and that we only wish to consider failure due to a single pair of those risks. We would need to think about combinations of 20 risks taken two at a time, or 190 scenarios.

Twenty risks taken three at a time generate 1,140 scenarios. I won't bother with the household exposed to more than 20 risks or those scenarios of 4 or 5 combinations of dependent risks except to note that 30 risks taken 2, 3, 4 or 5 at a time would require an unmanageable analysis of 174,406 scenarios. Copulae are a probabilistic approach to solving the problem at this scale.

Importantly, Klüppelberg and Stelzer also note that “For risk assessment it is mainly the dependence structure of extreme events that matters. Thus, measures for dependence in extreme observations provide useful dependence measures for combined risks.”  The impact of dependent risks are largely felt under extreme conditions and are far less an issue under normal economic conditions. By definition, "normal conditions" means relatively small bangs that are unlikely to start a chain reaction.

Clearly, there are far more potential risk scenarios than we can reasonably expect to consider for a retirement plan. We might, however, be able to identify and consider the most impactful scenarios. We might do that by identifying the most common causes of bankruptcy or “ruin”, the ultimate retirement plan failure, and then considering only extreme losses resulting from those risks. This only identifies the worst cases, of course, but that might be the only manageable analysis.

As I described in Why Retirees Go Broke, elder bankruptcies are most often the result of one, two, three, four or five of the following risks:
  • Credit card interest and fees,
  • Illness and injury,
  • Income problems,
  • Aggressive debt collection, and
  • Housing problems.
Aggressive debt collection is probably beyond our ability to manage, so let’s drop it from the list. Although neither market loss nor inflation is commonly cited as a cause of bankruptcy, they are common fears of retirees so I will add them to the list for the sake of a good night's sleep. This modified list of greatest concerns (biggest bangs) is then:
  • Credit card interest and fees,
  • Illness and injury,
  • Income problems,
  • Housing problems,
  • Market losses, and
  • Inflation.
Combined, these six scenarios considered one, two and three connections deep generate 41 scenarios. Still a lot, but perhaps manageable. Adding Klüppelberg and Stelzer's warning about extreme conditions, analyzing this smaller subset of risks only under such conditions might provide a good if incomplete start.

This also raises the issue of how we can best deploy our retirement assets to mitigate retirement risk. It appears that our goal should be to first avoid the worst case, a chain reaction leading to ruin. A chain reaction will likely have far worse outcomes than any individual risk.

This implies that we might want to use our risk-management assets first to "shield the biggest potential blasts" rather than spread these resources broadly to minimize all risks. Perhaps long-term care insurance and securing housing deserve priority consideration over market or inflation risk, for example, since the former are commonly-cited reasons for bankruptcy and the latter are not.

Because with dependent risk "it is mainly the dependence structure of extreme events that matters",  analyzing retirement risks independently may be adequate under normal conditions. But, we are probably underestimating our vulnerability under extreme conditions (think the 2007-2009 simultaneous crash of the mortgage and stock markets).

On the other hand, global financial meltdowns occur far more frequently than we might expect. Business Insider[9] claims there have been 57 stock market crashes, defined as a 20% or greater decline in one or more of the four major stock market indices, since 1950 and Wikipedia[10] provides a long, depressing list of global financial crises throughout history, leaving one to wonder how typical "normal conditions" actually are in this context.

Speaking of chain reactions and dependent risks, the Fukushima Daiichi nuclear disaster[11] resulted from a chain of dependent risks, which one might expect to have been thoroughly studied by the experts that designed a nuclear power plant.

The plant began to automatically shut down, as designed, when it detected an earthquake on March 11, 2001. About an hour later the plant was inundated by a tsunami, also anticipated in safety plans, although this one was 15-meters high. The tsunami topped a seawall and then flooded generators that powered the plant's cooling pumps causing the nuclear "accident." But, over one thousand people living near the plant died as the result of a fourth dependent risk – the evacuation plan.

What are the odds of experiencing an earthquake and a flood within the same hour? Probably quite low unless the earthquake causes the flood. This is the essence of dependent risks.

The string of dependent risk losses that resulted from Hurricane Katrina in 2005 disaster was similar[12]. New Orleans survived the hurricane but the resultant flooding of the Mississippi River from torrential rains upstream caused levees to fail, flooding the city. The flood from the breaches shut down most of the 149 pumps designed to pump flood water out of the city. Ultimately, many more people were killed or devastated by a failed evacuation. Like Fukushima and elder bankruptcy, the risk to New Orleans residents was much greater than the individual risks of a hurricane, failed levees or disabled pumps in isolation.

A reverse mortgage is a retirement example that also creates dependent risk. Borrowers are generally protected from foreclosure except in specific cases (inability to pay property taxes or maintain the property, for example) so long as they live in the home. It appears that actual foreclosures are, in fact, quite rare. In theory, a borrower needs only to continue to live in the home to avoid losing it but as a colleague of mine used to say, "just notice how easily that rolls off the tongue."

Imagine that a household experiences extreme medical expenses or the loss of a spouse after much of the home's equity has been spent and the survivor can no longer afford to live in the home or community or no longer wishes to. Leaving the home would render the mortgage due and payable with practically the same outcome as a foreclosure. The household would lose the home as a result of illness or death of a spouse triggering loss of standard of living exposing the risk associated with the reverse mortgage.

If the borrower set up the mortgage with tenure payments he or she would also lose those – yet another dependent risk – and be unlikely to have assets to replace that expected future income. Considering reverse mortgage risk, medical expense risk and loss of spouse risk separately without evaluating the dependent risks they create would not uncover this vulnerability.

(This is not an argument to avoid reverse mortgages, by the way – all financial strategies have risks and rewards. It is an argument to understand the risks as well as the rewards.)

Some general conclusions can be drawn:
  • Retirement risk is more than the sum of its parts, potentially much more. Mitigating individual risks independently ignores dependent risks which may be much greater.
  • The retirement field doesn't appear to have widely considered dependent risk nor do retirement plans.
  • A thorough statistical analysis of dependent risk is typically well beyond the reach of a financial planner or do-it-yourselfer.
  • Dependent risk grows under extreme economic conditions.
  • Analyzing the inter-dependence of the few risks generally responsible for financial ruin and only under assumptions of extreme conditions may be manageable and helpful.
  • The greater a retired household's safety margin (i.e., its wealth) the less likely a loss will be "extreme" enough to trigger dependent risk losses.
  • Households with marginal retirement resources are more susceptible not only to independent risks but also to dependent risks.
  • Dependent risk may result in the worst-case outcomes so consideration should be given to prioritizing them when allocating risk-management resources.
Bottom line, your retirement plan likely has a great deal more risk under extreme conditions than you know and it probably goes without saying that more wealth means less risk. These plans are acceptable if everything remains normal but if we could count on everything remaining normal we probably wouldn't need to plan much in the first place.

Evaluating retirement risks individually and in isolation, a common practice, is somewhat akin to analyzing the risk of driving your car by reviewing its safety features and ignoring the fact that there will be other drivers on the road.

Please note that I have made a few changes to the table of risks, including the downloadable version, in my previous post, Retirement is Risky Business.

Optional homework for this week's post is to play a game of Minesweeper[5] and to watch a short video of ping pong balls tripping mouse traps[6].


[1] The (Interconnected) Reasons Elder Americans File Consumer Bankruptcy, Dr. Deborah Thorne (download PDF).

[2] The Big Short, Michael Lewis.

[3] Top 10 Companies Held By Mutual Funds

[4] Dealing with Dependent Risk, Claudia Klüppelberg and Robert Stelzer, 2012. Download PDF

[5] Minesweeper game online.

[6] Mouse Trap Reactor video.

[7] Systematically Dependent Competing Risks and Strategic Retirement, dependent risk in election decisions.

[8] In probability theory and statistics, a copula is a multivariate probability distribution for which the marginal probability distribution of each variable is uniform. Copulas are used to describe the dependence between random variables. In the present context, random variables represent risk.

[9] Here's every stock market crash in the past 60 years, Business Insider, June 8, 2016.

[10] Financial Crises throughout history, Wikipedia.

[11] Fukushima Daiichi Accident, World Nuclear Association.

[12] Hurricane Katrina,


  1. Great post, Dirk. The "Minesweeper" and "blast radius" analogy really helps visualize the concept of dependent risk. You'll be happy to hear I watched the ping pong ball video, too, but I think the Minesweeper concept best explains dependent risk.

  2. The downside of the ping pong ball demo is that a retirement version would be better viewed in super slo-mo. The downside of the Minesweeper exercise is that people like me can't stop after one game!

  3. The Fukushima accident is a particularly interesting one from a risk management perspective. The earthquake and tsunami were larger than believed to be possible, so shaking and flooding that was going to cause problems was inevitable in retrospect due to that lack of knowledge.

    However, the placement of the generators and electrical switching gear was a critical element in turning a bad situation into a disastrous one. Three back-up generators were placed in the basement of the reactor buildings, so they got flooded by the tsunami. However, there were three other back-up generators in newer facilities on high ground. However, electrical switching gear that could have routed power from those dry back-up generators were located in the same location as the flooded generators, so the dry generators were unable to act as a back-up to the flooded generators because the switching gear was also flooded.

    So something as simple and relatively inexpensive as simply putting electrical switching gear in a location guaranteed to be dry could have prevented most of the radiation parts of the disaster. This was simply lack of imagination during the design of the retrofits.

    Key elements to risk management are to understand how to have relatively simple, inexpensive, robust elements that can help prevent bad things from getting worse. We often can't prevent the bad things from occurring, but we can do things to reduce their impacts. A simple example is buying cars that are highly-rated for safety compared to other vehicles costing the same amount; they may not prevent an accident, but they can significantly reduce the impacts of it which can be critical from a quality of life and financial standpoint (or allow for simple survival).

  4. Thank you, Dirk for the post. Here is a personal case example: Dependent risks may also have risks within ... for example, one kind of cancer may increase the risk of also getting another kind of cancer. We have some experience with this ... after the first diagnosis we set aside a TIPS ladder to address this future illness liability ... but the second cancer has a much larger "blast zone" due to required medical travel expense (more treatment, more often). So, it is easy to see how one or two additional kinds of risks such as market risk(the Big Short raises the issue of safety for the bond funds that we hold as "more secure" than the stock market)... or the death of a care taking spouse ... or a need for long-term care ... could cause real problems for many families. The one thing that we did, fortunately, to reduce the impact of these bad things ... was to live frugally for many years, and save ... save ... save. It does not go without saying that more wealth = less risk. It bears saying over and over again ... I suppose retirement planning seeks to answer the question "How much is enough"? Dependent risk analysis suggests "enough" could be more than you might think.