The Limits of Simulation

In a previous post, The “Future” of Retirement Planning, I explained that Monte Carlo simulation of retirement finances provides all the information available from a deterministic “spreadsheet” model and more. Among other advantages, it models sequence of returns risk.

Monte Carlo simulation, however, has its own limitations.

A reader commented on my previous post that Monte Carlo simulation “creates thousands of possible and impossible scenarios.”

The “impossible” part of that statement is wrong.

In fact, the opposite is true. Monte Carlo simulation’s biggest shortcoming is that most of the scenarios it produces will be the most likely and simplest scenarios while lots of possible but unlikely scenarios that could destroy a retirement will never be simulated.

Most retirement models, deterministic or stochastic, don't model the risks that are most likely to lead to lead to bankruptcy, like spending shocks, divorce or a combination of inter-related risks.[1]

Any planning exercise begins with the basics and is then augmented by a bunch of “what-if’s.”

Planning a picnic? You’ll need a blanket, some food and some lemonade. But, then, what if it rains? What if the park is closed? What if there are too many ants or mosquitoes? What if the sun is too intense? What if someone gets a bee sting? A good plan will consider these possible bad outcomes and prepare for them.

Monte Carlo simulation is a great way to quickly generate a few hundred thousand retirement “what-if” scenarios. Analyzing them with statistics allows us to comprehend the big picture without looking at each scenario individually (an impractical task). They allow much greater in-depth analysis than the spreadsheet approach because they consider more of the key factors of retirement success and provide a lot more what-if’s but here are some of their limitations.

1. They model questionable assumptions.

Most Monte Carlo simulation models assume that market returns are normally distributed, even though we know they aren’t. We see far more — and far more severe — market crises than a normal distribution predicts. We’re either living in a very unlucky universe or we’re using an optimistic distribution for market returns. We use a normal distribution because it's the closest parametric distribution we have and that simplifies the math but we’re pretty sure the market has fatter tails than a normal distribution.

We have a couple of hundred years of market return data but that isn’t enough to create anything near a reasonable confidence interval. That is to say, our (historic) sample size is way too small to make confident guesses of the mean market return and there is no convincing argument that the next thirty years of market returns will look like the last 30 or the last 130.

(These are also problems with deterministic models.)

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Monte Carlo is one of the best planning tools we have but it has its limits.

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In “Where is the Market Going? Uncertain Facts and Novel Theories”[2], John Cochrane notes that over the fifty years from 1947 to 1996 the excess return of stocks over T-bills was 8% but, assuming the annual returns are statistically independent, the standard confidence interval for the mean return ranged from 3% to 13%.

Let me say that in simpler terms. If you asked me the mean excess market return, then based on the sample data from that period I would guess it’s about 8%. But, if you then asked me how confident I am that 8% is the mean, I would say that I’m 95% confident (not totally) that it isn’t less than 3% or more than 13%. In other words, I’m not that confident. (This is also the reason that we can’t identify optimal asset allocations.)

Monte Carlo simulation addresses this uncertainty by generating scenarios with a fairly broad range of market returns. Some scenarios might have a return near 3%, for example, and others near 13%, though most would be closer to 8%. Contrast this with a spreadsheet model that assumes a single market return with no variance.

Some financial writers define market volatility as “risk” and they define “uncertainty” as not even knowing the underlying distribution. We don’t know the underlying distribution of market returns or if the underlying mean return changes over time.

The effect of all this uncertainty is that, while Monte Carlo simulations appear to generate accuracy to several decimal places, our sample size of 200 years or so of historical U.S. stock market returns is too small to inspire confidence. That doesn’t render simulation results irrelevant, however. Hurricane forecasts, as Larry Frank points out, are not very accurate but still very useful. It’s a good analogy for dynamic retirement planning.

When someone says, “My Monte Carlo planner says I have only a 5% probability of outliving my savings, so I’m good, right?”, my answer is, “Well, yes. . . assuming the market behaves much as it has in the past, that you invest your portfolio wisely and earn something near market averages, that you don’t experience a 3-sigma market crash early in retirement, that you experience no spending shocks and that you consider a 1-in-20 chance of outliving your savings “good”, then, yeah, you’re probably good.

2. Simulations are only as good as the strategy they model.

The first thing we need to know is what the simulation models. Most model the probability of outliving a portfolio of stocks and bonds but, as I explained in Three Degrees of Bad[3], portfolio depletion can’t be equated with retirement failure. Portfolio depletion can even be part of the plan.

Some retirement financing strategies are simply flawed. I believe fixed-spending strategies and set-and-forget strategies are hopelessly flawed, for example. Monte Carlo simulation of a flawed strategy for an individual household’s retirement plan is pointless.

I find the concept of “retirement ruin” to be meaningless (retirees don’t stop living and spending when their portfolio is depleted) so I have little confidence in retirement models based on probability of ruin[4,5]. U.S. retirees would declare bankruptcy if their retirement failed, emerge with some protected assets, and live off Social Security benefits. Their retirement wouldn’t simply end, though their standard of living might dramatically decline. Instead, I model the probability of not meeting desired spending.

So, when I respond, “yeah, you’re probably good”, I add, “. . . and assuming your Monte Carlo simulation used a reasonable model.”

3. Spending shocks are difficult to model, so they seldom are.

Spending shocks can decimate a retirement plan but they are difficult to model. Shocks typically have a low probability of occurring but potentially huge risk magnitude. These risks are usually better mitigated by insurance when affordable insurance is available than by relying on a low-probability of their occurrence. Even if we model them, insurance (Social Security benefits, annuities and pensions) will usually be the answer.

4. Simulations probably won’t generate rare but potentially catastrophic scenarios.

Monte Carlo simulation works by generating many of the most probable scenarios and fewer and fewer of less-probable scenarios. They won’t thoroughly analyze very low-probability market returns (tail risk), for example, because they are unlikely to generate more than a few such scenarios.

A normal distribution “tails off” at both ends. The “skinny tails” show that the probability of outcomes far from the mean are highly unlikely, which means they are equally unlikely to be included in a Monte Carlo simulation. We refer to this as “tail risk.” You can see the skinny tails of a normal distribution in the diagram above.

Outcomes in the tails are improbable but, as I recently read somewhere, the left tail should be labeled “There be dragons.”

Unlikely outcomes to the right of the mean (the right tail) aren’t a problem; those outcomes are improbably good. It’s the left tail risk that’s a problem because the distribution tells us that outcomes there are improbable but it doesn’t tell us they’re magnitude.

The reality is that we can’t estimate tail risk for the market because we don’t know the distribution of market returns. We guess that it is “normal-ish” tail risk but we know that market crashes occur far more often than a normal distribution would predict. Monte Carlo simulation isn’t helpful in predicting very unlikely but catastrophic events but then, nothing is.

In Antifragile[7], Nassim Taleb says, "[Antifragility] provides a solution to what I have called the Black Swan problem — the impossibility (emphasis mine) of calculating the risks of consequential rare events and predicting their occurrence."

5. Complex scenarios are difficult to model, so they seldom are.

Complex scenarios are difficult to conceive, let alone model. Elder bankruptcy research by Deborah Thorne[6] showed that most of the worst-case retirement finance outcomes (those that end in bankruptcy) are not caused by a single factor, like spending too much on credit cards, but by a complex self-reinforcing cycle of interdependent risks. These numerous complex combinations of risk are unlikely to be modeled.

Here’s an example that would be difficult to anticipate and therefore difficult to generate with a simulation model.

A retiree borrows a reverse mortgage, feeling secure in the fact that it is non-recourse. He knows that his loan can’t be foreclosed unless he moves out of the home, which he doesn’t plan to do. His wife becomes ill and runs up huge medical bills. They spend home equity to pay bills, then run up credit card debt and eventually file for bankruptcy. They can no longer afford to live in the home and when they leave, repayment of the reverse mortgage will be triggered.

Monte Carlo simulation can generate hundreds of thousands of possible future scenarios but they won’t include complex, interdependent risks like this one. On the other hand, Monte Carlo simulations may surprise you by showing scenarios, for example, in which purchasing an annuity actually results in a greater legacy.

7. Simulation can’t predict your future.

I recently wrote about a blog post that suggested that Monte Carlo simulation has no value because a retiree can’t know which of the thousands of possible future paths her future will track. That is absolutely true — your individual path is unknowable — but the argument is irrelevant. That argument is based on the false premise that we run simulations in order to find that path. We run simulations to collect information on the range of many paths.

A retiree shouldn’t look at simulation results, regardless of the number of scenarios simulated, and assume his or her future is in there somewhere. More often than not it will be but a good retirement plan doesn’t rely on that. A good retirement plan should also consider what happens when really bad, improbable things happen.

8. Many Monte Carlo models underestimate risk.

Many, and probably most, Monte Carlo models calculate risk of ruin simply by counting the percent of scenarios that end in ruin. Some scenarios that are counted as successes, however, may have been exposed to significantly greater risk than others. That 95% probability of success is probably best case.

At this point, you may be asking yourself why I recommend a tool with so many shortcomings. One answer is that it has fewer shortcomings than the alternatives. It considers more factors and generates more information. We look at simulation results to get an overall view of the most probable outcomes and the perspective we gain is, like weather forecasts, imperfect but highly useful.

Understanding what will probably happen and what might happen in most scenarios is a great place to start.

The important takeaways are these. Monte Carlo simulation can be a powerful tool for retirement planning because it provides more information than other approaches. Ultimately, however, we must realize that, as Yogi is credited with saying, predictions are really hard — especially about the future. The results are more of a distribution of a ballpark estimate than a single answer but it's more useful to estimate a 40% chance of rain tomorrow than to maintain that we can't know for sure so it isn't worth considering. Monte Carlo simulation will not predict or protect your retirement from "consequential rare events."

The results are also better used to compare the relative risk of one strategy to another than to measure their absolute risk. If simulation tells you that 3% spending is half as risky as 5% spending, then you can be more confident that one is safer than the other than you can be that there is actually a 3% risk that the former will result in ruin.

If this is all a little too confusing, bear with me. You can learn to use the information provided by simulations without a complete understanding of Monte Carlo models. You probably couldn't build a GPS device, either, but you're probably confident using one. Perhaps, you just need to find a planner that will run one for you. Maybe you have a perfectly fine plan built with a different type of model or no model at all and you just need simulation to improve your confidence.

Next time I’ll discuss the relationship between Spending Rules and Simulation.

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REFERENCES

[1] The Retirement Café: Why Retirees Go Broke.


[2] Where is the Market Going? Uncertain Facts and Novel Theories, John H Cochrane.


[3] The Retirement Café: Three Degrees of Bad.


[4] The Retirement Café: Time to Retire the Probability of Ruin?.


[5] Financial Analysts Journal: It’s Time to Retire Ruin (Probabilities) | CFA Institute Publications, Moshe Milevsky.


[6] The (Interconnected) Reasons Elder Americans File Consumer Bankruptcy, Deborah Thorne.


[7] Antifragile: Things That Gain from Disorder (Incerto), Nassim Taleb.

Unraveling Retirement Strategies: Variable Spending from a Volatile Portfolio

 In Unraveling Retirement Strategies: Constant-Dollar Spending (4% Rule), I described retirement funding strategies like the “4% Rule” that base portfolio spending on a calculation made at the beginning of retirement that remains unchanged in real dollars regardless of how the household’s finances unfold over time.

Constant-dollar spending is like the Stephen Colbert joke about a man whose beliefs are constant. He believes the same thing on Thursday that he believed on Tuesday ... no matter what happened on Wednesday.

That doesn't work well for retirement planning, either.

Variable-spending strategies are similar to constant-dollar strategies in that they spend periodically from an investment portfolio but differ in that they spend a periodically updated amount based on portfolio performance – they spend more in good markets and less in bad markets.

This is a huge difference. We have two basic choices in portfolio-drawdown strategies: spend a predictable amount annually and risk depleting our portfolio or spend an unpredictable, possibly painful, amount annually to avoid portfolio depletion.

Spending strategies, including these two, explore ways to draw down a portfolio without outliving it but they do so without considering the expense side of the equation.

Regardless of which of these strategies you choose, you will spend the amount you need to spend after retiring. If you need a kidney operation or a new roof or a check for the IRS, you will pay for those things regardless of what your spending strategy recommends. That will increase your chances of outliving your savings but that risk isn't considered by these "income-side" strategies.

There are many variable spending strategies. I recently attended a webinar in which Wade Pfau identified a half dozen of the better known and in Making Sense Out of Variable Spending Strategies for Retirees[1] he compares several more.

Joe Tomlinson, Steve Vernon and Wade Pfau recently recommended using the spending percentage for Required Minimum Distributions (RMDs) from qualified retirement accounts[2]. Vernon provides a summary of the study in "How to Pensionize Any IRA or 401(k)."[6]

RMD is based on the assumption of a retiree and a spouse 10 years younger. Retirees closer in age to their spouse can perhaps use the Modified RMD strategy and spend 10% more. Your investment company will calculate RMDs for your qualified retirement accounts when the time comes or you can find a calculator online.[3] You are required by tax law to use these calculations on tax-deferred retirement accounts but you can, of course, use them on all types accounts if you choose.

Another strategy is to spend a fixed percentage, say the same 4%, of the new portfolio balance each year, though the safe spending rate actually increases as life expectancy decreases. It makes more sense to spend that gradually-increasing percentage of one’s current portfolio balance each year than to always spend a fixed percentage of a changing portfolio balance. It approaches 10% late in retirement but grows slowly at first.

Most Americans are eligible for Social Security benefits so most have a floor. It may not be an adequate floor in the event that your portfolio is depleted, but it is a floor. The variable spending strategies and the constant-dollar strategies, therefore, technically manage the upside portfolio of a floor-and-upside strategy and will rarely be a standalone strategy.

I recommend, once again, reviewing this strategy in Pfau and Jeremy Cooper’s The Yin and Yang of Retirement Income Philosophies[4]. I particularly recommend the introduction to the work of Blanchett, Mitchell and Frank[6] on dynamic spending at the end of the variable spending strategies review. Their strategy periodically updates the critical assumptions of a retirement plan. (Frankly, I don’t see a rational alternative.)

It effectively says, “When the road in front of you turns or ends, modify your car’s behavior accordingly.”

A light pole oddly stood in the middle of the Sears gravel parking lot in my hometown. Some wise person had painted two arrows on the pole curving away in opposite directions. Below the arrows were the words, “Turn. Go left or right.”

Sounds like sage advice.

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Variable-spending strategies make a lot more sense.

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The challenge with the dynamic spending strategy is that it is mathematically complex and will be difficult for most retirees or even planners to implement. I suspect, however, that you would achieve similar results with any variable spending strategy if you updated your spending percentage annually to reflect decreasing life expectancy (strategies like RMD do this for you) and based the spending amount on your current portfolio balance. Blanchett, Frank and Mitchell point out that asset allocation plays a smaller role.

The Blanchett-Frank-Mitchell study shows that life expectancy plays a critical role in determining a safe spending amount. Life expectancy declines as we age. Some variable-spending strategies, like RMD and actuarial approaches, consider decreasing life expectancy in their calculations while others, like spending 4% of remaining portfolio balance, don't. I recommend you choose one that does — it's a key factor.

To implement a variable spending strategy, choose a variable spending rule that suits your fancy[1]. Which you choose probably has less impact on portfolio depletion risk than the act of recalculating it annually, so long as it incorporates changing life expectancy.

I personally prefer the dynamic strategy, Modified RMD for simplicity, Milevsky’s formula[4], and actuarial strategies[5].

I’ve written several posts on asset allocation and it has been thoroughly discussed in several threads, including Unraveling Retirement Strategies: Constant-Dollar Spending (4% Rule). You won’t go terribly wrong with an equity allocation between 40% and 60% and it’s difficult to prove that another will work better across a broad range of outcomes. The same rules apply to variable spending portfolios.

I recommend a floor to go along with an upside variable spending portfolio to make sure you can survive if the improbable happens.

Constant-dollar strategies tell you to spend the same amount every year and that you probably won't run out of savings over a fixed thirty-year retirement. They don't consider what happens if you do.

Variable spending strategies tell you to spend more when you have more money and spend less when you have less money. The better variable spending strategies also consider remaining life expectancy and tell you that you can spend a higher percentage of your remaining savings as you age. Annual spending isn't predictable but you are unlikely to outlive your savings.

Again, seems like sage advice. Variable-spending strategies are so much more rational that I personally dismiss constant-dollar spending strategies entirely.

Retirees who have a pension, Social Security benefits or have purchased an annuity, which covers practically all American retirees, will actually be building a floor-and-upside strategy and managing the upside portfolio with a variable-spending strategy. Floor-and-upside strategies, however, will focus more on the floor and will likely recommend one higher than Social Security benefits alone are likely to provide.

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REFERENCES

[1] Making Sense Out of Variable Spending Strategies for Retirees, Pfau.



[2] Optimizing-Retirement-Income-Solutions-November-2017-SCL-Version.pdf, Pfau, Tomlinson, Vernon. (Very lengthy, consider [6], instead.)



[3] Estimate your required minimum distributions in retirement, Vanguard.



[4] The Yin and Yang of Retirement Income Philosophies, by Wade D. Pfau, Jeremy Cooper.



[5] How Much Can I Afford to Spend in Retirement?: Spreadsheets, Ken Steiner.



[6] How-to-pensionize-any-IRA-401k-final.pdf, Steve Vernon.



[7] An Age-Based, Three-Dimensional Distribution Model Incorporating Sequence and Longevity Risks, David Blanchett, Larry Frank, John Mitchell.

Retirement Roulette

Phyllis loves to play roulette at the casinos. She knows there are games with better odds but there's something about the large spinning wheel and the big green table with its field of many bets that she finds irresistible.

Phyllis has a roulette strategy – she calls it a "system" – that she adheres to rigorously. Because a fair roulette game is totally random and the odds favor the house her strategy isn't statistically profitable but that isn't something that concerns a typical gambler. Watching a YouTube video of a roulette game, I heard one player say he watches for trends in the random winning numbers (humans are really good at seeing trends, even when they don't exist) and I hear another say that he seems to win a lot with the number 26.

Phyllis' strategy is to place several small bets on the first spin of the wheel and to double the bets each time she loses. After a winning bet, she bets the same amount on the next spin.

She places a bet on red, another bet on 36, a corner bet, and a street bet for each spin. (Watch a few minutes of this YouTube video[1] if you've never seen a roulette game. Notice the multiple bets placed by each player at each spin of the wheel.)

After each spin, she calculates the revised amount of her bankroll and places another set of bets on the next round. Her strategy is to stop playing should she double her initial bankroll and, of course, she will stop playing when she is ruined.

At this point, you may wonder what Phyllis and her roulette strategy have to do with financing retirement. The answer is that the mechanics of her roulette game are somewhat analogous to the way in which retirement should be played. Visualizing retirement funding as a roulette game can demonstrate the process as a whole as opposed to seeing a set of related but independent strategies for income generation, asset allocation, annuitization, and the like.

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Life is like a box of chocolates. Retirement is like a game of roulette.

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We start with a grand strategy, hopefully one that is more profitable than a roulette strategy, and play one year at a time in the same way that Phyllis plays one spin of the roulette wheel at a time. We stop playing retirement when no one in our household is still alive.

It's not a perfect analogy. Phyllis stops playing roulette when she runs out of money but, unlike roulette players, we can't stop being retired when we go broke. We have to figure out how to continue playing retirement until the end, perhaps getting by on Social Security benefits alone – not a pleasant prospect[2].

Now, let's play a game of Retirement Roulette. Over my working life, I have accumulated wealth that I can use to pay for retirement. That wealth is represented by the three stacks of chips in front of me that constitute my "bankroll."

My financial capital (pink), social capital (red) and human capital (blue) at retirement. Image from designinstruct.com.

The first stack of chips represents my financial capital[3]. It represents my wealth held in taxable accounts, retirement accounts, home equity, etc. The second stack of chips represents my human capital, my ability to generate income from labor. Perhaps I can retire as a college professor and still teach a couple of classes each semester for a few years. This stack of chips will shrink over time whether or not I use it as my ability to generate income from labor diminishes.

The third stack of chips represents my "social capital" and includes my Social Security benefits and a small pension I earned from a previous employer. I have three chips. The first represents my pension, the second represents my wife's Social Security benefits and the third chip represents my own Social Security benefits.

My social capital.

On the "Retirement Roulette" table in front of me lies a broad array of potential retirement bets including:

• a bet on a retirement date
• a bet on an amount to spend this year
• a bet on stocks
• a bet on bonds
• a bet on cash
• a bet to claim or delay Social Security benefits
• a bet to purchase an annuity
• a bet to purchase long-term care insurance
• a bet on a legacy for our heirs

I refer to these as "bets" because each has a cost, each has a payoff, and each payoff is uncertain.

I use my strategic retirement plan[4] to guide my bets in much the same way Phyllis uses her strategy to place roulette bets. That plan identifies my strategic objectives – the long-term financial retirement goals I'm trying to achieve. I now need to identify the best tactical moves I can make in the present round (this year) to further those long-term objectives. For example, I have a strategic goal to not outlive my savings so perhaps a good tactic for the current round is to not claim my Social Security benefits, yet.

First, I bet that I have enough retirement resources to retire this year at age 65.

I decide to wager the pension bet immediately because I am 65 years old and, unlike postponing Social Security benefits, delaying my pension claim has no financial benefit. The payoff for this bet is $1,000 of income monthly for as long as I live.

I have determined that the optimal Social Security claiming strategy for our household is for my wife to claim at age 66 and for me to claim at age 70. Since she is now 66, I will bet her Social Security benefits chip now and save mine for the year I turn 70. Of course, I can decide to bet my chip sooner should I need the money.

The payoff for this bet is some immediate income from my wife's benefit and maximum lifetime retirement and survivor benefits for both of us should we live longer than an average life expectancy at the claiming age.

I won't bet the home equity chips right away in case I need those for an emergency later in retirement.

My strategic retirement plan calls for a floor-and-upside retirement strategy so I will add a small pension bet to my wife's Social Security benefits to create the floor. I move chips from my financial capital pile to the pension bet.

After calculating the income from my floor bet, I decide that I will need to spend 3% of my remaining portfolio balance on expenses for the coming year. I move that amount of chips to the spending bet on the table.

I count the number of chips left in my financial assets pile and decide on an asset allocation. I move 5% of the chips remaining in that pile to the cash bet on the roulette table, 35% to the bonds bet, and 60% to the stocks bet. All of my chips are now on the table on eight different bets and they look something like this:

I am actually making 12 bets, not eight, because not buying Long-term Care Insurance (LTCi), for example, is also a bet. It's a bet that I won't need the insurance in the coming year and that I will have both the resources and the health to enable me to make that bet a year from now should I so decide.

I win this "non-bet" when I don't need to claim LTCi in the coming year and the payoff is a year of typically substantial premiums. I lose this non-bet when I do need to make a claim but don't have insurance or when my health deteriorates to the point that I can't qualify for the insurance in the future. I would lose a purchase bet if the insurer raises my future premiums so much that I am forced to let the policy lapse before I need it. And, of course, I lose the bet if delaying the purchase results in significantly higher premiums when I eventually do buy. Retirement bets can be very complicated and understanding them in their entirety is critical.

In Retirement Roulette, we bet all of our chips every year and we make every bet even if the bet is that we should wager nothing on it.

I "spin the wheel" and nature takes its turn. A year later the results are in.

The payoff on my stock bet will be about 8% with a standard deviation of about 12%, meaning that about two-thirds of annual returns will fall between a 4% loss and a 20% gain. The payoff on my bonds bet will be about 3% with a standard deviation of about 3%. My cash bet will return about the rate of inflation, or about zero in real dollars.

My pension bet will pay off $12,000 and my wife's Social Security benefit will pay off about $20,000. My cash will increase by about the rate of inflation but decrease by about the 3% I planned to spend. Of course, expenses are unpredictable and I may actually spend more or less. The "payoff" for the spending bet will be about a 3% loss.

My life expectancy and that of my wife have decreased by a little less than one year. (Life expectancy is a key factor in many retirement decisions.)

And so ends round one.

To prepare for round two I must evaluate the results of all my bets, changes in my life expectancy and my wife's, changes in our health, our expectations for the financial markets going forward, and other critical factors to decide which if any of my bets I should change for the coming round.

How will I bet in future rounds? I won't know for certain until I see how retirement unfolds between now and then, but my plan is to play my Social Security chip when I reach 70. My spending next year might go up or down a little depending on this year's market returns. I may move some chips from the stocks bet to the bonds bet after a really good run for stocks, or vice versa after a poor run, but only if the percentages get seriously out of whack. Most years I will tweak my bets just a little and spin again.

The game will continue as long as one of us survives. Unlike roulette, our game doesn't end if we deplete our bankroll, though our lifestyle is likely to be severely curtailed in that event.

The important perspectives of the roulette analogy are:

• Like roulette, retirement funding has a very large element of uncertainty. This includes the length of our careers, how long we will live, market returns, interest rates, annuity payouts, inflation, discretionary spending and spending shocks, which is to say all of the critical factors are uncertain. Even households who generate retirement income completely with "risk-free" assets will be exposed to expense risk.
• Like roulette, retirement funding is a series of "rounds"(typically years) during which the retiree makes a series of decisions (bets) and the universe responds. These first two characteristics define what game theorists refer to as a sequential stochastic game against nature[5].
• Retirement ends with death; roulette ends when the gambler decides to walk away or is ruined. Retirees can't walk away but they can lose their standard of living.
• Unlike roulette, a retiree plays all her wealth every round. Some bets, like cash, will have very little risk. Bets we don't make are as important as those we do. 
• A "round" typically involves multiple bets that are separate, yet the ultimate result of the round is the sum of the bets won less the sum of the bets lost.
• Critical factors can change from one round to the next and these must be considered when placing next year's bets. Retirement funding is dynamic, not set-and-forget.

Retirement Roulette ties back to my posts on strategic retirement planning; The Opening, the Middle Game and the Endgame[6]; and A Mission Statement for Retirement[7].

Next time, I'll tie these together.

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REFERENCES

1. YouTube video of a roulette game. [click here]
2. The Tightwire Act of Living Only on Social Security, Washington Post.
3. Sullivan and Sheffrin (2003) defined human capital as "the stock of competences, knowledge and personality attributes embodied in the ability to perform labor so as to produce economic value", in other words, our capacity to generate wealth from our labor. Social capital is defined as capital from "social structures" like Social Security and pensions. Financial capital consists of debt and equity.
4. Strategic retirement planning, The Intersection of What's Desired and What's Possible, The Retirement Cafe´.
5. Sequential stochastic games against nature, A Tiny Bit of Game Theory, The Retirement Cafe´.
6. The Opening, the Middle Game and the Endgame, The Retirement Cafe´.
7. A Mission Statement for Retirement, The Retirement Cafe´.

A Random Walk, A Sequential Game, Part 3

In A Model of Retirement Planning, Part 1, I wrote that the challenge of retirement income planning is to best position ourselves to maintain our desired standard of living throughout an unpredictable length of retirement with somewhat-predictable future income but largely unpredictable future expenses. A mighty challenge.

In Adding Risk to the Model, Part 2, I added to the model tolerance toward the risk of losing standard of living, because within a fairly small range of expected income and expenses, some households will choose to spend more early in retirement at the risk of having less to spend late in retirement, and some households will choose the opposite. Some can live with more risk than others.

We need to add one last important characteristic to the top-level model of retirement finance, its “chained state” nature. Retirement finance is not a “set-and-forget” decision that we implement and never revisit. It's a series of moves in a sequential game.

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Retirement finance is not a “set-and-forget” decision that we implement and never revisit. It's a series of moves in a sequential game.

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I often use the sailing metaphor. At the end of a day of sailing – or a year of retirement – we will find that we have drifted off course and we need to correct our heading. We can't just continue using the heading we set at the start.

Game theorists refer to this as a sequential game against nature, meaning that the game is a series of alternating moves in which Player 1 (your household) makes a move and nature (defined in game theory as "a fictitious player having no known objective and no known strategy") responds.

Although personal finances are practically time-continuous, it is easier to think of them as a series of years, or “discrete-time states”, so that’s how we plan. The age of death for a healthy person is unpredictable, but we often think of people retiring around age 65 and living until age 100, or so. In that case, retirement would consist of one to 36 discrete time states representing ages 65 through 100.

 Following is a simple state diagram for a retiree who retires at age 65 and turns out to live to age 76. Of course, life span is unpredictable for a healthy retiree, so we don’t know beforehand if our own chain will contain one state or dozens.

An individual state can be identified by the age of the retiree, so we can use the terms “state” and “age” synonymously in this example. Each state has associated with it information about income, expenses, net worth, remaining lifetime, portfolio balance, desired standard of living, risk tolerance and other critical financial information.

This information is known with the most certainty in the state that is current, in other words, at our present age. For example, we can know our current portfolio balance, interest rates, current desired standard of living, and current risk tolerance fairly well. We can't know with as much confidence what these values will be for next year, and the uncertainty increases every future year.

For example, if state zero represented 2007, the market crash in October of that year might significantly change all future expectations for portfolio balance, portfolio spending, and net worth and it might even affect our decision to delay Social Security benefits. For some households, it postponed the planned retirement date.

The following table illustrates some of the plan's forecasted financial data for each year in the diagram above as of the starting state (age 65). Age 66 data is less certain when predicted at age 65, age 67 data predicted at age 65 is even less certain, etc. (Click to enlarge.)

Large changes in expectations might also result from out-sized market gains, unexpected medical expenses or the loss of a spouse. Our view of the future can change significantly in a short time. In 2006, our forecast for 2008 would not have included a 55% market crash and a housing crash.

Also, note that the state data we are forecasting are moving targets. Income changes when we claim Social Security benefits. Life expectancy decreases at each new state. Spending, our desired standard of living, tends to decline with age. The sustainable withdrawal percentage from our savings portfolio increases with age. The purchasing power of a dollar changes. Our forecasts constantly change, but so do our targets. We can't simply say we're going to spend $50,000 a year in retirement or receive $50,000 of income annually in retirement because those numbers change over time.

What about the past?

This series or “chain” of discrete states (ages) has the characteristic that the values of next year's state are dependent only upon the information provided in the current state and what happens this year. Anything that happened before reaching the current state is no longer relevant. (Mathematicians refer to this as a discrete-time Markov chain.)

A Monopoly board provides a simpler example of a Markov chain. If your race car or thimble is currently parked on Illinois Avenue, where you will end up next depends solely on where your thimble or race car currently sits and the next roll of the dice. It doesn't matter if you got to Illinois Avenue by sitting on New York Avenue and rolling a five or States Avenue and rolling eleven. That won't affect where you will move next.

This is an important concept that points out, for example, the absurdity of a fixed sustainable withdrawal strategy basing how much you can spend in year 12 of retirement on how much savings you had at the beginning of retirement. If you reach year 12 of retirement with a half million dollars in your savings portfolio, it doesn't matter if you got there by starting retirement with $1M and depleting half of it, or by starting retirement with $250,000 and doubling it. All that matters is where you are now and what happens next.

This is also an important concept in retirement planning because the states you “land on” will be a random walk through retirement-wealth “state space” resulting from those unpredictable incomes, expenses, market returns, and lifetimes, etc.

(State-space is simply the set of all possible future states of a dynamic system – or all possible states of retiree wealth in this explanation. In the simple game of tic-tac-toe, for instance, there are 765 essentially different states that can be reached. The state space for a coin-toss consists of only a head and a tail. There are only two possible future states. In reality, there are an infinite number of possible wealth states for a retiree and time is continuous. It simplifies the explanation, however, if we imagine time in discrete years (snapshots) and a finite number of essentially-different wealth states.)

The state diagram above shows the path moving forward in a straight line, but your path will actually wander through wealth “state space” depending on the draws from those random variables, incomes, expenses, market returns, etc., as illustrated in the following diagram.

When you reach the darker-blue state at age 67 in the above diagram, for example, it won't matter how much or how little wealth you had at ages 65 or 66. Those gray states and the information they contained will no longer be relevant. At age 67, we can only guess the future positions of the light blue states and when we reach age 68 and gray-out age 67, our predictions of the position of future light blue states may change then, perhaps dramatically.

This Markov-chain, or "Markovian", nature of retirement finance has a number of implications for the retirement model. First, since year three's finances depend solely on year two's financial state plus some unpredictable events, and year two's finances are also unpredictable, predicting our future finances with any accuracy quickly becomes untenable. We are trying to predict where we will be in the future by moving an unpredictable distance and direction from an unknown starting point.

Our ability to predict future states decays quickly. We can perhaps predict a year in advance with a little accuracy, but this foresight decreases with each year beyond that and quickly becomes unpredictable. No one predicted the 2008 financial disaster in 2006.

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Our ability to predict our financial future decays quickly. No one predicted the 2008 financial disaster in 2006.

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Second, thinking of retirement as a Markov chain that renders past information irrelevant means each new year of retirement becomes a new puzzle to solve, possibly quite different than the one we faced the previous year, so dynamically updating our plans becomes an obvious necessity. It also rids us of the notion that our financial situation years ago remains relevant.

The top-level model for retirement finance, then, should look something like this.

"Retirement finance is a random walk of unpredictable length ranging from one year to several decades. At a given age, only the present financial data are known with any certainty. Data from previous years can be known but are irrelevant. The reliability of forecasts of data for future states decays rapidly with time and forecasts beyond five years are probably sheer conjecture. The key determinants of retirement wealth are random variables: income, expenses, life span, and risk tolerance. Retirees can choose to spend more or less, within a reasonable range, depending on their risk tolerance. Retirees with high risk tolerance can increase spending early in retirement and consequently increase the risk of a lower standard of living in late retirement while more risk-averse retirees can decrease spending early in retirement and consequently decrease the risk of a lower standard of living in late retirement.”

Retirement finance is a random walk along a Markov chain, or to a game theorist, a sequential game against nature. Each year we make forecasts based on what we know (our current financial status and the financial environment), what we expect to happen in the future, and what unexpected outcomes we believe we might experience in the future (risks). We make our move based on this analysis and our risk tolerance. Then nature takes its turn and we repeat.

Once we have a high-level model of retirement finance, we can start to think about how to plan for it. Surprisingly, I have been able to find very little literature that addresses the best way to develop a plan. A good place to start, I think, would be to answer this question: How can you know a good plan when you see one?

Positive Feedback Loops: The Other Roads to Ruin

Positive feedback like, “Nice post!” is always welcome, but positive feedback that gets stuck in a loop can have catastrophic results.

The most memorable experience of positive feedback is the head-splitting screech that fills an auditorium when the PA system experiences feedback. Someone speaks into the microphone and the sound is amplified. Amplified sound from the speakers is picked up by the microphone and amplified again through the speakers and back to the microphone and . . . well, by about the fifth cycle through the amp everyone in the room is holding their hands over their ears and mouthing silent profanities.

The most common experience of a negative feedback loop is your home thermostat that reduces heat when the temperature gets higher. You’d think that a screeching PA system would be negative and a thermostat controlling your home heating and cooling would be positive, but that isn’t how feedback loops are named.

According to one website, a more formal explanation of the difference is this:

“Positive feedback loops enhance or amplify changes; this tends to move a system away from its equilibrium state and make it more unstable. Negative feedback loops tend to dampen or buffer changes; this tends to hold a system to some equilibrium state, making it more stable."

So, when does a retirement income system “tend to move away from its equilibrium state and become unstable”?

To answer that, I'll tell a story about a retired couple in 2007, because I was raised in the South where every question is answered with a story. My story is not strictly true (a long-standing tradition of Southern stories). I will build a composite retired household from personal observations of multiple actual households from that time, some of whom weren't really even retired but, as my grandfather would’ve said with a grin if he were telling this story, “they might'a been.”

Jim and Linda retired in Omaha in 2005. The family seemed well-to-do, but they lived in a large, heavily mortgaged home. Jim had built a small fortune over his working career investing in rental homes, also heavily mortgaged, and most of their retirement income came from those properties. They both had retirement accounts invested in index funds worth about $200,000 and significant income from several CD’s and a money market fund.

Life went pretty much as planned until late 2007 when the stock market began a 50%, 18-month drop, interest paid on safe investments dropped to zero and, worse for Jim and Linda, the real estate market tanked, all simultaneously. Though most people would eventually recover from these crises, Jim and Linda wouldn't – a financial crisis can be a very personal thing.

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Market losses aren't the only road to ruin in retirement.

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With the rental income gone and the CD's and money market funds now paying a pitiful fraction of one percent, Jim could no longer afford the mortgage on his home plus the mortgages on fifty or so rental properties so he let the unprofitable rentals go. There were no buyers, so “letting go” meant skipping mortgage payments until the banks foreclosed.

The family’s rental business had drifted into a positive feedback loop wherein foreclosed properties reduced income, which reduced their ability to pay other mortgages, which resulted in more foreclosures, which resulted in even less income. It didn't stop until all the properties, including their home, were foreclosed. In less than a year, Jim and Linda's once-shiny finances looked like PA system feedback sounds.

The couple’s plan had assumed that their portfolio of rental properties was well diversified. Sure, a few of the fifty properties might fail from time to time, but what were the odds that a catastrophic number of them would fail in short order? Incidentally, this is the same assumption that led to the Wall Street collateralized mortgage obligations crisis on a much grander scale and as Jim, Linda and several Wall Street giants soon learned, the correlations had been much higher than they had believed.

Jim needed to sell their stocks, intended to fund decades of retirement, at lower and lower prices as the stock market continued its collapse. The stock market would recover years later, as stock brokers promise it always will, but Jim and Linda wouldn't participate in that recovery. Their stocks had long been sold. The stock market had also entered a positive feedback loop with selling encouraging more selling for a year and a half.

Their retirement planner had told them that they could safely spend 4% of their portfolio value each year, or about $8,000. There was a small chance, around 5%, that a series of poor returns early in retirement would result in their outliving their savings, but an even smaller chance if they spent less when their portfolio declined in value. Unfortunately, they did realize that unlikely poor performance right after they retired.

Jim, Linda and their planner had assumed that spending might need to be reduced during a bad market spell. (We say “spell” in this context a lot in Southern stories. It’s a very versatile word. We can sit for a spell, Uncle Howard can have one of his spells, or in Louisiana we might even cast one.) What they hadn’t considered is that forces other than market volatility – like expense surprises and lost income, for example – might preclude their ability to make those needed spending cuts.

Each year that Jim and Linda spent more than planned from their portfolio increased their probability of ruin. The continual shrinking of their portfolio value as the market fell increased it even more. Soon that probability of ruin was a lot more than the original 5%. An example is provided in the table below.

Their portfolio spending strategy had drifted into a positive feedback loop (that's three if you're keeping score), wherein every year that they overspent from their savings they increased the risk of portfolio ruin, reduced their capacity to recover when the market did, and decreased the amount of spending that would be considered safe the following year, increasing the probability that they would need to overspend yet again. The way to escape this loop would have been to reduce spending from their portfolio. Without the rental income and fixed income interest, they couldn’t.

The good (and coincidentally true) ending to this story is that today, eight years later, all of the households in this composite have recovered to some degree, though one middle-aged couple divorced under the strain. The investment portfolio is gone, as is the real estate wealth, but they have a "spell" to recover because, as I said, none of them were actually retired. The outcome would have been worse had they been. Younger people have more risk capacity and remaining human capital.

Most people survived and completely recovered from these simultaneous stock, interest rate and real estate crashes, but Jim and Linda did not. Had their investment properties not simultaneously tanked, they would have easily survived the bear market and kept their home.

What types of spending shocks can initiate a positive feedback loop? There are several candidates. A late-life divorce can be financially devastating and, though you may imagine them rare, they are not. I am aware of three among my circle of acquaintances over the past five years. (One gentleman was 80 and he married again within a year.)

Unexpected medical expenses, particularly onerous with dementia (see Costs for Dementia Care Far Exceeding Other Diseases), aren't uncommon. Two families within my circle of acquaintances are retired and financially stressed by the high support costs of their grown children who have medical problems. A combination of small underestimates of spending, expected market returns, and longevity could also do the trick in an otherwise survivable economic downturn. (As I showed in 100% Certain That We're Not Sure, there is no certainty that you picked the correct portfolio spending rate to begin with. You may already be overspending.)

Research shows that well-diversified retirement portfolios are unlikely to completely fail as a result of market volatility. (See, for example, Larry Frank.) The portion of the portfolio that is unlikely to disappear is sometimes referred to as a “soft floor.” Stout and Mitchell (download PDF) showed that retirees who reduce spending when their portfolio is stressed can reduce the risk of ruin by 30% to 40%.

These studies don't address spending volatility, however, so they don't predict what happens if retirees, like Jim and Linda, are unable to make the needed spending reductions. Mean reversion and diversification won't save those who can't due to divorce, dementia, debt or dependents.

The positive feedback loops are present in these studies if you look for them carefully. Observe what happens to a portfolio in a constant-dollar spending model and you will see that when a portfolio declines in value and the retiree keeps spending a constant-dollar amount, she increases the risk of portfolio ruin going forward. When this happens several years in a row, the probability of ruin grows quite quickly. In the following table, a 65-year old couple in 1974 with a 50% equity portfolio wishing to spend $52,000 from a $1M portfolio each year would see their probability of ruin nearly triple in five years. (Probability of ruin calculated using Milevsky formula.)

Year	Return on 50% Equity Portfolio	Portfolio Balance	Withdrawal Rate for $52k Spending	Probability of Ruin
Initial		1,000,000		5.0%
1974	-8%	872,160	6.0%	5.2%
1975	-11%	729,942	7.1%	8.5%
1976	18.5%	803,362	6.5%	14.4%
1977	6.5%	800,200	6.5%	10.6%
1978	-4%	718,272	7.2%	14.4%

The table above demonstrates a positive feedback loop that would have developed had the retiree felt it was safe to continue the same amount of spending yearly as the market declined (it isn't), but it would also have developed if the retiree hadn't been able to reduce spending.

Positive feedback loops disappear in dynamic-updating models that assume that the retiree will be able to cut spending when necessary. Since there are no unmet liabilities (overspending) in these models, there are no positive feedback loops. The difference between probabilities of ruin between the two types of models offers an estimate of the risk of not being able to reduce spending.

Stout and Mitchell found that adjusting spending reduces risk of ruin 30% to 40% compared to constant-dollar spending, so we can infer that not adjusting spending is about 43% to 67% riskier than adjusting it. The risk that we will deplete our portfolio because we can't adjust our spending is that 43% to 67% probability times the probability that we won't be able to reduce spending. The probability that we can't is far more difficult to estimate.

We can, however, ballpark that probability by considering our financial risk capacity. If we have lots of money saved relative to our spending needs, we have lots of risk capacity and the odds are better that we won't find ourselves unable to reduce spending from our portfolio when needed. The less savings we have relative to our spending, the greater the likelihood that we may be unable to reduce spending when necessary and the greater the chances that we will trigger a positive feedback loop that ends in ruin.

(Another way to look at risk capacity is your portfolio spending rate. If you only need to spend 1% to 2% annually, you're far safer from spending crises than if you need to spend 4% or more annually.)

Most Southern stories have a moral and this one is no exception. Market volatility isn't the only road to portfolio depletion. Studies that ignore spending risk understate the probability that a retiree will outlive savings.

Here's my intuition: retirees are more likely to outlive their savings as the result of a spending crisis that triggers a downward, self-feeding spiral than they are to outlive their savings as a result of slowly overspending 4% a year instead of 3.5%, especially if they dynamically update their plans. I readily admit I don't have data to back that up, so take it for what it is. I also suspect that long-term persistent overspending and sequence risk are far more likely to result in a permanent loss of standard of living than outright ruin.

Retirement income systems are vulnerable to positive feedback loops that can preclude the option to reduce spending in times of portfolio stress. Nor is retirement uniquely the domain of positive feedback loops. My personal experience with pre-retirement households that ended in personal bankruptcy displayed evidence of loops. Long bouts of unemployment or disability trigger them; consumer debt, divorce and foreclosure combine to finish them, in good stock markets and bad.

Another impression I have is that most of us have far more confidence in retirement models than our understanding of them merits, and "us" includes financial planners. I appreciate models as research and learning tools and as tools that can support a good retirement plan, but I've been building and studying them for perhaps 20 years and the list of their weaknesses is long. They can't predict an individual household's future and they are not by themselves a retirement plan (see Michael Kitces' recent post.)

Positive feedback loops are a characteristic of chaos theory. Is our retirement income system a chaotic system that is normally in equilibrium but can unpredictably be drawn into the influence of a point attractor like ruin? I'm not certain, but I have been doing some research and having some interesting discussions. Check out Retirement Income and Chaos Theory.

The Chain of Longevity Risk

I've spent the last several weeks working on some interesting portfolio survival research with my son and daughter, so my posts have been a bit few and far between. My apologies. Cary and I realized one day this summer, over a local craft beer after a round of sporting clays, that retirement portfolio survival and the medical research he does are largely the same research problem. I hope to have something here on my blog about our findings in a few weeks. In the meantime, here are some thoughts about portfolio survival in general.

Longevity risk is the risk that a retiree will outlive his or her retirement savings. It develops in four stages as we make decisions about funding retirement.

Let’s consider those risks by imagining a retiree who splits his retirement savings portfolio in half on the day he retires. The first "legacy" portfolio is intended for his heirs and the second “funding” portfolio is intended to fund his retirement expenses.

To simplify the example, let’s assume he invests both identically in the same 40%-equity index fund on the same day. The only difference between the funding portfolio and the legacy portfolio is that he will spend annually from the funding portfolio and then re-balance it to 40% equities. The legacy portfolio will remain untouched to be left to his estate.

A retiree can pretty much avoid longevity risk altogether by purchasing life annuities or TIPS bonds. There are plenty of good reasons to invest at least some of our savings in stocks and bonds, though, and that decision leads to the first risk, known as market risk. Market risk refers to the volatility of stock prices over time. Once we invest in risky assets like stocks, outliving our savings becomes a possibility.

We can mitigate market risk by reducing our equity exposure or we can completely eliminate it, by purchasing life annuities or TIPS bonds. Our imaginary retiree has decided to mitigate market risk in both portfolios by investing only 40% in equities, but he has not avoided market risk altogether.

If this retiree never spends from or saves to either portfolio, those portfolios will have equal values at the end of retirement. We don't know what that value will be, however, because both are exposed to unpredictable market risk. We only know that they will be exposed to identical market risk and that their "terminal value", or value at the end of life, will be the same.

When a retiree begins to spend from her funding portfolio, the outcomes of those two portfolios go their separate ways. No matter how little our retiree spends each year, so long as there is net spending, there is no future in which the terminal value of the legacy portfolio will not be larger than the terminal value of the funding portfolio at the end of retirement for two reasons.

The first cause is obvious – her funding portfolio will be smaller  because she is spending some of it – but the second cause, path-dependent risk, can make her legacy portfolio's terminal value larger or smaller. The funding portfolio will always, however, have less value than her legacy portfolio, again because she is spending some wealth and never saving, but path-dependent risk can leave the funding portfolio fatter or thinner than it would have been with no path-dependent risk.

Path dependence refers to the fact that, once we begin spending from a volatile portfolio, the order of market returns can change the portfolio’s value. A buy-and-hold portfolio has no path dependence (“Path dependence” means the outcome depends on the path we take to get there, which in this discussion refers to the order of annual portfolio returns.)

Let me provide a quick example to explain path dependence. Assume that over the next five years, the stock market will provide the following returns in the following order: 5%, -7%, 9%, 3% and 4%. If we invest $1,000 in this market at the beginning and neither buy nor sell additional shares, we will end up with $1,140 five years later, no matter which order those returns occur.

If we spend $30 at the beginning of each of the five years, however, the order of returns does matter. There are 120 different ways (5 factorial) those five returns can be ordered and each will provide a different outcome. The outcomes will range from $966 to $988, but always less than $1,140. Once we spend from or save to a volatile portfolio, the outcome is path-dependent.

Note that in none of these 120 permutations is our account balance depleted. Path dependence isn't the same as risk of ruin and if we are only spending 3% annually ($30), it is very unlikely that we will exhaust our savings.

Some refer to path dependence as “sequence of returns risk” but the term isn’t always used in that way, so I prefer to avoid it whenever possible. If returns are experienced with the highest gains early in retirement and the lowest gains toward the end, this path dependence helps our portfolios over time and if returns are experienced with the worst returns early in retirement, path dependence hurts our portfolio.

The best possible outcome is achieved when our market returns are ordered from best to worst. The worst possible outcome is the reverse. With 30 years of annual market returns over a long retirement, the odds of experiencing the best or worst outcome are literally astronomical (1 in 30 factorial, each – there are fewer than 30 factorial stars in the visible universe).

The source of path-dependent risk is selling in the spending phase of retirement finance and buying in the accumulation phase. We have no idea what price we will receive for the securities we will sell (or buy) in the future and that price risk is path-dependent. TIPS bond ladders held to maturity and life annuities have no path dependence risk because we know their future values relatively accurately.

(As an aside, savings portfolios during the accumulation phase also have path-dependence risk because we don’t know the future price at which we will buy equities. A lot less attention is paid to path-dependence in the saving phase because it doesn't lead to portfolio ruin. It does, however, greatly impact wealth accumulation.)

So far, our retiree’s legacy and funding portfolios are both exposed to market risk, and the funding portfolio is exposed to additional risk (path-dependent risk) once she starts spending from it. Note that this risk is introduced by the retiree’s decision to sell shares. Path dependent risk is not market risk, cannot be diversified away like market risk, and therefore we can’t be compensated for it. In general, more risk means a greater expected return, but the market doesn’t compensate us for taking path-dependence risk.

Our retiree will make another decision that affects path-dependence risk, how much to spend annually. The more she spends each year, the more she exposes her portfolio to that selling-price risk each year and the more path dependence risk and risk of ruin she accepts. Simply said, a 4% “sustainable withdrawal rate” is riskier than a 3% rate.

The term “sequence of returns risk” is also sometimes used to refer to the probability that a retiree will outlive his savings, which I refer to as "risk of ruin." Path dependence doesn’t cause a retiree’s portfolio to fail, at least it is not the proximate cause. Refusing to reduce spending when our portfolio declines in value causes portfolios to fail is the proximate cause of portfolio failure. This is not a market risk or path-dependence risk, but a poor decision on the part of the retiree. If your portfolio declines significantly in value and you don't start spending less, you risk ruin.

Most spending strategies, like ARVA, constant-percentage spending and "RMD" rarely or never deplete a portfolio because they reduce spending as a portfolio declines in value, lowering the risk of ruin. Constant-dollar spending is the exception.

I wrote a post some time ago entitled, "When You Have Less Money, You Probably Ought to Spend Less", showing that portfolio failure occurs under the (absurd) assumption that a retiree will continue to spend the same amount from his portfolio every year, even when it becomes obvious that the portfolio will soon be depleted. This is an interesting technique to use in research, but it is not a realistic retirement spending strategy. We sometimes refer to this as “constant dollar spending.”

That post also shows that retirees who spend a reasonable constant percentage of remaining portfolio balance each year will not deplete their savings. Their portfolio will eventually recover and spending can increase.

The  “RMD” spending strategy avoids ruin, as well, by dividing the remaining portfolio balance by your remaining life expectancy to calculate a safe withdrawal amount, similar to the manner in which the IRS calculates required minimum distributions for IRA's. Waring and Siegel's ARVA strategy (download PDF) does something similar. Both strategies reduce spending when a portfolio is faltering. In fact, constant-dollar spending is the only widely acknowledged spending strategy that results in portfolio ruin under reasonable spending assumptions.

The third layer of risk in the chain of longevity risk is that of portfolio ruin. It is introduced when a retiree decides to keep spending the same amount after significant portfolio losses. Rational, knowledgeable retirees will reduce spending when their portfolio wealth dwindles dangerously low, but they expose themselves to the risk of a permanent reduction of spending if they wait too long to adjust. (This is a key reason I recommend dynamic spending and annual adjustments. Small, annual adjustments are easier to tolerate and help avoid larger, permanent adjustments by limiting damage.)

To summarize, our decisions can lead us down a chain of retirement wealth risk. It begins when we decide to invest some of our savings in equities. We increase risk by allocating more of our portfolio to equities and decrease it by allocating less.

The next step is our decision to spend from our savings portfolio. Spending more raises the risk and spending less lowers it.

The final step in the chain of risk depends on the decisions we make when our portfolio dwindles in value.  Path-dependence can lead to portfolio ruin, but it probably won't if we lower spending when our portfolio is stressed.

Each step we take, we add more risk. Except for the final, "overspending" step, these can all be reasonable risks to assume. Understanding them can help retirees understand how much of each risk they should accept.

Retirement Expenditures and Costs of Retirement

Some great questions and comments about my previous posts on spending in retirement, beginning with Spending Typically Declines as We Age, suggest that I should add a bit more to my explanation. Or as Ricky Ricardo might have said, "I got some 'splainin to do."

Will the cost of retirement decline as you age?

The fact is I don't have any idea how much you will spend late in retirement, nor does anyone else. I can't predict what a household's finances will look like in two or three decades (which is why glide path discussions don't much interest me). My arguments about declining expenses as we age and dynamic updating are about how much you can spend now based on what you now know, not about how much you will spend later in life.

(Reminder to readers: Hover your mouse pointer over yellow text for further explanation. Double-click any chart to see a larger version. Orange text is a hyperlink. "PDF" denotes that clicking will download a PDF of the referenced document.)

The Banerjee and Blanchett studies show that retirement expenditures typically decline with age. Expenditures, however, are not the same as the generally accepted definition of “cost". Think of expenditures as consisting of non-discretionary spending (“basic costs") and discretionary expenses (“lifestyle costs”). In fact, Blanchett showed that the group of retirees with high net worth and low spending are the ones most likely to experience an increase in expenditures, not because their costs go up in many cases, but because at some point they realize they can safely spend more money on their lifestyle than they have been.

No one knows if your spending or your costs will decline as you age, but these studies (and many others) show they are very likely to. Banerjee shows that expenditures decline for two out of three retired households. That is the best initial assumption until experience with your actual retirement results indicates that you are on a different track. (You can refine that initial assumption, as I explained in Retirement Spending Assumptions and Net Worth.)

Is it dangerous to assume that costs will decline?

Not really, and for two reasons. Theoretically, using this approach, if we assume costs will decline and they don’t, we will spend money early in retirement that we might come to need late in retirement. That’s a risk.

It's important to note that the risk of overspending early in retirement isn't exclusive to a plan that assumes decreasing spending. 

But, Banerjee showed that spending declines for about 66% of retirees and increases for about 16% in real dollars. If many of the 16% of retirees who eventually spend more do so because they realize they can afford to, then the danger zone is the 18% chance that spending will remain flat.

However, assuming declining costs in order to provide the most accurate assessment of how much money a retiree can spend today isn’t a one-time calculation, at least it shouldn't be. These calculations should be made annually (see Dominated Strategies and Dynamic Spending). A retiree who initially assumes declining expenditures but ends up in the 18% or so of retirees who don’t see declines in spending should quickly notice the divergence from plan and correct spending within a few years. Annually adjusting spending and assumptions about future spending should should provide for a quick and relatively smooth correction. This is the first way we hedge the risk of assuming declining expenditures.

The second hedge is control of our discretionary spending. We can budget discretionary spending to target a planned decline in spending as we age to increase the probability that our spending does, in fact, decline as we assumed it would. In other words, we have some control over those spending declines. As Blanchett shows, the larger the portion of our budget that consists of discretionary expenses, the more our spending is likely to decline with age. If your spending is largely non-discretionary, then your expectations for spending declines should be modest from the beginning.

There are other arguments for assuming flat spending, including building in a margin of error and having the excess available to pass to heirs. Perhaps the first argument is a matter of personal choice, but I prefer to make the best prediction that I can of future expenses and allow for a margin of error separately. I like to understand both the expected costs and the risk, and not have risk tossed in as an afterthought.

Assuming flat spending as a safety margin is, after all, quite arbitrary. Why not assume a half-percent annual increase in spending, instead of flat spending? Without studies like Banerjee and Blanchett, most retirees and planners couldn’t identify the magnitude of that margin, let alone determine if that is the correct safety margin. Regardless, in my opinion, the risk of running out of savings should be addressed in the floor portfolio, not as additional margin in the risky portfolio.

I have a similar concern with planning legacies as an afterthought of spending, first because I believe that any serious concern about a legacy deserves its own plan and, second, because Scott, Sharpe and Watson (PDF) have shown that planning with “reserves” (hedging sequence of returns risk with over-saving) can be very costly.

In my next post, Retirement Expectations: A Reality Check, I'll write about what we should hold as reasonable expectations of retirement. Hope to see you there.