Saturday, August 11, 2018

The Critical Factors of Portfolio Ruin Aren't Predictable

Probability of ruin and sequence of returns risk are probably the most widely-discussed topics in all of retirement finance and perhaps the least understood.

Probability of ruin is not sequence of returns (SOR) risk. The sequence of portfolio returns we experience after retiring is one determinant of premature portfolio depletion (ruin) but so are life expectancy, the market returns, themselves, the volatility of those returns, the amount we choose to periodically spend and the value of our portfolio.

For a given sequence of returns, the probability of prematurely depleting our savings increases if we expect to live longer or spend more, start out with a smaller portfolio, receive better average market returns or experience less volatility of those returns. As I will explain below, some of these factors have a significantly larger impact on expected terminal (end-of-retirement) wealth than others.

The fact that some of those key variables, our life expectancy and the size of our portfolio, invariably change as we age tells us that probability of ruin also changes as a result of aging. The amount we need to spend annually might also change over time, as might our expectations of future portfolio returns and these will also alter our updated estimate of probability of ruin.

But, the size of our portfolio and our life expectancy are certain to change as we age. They are critical factors of portfolio survival and I suspect nearly everyone would agree that he or she can't know how much money will be left in the retirement-funding portfolio in 10 or 20 years or whether he or she will live that long.

This should dispel the notion some have that a 95% probability of success at the beginning of retirement remains 95% throughout retirement. It probably changes the next year, perhaps meaningfully. That also means that spending 4% of initial portfolio value could become far riskier or far less risky as we age.

“Sequence risk” is introduced when we periodically spend from or invest in a volatile portfolio of stocks and bonds. If we plan to sell stocks every year for the next 30 years, we have no idea today what the selling price will be when those 30 times arrive. That uncertainty of future selling prices creates sequence risk.

Notice I said, “or invest in a volatile portfolio.” When we are accumulating a retirement portfolio with periodic stock purchases before retiring, we don’t know future purchase prices today, either, and that uncertainty also creates sequence risk.

The best way to see the cause of sequence risk is to look at what happens when it isn’t present. Any given thirty years of market returns, for example, will result in the same terminal portfolio value for a buy-and-hold strategy regardless of the order of those returns.

Imagine three years of portfolio returns of 10%, -7% and 12%. These equate to growth rates of 1.1, 0.93 and 1.12, respectively. Multiply those in any order and you get a three-year growth factor or 1.146.  One dollar invested returns $1.15 after three years. The sequence of the returns doesn’t matter.

When you add (save) or subtract (spend) numbers from each of those years, however, no matter where those numbers come from (constant-dollar spending, constant-percentage spending or whatever) the order of the sequence does matter. This is sequence risk. We see sequence risk when we periodically spend from or invest in a volatile portfolio. We see no sequence risk with a buy-and-hold portfolio, so the sequence risk comes from either periodic savings or periodic withdrawals.

The critical factors of portfolio ruin aren't predictable.
[Tweet this]

This periodic spending, if too large, can result in depleting our portfolio after retirement, so we are exposed to both sequence risk and a “risk of ruin.” Losing 100% of a savings portfolio, however, is extremely unlikely and while we save for retirement we have sequence risk but almost zero probability of ruin.

So, probability of ruin and sequence risk aren’t the same thing. A poor sequence of returns combined with unsustainable spending can lead to ruin after retirement but a good sequence of returns decreases probability of ruin given the same average return.

The cost of sequence risk is lost compounding of returns. When we have a losing year with a buy-and-hold portfolio, we lose money. When we spend from a volatile portfolio we also lose money during that same losing-market year but our portfolio balance further loses the money we spend plus all potential future compounded gains on the amounts we sold.

Losses hurt more when we spend from a volatile investment portfolio than when we buy and hold. This is why it takes longer for a spending portfolio to recover from a bear market than it takes a buy-and-hold or accumulation portfolio.

(It is often noted that the market recovered fairly quickly after the Great Depression when dividends are considered. A buy-and-hold portfolio would have, too. An accumulation portfolio would have recovered even faster as cheap stocks were subsequently purchased. But, a retiree's spending portfolio would have recovered much more slowly, assuming the portfolio had survived, of course.)

Losses early in retirement hurt more than later losses because those earlier losses leave less capital to compound over time. As Michael Kitces has explained, good returns late in retirement aren't helpful if your portfolio doesn't survive long enough to see them.

The best possible sequence of your annual portfolio returns would result if those returns happened to materialize ordered from best annual return in the first year to worst return in the last. The opposite order would be the worst. That’s why we’re warned that significant portfolio losses early in retirement are the most severe.

Of course, we have no control over the sequence of returns we receive nor can we predict the sequence.

Sequence risk never completely goes away. It is present in a 30-year retirement (and greater in the early years) and it is present in a 5-year retirement (and greater in the early years). Note that a 30-year retirement will eventually become a 5-year retirement if we live long enough.

The challenge of savings decumulation is to optimally spread one's portfolio over one's remaining lifetime but a healthy individual's lifetime is unpredictable. Will sequence risk be reduced when a 60-year old reaches 85? That depends on how much longer the 85-year old will live, how much of her wealth remains and how much she will spend. It requires a new calculation of safe spending based on these new variable values.

A reduced range of life expectancy reduces that component of risk compared to 25 years earlier. However, the amount of wealth we will have 25 years into the future is wildly uncertain. If the retiree's portfolio performs well, she may reach age 85 with reduced probability of ruin compared to age 65 because she has greater wealth and fewer years to spread it over. If her portfolio performs poorly, however, she may reach age 85 with fewer years to fund but far less wealth to fund them and, therefore, increased probability of ruin.

Many SWR analyses suggest that risk decreases because the safe withdrawal percentage increases as we age. Those analyses estimate a safe withdrawal rate when a retiree experiences a 30-year retirement beginning with initial savings of say, a million dollars, and an SWR for a 10-year retirement beginning with the same million dollars.

Risk then appears to decrease with age because the analysis assumes the retiree will have the same million dollars with 10 years remaining as he had with 30 years remaining.  But, in real life there is no guarantee that the retiree will still have a million dollars after 20 years.

An SWR model of historical market returns since 1928 with 4% spending produced a maximum TPV after 20 years of $10.8M and a minimum non-zero TPV of $106K. With continued 4% spending, the former scenario would clearly have a far lower probability of ruin than the latter after 20 years. Add the risk of future portfolio value back into the mix and sequence risk doesn't diminish.

Said differently, the percentage of your remaining portfolio that can be safely spent increases as you age because your life expectancy decreases. The problem is knowing "the percentage of what?" Spending 7% of $106K isn't better than spending 7% of $10.8M even though 7% is larger than 4%.

Probability of ruin doesn't always decline with time but it does change as our savings balance and our remaining life expectancy change. We need to recalculate periodically.

We can estimate a terminal portfolio value (TPV), say after 30 years, for a given sequence of returns and we can estimate how often that will deplete the portfolio in less than 30 years (probability of ruin). These are two different measures. TPV says, "you might have this much money left at the end of retirement", while probability of ruin tells us the likelihood that amount will be more than zero.

The EarlyRetirementNow blog[1] estimates the impact of sequence of returns on the sustainable withdrawal rate* and summarizes its findings: "Precisely what I mean by SRR matters more than average returns: 31% of the fit is explained by the average return, an additional 64% is explained by the sequence of returns!" 

However, the sequence of returns explains 100% of portfolio ruin. To illustrate, we can take a series of portfolio returns that result in premature portfolio depletion (ruin) and rearrange those exact same returns in a better way that avoids premature depletion. We simply swap some of the poor early returns with better late returns. As I explained above, doing so doesn't change the average portfolio return we would receive but it does increase the resulting terminal portfolio value. The difference between success and failure is the sequence, not the returns, themselves.

Focussing on portfolio ruin, however, can be misleading. Sequence risk can dramatically decrease consumption (standard of living) in retirement without resulting in portfolio depletion. (This happens when you end retirement with a small portfolio value that is greater than zero.)

As Jason Scott told me years ago, probability of ruin treats a scenario that successfully funds 29 years as a failure and a scenario that successfully funds 50 years of retirement as no better an outcome than one that funds 30 years. I would add that for a retiree who lives less than 30 years, all three scenarios are winners. It's important to also model life expectancy.

Readers often comment that variable-spending strategies eliminate sequence risk. They don't but they can lower the probability of portfolio depletion by not foolishly spending the same fixed amount annually when savings dwindle. Reducing the chances of depleting the portfolio, however, comes at the expense of lower spending.

Think of it this way: a poor sequence of returns reduces our wealth. We can ignore that reduced wealth and keep spending the same constant amount, risking portfolio depletion, or we can spend less (variably) when our savings are stressed. Either way, we have less wealth so variable spending didn't eliminate the consequences of a poor sequence of returns. It simply changed the impact of sequence risk from portfolio depletion to a lower standard of living.

There is a problem with variable spending strategies, though I still consider them vastly superior to mindless constant-dollar strategies. There is no guarantee that the varying amount you can safely spend every year will maintain your standard of living.

If I am stranded on a desert island with a limited water supply, I can choose to drink decreasing amounts as the supply dwindles but at some point, I can't drink less and survive. Likewise, when variable "safe" spending drops below non-discretionary spending for a sustained period I still have to buy food and pay the mortgage even if that entails an "unsafe" level of portfolio spending. Variable spending isn't a flawless strategy but it seems more sound than the alternative.

I mentioned that the sequence of your future portfolio returns can’t be predicted but the risk can be mitigated. We can do this by spending less from the portfolio, for example, or by changing bond-equity allocations. Sequence risk is moderated by safety-first advocates by ensuring an acceptable income from assets not exposed to market risk in the event of portfolio failure.

To summarize some key characteristics of sequence risk:
  • The sequence of future returns is critical for the survivability of a spending portfolio — but unknowable.
  • Sequence risk and the "safe" amount we can spend vary throughout retirement. They can become much safer or much riskier. We need to modify the amount of portfolio withdrawals to compensate — if we can. 
  • Sequence risk can be helpful or harmful and it has different impacts (generally better) during the accumulation phase than after retirement.
  • Sequence risk can result in portfolio depletion (ruin) or lowered standard of living after retirement but probably not before.
  • The sequence of returns matters more than average returns. To avoid premature portfolio depletion you need a fortunate sequence of portfolio returns about twice as badly as you need really good returns.
  • Althought we can't predict or control our sequence of future portfolio returns, the risk it introduces can be mitigated in various ways.
  • Sequence of returns explains most of sustainable withdrawal rate and all of portfolio ruin.
  • The portfolio return of the first five and ten years of a 30-year retirement are much better predictors of a sustainable withdrawal rate than the mean return for 30 years.[1] You can experience good average returns for thirty years and see your portfolio fall to a poor sequence of those returns or experience mediocre average returns and be saved by a good sequence.
  • A terrible bear market isn't required to sink a retirement portfolio. To quote Michael Kitces, "a “merely mediocre” decade of returns can actually be worse than a short-term market crash..."[2] Retiring in the 1960's was a perfect example. Retiring around the beginning of the Great Depression offers a similar example of how a shorter period of dramatic losses can also result in portfolio failure.
  • Sequence risk never goes away but it can become quite small if your wealth is (or becomes) very large relative to your spending needs and remaining life expectancy — in other words, when your portfolio performs well throughout retirement. Sequence risk can become quite high under the opposite circumstances.
The key takeaways are that the sequence of the returns your retirement portfolio experiences is a major determinant of portfolio survival and is about twice as important as your mean portfolio return. The most important factor is how long you will be retired. And, neither of these is predictable for an individual household.

EarlyRetirementNow's analysis calculates the safe withdrawal rate that would deplete the portfolio in exactly 30 years.


[1] The Ultimate Guide to Safe Withdrawal Rates – Part 15, Early Retirement Now blog.

[2] Understanding Sequence Of Return Risk – Safe Withdrawal Rates, Bear Market Crashes, And Bad Decades, Michael Kitces, Nerd's Eye View blog.


  1. "The best possible sequence of your annual portfolio returns would result if those returns happened to materialize ordered from worst annual return in the first year to best return in the last": did you mean the opposite? Or have I misunderstood?

    1. Thanks! You understood perfectly. I missed that (even after proofing it dozens of times). Corrected.

  2. What do you think of Maxifi planner? I get the impression that it is going to replace ESPlanner. I thought I had read about ESPlanner in one of your articles so I thought you were familiar with that software. Maxifi planner states that it can be used to compute consumption smoothing. When my husband retires I was thinking of using that to see if our current budget is ok to not deplete our portfolio. If it is not I was thinking that the software would give us guidelines as to what amount we could spend. Do you think Maxifi planner could be used for that purpose?

    Basically, my husband plans to retire next year no matter what our portfolio is doing. He has had some health issues and it is time for less stress. We just need to figure out what amounts can be spent each year compared to our budget and portfolio. I've done a spreadsheet and it seems like our projected retirement budget is doable with inflation increases each year and conservatively increasing our income each year. I project that our income should last till 100, but I would like some software that I can run to verify my calculations, especially since this should be re-run every year.

    As a side note when I prepared our retirement budget I was amazed at how much of a percentage our budget is spent on medical insurance and expenses. That was a eye opener. Also I have several retired friends that are 10-15 years older than me and apparently dental bills can really increase as you age. I have always kept an informal budget but have just started using budgeting software. I wish I had started using budgeting software several years ago, that would definitely help with retirement planning.

    1. MaxiFi is apparently the intended replacement for ESPlanner, although there doesn't seem to be much difference between the two at this point in time. ESPlanner was written in Visual Basic, which is going away, hence, the rewrite of ESPlanner.

      I used ESPlanner for a long time and I like it a lot, though I suspect you will find it difficult to use. Furthermore, I don't think it will answer the question I believe you are asking, which is the proverbial "how much can I safely spend in retirement if I invest in a volatile portfolio of stocks and bonds?"

      We can make guesses about how various spending strategies would perform if you retired many times but you will only retire once. We can't predict safe spending for a unique household, especially one that spends from investments.

      Specific to MaxiFi, you are correct that it calculates a consumption-smoothing path. If you understand what consumption-smoothing is and have decided that is how you want to plan retirement, then MaxiFi will probably do it well. In essence, it applies the life-cycle economics theory that people should prefer their consumption to be smooth instead of spending a lot one year and a lot less the next, for example. If you don't understand what the consumption-smoothing software is calculating for you, then the calculation will be of limited value.

      I will also tell you that spreadsheets won't answer your question very well and you should have little confidence in their results.

      Let me offer a simpler starting point. The best way to know how much you can spend for the next 30 years is to think about an annuity (I'm suggesting you think about one, not necessarily buy one). An annuity promises to pay you for as long as you and a surviving spouse live. For several reasons, it may not be ideal to annuitize all your wealth but then you don't have to.

      Wade Pfau's Retirement Researcher Dashboard quotes payouts for a fixed annuity without inflation protection as currently 5.67%. It quotes a CPI-U inflation-adjusted annuity payout at 3.85%.

      If you had a portfolio worth $100,000 (plug in your own portfolio value here), you could receive lifetime payments of $5,670 per year, subject to inflation. You could receive 3.85%, or $3,850 per year compensated for CPI-U-calculated inflation each year. That is about as certain as future retirement income can be. There are some risks, but they aren't longevity risk or market risk.

      You can take some risk by investing some or all of this money in a stock and bond portfolio instead of purchasing an annuity and you will be able to spend more or less than the annuity payout depending on how your investments perform. You will have introduced market risk and you may or may not be rewarded for it. It's a bet.

      I suggest you calculate the annuity payouts for the size of your portfolio and, based on those amounts, decide whether you would like to perhaps generate more income at the risks of both generating less income and depleting your savings. You can adjust the amount of risk you are willing to accept by allocating partly to annuities and partly to your portfolio.

      If you invest in a portfolio (and probably even if you don't) you need to determine how much you can safely spend each year of retirement when that year begins. There is no financial magic that let's you predict what your spending can be in 20 years, although annuities come closest.

      I don't think that MaxiFi or spreadsheets will provide the answer you're looking for. Hope this helps.

      Thanks for writing!

  3. I believe that the new Monte Carlo Risk Analysis, recently rolled out, will help with this in MaxiFi. There's a new case study that refers to Kitces and sequence of return risk specifically. It directly addresses this concern and how MaxiFi provides some insight.

    1. Dan, I find MaxFi's approach of optimizing standard of living far superior to minimizing probability of ruin, which is simply a flawed metric.

      However, I don't believe sequence of returns is at all predictable so I know of no credible way to model it. If you do, please share!

      Two additional points. The Kitces piece (and many others) describe MC as equivalent to "MC that minimizes p(ruin)". MC doesn't have to model p(ruin), as MaxiFi demonstrates.

      Also, Big Ern at found that the first 5-years of retirement returns have even greater explanatory power than the first 10.

      Thanks for writing!

  4. Yes, OK, well the with MaxiFi's MC using an all-stock investment strategy to get the most volatility possible, I am able to create some pretty unlucky return sequences in the first five or ten years. It's not strictly predictable (if I understand what you mean by that), but the pattern of unlucky return sequences drawn from the inherent probabilities of the asset class is fairly reliable. That is, I see similar patterns of poor returns at the fifth percentile over and over even if they are not strictly predictable. We can see the sequence of returns in each of the five percentile stops shown in the rate of returns sequence reports. These are the returns sequences randomly drawn (at these 5 stops) from the 500 models run. I would think that enough to represent some pretty realistic bad luck. But I guess your point is that we're always dealing with probabilities of one sort or another. I like our work here!

  5. Actually, Dan, that is not my point, though it is obviously true.

    By varying the asset allocation (in your example to 100% equities) you change the mean return and volatility but not the sequence of those returns. You will generate more very bad returns (and more very good ones) and even more failed scenarios.

    But the sequence of returns explains about 70% of sequence of returns risk, while the mean return itself explains only about 30% (see Big Ern).

    I assume MaxiFi makes random draws of returns from a normal distribution (only because I'm yet to see an MC model that doesn't do that) and accepts the sequence of those draws as produced by the random number generator. The sequence of those draws will be uniform random unless MaxiFi models sequence of returns differently than most models. Looking at historical sequences of returns, they do not appear to me to be uniform random, the caveat being that we don't have many historical sequences to consider.

    Ultimately, I believe the original question was "how much can [our household] spend each [future] year?" and sequence risk was mentioned by you and not the original poster. My advice is, given the massive uncertainty involved, this household not to be overconfident in any model's ability to predict their future financial situation several years down the road.

    Do you disagree?

  6. Right, definitely agree. Interesting articles, I'll have to do some more studying of sequence of risk! I was just thinking that because MaxiFi is running 500 lifetime trajectories or sequences, even though the returns are random overall, in some of the worst performing trajectories there must be at least short sequences of bad returns--in that case there's what 5 double-digit negative returns in the first decade? And the reports show you the real rate of returns used. Looking at that 5th percentile sequence looks bad. I mean it's not a black swan, but it's sure a run of bad luck and you can see thus the impact on household annual spending. So you can get at least some sense of how sensitive your model is to bad (and good) sequences, but I agree it's not testing long sequences of consistently bad returns like major economic downturns or long periods of high inflation. It's limited to poor, but not improbable, sequences of returns. At least that's how I understand it. I'll do some more thinking about it. Thanks!

    1. I think that's exactly correct. There will no doubt be some bad sequences from MaxiFi. My only point is that changing the asset allocation to more aggressive causes shortfalls that result from poor returns and perhaps not from poor sequences of those returns. But, sequence risk is a bit of an unnecessary distraction here.

      MaxiFi generates some bad outcomes and that's important. It's less important with MaxFi than with most MC models because MaxiFi uses a more robust metric than p(ruin). That's one of the reasons I prefer your model.

      Black swans are impossible to predict and MC isn't a very good tool for analyzing tail risk. I would recommend that people mitigate black swans with insurance.

      I believe the original poster was asking how to predict future expenses (her budget) with a spreadsheet and I was trying to explain that isn't possible. It's not possible with MC, either, though one can test many more scenarios. MaxiFi doesn't try to predict expenses, as I understand it, but to calculate optimal smoothed consumption given a set of resources. Said differently, she can estimate how much she might be able to spend in the future but can't know whether that will be enough.

      Regardless, I think MaxiFi is her best bet if she insists on planning retirement without a qualified human planner. That's my second concern -- a retirement planning toolkit is only as good as the person using it.

      Cheers. . .