Sequence of returns

Introduction to Sequence of Returns and Buying a Boat in Retirement

Do you know what has been one of my favorite parts of writing a blog?

Has it been diving into the detail on some area of research that I’ve always wanted to investigate? Or is it receiving kind words from my readers who share my enthusiasm? Or is it having fellow actuaries reach out and offer support for my mission? (ooooh it’s a ‘mission’ now? Well la-de-da!)

Nope, it’s getting down and dirty with the numbers and the models!

Seriously though; I certainly enjoy building the models and investigating the results, but can you let me know if anything is inaccessible? Because this stuff can polarize people, and I want everyone to be able to take away something from this blog, irrespective of whether you are a numbers person or not. I’m not talking about dumbing things down, I’m talking about getting sophisticated messages across in a fun way that doesn’t blow up your brain (or mine).

Have you read the important notes? It’s a condition for reading this blog.

Inflation Risk Series

Were you expecting the next episode in the series of Inflation Risk for Early Retirees that Karsten/ERN and I have been running? Following Karsten’s last episode I had to lie down in a darkened room and digest it all, and I’ll be coming back at some point with a new episode, so stay tuned! But here is my last episode on personal inflation rates when you have read ERN’s.

Sequence of Returns

Let’s get back to sequence of returns.

Since starting this blog I have become totally obsessed with sequence of returns (SOR). I am planning a new article on this subject that will take a novel view on the classic ‘Trinity Study’ but first I wanted to do a short primer on sequence of returns in preparation. I have many new readers that may not have seen some of my early articles on the subject, here and here So I think it is worth a quick review.

Sequence of returns addresses the fact that it’s not just the value of stock and bond returns that are important in retirement, it’s also how those returns are sequenced that can have a big impact on your retirement success. Enduring a significant market crash early in your retirement can be much more damaging than experiencing it later in retirement if you continue to drawdown your portfolio at the same rate.

I’m not going to discuss ways to mitigate this risk today, but instead I’m going to look at one aspect that can make this risk more acute…. buying a boat.

Quantifying Sequence of Returns Risk

First we need to quantify SOR and how it might impact on our retirement success.

I’m going to look at a 50 year retirement period and take a portfolio of 70% stocks and 30% bonds, and simulate using real returns over the last 50 years. Here is the results showing the growth of a $1,000,000 portfolio.

Sequence of returns
Growth of $1m

Over the last 50 years it would have grown to a huge $12m sum. And that’s in real terms! In order to look at the impact of sequence of returns I’m going to scramble up those 50 years’ of returns in a different order?


Because over the period the total return will still be same, but only the sequence of returns will differ. Here is a chart showing 100 different versions of these 50 returns, and you can see that the $1m still rolls up to the same $12m sum. that’s just math.

Sequence of returns
Growth of $1m with sequence of returns

It’s not until you start introducing withdrawals from the portfolio that you see the impact of SOR. Here is the same simulation with $40k withdrawn every year.

Sequence of returns
Withdrawal of $40k per year and sequence of returns

There is suddenly a big spread in ending values! And there are even some values that have gone to zero. That is the power of SOR. Remember that the total return for equities and bonds for all these simulations is identical only the SOR has changed.

In fact in my simulations I found that the 4% rule failed around 11% of the time for this 50 year time horizon and using 10,000 different SOR simulations of the last 50 years’ of returns. So let that sink in for a minute. Just by changing the SOR the 4% Rule is not so safe. But that will be a subject of another post. Let’s now look at boats.

Buying a Boat

So what has this got to do with buying a boat?

Well, it doesn’t have to be a boat, but that’s just actuarial shorthand for retiree profligacy. If you are considering any kind of capital outlay in retirement how could SOR impact your overall retirement solvency?

We know from the above example that cashflows will magnify SOR. So how does buying a boat (or any large purchase) impact the SOR risk in retirement?

I’m going to look at four situations, and in all cases I will start the simulation with $1m.

  • Not buying a boat and just have regular spending of $40k a year.
  • Buying a boat worth one year’s spending ($40k) along with regular spending.
  • Buying a boat worth two year’s spending ($80k) along with regular spending.
  • Buying a boat worth three year’s spending ($120k) along with regular spending.

Don’t get hung up on the actual dollar amounts here. You might not have $1m in your retirement pot, you might have much more, or much less. You also might not be interested in a boat. The point is that we are looking at a large capital purchase worth a multiple of your annual spend. It might be a boat, it might be a down payment on a house, or fees to go to actuary school, so just go with it ok?

Also it might not be a pleasant thing… You might have a large capital outlay due to a medical emergency. So it’s useful to understand how this might hurt your retirement success.

Sequence of returns

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Impact of SOR on Your Boat Purchase

The key measure I am going to use is whether you run out of money in the 50 years. In actuary circles we call this “solvency probability” (oooooh I love it when we talk all actuary-like!).

This might sound odd, but remember that I’m not really interested in the absolute probability of success, I’m interested in the relative impact on success of buying a boat. In particular, I’m interested in how SOR will affect this success. There is loads of information out there about the probability of success of a 4% withdrawal rate over different time periods and using different investment strategies. See for example ERN’s SWR series.

Also remember I’m not looking at different historical time periods. I’m only looking at one time period, and that is the last 50 years’ of returns. But I take 10,000 different permutations of these returns. It sounds crazy, but this ensures that the total return for each simulation is identical, and only the sequence of those returns has changed.

Let’s look at the results.

Sequence of returns
Decrease in chance of retirement success

The above shows the impact on the probability of retirement success from buying various boats at different points in your retirement whilst continuing to maintain a $40,000 per year withdrawal.

Suppose you buy a boat worth one year’s spending in year 10 of your retirement. You can see that this will reduce your probability of success by around 2% simply from SOR and the additional spend.  That’s not a big impact, because it’s a pretty small boat, and quite a long way into your retirement.

Now look at buying a really large boat worth three year’s of spending in the first year of retirement. The reduction in probability of success is now almost 12%, just from SOR and the additional spend. In other words, you are 12% more likely to run out of money compared to the baseline of regular $40k a year spending. This is a material impact on your retirement success.


If you want to make a large capital outlay in retirement then there is no doubt that it will reduce your chance of remaining solvent. However if you are only spending about one year’s worth of spending as a special project then that might only reduce your success probability by 2-3%. Not much.

However if you’re planning to spend 2-3 times your annual spend on a special project then that could materially impact your chance of retirement success. It might reduce your probability anywhere from 8-12% compared to the baseline of constant spending.

Are you planning to make a capital expenditure in retirement? Have you simply wrapped that in your total assets, or have you carved it out, and think about your annual income retirement assets differently to a one-off spend?  Are you a not a numbers person, but still want to get something out of this blog? Drop me a line or comment below. Thanks!

(c) Actuary on FIRE 2018

9 thoughts on “Introduction to Sequence of Returns and Buying a Boat in Retirement”

  1. I have two thoughts on this issue, that relate to my personal circumstances and no doubt others.

    At some point during my retirement, I expect to pay for a wedding. A wedding is kind of like a boat in that it is an expensive outlay, but unless you stiff the caterer and get sued, you typically do not have to keep paying for it. My guess is that the wedding outlay would be about 1/2 of the yearly spend, so it would appear that it would have little negative impact on the success probability.

    Also, at some point in my retirement, I will likely be gifted 4 1/2 boats. Okay, they are not really boats, but it will be an inheritance in the range of between three and six times my expected annual spend. Because I truly do love my 86 year old father, I hope it is later rather than sooner, but he would be the first to admit that his best days are behind him. Nonetheless, it would be interesting to add this also to a SOR model to see how this might affect planning and if it might permit a higher SWR.

    1. actuary on FIRE

      That’s a good couple of points. I hadn’t really thought about cash inflows from inheritance, but SOR works in reverse then.

  2. One thing about a boat is you have a physical investment you can sell and recoup something.

    I’ll see your boat and raise you a Roth IRA conversion. I’ve been studying this problem for a while. I’ll use an example close to my own. I have an IRA worth $1.5M, I’m 66 and fully retired. I’m waiting to take SS at my RMD age of 70.5. My SS at that age will be about $42K and rising with COLA to about $53K at 82. My wife who is younger will add about 18K from SS to the mix when she retires rising to about 21K at my age 82. She will also eventually add some money from her RMD. RMD from my IRA at 70.5 will be $55K rising to 83K at age 82. I chose 82 to just give some convenient number to look at how things change over time. The comparison is to show how the tax bite can get out of control. So at 70.5 My income will be $97K. The top end of the 12% married joint over 65 with standard deduction is $104K So at RMD I will barely be in the 12% bracket, The advantage of the 12% bracket is you can pull money out of post tax accounts at 0% cap gains and most of my money is post tax. Within 2 years I will be into the 22% bracket and at 82 I will be closing on the 24% bracket and my beloved 12% cap gain rate will be distant in the rear view mirror. If one spouse dies the bracket goes up to 32%. Once you RMD there isn’t much you can do because you pay taxes on the taxes if you try to Roth convert while RMDing.

    So of course I’m going to Roth convert. The question is how much and how often and how to do it efficiently. If I Roth convert 250K for 4 years and I live off cash on hand, my tax bill will be $42.2K x 4 or $168,800. If I pull this out of the portfolio it’s like a SORR. I will have moved a compounded 1.1M into the Roth after 4 years and 700K will remain in the IRA after 4 years. RMD on 700K is 25K at 70.5 and $38K at age 82 so this means I live in the 12% bracket for a long time, At 82 our combined income will be 112K and I have some LTcap loss to use against the over 12% cap gain which keeps my cap gains at 0 and my income tax very low as well. If I need more money than my income I just take some out of post tax. So this is clearly efficient. I did the analysis for longer smaller conversions like 100K for 10 years, and for larger conversion to the top end of the 24% bracket 340K which virtually cleans out my IRA, The problem with smaller/longer is you need a LOT of cash to live on while converting. The problem with cleaning out the IRA (340K) is the total taxes on that would be $256K in the first 4 years, a huge SORR. I worked the effect through to the end and if the portfolio survives SORR on the average at age 90 the portfolio would be worth an extra $200K due to the fact you have much better control of the tax bite and eventually tax savings over power SORR (assuming you do’t have SORR from Roth conversion and SORR from Mr Market eating your lunch). Dual SORR is the risk of this scheme. But ever increasing taxes and market SORR is the risk of not converting so you have dueling risks. The kicker for me was when I analyzed going from two spouses to one the taxes get REALLY bad.

    This is a real problem many if not most will be facing. You often hear how taxes are too complicated to deal with and everybody is different. That’s a dodge. Taxes are perfectly understandable but complex for sure. The way to deal with this is to plan during the accumulation phase by stashing cash on hand and tax dough during the working years. Do the conversion while leaving the portfolio alone, or have a lot of money post tax to play with and some LT cap loss. Again this is a plan to make long before you pull the plug and have a clear understanding of the moving parts.

    And you thought it was “max out the pretax, save 25x and spend 4% and figure out the taxes when they happen. The government has other plans for their part of your money and an ever increasing tax burden is its own systematic SORR

    AoF your articles are always so thought provoking and timely! I’ll have an article coming out on DadsDollarsDebts site in a couple weeks (around tax day!) with tables to better elucidate the moving parts. How’s the saying go? Parts is parts!

    1. actuary on FIRE

      Aww man! I do a simple puff piece on SOR and you raise all these great points on tax impact. You’re right though, I shy away from tax given the complication but it’s such a massive part of an optimal strategy.
      I should pull my finger out and do a post on that.
      Hey – I’m really looking forward to your article at DDD!

      1. I think 2 things are important for the FIRE bug.

        1 you have to optimize a plan before RMD by as much as a decade. To do that you need some at least qualitative idea of the opposing forces. You don’t necessarily need exact dollar amounts but some “what if” idea of what will hurt you.

        2 You need to run out end games till death of each spouse. The govt has all kind of little trap doors they have set.

        Just broaching the topic will help people get off the dime.

    2. I am in somewhat similar circumstances except with a 44k pension at 62 years old. My accountant says no ( they are trained never to pay tax when not necessary) but I think rates have only one way to go. I am reluctant though

  3. I realize the point of this article isn’t about boats specifically, but man is a boat a terrible investment. Do you know what BOAT stands for? Break Out Another Thousand.

    Kudos on another engaging and accessible discussion about SORR.

    1. actuary on FIRE

      Ha ha. Thanks for the kind words.
      They say the two happiest days of your life are the day you buy a boat and then the day you sell it.

  4. Pingback: The Trinity Study In Another Dimension - actuary on FIRE

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