Have you thought much about sequence of returns risk, and how it will affect your withdrawal strategy? I’ll tell you that it’s been absorbing a lot of my thinking lately.

Like me, you might have seen a lot of information on safe withdrawal rates and investment strategy in retirement. We can then argue about whether the historical experience that informs those results will be relevant in the future, but what I really want to revisit is the impact sequence of returns risk (SORR) might have on your strategy.

# Sequence of returns risk

I say revisit, since you may have seen my last post on this issue. In that post I introduced a method to isolate SORR and show its impact without varying the overall return over a period. Remember? No? Maybe give that post a quick looks to get you upto speed, but don’t be long we’ve got some new ground to cover!

## Isolating SORR

To quickly summarize I take the last 33 years of equity and bond returns and simulate different withdrawal rates in retirement. So far so good… but… I then take different permutations of these returns and re-simulate to get different paths.

*Huh – why? *

Because over the total period all these permutations and paths have **exactly the same total return.** For a 70% equity/30% bond portfolio the total compound annual growth rate over the period was 7.8% – not bad! The only thing that has changed is the sequence of returns. See the example below where I’ve shown the growth of $100 with no withdrawals. Without withdrawals all the paths end on the same point of $1,217. Note that I work in today’s money so I adjust for inflation over the period, but that’s not that important in what we’re going to do.

## Do we have to part ways?

Now, listen to me – this analysis is not for everyone. If you think about what I have done, I have taken a perfectly respectable historical time period of investment return data and then scrambled them up. I must emphasize that there is absolutely no financial or economic justification for this. I am creating almost random sequences of returns that are not justifiable in any economic sense. So if this jiggery pokery makes you queasy as to the lack of sound financial justification then you might have to leave now.

But… if you think these different permutations of returns might be possible over the next few decades, and you think this might be a useful exercise to glean some insight into SORR then take a seat.

Ok – ready to go?

## Withdrawal rate and SORR

There are two key levers to pull in retirement; your investment strategy and your rate of withdrawal. It’s worth noting that these two are linked. A more aggressive investment strategy with a higher equity allocation is required to sustain a high withdrawal rate, and conversely a lower withdrawal rate will permit a less risky investment strategy with fewer equities and more bonds. I’m not going to address that in this post, I’m going to concentrate on how the SORR changes when we pull these two levers.

The following example shows a 4% withdrawal rate with an equity allocation of 50% and the remaining 50% bonds.

The key thing to note is that the end-point of the simulations is not all the same point. SORR has bitten us on the ass! Remember the total return over the period is the same for all the simulations. The only thing that is different is the sequence of those returns. *I know! crazy!*

Now look at this example of 50% equities, but the withdrawal rate is halved at 2% per year.

First thing to see is that the end point is higher. Well done Sherlock! No surprise! If you only withdraw half the amount then you will have a bigger pot at the end.

What I really want to focus on is the spread in end values. Does that spread look tighter than the last chart? Yep – there is no doubt that decreasing the withdrawal rate decreases the SORR.

## Enough with the hairy charts! Measuring SORR

There is only so many of these hairy charts that you can look at, so we need some kind of way of quantifying the SORR.

Suppose we have two retirees, one who invests for the period and has a reasonable sequence of returns, and ended up in the middle of the pack (the “median” as we say in actuary-land). The other retiree was less fortunate with the sequence of returns and ended up near the bottom (“5^{th} percentile”). They can look back at their annual return on their money over the period. The median retiree might calculate an effective annual return of 7% say, and the other might calculate an effective return of 5%. So in this case we say that SORR can potentially have an impact of 2% per year.

## Show me some results!

We’re now going to repeat this for all investment strategies from 0% equities to 100% equities in 10% increments and withdrawal rates from 0% to 5% in 1% increments.

Each color in the chart above shows the return impact on SORR. So the dark red represents a 4.5% per year return ‘drag’ purely from SORR if you are unlucky. Ouch!

These numbers are high, even with a relatively modest asset allocation. Look along at 50% equities and up at a withdrawal rate of 3%. We’re in the fairly dark blue territory which means the SORR drag could be ~1% a year (in real terms).

You can see two key things here:

- Increasing the equity allocation increases the potential drag from SORR. A more risky strategy makes you more susceptible to SORR.
- Increasing your withdrawal rate also increases your susceptibility to SORR.

I would say that as soon as you end up in the yellow or red region you are taking on significant SORR risk. This could happen with a 4% withdrawal rate and 90%+ equities.

## But the equity market has historically delivered?

One common refrain you hear is that the stock market has always bounced back and delivered after a rocky period, and this is cited as evidence to hold a very stock-heavy portfolio. This is true, in historical terms stocks have performed over the long run. But when you are drawing down your portfolio the sequence of those returns matter.

Remember we have taken the market out of this analysis completely. I’m not showing good nor bad returns here. I am showing the **same total return **over the period. When there were no withdrawals we found the annual growth rate over the period as 7.8%. That’s a good period of stock and bond growth. So you can’t blame the red/bad scenarios above on a market downturn, or period of inflation. I’ve chosen a pretty benign 33 year period of growth. Remember the $100 growing to $1,217 ? This a pretty good sequence of returns in terms of total return, but simply by taking the returns in a different order you could face total ruin!

**Overly dramatic? Nope.**

Therefore you can use the Trinity Study, and the other derivatives of this work, to justify a 4% withdrawal rate with a very high equity allocation, but these historical periods simply do not show enough permutations of those returns to reveal the full extent of the risk.

*Have you signed up for email updates? It’s on the left if you’re on a desktop and in the menu if you’re on a phone – or follow me on twitter @actuaryonfire to get all the hot new updates.*

## Frequency of withdrawals

Now let’s look at how the frequency of withdrawals might impact on SORR. The following chart is our old friend that shows a 4% per year withdrawal and a 50% equity strategy.

The next chart shows the same investment strategy of 50% equities but we have changed the withdrawal rate to 16% every four years.

It’s difficult to tell whether SORR is changing here so we need to do some calculations. Like before, we vary the investment strategy, but this time we will consider six different withdrawal frequencies:

- 4% per year
- 8% every two years
- 12% every three years
- 16% every four years
- 20% every five years
- 24% every six years

It’s time for another colorful chart!

Again each color shows the potential return drag from SORR. What do you notice?

- Lengthening the withdrawal period does not have a big impact on SORR, but it slightly increases.
- As before a risky investment strategy has a major impact on SORR.

It’s better to take your withdrawal frequently and not hold onto a significant sum in cash over a long period. This is a fairly surprising result in my opinion. This is not saying that a frequent withdrawal rate is ‘better’ in terms of providing a greater end sum, this is concerned with the SORR. Basically, making your cashflows more lumpy will make you more susceptible to SORR.

Note again that an equity heavy portfolio can really screw you with SORR, irrespective of withdrawal frequency.

## Putting it all together

I think for most seeking financial independence there are going to be certain parameters to stay within, that I set out below.

- An investment strategy that has more than 50% equities. Anything less is going to produce too low a return over the long term for most early retirees.
- A withdrawal rate of more than 3%. Yes, I know, some have sufficient assets to support a lower withdrawal rate. But for most, accumulating sufficient assets to support anything less than a 2% withdrawal rate is going to be impractical.

**So given the above, what constraints would we impose based on what we’ve learned about SORR?**

The chart above shows the results we saw previously but I have imposed the constraints discussed above; equities greater than 50%. Based on a relatively arbitrary threshold on sequence of returns risk I would recommend tapering down the equity allocation if you are inclined to take make your withdrawals particularly “lumpy”.

Let’s now look at the amount of withdrawals, rather than the lumpiness of them.

Having a low withdrawal rate of around 3% gives you a lot of immunity to SORR. It doesn’t matter a whole lot what your investment strategy is, within the 50-80% equity range. However, as you ramp up the withdrawal rate I think it is prudent to taper down the equity allocation as the withdrawal rate increases so as to contain a manageable SORR. Note that this is the opposite of what you might want to do, since to support a higher withdrawal rate you need a higher equity allocation. More on this tension in a later post…

## So what’ve we found?

We’ve found that the lumpiness of withdrawals don’t make a whole lot of difference to SORR, although it is preferable to have less lumpy withdrawals. We’ve also seen that the withdrawal amount makes a big difference to SORR, particular north of 4% withdrawals. In fact, at a 4% withdrawal rate I wouldn’t recommend an equity allocation of much more than 70%, in order to contain SORR to a manageable level

*So how did you find that? Too many words? Any burning questions that you think are remaining that we need to address?*

**Technical notes**: I upgraded my analysis from last time and am now doing 10,000 simulations rather than 1,000. I noticed that the 5th percentile was not stable under 1,000 simulation so needed more. This in itself tells you that SORR is big deal if need as many as 10,000 simulations. I also changed the return methodology to be a proper internal rate of return (IRR) method to take account of the time varying payments I introduced. I define the SORR drag as the IRR on the 50th percentile scenario less the IRR on the 5th percentile return over the period. You made it to the end – yay!

Handy MillennialGreat post! I really enjoyed your analysis. One key fact stands out for me – permuting the returns gives you the same total return. Duh!!! That’s such an obvious statement, yet one I never considered. But it enables you to do this cool analysis on return rates. I also really like the drag on the return that you quantify. That’s a great way of looking at portfolio allocation SWRs.

actuary on FIREThanks for stopping by and the encouragement. Glad you found it insightful!

Dr. MomThinking about sequence of returns risk as a quantifiable drag on your portfolio is very interesting and helpful. Most of what I have read about SORR stresses the last few years of your accumulation phase and the first 10 years of the withdrawal phase. Do you have a way to look at varying the first 10 years of withdrawal to a less equity heavy portfolio and then start increasing your equity allocation for the remainder of your withdrawals? Kitces has written on Bond Tents to help with SORR and ratcheting withdrawal rates. Just wondering if you could play with those ideas? Thanks again!

actuary on FIREYes, there is more to do on this. I think I can unpick this into three different hypotheses:

(1) Test the assertion that SORR is more important late in the accumulation phase, and early in the spendown phase. I hear this a lot, but I want to quantify it.

(2) Can you mitigate SORR with a smarter investment strategy. e.g. Kitces “bond tent”?

(3) Can you mitigate SORR with varying withdrawal rates.

You’re keeping me busy – thanks for dropping by (again)

hatton1Good Post. I always agree with DoctorMom. It looks like 68% equities is ok.

actuary on FIREDepends what your goal is! But I agree, I always agree with DrMom

Dr. MomLol to you both!

Muad'GrumpsBut what if bonds turn out to be the problem? If they turn out to be the big losers the next thirty years?

There’s also another asset class that’s missing from your analysis. An asset that can compensate for negative real yields on financial assets.

actuary on FIREOne of the issues that I have to look into, and I owe my readers, is any inherent bias in the data set I am using. I have used the last 33 years, and I didn’t initially think it made a lot of difference because I am just permuting the returns, but I need to test this with some other data sets. So I’ll get back to you on this…

Thanks for raising this.

GasemThis “asset” is called the VIX As stock/bonds crash the VIX tends to grow exponentially. The problem is the carry charge, the VIX is very expensive to own. Gold is a rational though imperfect substitute.

Muad'Grumps33 years isn’t long enough. Heck, 46 years isn’t long enough. What happened 46 years ago?

This is why so many of you young uns are going to be blindsided by what’s coming. You’ve only experienced one part of a cycle.

GasemGreat analysis. It answered my question. Lately I’ve been playing with efficient frontier ratios using this calculator:

https://www.portfoliovisualizer.com/efficient-frontier

under the “gear” icon are some standard internet portfolios. Your 2 asset portfolio is on the efficient frontier, but the frontier for a 2 asset portfolio after you pass the tangent portfolio is just a straight line. You can run up and down the line and choose which risk/return you want. I think sequentially increasing vol (associated with more stocks) probably accounts for a lot of SORR given what I just read of your great work.. So would a better diversified portfolio (which yields a lower vol for a given return) be another way to reduce SORR? If that’s true then a reduction in SORR may be the “free money” associated with proper diversification in Modern Portfolio Theory.

For example look at the “Yale Endowment” portfolio and then add gold to the mix and let the program optimize the asset ratios. You get a portfolio that is the tangent portfolio (most efficient compared to “risk free” 1mo T-Bills) This portfolio is much less volatile than Yale Endowment but returns nearly the same. So does living on the efficient frontier with better diversity help SORR?

give me your email or the sites email, and I’ll send you a paper I just wrote on this.

TNX!

actuary on FIREThis looks like a great tool. Let me have a play around and get back to you. Thanks a lot.

GasemTo add gold just add the asset and set the % to 0 The program will do the rest. Also look at the optimized tangent portfolio before gold.

CubertEggzcellent analysis my friend! However, my head hurts substantially from all this early AM thinking. Our plan is mostly predicated on cash flow from our rentals, but this is certainly good food for thought should we find some dollars to use in a post-tax investment account.

actuary on FIREThanks for visting! Good work on the rentals hopefully a decent inflation linked return for you.

Pingback: The Sunday Best (10/29/2017) - Physician on FIRE

earlyretirementnow.comI still prefer a 100% equity portfolio, 3.5WR and a drag of 3% over a 50/50 portfolio with 1% drag because the expected return net of “drag” is still be higher in the 100% equity portfolio. Portfolios with a high equity share definitely have a higher success rate, see Part 2 of my SWR series.

https://earlyretirementnow.com/2016/12/14/the-ultimate-guide-to-safe-withdrawal-rates-part-2-capital-preservation-vs-capital-depletion/

actuary on FIREYou’re right, one thing I don’t consider is the net drag. i.e. a higher equity allocation gives you a higher expected return but a higher SORR “drag” and the net amount is the key in determining likelihood of success. But my purpose here wasn’t really to address the likelihood of success, that has been covered by you and others. I’m looking at quantifying the impact of SORR.

One of my concerns is that taking 60yr simulation periods since 1871 will give you 86 separate scenarios. I just don’t have a feel for whether observing 86 successes is statistically significant with so few potential sequence of returns. It feels like it’s pretty nailed-on, but I’m attempting to uncover what the potential for catastrophe is if some of those returns were in a different order. And for 100% equity it feels like the risk ramps up too much (for me).

Thanks for swinging by, I appreciate it.

Pingback: College Investment Strategies - actuary on FIRE

Pingback: Travel Hacking actuary on FIRE Style, and Embrace Your Inner Curmudgeon - actuary on FIRE

Pingback: Lump Sum or Dollar Cost Average Investing? Part 1 - actuary on FIRE