Sequence of Return Risk impact on Retirement

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KlangFool
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Sequence of Return Risk impact on Retirement

Post by KlangFool » Tue Jan 09, 2018 8:24 pm

Hi,

As I read and studied a lot more, I get to know that I do not know what sequence of return risk meant. I need some numbers and examples in order get it.

Let's assume the followings, AA of 60/40 and a portfolio of 1.5m with 60K annual expense. Let's assume that it is at the age of 57 and this person is planned to retire at 62 years old. So, this person is 5 years from retirement.

What is a bad sequence of return for this person?

A) Bear market before retirement and bull market after retirement

Or,

B) Bull market before retirement and bear market after retirement

(A) or (B)? Please enlighten me.

Thanks.

KlangFool

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Tycoon
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Re: Sequence of Return Risk impact on Retirement

Post by Tycoon » Tue Jan 09, 2018 8:26 pm

I pick B.
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KlangFool
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Re: Sequence of Return Risk impact on Retirement

Post by KlangFool » Tue Jan 09, 2018 8:30 pm

Tycoon wrote:
Tue Jan 09, 2018 8:26 pm
I pick B.
Tycoon,

Why (B) is bad? There is something simple that I just do not get it. Pardon my stupid question. I am stuck.

KlangFool

2Birds1Stone
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Re: Sequence of Return Risk impact on Retirement

Post by 2Birds1Stone » Tue Jan 09, 2018 8:32 pm

B

It's the first few years of retirement going relatively poorly year after year and you blindly withdrawing from your portfolio as though everything is peaches and rainbows.

Simply being able to scale back a tiny bit on the spending front, or making some side income can greatly reduce this risk.

Many make a mistake of keeping too high of a cash buffer to "wait out the bad years" which ultimately creates a detrimental drag on the portfolio.

All of this is largely irrelevant with WR's that are 3.5% or less.....which have never failed.

:sharebeer

radiowave
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Re: Sequence of Return Risk impact on Retirement

Post by radiowave » Tue Jan 09, 2018 8:33 pm

I'll also pick b.

There was (still is) an excellent SOR thread recently viewtopic.php?f=1&t=236665 KlangFool I see you posted there. I think I'm in the same boat as you, just a few years out from retirement, wondering what happens if the market takes a nosedive and that affects a lot of decisions, e.g. one more year, bulk up on CDs in taxable, change current asset allocation to more bonds, etc. Reading through that tread helped me sort through a number of decisions I need to make in the short term. I'm not going to worry about either a or b scenario. I have a good IPS in place and working with my spouse on our different options.
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2Birds1Stone
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Re: Sequence of Return Risk impact on Retirement

Post by 2Birds1Stone » Tue Jan 09, 2018 8:34 pm

KlangFool wrote:
Tue Jan 09, 2018 8:30 pm
Tycoon wrote:
Tue Jan 09, 2018 8:26 pm
I pick B.
Tycoon,

Why (B) is bad? There is something simple that I just do not get it. Pardon my stupid question. I am stuck.

KlangFool
Say you experience significant drops in the first 3-5 years of your retirement, and keep spending at your planned 4% withdrawal rate....mathematically it's much worse for portfolio survivability than it happening just a few years (or much later) into a retirement.

If you're worried about it, just work until you can support yourself on a 3.5% or lower WR. Or don't factor in SS and it will mitigate 99.9% of your risk.

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onthecusp
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Re: Sequence of Return Risk impact on Retirement

Post by onthecusp » Tue Jan 09, 2018 8:39 pm

Typically you would still be contributing before retirement (accumulation phase) so a bear would let you buy at lower prices. Then at your desired retirement you could (presumably) decide if you still had enough. Maybe your contributions kept the balance at 1.5MM despite the bear market.

Or go for one more year, or maybe even decide that the market is low enough, with recovery started, that you will take 5% withdrawal and that is enough. If the subsequent market is good you will be that many years closer to the end of your planning period and the "early years sequence of return danger phase" is over.

That is how I see it. The inverse is retiring at a market "high". If you believe that 4% gets you through this "worst case" like the guy who retired in the year 2000 you will be good, but bad sequence of returns right after retirement may give you some pause a few years into it.

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Tycoon
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Re: Sequence of Return Risk impact on Retirement

Post by Tycoon » Tue Jan 09, 2018 8:44 pm

KlangFool wrote:
Tue Jan 09, 2018 8:30 pm
Tycoon wrote:
Tue Jan 09, 2018 8:26 pm
I pick B.
Tycoon,

Why (B) is bad? There is something simple that I just do not get it. Pardon my stupid question. I am stuck.

KlangFool
The way I see it (and I could be wrong), if a bear market hits before I retire I can continue to work and replenish my portfolio. Alternately, once I retire I plan on living on our investments until we die. I don't plan on working ever again. Consequently, a bad bear market will stress my normally calm demeanor and ruin my happy retirement by making me worry about having to eat cat food.
Appeal to Pity:When pity is envoked to support a statement | Appeal to Popular Sentiment:Appealing to unrelated prejudices and attitudes | Hasty Generalization:Too little evidence to support the conclusion

Thesaints
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Re: Sequence of Return Risk impact on Retirement

Post by Thesaints » Tue Jan 09, 2018 8:53 pm

-10%, -20%, -10%, -20%, -30%, +25%, +25%, +25%, +25%, +25%

+25%, -10%, +25%, -20%, +25%, -10%, +25%, -20%, +25%, -30%

average return is obviously the same as well as the volatility distribution (not just its value !).

If you withdraw 5% of initial amount every year in the first case you end up with ~20% of initial capital and in the second with more than three times as much.
We may know the statistical properties of the stock market, but have no control on the form they decide to show up in.
The real problem is not when thew "bad" realization decides to show before you retire, but when it does after you have retired. Before you realize you indeed went through a bad sequence of returns, you may very well be too old to be employable.

KlangFool
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Re: Sequence of Return Risk impact on Retirement

Post by KlangFool » Tue Jan 09, 2018 9:03 pm

Thesaints wrote:
Tue Jan 09, 2018 8:53 pm
-10%, -20%, -10%, -20%, -30%, +25%, +25%, +25%, +25%, +25%

+25%, -10%, +25%, -20%, +25%, -10%, +25%, -20%, +25%, -30%

average return is obviously the same as well as the volatility distribution (not just its value !).

If you withdraw 5% of initial amount every year in the first case you end up with ~20% of initial capital and in the second with more than three times as much.
We may know the statistical properties of the stock market, but have no control on the form they decide to show up in.
The real problem is not when thew "bad" realization decides to show before you retire, but when it does after you have retired. Before you realize you indeed went through a bad sequence of returns, you may very well be too old to be employable.
Thesaints,

You lost me.

<<-10%, -20%, -10%, -20%, -30%, +25%, +25%, +25%, +25%, +25%>>

This could be (A).

<<+25%, -10%, +25%, -20%, +25%, -10%, +25%, -20%, +25%, -30%>>

But, this is neither (A) or (B).

Is (A) or (B) worse?

KlangFool

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iceport
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Re: Sequence of Return Risk impact on Retirement

Post by iceport » Tue Jan 09, 2018 9:05 pm

KlangFool wrote:
Tue Jan 09, 2018 8:24 pm
Let's assume the followings, AA of 60/40 and a portfolio of 1.5m with 60K annual expense. Let's assume that it is at the age of 57 and this person is planned to retire at 62 years old. So, this person is 5 years from retirement.

What is a bad sequence of return for this person?

A) Bear market before retirement and bull market after retirement

Or,

B) Bull market before retirement and bear market after retirement

(A) or (B)? Please enlighten me.

Thanks.

KlangFool
KlangFool,

I don't think it's that simple at all. You are attempting to generalize something which is — in my understanding by definition — unique to each retirement year. The sequence of returns in the 5-10 years before and after each starting year of retirement are probably the most critical, but the point is that for each starting year, each sequence of returns is unique.

A graph in a Michael Kitces article drove home this point for me. From Ratcheting the 4% rule for saner retirement spending:

Image

Notice how discontinuous the graph can be from one year to the next.
"Discipline matters more than allocation.” ─William Bernstein

dbr
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Re: Sequence of Return Risk impact on Retirement

Post by dbr » Tue Jan 09, 2018 9:10 pm

Sequence of return "risk" is a concept that applies in the following context. Pay close attention to exactly what is and what is not involved here.

1. The problem envisages annual (or whatever period) returns that if compounded would result in a known compound average growth rate for a series of time periods. For specificity one might image annual returns for thirty years as that might be a typical accumulation period or retirement period and we usually are comfortable being familiar with annual returns.

2. We haven't specified the sequence in which this set of thirty returns might occur, only the CAGR that would be produced for an investment placed at the beginning and held for the duration. In that case the sequence in which the returns occur makes no difference to the result at the end of the time period.

3. Now for a real investor there will be contributions placed during the entire period of accumulation and presumably withdrawals during the period of retirement. In this case the sequence in which the returns occur matters. For an accumulator there will be more money accumulated at the end if the smaller returns occur early and the larger returns occur late. For a person withdrawing the assets will decline more if the smaller returns occur early and the larger returns occur later. In this sense there is extra variation in the results due to the random sequence in which the returns occur even though the compound average annual growth rate per se of that set of returns is fixed. Phenomenon could include the infamous fear that the market would crash in the first year of retirement but can also include that the first half of retirement just gets all the low returns and second half the good ones rather than vice-versa. A consequence of this mathematical fact is that the amount you can safely withdraw from a portfolio in the worst case is lower than it would be if all the returns were the same every year and the sequence would therefore not matter.

4. Since we have just said that sequence of returns risk is greater the wider the range over which the set of returns varies it might be presumed that reducing that variability would solve the problem. That is not so simple because in the real world portfolios with less variability also have less return on average. In other words that assumption of the expected CAGR being fixed across scenarios is violated. What actually happens is that reduced sequence of returns effect is offset by reduced return effect and models of retirement withdrawal are painfully insensitive to asset allocation. The exception is when return is reduced so far by inadequate allocation to stocks that lack of return finally dominates and produces retirement ruin. Of course, it also true that if withdrawal rates are far enough reduced, the retirement ruin is also impossible, but that has nothing to do with sequence of returns.

5. Sequence of returns "risk" should not be confused with the risk that the actual average return that one gets during a period may not be what is expected. You could just have a period of investment for which the compound average of the returns is lousy even with a good sequence. While that might seem like the same thing in the sense of having a bear market the whole time one is retired being a bad "sequence" that is not what is meant. Sequence of return risk is in reference to all else being equal.

smitcat
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Re: Sequence of Return Risk impact on Retirement

Post by smitcat » Tue Jan 09, 2018 9:19 pm

KlangFool wrote:
Tue Jan 09, 2018 9:03 pm
Thesaints wrote:
Tue Jan 09, 2018 8:53 pm
-10%, -20%, -10%, -20%, -30%, +25%, +25%, +25%, +25%, +25%

+25%, -10%, +25%, -20%, +25%, -10%, +25%, -20%, +25%, -30%

average return is obviously the same as well as the volatility distribution (not just its value !).

If you withdraw 5% of initial amount every year in the first case you end up with ~20% of initial capital and in the second with more than three times as much.
We may know the statistical properties of the stock market, but have no control on the form they decide to show up in.
The real problem is not when thew "bad" realization decides to show before you retire, but when it does after you have retired. Before you realize you indeed went through a bad sequence of returns, you may very well be too old to be employable.
Thesaints,

You lost me.

<<-10%, -20%, -10%, -20%, -30%, +25%, +25%, +25%, +25%, +25%>>

This could be (A).

<<+25%, -10%, +25%, -20%, +25%, -10%, +25%, -20%, +25%, -30%>>

But, this is neither (A) or (B).

Is (A) or (B) worse?

KlangFool
Good example by Thesaints,

The strings of numbers represent rates of returns each year right after retirement - each string has the same total amount of positive and negative returns over the 10 year timeframe.
But even with the same total amounts of returns the top sequence represents the 'Sequence of return risk' by the order in whcih they come.

KlangFool
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Re: Sequence of Return Risk impact on Retirement

Post by KlangFool » Tue Jan 09, 2018 9:21 pm

radiowave wrote:
Tue Jan 09, 2018 8:33 pm
I'll also pick b.

There was (still is) an excellent SOR thread recently viewtopic.php?f=1&t=236665 KlangFool I see you posted there. I think I'm in the same boat as you, just a few years out from retirement, wondering what happens if the market takes a nosedive and that affects a lot of decisions, e.g. one more year, bulk up on CDs in taxable, change current asset allocation to more bonds, etc. Reading through that tread helped me sort through a number of decisions I need to make in the short term. I'm not going to worry about either a or b scenario. I have a good IPS in place and working with my spouse on our different options.
radiowave,

But, why is it worse? This person has at least 10 years worth of annual expense in fixed income. Let's assume that the stock market drops 50% and stay down for 5 years. The bond portion is 600K and the stock portion is 450K (drop by 50%). If this person keeps his AA at 60/40, the person will sell 180K of bond and buy stock. He is down to 420K of bond = 7 years of expense. He can survive 7 years while buying the stock at the bottom.

KlangFool

zengolf2011
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Re: Sequence of Return Risk impact on Retirement

Post by zengolf2011 » Tue Jan 09, 2018 9:23 pm

Poor returns early in retirement coupled with withdrawals deplete a portfolio faster than poor returns with withdrawals later. I think it's the power of compounding, but in reverse.

dbr
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Re: Sequence of Return Risk impact on Retirement

Post by dbr » Tue Jan 09, 2018 9:24 pm

smitcat wrote:
Tue Jan 09, 2018 9:19 pm
KlangFool wrote:
Tue Jan 09, 2018 9:03 pm
Thesaints wrote:
Tue Jan 09, 2018 8:53 pm
-10%, -20%, -10%, -20%, -30%, +25%, +25%, +25%, +25%, +25%

+25%, -10%, +25%, -20%, +25%, -10%, +25%, -20%, +25%, -30%

average return is obviously the same as well as the volatility distribution (not just its value !).

If you withdraw 5% of initial amount every year in the first case you end up with ~20% of initial capital and in the second with more than three times as much.
We may know the statistical properties of the stock market, but have no control on the form they decide to show up in.
The real problem is not when thew "bad" realization decides to show before you retire, but when it does after you have retired. Before you realize you indeed went through a bad sequence of returns, you may very well be too old to be employable.
Thesaints,

You lost me.

<<-10%, -20%, -10%, -20%, -30%, +25%, +25%, +25%, +25%, +25%>>

This could be (A).

<<+25%, -10%, +25%, -20%, +25%, -10%, +25%, -20%, +25%, -30%>>

But, this is neither (A) or (B).

Is (A) or (B) worse?

KlangFool
Good example by Thesaints,

The strings of numbers represent rates of returns each year right after retirement - each string has the same total amount of positive and negative returns over the 10 year timeframe.
But even with the same total amounts of returns the top sequence represents the 'Sequence of return risk' by the order in whcih they come.
But it is critical that there are withdrawals, the 5% of the initial portfolio amount taken each year. By commutivity of multiplication the order makes no difference when there are no contributions or withdrawals.

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Ditchwitch
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Re: Sequence of Return Risk impact on Retirement

Post by Ditchwitch » Tue Jan 09, 2018 9:25 pm

KlangFool wrote:
Tue Jan 09, 2018 8:24 pm
Hi,

As I read and studied a lot more, I get to know that I do not know what sequence of return risk meant. I need some numbers and examples in order get it.

Let's assume the followings, AA of 60/40 and a portfolio of 1.5m with 60K annual expense. Let's assume that it is at the age of 57 and this person is planned to retire at 62 years old. So, this person is 5 years from retirement.

What is a bad sequence of return for this person?

A) Bear market before retirement and bull market after retirement

Or,

B) Bull market before retirement and bear market after retirement

(A) or (B)? Please enlighten me.

Thanks.

KlangFool
As usual "it depends" on the parameters of "bull vs bear", i.e. the duration, timing and intensity (e.g. 3yr duration, 5 yr. prior to retirement, -50% etc.) but all else being equal you always want a bull before a bear. In a simple scenario if your portfolio advances the same amount in a bull as in a bear with the same timing etc you should come out ahead with the bull first.
“Anyone who has never made a mistake has never tried anything new.” | ― Albert Einstein

KlangFool
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Re: Sequence of Return Risk impact on Retirement

Post by KlangFool » Tue Jan 09, 2018 9:26 pm

iceport wrote:
Tue Jan 09, 2018 9:05 pm
KlangFool wrote:
Tue Jan 09, 2018 8:24 pm
Let's assume the followings, AA of 60/40 and a portfolio of 1.5m with 60K annual expense. Let's assume that it is at the age of 57 and this person is planned to retire at 62 years old. So, this person is 5 years from retirement.

What is a bad sequence of return for this person?

A) Bear market before retirement and bull market after retirement

Or,

B) Bull market before retirement and bear market after retirement

(A) or (B)? Please enlighten me.

Thanks.

KlangFool
KlangFool,

I don't think it's that simple at all. You are attempting to generalize something which is — in my understanding by definition — unique to each retirement year. The sequence of returns in the 5-10 years before and after each starting year of retirement are probably the most critical, but the point is that for each starting year, each sequence of returns is unique.
iceport,

I am asking a very simple question in order to further my understanding. What is a bad sequence of returns for 5 years before and after retirement?

Is it

A) Bear market (sequence of 5 years of bad returns) before retirement and bull market at retirement (sequence of 5 years of good returns).

Or

B) The reverse.

KlangFool

dbr
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Re: Sequence of Return Risk impact on Retirement

Post by dbr » Tue Jan 09, 2018 9:28 pm

zengolf2011 wrote:
Tue Jan 09, 2018 9:23 pm
Poor returns early in retirement coupled with withdrawals deplete a portfolio faster than poor returns with withdrawals later. I think it's the power of compounding, but in reverse.
Not power of compounding but internal rate of return, which is a more subtle bit of mathematics that includes compounding. There is also the constraint that one is comparing histories in which the compound annual average of the returns is the same but annual returns occurring in different order. That is a much more restricted case than one retirement just having the bad luck of getting poor returns altogether.

KlangFool
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Re: Sequence of Return Risk impact on Retirement

Post by KlangFool » Tue Jan 09, 2018 9:33 pm

Folks,

1) It is bad to withdraw from the portfolio while the return is bad. Hence, it depletes the portfolio faster.

2) But, what if we deplete the bond portion while the stock market is down? Or, only deplete the bond portion for the first 5 years of retirement. Then, what happened? Isn't this concept of increasing equity portion as part of the glide path AA during retirement?

KlangFool

bhsince87
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Re: Sequence of Return Risk impact on Retirement

Post by bhsince87 » Tue Jan 09, 2018 9:35 pm

I'm with Klang. This is a topic I have a hard time grasping.
Retirement: When you reach a point where you have enough. Or when you've had enough.

Thesaints
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Re: Sequence of Return Risk impact on Retirement

Post by Thesaints » Tue Jan 09, 2018 9:37 pm

KlangFool wrote:
Tue Jan 09, 2018 9:03 pm
But, this is neither (A) or (B).

Is (A) or (B) worse?

KlangFool
What happens before and what happens after retirement is a false problem. If market drops before retirement, you simply keep working (hopefully you have this option), because you haven't reached sufficient capital for retiring safely with the withdrawal rate you have in mind.

The real problem with a negative sequence of returns is after you retire. You have done your due diligence and concluded that a portfolio with expected return X and volatility Y will allow you to withdraw this many dollars for at least this many years.
That's all very well in theory, but there are many ways volatility Y can manifest itself. Without even taking into accounts different distributions, which can have identical volatility, but some of which can kill you right away (the infamous black swans), there are possible realizations of the same statistical distribution, which can also ruin you not instantly, but in the course of many years.

As a rule, negative returns concentrated at the beginning of retirement (i.e. when you start withdrawing instead of contributing) are the nasty ones.
It is the combination of withdrawals and negative return, which creates the phenomenon. If you were still contributing, you would not care: There is no sequence of returns risk for those who keep investing, or at a minimum do not withdraw.

aristotelian
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Re: Sequence of Return Risk impact on Retirement

Post by aristotelian » Tue Jan 09, 2018 9:39 pm

B is much worse because there is nothing that can be done to mitigate the damage. A is less bad because he can work a couple more years.

KlangFool
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Re: Sequence of Return Risk impact on Retirement

Post by KlangFool » Tue Jan 09, 2018 9:42 pm

Thesaints wrote:
Tue Jan 09, 2018 9:37 pm
KlangFool wrote:
Tue Jan 09, 2018 9:03 pm
But, this is neither (A) or (B).

Is (A) or (B) worse?

KlangFool
What happens before and what happens after retirement is a false problem. If market drops before retirement, you simply keep working (hopefully you have this option), because you haven't reached sufficient capital for retiring safely with the withdrawal rate you have in mind.
Thesaints,

1) I do not have that option. So, please answer my question.

2) No, I am not interested in the more complicated statistical answer with volatility.

3) Let's start with the basic. Bull market = continuous 10% per year return. Bear market continuous 10% per year negative return.

KlangFool

KlangFool
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Re: Sequence of Return Risk impact on Retirement

Post by KlangFool » Tue Jan 09, 2018 9:46 pm

aristotelian wrote:
Tue Jan 09, 2018 9:39 pm
B is much worse because there is nothing that can be done to mitigate the damage. A is less bad because he can work a couple more years.
aristotelian,

That statement is not necessarily true. This is the claim of having a glide path AA that increases the equity portion for the first few years of retirement. The impact of that is you will spend down your bond portion. Hence, even if there is a bear market, the impact will be less.

In summary, what if you sell your bond for the annual expense for that 5 years?

KlangFool

dbr
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Re: Sequence of Return Risk impact on Retirement

Post by dbr » Tue Jan 09, 2018 9:52 pm

KlangFool wrote:
Tue Jan 09, 2018 9:33 pm
Folks,

1) It is bad to withdraw from the portfolio while the return is bad. Hence, it depletes the portfolio faster.

Sequence of returns risk is a subset of that scenario. Withdrawal while return is bad altogether is a larger case of bad luck. Sequence of returns risk is poor returns early in a period compared to later in a period where the overall result is neither good returns or bad returns in particular. You aren't following the math.

2) But, what if we deplete the bond portion while the stock market is down? Or, only deplete the bond portion for the first 5 years of retirement. Then, what happened? Isn't this concept of increasing equity portion as part of the glide path AA during retirement?

Now you are asking about the effect of changing asset allocations while other things are going on at the same time. That is a complicated mathematical problem that has to be modeled. I don't think there is an intuitively evident answer to what should happen. That is why it makes sense to read people like Pfau who actually try to look and see what happens and ignore trying to think things are obvious. That is also why approaches like variable percent withdrawal, which is also a complicated mathematical model, are worth looking at as far as they go. The results may also be complicated. A problem in general with changing asset allocations is that not only risk but also return is being changed and in ways that have opposite effects on what we are interested in. On the other hand we know reducing withdrawal is always a powerful lever on preserving assets, but the timing of more or less withdrawal is hard to figure out. In the meantime everything is dominated by overall luck of history in both catastrophic (market crash) sense and in the secular sense (bull bear markets with multi decade periods). Also the secular course of inflation affects the outcome.

KlangFool

Thesaints
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Re: Sequence of Return Risk impact on Retirement

Post by Thesaints » Tue Jan 09, 2018 9:57 pm

KlangFool wrote:
Tue Jan 09, 2018 9:42 pm
Thesaints,

1) I do not have that option. So, please answer my question.
Then naturally a bear market before you retire is worse, everything else being equal, because it will force you to enter retirement with a smaller capital.
Don't commit the error to think that because there was a bear market before retirement there will have to be a bull market after retirement. That is not how aleatory variables work.
2) No, I am not interested in the more complicated statistical answer with volatility.
Forget volatility. Focus on the fact that withdrawings amplify the negative effects of bear markets and lessen the positive effects of bull markets, so that it takes a larger bull market to compensate for a bear market. Whereas bear and bull markets are equally powerful, as long as you don't withdraw.
Last edited by Thesaints on Tue Jan 09, 2018 10:05 pm, edited 1 time in total.

KlangFool
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Re: Sequence of Return Risk impact on Retirement

Post by KlangFool » Tue Jan 09, 2018 10:00 pm

dbr wrote:
Tue Jan 09, 2018 9:52 pm
KlangFool wrote:
Tue Jan 09, 2018 9:33 pm
Folks,

1) It is bad to withdraw from the portfolio while the return is bad. Hence, it depletes the portfolio faster.

Sequence of returns risk is a subset of that scenario. Withdrawal while return is bad altogether is a larger case of bad luck. Sequence of returns risk is poor returns early in a period compared to later in a period where the overall result is neither good returns or bad returns in particular. You aren't following the math.

2) But, what if we deplete the bond portion while the stock market is down? Or, only deplete the bond portion for the first 5 years of retirement. Then, what happened? Isn't this concept of increasing equity portion as part of the glide path AA during retirement?

Now you are asking about the effect of changing asset allocations while other things are going on at the same time. That is a complicated mathematical problem that has to be modeled. I don't think there is an intuitively evident answer to what should happen. That is why it makes sense to read people like Pfau who actually try to look and see what happens and ignore trying to think things are obvious. That is also why approaches like variable percent withdrawal, which is also a complicated mathematical model, are worth looking at as far as they go. The results may also be complicated. A problem in general with changing asset allocations is that not only risk but also return is being changed and in ways that have opposite effects on what we are interested in. On the other hand we know reducing withdrawal is always a powerful lever on preserving assets, but the timing of more or less withdrawal is hard to figure out. In the meantime everything is dominated by overall luck of history in both catastrophic (market crash) sense and in the secular sense (bull bear markets with multi decade periods). Also the secular course of inflation affects the outcome.

KlangFool
dbr,

1) Sorry. You lost me. I need to understand at a basic and fundamental level before we get into a serious math.

2) Yes, I understand due to reversion to mean and so on, it may even out eventually.

3) But, it still comes down to why a sequence of bad returns during retirement is bad?

KlangFool

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Re: Sequence of Return Risk impact on Retirement

Post by KlangFool » Tue Jan 09, 2018 10:04 pm

Thesaints wrote:
Tue Jan 09, 2018 9:57 pm
KlangFool wrote:
Tue Jan 09, 2018 9:42 pm
Thesaints,

1) I do not have that option. So, please answer my question.
Then naturally a bear market before you retire is worse, everything else being equal, because it will force you to enter retirement with a smaller capital.
Don't commit the error to think that because there was a bear market before retirement there will have to be a bull market after retirement. That is not how aleatory variables work.
2) No, I am not interested in the more complicated statistical answer with volatility.
Forget volatility. Focus on the fact that withdrawings amplify the negative effects of bear markets and lessen the positive effects of bull markets, so that it takes a larger bull markets to compensate for a bear market. Whereas bear and bull markets are equally powerful, as long as you don't withdraw.
Thesaints,

In summary,

A) It is bad to have a bear market while withdrawing.

B) While accumulating, it may not matter whether it is a bear or bull market.

Is that what you are saying?

KlangFool

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Re: Sequence of Return Risk impact on Retirement

Post by Thesaints » Tue Jan 09, 2018 10:08 pm

KlangFool wrote:
Tue Jan 09, 2018 10:04 pm
Thesaints,

In summary,

A) It is bad to have a bear market while withdrawing.

B) While accumulating, it may not matter whether it is a bear or bull market.

Is that what you are saying?

KlangFool
Yes, with minor adjustments

A) it is worst to have a bear market while withdrawing than while contributing.

B) It does not matter, provided the average return in the end is the same.

While withdrawing, instead, two particular sequences of market returns with the same average can have very different outcomes. That is why it is called "sequence of returns risk".

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Re: Sequence of Return Risk impact on Retirement

Post by dbr » Tue Jan 09, 2018 10:11 pm

KlangFool wrote:
Tue Jan 09, 2018 10:00 pm


dbr,

1) Sorry. You lost me. I need to understand at a basic and fundamental level before we get into a serious math.

2) Yes, I understand due to reversion to mean and so on, it may even out eventually.

3) But, it still comes down to why a sequence of bad returns during retirement is bad?

KlangFool
The answer to that is the serious math you don't want to do. Sequence of returns risk is a reference to a certain piece of mathematical calculation that appears when you try to figure out what happens to portfolios given assumed returns together with contributions or withdrawals. A couple of posters have offered some examples.

If I were presenting this discussion to some math students I would probably have them get into a spreadsheet and work some examples in detail to see how different scenarios work out. That would include that the students would have to devise what kind of calculations are needed to be done. You could start by reproducing the results quoted in the example posted by Thesaints, the one with the 5% withdrawals.

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Re: Sequence of Return Risk impact on Retirement

Post by dbr » Tue Jan 09, 2018 10:13 pm

Thesaints wrote:
Tue Jan 09, 2018 10:08 pm
KlangFool wrote:
Tue Jan 09, 2018 10:04 pm
Thesaints,

In summary,

A) It is bad to have a bear market while withdrawing.

B) While accumulating, it may not matter whether it is a bear or bull market.

Is that what you are saying?

KlangFool
Yes, with minor adjustments

A) it is worst to have a bear market while withdrawing than while contributing.

B) It does not matter, provided the average return in the end is the same.

While withdrawing, instead, two particular sequences of market returns with the same average can have very different outcomes. That is why it is called "sequence of returns risk".
Don't forget sequence of returns has an effect while contributing as well. It is just that premature reduction of the portfolio to zero is not one of the consequences. It is only when a single sum is held without contributions or withdrawals that the sequence of returns has no effect at all.

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iceport
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Re: Sequence of Return Risk impact on Retirement

Post by iceport » Tue Jan 09, 2018 10:37 pm

KlangFool wrote:
Tue Jan 09, 2018 9:26 pm
iceport,

I am asking a very simple question in order to further my understanding. What is a bad sequence of returns for 5 years before and after retirement?

Is it

A) Bear market (sequence of 5 years of bad returns) before retirement and bull market at retirement (sequence of 5 years of good returns).

Or

B) The reverse.

KlangFool
I guess I wasn't seeing that simple scenario as a realistic or even necessarily illuminating example. Usually the sequence is more complex. And the difference of even a single year in the starting point of retirement, with everything else being equal, can result in significantly different outcomes.

But even if I am forced to consider only the two rather extreme options you've provided, it still involves some nuance. You need to define "bad."

Scenario A results in a smaller nest egg at retirement. There is a target retirement year, and working longer is not an option you specified. (If working longer is feasible, that's still bad, because the extended working years cut into the planned retirement years.) So in Scenario A, the portfolio might theoretically support a lower withdrawal rate than desired or required. That's bad. At a lower withdrawal rate, and with the following bull market, even with a variable withdrawal strategy the retiree might end up leaving a large unspent balance. If the retiree would have preferred to enjoy more spending and leave less at the end, that could be considered a bad outcome.

Scenario B results in a higher starting balance, and larger retirement withdrawals. But there is greater risk of depleting the portfolio before death. Obviously, that would be bad.

In practice, I wonder how obvious the outcome will be as the time slowly goes by. Because in reality, it's not just the sequence of market returns that affects the outcome. The sequence of inflation is also an important factor. I wonder how obvious the interaction of the two will be over time.
"Discipline matters more than allocation.” ─William Bernstein

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Re: Sequence of Return Risk impact on Retirement

Post by radiowave » Tue Jan 09, 2018 11:34 pm

In practice, I wonder how obvious the outcome will be as the time slowly goes by. Because in reality, it's not just the sequence of market returns that affects the outcome. The sequence of inflation is also an important factor. I wonder how obvious the interaction of the two will be over time.
Excellent point. In my spreadsheet model, I include different scenarios of inflation and expected return on investment for retirement planning. I was quite surprised on the effects of even a modest increase in inflation, > 3% has on the later years of retirement.

I haven't answered KlangFool's question to me above, let me think about this some. I'm more oriented towards looking at cash flow in retirement and effects of withdrawing from bonds which are in tax-deferred and incur income taxes, vs. selling equity in taxable and hopefully minimizing capital gains. My current thinking is to bulk up cash/CDs on the taxable side for the early years in retirement (< 70) to offset paying tax on selling bonds in an IRA/401k before needed at RMD in a scenario of bear market and unrealized equity loss.
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Re: Sequence of Return Risk impact on Retirement

Post by aristotelian » Tue Jan 09, 2018 11:39 pm

dbr wrote:
Tue Jan 09, 2018 10:11 pm
The answer to that is the serious math you don't want to do. Sequence of returns risk is a reference to a certain piece of mathematical calculation that appears when you try to figure out what happens to portfolios given assumed returns together with contributions or withdrawals. A couple of posters have offered some examples.

If I were presenting this discussion to some math students I would probably have them get into a spreadsheet and work some examples in detail to see how different scenarios work out. That would include that the students would have to devise what kind of calculations are needed to be done. You could start by reproducing the results quoted in the example posted by Thesaints, the one with the 5% withdrawals.
A simple explanation would be that a good sequence enables you to purchase stocks in accumulation when prices are cheap and sell when prices are high. This is what we all hope for. If you buy low and sell low, you are probably OK. If you buy high and sell high, you are probably OK. A bad sequence forces you to buy stock in accumulation when prices are high, and sell stock in retirement when prices are low. You get less for your investment than any other scenario. You could have the same average returns but depending on the sequence you will have very different outcomes.

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Re: Sequence of Return Risk impact on Retirement

Post by Thesaints » Wed Jan 10, 2018 1:51 am

Don't forget sequence of returns has an effect while contributing as well. It is just that premature reduction of the portfolio to zero is not one of the consequences. It is only when a single sum is held without contributions or withdrawals that the sequence of returns has no effect at all.
Well, no. For a given realized return it does not matter which particular sequence the market follows if one is contributing, or not withdrawing.
It is only during withdrawals (of fixed amounts) that the particular sequence can help, or hurt.

Even with a cost averaged investment, while higher volatility always helps, the sequence is irrelevant.

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Re: Sequence of Return Risk impact on Retirement

Post by randomguy » Wed Jan 10, 2018 3:12 am

Thesaints wrote:
Wed Jan 10, 2018 1:51 am
Don't forget sequence of returns has an effect while contributing as well. It is just that premature reduction of the portfolio to zero is not one of the consequences. It is only when a single sum is held without contributions or withdrawals that the sequence of returns has no effect at all.
Well, no. For a given realized return it does not matter which particular sequence the market follows if one is contributing, or not withdrawing.
It is only during withdrawals (of fixed amounts) that the particular sequence can help, or hurt.

Even with a cost averaged investment, while higher volatility always helps, the sequence is irrelevant.

Pretty sure he is right.:) Real simple example. You invest 1k/year at the start of each year for 2 years.
a) your earn 0% followed by 10%
1k+0 yearly earnings + 1k + 10% yearly earnings (200 bucks) = 2.200

b) You earn 10% followed by 0%
1k+ 10% earnings(100 bucks) + 1k + 0k earning = 2.1k

Sequencing of returns gives a an extra 100 bucks.

Obviously the real world is more complicated but in general you want higher returns when you have a lot of money invested and low returns when you don't.

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Re: Sequence of Return Risk impact on Retirement

Post by magneto » Wed Jan 10, 2018 3:45 am

One simple point to hang on to, is that in an ideal world, the investor should only be selling Stocks if :-

+ Stocks are at an all-time high and also

+ Fully Valued
Repeat :-
+ And also Fully Valued !!!

Selling for anything else must on reflection be sub-optimal?

This aim can lead investors to various designs of Investment Plan to avoid selling at bad prices.
A well designed Investment Plan, such as the 'Natural Yield' for the more wealthy, or the Frank Armstrong 'buckets' proposal, the latter not entirely without failings; should hopefully enable the investor to sail through those bad Stock price scenarios esp (B), without damaging the portfolio. A slight over-simplification perhaps?

Retirees are presently experiencing a purple patch. :)
'There is a tide in the affairs of men ...', Brutus (Market Timer)

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Re: Sequence of Return Risk impact on Retirement

Post by burt » Wed Jan 10, 2018 7:11 am

William Bernstein does a good job of explaining Sequence of Returns in his paper "The Retirement Calculator from Hell".

http://www.efficientfrontier.com/ef/998/hell.htm

burt

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Re: Sequence of Return Risk impact on Retirement

Post by Lloydo » Wed Jan 10, 2018 7:30 am

radiowave wrote:
Tue Jan 09, 2018 11:34 pm
In practice, I wonder how obvious the outcome will be as the time slowly goes by. Because in reality, it's not just the sequence of market returns that affects the outcome. The sequence of inflation is also an important factor. I wonder how obvious the interaction of the two will be over time.
Excellent point. In my spreadsheet model, I include different scenarios of inflation and expected return on investment for retirement planning. I was quite surprised on the effects of even a modest increase in inflation, > 3% has on the later years of retirement.

I haven't answered KlangFool's question to me above, let me think about this some. I'm more oriented towards looking at cash flow in retirement and effects of withdrawing from bonds which are in tax-deferred and incur income taxes, vs. selling equity in taxable and hopefully minimizing capital gains. My current thinking is to bulk up cash/CDs on the taxable side for the early years in retirement (< 70) to offset paying tax on selling bonds in an IRA/401k before needed at RMD in a scenario of bear market and unrealized equity loss.
Looking at your “current thinking”, would it change if you had 100% equities in taxable but could still fund 8+ years of withdrawals even following a very significant (30% +) drop in market value? I other words, one could sell equities in taxable and rebalance the equity position in tax deferred. Would it still make sense to “bulk up cash”in taxable?

Thanks.

Lloyd

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Re: Sequence of Return Risk impact on Retirement

Post by carolinaman » Wed Jan 10, 2018 8:06 am

burt wrote:
Wed Jan 10, 2018 7:11 am
William Bernstein does a good job of explaining Sequence of Returns in his paper "The Retirement Calculator from Hell".

http://www.efficientfrontier.com/ef/998/hell.htm

burt
Good article by Bernstein. He describes a 30 year period between 1966 and 1995. The first 15 years had zero real return on equity. He did not state what bond return was, but it had to be negative the first 15 years given the very high inflation of the 70s and early 80s. The only return that worked was one based on a percentage withdrawal. Of course in actual dollars, the withdrawal may be 30% to 50% less in a really bad bear market. Many people would be severely challenged to live on that much of a reduced withdrawal.

We tend to think of bear markets and ensuing recoveries in relatively short periods whereas the one Bernstein described was much longer. Most bear/bull cycles are relatively short but some are like the 1966 to 1981 in impact although they may have different characteristics.

I think any viable strategy to deal with SORR needs to include a decent buffer to allow for more severe markets. If you need $40k from a $1M portfolio, then perhaps increase your portfolio to $1.5M or higher so you can more realistically survive on a constant percentage withdrawal rather than a constant amount. You should also review your expenses for areas to cut in the event of a bad market and reduced withdrawals. Some combination of expense reductions and higher portfolio should give you greater protection.

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Re: Sequence of Return Risk impact on Retirement

Post by smitcat » Wed Jan 10, 2018 9:12 am

Another good article on SOR risk by KItces....

https://www.kitces.com/blog/understandi ... d-decades/

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Re: Sequence of Return Risk impact on Retirement

Post by Da5id » Wed Jan 10, 2018 9:26 am

You may like this article too:
It (and the next one) discuss the topic both for savers and those withdrawing...

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Re: Sequence of Return Risk impact on Retirement

Post by KlangFool » Wed Jan 10, 2018 10:10 am

aristotelian wrote:
Tue Jan 09, 2018 11:39 pm
dbr wrote:
Tue Jan 09, 2018 10:11 pm
The answer to that is the serious math you don't want to do. Sequence of returns risk is a reference to a certain piece of mathematical calculation that appears when you try to figure out what happens to portfolios given assumed returns together with contributions or withdrawals. A couple of posters have offered some examples.

If I were presenting this discussion to some math students I would probably have them get into a spreadsheet and work some examples in detail to see how different scenarios work out. That would include that the students would have to devise what kind of calculations are needed to be done. You could start by reproducing the results quoted in the example posted by Thesaints, the one with the 5% withdrawals.
A simple explanation would be that a good sequence enables you to purchase stocks in accumulation when prices are cheap and sell when prices are high. This is what we all hope for. If you buy low and sell low, you are probably OK. If you buy high and sell high, you are probably OK. A bad sequence forces you to buy stock in accumulation when prices are high, and sell stock in retirement when prices are low. You get less for your investment than any other scenario. You could have the same average returns but depending on the sequence you will have very different outcomes.
aristotelian,

Thank you. This is the level of detail that I am looking for.

KlangFool

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Re: Sequence of Return Risk impact on Retirement

Post by KlangFool » Wed Jan 10, 2018 10:25 am

Folks,

In general, we reduce our equity exposure via a glide path AA adjustment as we get closer to the number. Then, we arrive at our number and we retired. For the first 5 or 10 years of retirement, if we hit a bear market, we are in serious danger of running out of money. So, there is a suggestion of a reverse glide path of spending down the bond and increasing stock equity allocation in order to handle that.

Yes, there are a lot of paper and reference that talked about this. And, they confused me. I could use a simple example to show how it supposed to work.

So, at retirement, with a portfolio of 1.5 million with AA of 60/40 and the annual expense of 60K per year. What would be the reverse glide path look like?

Year 0 -> 60/40
Year 1 -> 64/36
Year 2 -> 68/32

The above example spends 4% on the bond. Or, the percent adjustment per year is based on something else?

KlangFool

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Re: Sequence of Return Risk impact on Retirement

Post by dbr » Wed Jan 10, 2018 10:40 am

KlangFool wrote:
Wed Jan 10, 2018 10:25 am
Folks,

In general, we reduce our equity exposure via a glide path AA adjustment as we get closer to the number. Then, we arrive at our number and we retired. For the first 5 or 10 years of retirement, if we hit a bear market, we are in serious danger of running out of money. So, there is a suggestion of a reverse glide path of spending down the bond and increasing stock equity allocation in order to handle that.

Yes, there are a lot of paper and reference that talked about this. And, they confused me. I could use a simple example to show how it supposed to work.

So, at retirement, with a portfolio of 1.5 million with AA of 60/40 and the annual expense of 60K per year. What would be the reverse glide path look like?

Year 0 -> 60/40
Year 1 -> 64/36
Year 2 -> 68/32

The above example spends 4% on the bond. Or, the percent adjustment per year is based on something else?

KlangFool
The glide path one might choose is arbitrary. You have an illustration using a 4% change every year. There is no reason whatsoever that glidepath would be preferred over any other until you have tabulated the outcomes for many different possibilities and compared them. That is more or less what is going on in the various references you refer to. Your sentence "spends 4% in the bond" I don't understand. How you actually manipulate the asset allocation depends on what has to be done each year regarding selling and buying assets after their market values have moved and including that something has to be sold to take the withdrawal. An example is that if stocks are down, one sells enough in bonds to withdraw and enough additionally in bonds to increase the allocation to stocks. If stocks are up one might sell stocks to fund the withdrawal and additionally sell more stocks to bring the proportion in bonds to whatever it should be. A person could also just always sell bonds and never stocks no matter what happens. I have no idea what the comparative outcomes for these different suggestions actually turns out to be as a statistical estimate. Note all estimates of future results are by their very nature statistical as our estimates of what future returns will be must be statistical in nature.

I am not aware of an algorithm that comes up with an optimum path for asset allocation over time given some desired figure of merit for an outcome. It might look like some sort of variational principal, but I wouldn't know if that really works for something like retirement planning: https://en.wikipedia.org/wiki/Variational_principle

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Re: Sequence of Return Risk impact on Retirement

Post by KlangFool » Wed Jan 10, 2018 10:51 am

dbr wrote:
Wed Jan 10, 2018 10:40 am
KlangFool wrote:
Wed Jan 10, 2018 10:25 am
Folks,

In general, we reduce our equity exposure via a glide path AA adjustment as we get closer to the number. Then, we arrive at our number and we retired. For the first 5 or 10 years of retirement, if we hit a bear market, we are in serious danger of running out of money. So, there is a suggestion of a reverse glide path of spending down the bond and increasing stock equity allocation in order to handle that.

Yes, there are a lot of paper and reference that talked about this. And, they confused me. I could use a simple example to show how it supposed to work.

So, at retirement, with a portfolio of 1.5 million with AA of 60/40 and the annual expense of 60K per year. What would be the reverse glide path look like?

Year 0 -> 60/40
Year 1 -> 64/36
Year 2 -> 68/32

The above example spends 4% on the bond. Or, the percent adjustment per year is based on something else?

KlangFool
The glide path one might choose is arbitrary. You have an illustration using a 4% change every year. There is no reason whatsoever that glidepath would be preferred over any other until you have tabulated the outcomes for many different possibilities and compared them. That is more or less what is going on in the various references you refer to. Your sentence "spends 4% in the bond" I don't understand. How you actually manipulate the asset allocation depends on what has to be done each year regarding selling and buying assets after their market values have moved and including that something has to be sold to take the withdrawal. An example is that if stocks are down, one sells enough in bonds to withdraw and enough additionally in bonds to increase the allocation to stocks. If stocks are up one might sell stocks to fund the withdrawal and additionally sell more stocks to bring the proportion in bonds to whatever it should be. A person could also just always sell bonds and never stocks no matter what happens. I have no idea what the comparative outcomes for these different suggestions actually turns out to be as a statistical estimate. Note all estimates of future results are by their very nature statistical as our estimates of what future returns will be must be statistical in nature.

I am not aware of an algorithm that comes up with an optimum path for asset allocation over time given some desired figure of merit for an outcome. It might look like some sort of variational principal, but I wouldn't know if that really works for something like retirement planning: https://en.wikipedia.org/wiki/Variational_principle
dbr,

<< How you actually manipulate the asset allocation depends on what has to be done each year regarding selling and buying assets after their market values have moved and including that something has to be sold to take the withdrawal. >>

My glide path leading towards retirement is based on the portfolio size as a ratio of my annual expense. So, the AA at 25 X my annual expense is 60/40.

The question here is if I would create a glide path AA for retirement, what would it be based on? Portfolio size as a ratio of retirement expense? Years after retirement? We can go down to the specific much later. But, what would this AA be based on?

One of the example which may be wrong is to adjust the AA by 4% per year. That will trigger either selling bond or stock to reach that AA. But, this method does not take into account of portfolio size that may increase or decrease due to market.

KlangFool

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Mountain Doc
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Re: Sequence of Return Risk impact on Retirement

Post by Mountain Doc » Wed Jan 10, 2018 11:33 am

The math is below. In both scenarios, the S&P 500 starts at 2500 and ends at 6000 for a CAGR of 6%. However, the first scenario involves an initial bear market followed by a bull market. The second scenario involves a bull market followed by a flat market. You end up with totally different final balances even though in both scenarios the S&P 500 returned 6% compounded annually. This is because your withdrawals from 65-69 in the first scenario cause you to have less money in the market at the bottom, therefore you do not participate in the subsequent climb as much.


Age Balance S&P 500 Withdrawal S&P 500 Final balance
65 $1,500,000. 2500 -$60,000 2300 $1,324,800
66 $1,324,800. 2300 -$60,000 2200 $1,209,809
67 $1,209,809. 2200 -$60,000 1800 $940,753
68 $940,753 1800 -$60,000 1400 $685,030
69 $685,030 1400 -$60,000 1300 $580,385
70 $580,385 1300 -$60,000 1400 $560,414
71 $560,414 1400 -$60,000 1900 $679,134
72 $679,134 1900 -$60,000 2200 $716,892
73 $716,892 2200 -$60,000 2500 $746,468
74 $746,468 2500 -$60,000 3000 $823,762
75 $823,762 3000 -$60,000 3500 $891,055
76 $891,055 3500 -$60,000 4000 $949,777
77 $949,777 4000 -$60,000 4500 $1,000,999
78 $1,000,999 4500 -$60,000 5000 $1,045,555
79 $1,045,555. 5000 -$60,000 5500 $1,084,110
80 $1,084,110. 5500 -$60,000 6000 $1,117,211

Age Balance S&P 500 Withdrawal S&P 500 Final balance
65 $1,500,000 2500 -$60,000 2700 $1,555,200
66 $1,555,200 2700 -$60,000 3400 $1,882,844
67 $1,882,844 3400 -$60,000 3700 $1,983,684
68 $1,983,684 3700 -$60,000 4200 $2,183,641
69 $2,183,641 4200 -$60,000 4900 $2,477,581
70 $2,477,581 4900 -$60,000 5000 $2,466,919
71 $2,466,919 5000 -$60,000 5100 $2,455,058
72 $2,455,058 5100 -$60,000 5200 $2,442,020
73 $2,442,020 5200 -$60,000 5300 $2,427,828
74 $2,427,828 5300 -$60,000 5400 $2,412,504
75 $2,412,504 5400 -$60,000 5500 $2,396,069
76 $2,396,069 5500 -$60,000 5600 $2,378,543
77 $2,378,543 5600 -$60,000 5700 $2,359,945
78 $2,359,945 5700 -$60,000 5800 $2,340,295
79 $2,340,295 5800 -$60,000 5900 $2,319,611
80 $2,319,611 5900 -$60,000 6000 $2,297,909

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Re: Sequence of Return Risk impact on Retirement

Post by remomnyc » Wed Jan 10, 2018 1:43 pm

I entered your data into cfiresim.com. Retirement start 2022 (age 62), end 2055 (age 95). Portfolio value $1.6M, 60/40. Spending $60k adjusted for inflation. Rebalance until 2022. Then target asset 100% equities start 2022 (at retirement), end 2030 (8 yrs later, to simulate spending down all bonds). Lowest portfolio is $560,778. No failures. It appears the rising equity path saves you in the years with bad sequence of returns.

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Re: Sequence of Return Risk impact on Retirement

Post by KlangFool » Wed Jan 10, 2018 1:55 pm

Folks,

Let's start with a baseline of 60/40, 1.5 million, and with 60K per year.

Let's assume that the stock market crash 50% and stay down for 5 years. The bond stays at 0%.

Option 1) This person rebalances to 60/40 every year.

Year 0 -> 1.5 went down to 1.05 million
Year 1 -> 990K
Year 2 -> 930K
Year 3 -> 870K
Year 4 -> 810K
Year 5 -> 750K

After year 5, the stock market doubles. The portfolio went up 60%. 750K * 1.6 = 1.2 million

Option 2) Only sell bond

Year 0 -> 1.5 went down to 1.05 million = 630K stock and 420K bond.
Year 1 -> 990K
Year 2 -> 930K
Year 3 -> 870K
Year 4 -> 810K
Year 5 -> 750K

After year 5, the portfolio consists of 630K stock and 120K bond. After year 5, the stock market doubles. Portfolio size = 630K X 2 +120K = 1.38 million.

KlangFool

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