A Simple (not easy) Elimination of SOR Risk

[David Jay]

I have laid out over several recent threads that Sequence of Return (SOR) risk has two components: Portfolio volatility and relatively level withdrawals. If there is no portfolio volatility, there can be no SOR issue. If there are no withdrawals (or deposits, as there is SOR impact for those in accumulation), there can be no SOR issue. Both must be present in order for sequence of return issues to exist. If either is missing then the commutative property controls and sequence does not matter.

Much as been publicized about reducing volatility. I myself utilized a "bond tent" in early retirement because I had relatively thin safety margins and sought to minimize portfolio volatility in the early years of retirement. But I have not seen a published evaluation looking at the withdrawal side:

Here is the simple (not great in practice) way to eliminate all SOR risk: If withdrawals are proportional to portfolio size, there can be no sequence of return issue. The commutative property of multiplication applies and the sequence of returns is immaterial. So a fixed percent of portfolio withdrawal removes all SOR risk.

Examples with fixed, 5% of portfolio balance annual withdrawal:

Sequence 1 - Early poor performance, 3 down years(-20%), followed by 27 up years (+7%).
Note: the 5% withdrawal subtracts from the annual percentage of portfolio change - i.e. down years are down 25% (-20%-5%) and up years are up 2% (7%-5%).

Starting Portfolio Balance * .75³ * 1.02²⁷ = Ending portfolio balance

Sequence 2 - Late poor performance, 27 up years (+7%), followed by 3 down years (-20%)

Starting Portfolio Balance * 1.02²⁷ * .75³ = Ending portfolio balance

Anyone with a knowledge of basic math will recognize that (.75³ * 1.02²⁷) = (1.02²⁷ * .75³)

Again, I want to state for the record that this is not a recommended withdrawal strategy for the typical retiree, it is an inductive evaluation of Sequence of Return. But intuitively, this would suggest that reducing withdrawals in down years and increasing withdrawals in up years would reduce SOR impact.

[Marseille07]

Here is the simple (not great in practice) way to eliminate all SOR risk: If withdrawals are proportional to portfolio size, there can be no sequence of return issue. The commutative property of multiplication applies and the sequence of returns is immaterial. So a fixed percent of portfolio withdrawal removes all SOR risk.

This is an important point, and what "constant-percentage" approaches solve (such as constant-%, VPW, ABW and what have you).

[scout1]

This is a great point that I did not realize. Thank you!

[Marseille07]

Imo percentage-based methods make more sense than constant-dollar + inflation, anyway. When your portfolio is down 40%, you cut back on travel plans, spend down your EF etc etc.

[jarjarM]

So basically reduce spending when SOR is going against the retiree. That's why I think one needs some buffer in the spending so that can happen in a down year. Thanks for the analysis.

[vineviz]

Here is the simple (not great in practice) way to eliminate all SOR risk: If withdrawals are proportional to portfolio size, there can be no sequence of return issue. The commutative property of multiplication applies and the sequence of returns is immaterial. So a fixed percent of portfolio withdrawal removes all SOR risk.

A percentage-based withdrawal strategy does not remove sequence of returns risk. It just moves the impact of the risk from the terminal value to the amount of income withdrawn.

Take a look at what happens to the real (inflation-adjusted) portfolio income using the annual returns of a portfolio from 1991 to 2020. The returns are organized in three different sequences:

1) Chronological (actual) order;
2) Highest returns first;
3) Lowest returns first;



Despite the fact that all three sequences generate the same ENDING portfolio value, they do NOT generate the same income. In fact, sequence 2 generates over 6 times as much lifetime income as sequence 3.

Even if the investor knew with perfect certainty that their portfolio would earn an average return of 10% with 2.2% inflation, they still would be facing a significant risk: the average income from a $100k portfolio could range anywhere from $2,700 to $16,700.

[MathIsMyWayr]

Here is the simple (not great in practice) way to eliminate all SOR risk: If withdrawals are proportional to portfolio size, there can be no sequence of return issue. The commutative property of multiplication applies and the sequence of returns is immaterial. So a fixed percent of portfolio withdrawal removes all SOR risk.

A percentage-based withdrawal strategy does not remove sequence of returns risk. It just moves the impact of the risk from the terminal value to the amount of income withdrawn.

David's statement is not wrong. However, it is misleading: a matter of the truth in advertising.

How to avoid gaining weight: eat only when you are not hungry.

[David Jay]

Here is the simple (not great in practice) way to eliminate all SOR risk: If withdrawals are proportional to portfolio size, there can be no sequence of return issue. The commutative property of multiplication applies and the sequence of returns is immaterial. So a fixed percent of portfolio withdrawal removes all SOR risk.

A percentage-based withdrawal strategy does not remove sequence of returns risk. It just moves the impact of the risk from the terminal value to the amount of income withdrawn.

Take a look at what happens to the real (inflation-adjusted) portfolio income using the annual returns of a portfolio from 1991 to 2020. The returns are organized in three different sequences:

1) Chronological (actual) order;
2) Highest returns first;
3) Lowest returns first;



Despite the fact that all three sequences generate the same ENDING portfolio value, they do NOT generate the same income. In fact, sequence 2 generates over 6 times as much lifetime income as sequence 3.

Even if the investor knew with perfect certainty that their portfolio would earn an average return of 10% with 2.2% inflation, they still would be facing a significant risk: the average income from a $100k portfolio could range anywhere from $2,700 to $16,700.

Nicely done. You have moved the discussion away from sequence of risk to other portfolio risks (which you continue to call SOR, though I do not know why, other than obfuscate). Which truly exist. Income generation is a risk, but just because you put a label on the top that says "SORR" does not make it a sequence of return question.

[David Jay]

Here is the simple (not great in practice) way to eliminate all SOR risk: If withdrawals are proportional to portfolio size, there can be no sequence of return issue. The commutative property of multiplication applies and the sequence of returns is immaterial. So a fixed percent of portfolio withdrawal removes all SOR risk.

A percentage-based withdrawal strategy does not remove sequence of returns risk. It just moves the impact of the risk from the terminal value to the amount of income withdrawn.

David's statement is not wrong. However, it is misleading: a matter of the truth in advertising.

How to avoid gaining weight: eat only when you are not hungry.

At least you understand the math.

As I said to Vineviz, there are many, very real portfolio risks. SOR has been incorrectly used to describe many of these risks.

[corn18]

Here is the simple (not great in practice) way to eliminate all SOR risk: If withdrawals are proportional to portfolio size, there can be no sequence of return issue. The commutative property of multiplication applies and the sequence of returns is immaterial. So a fixed percent of portfolio withdrawal removes all SOR risk.

A percentage-based withdrawal strategy does not remove sequence of returns risk. It just moves the impact of the risk from the terminal value to the amount of income withdrawn.

Take a look at what happens to the real (inflation-adjusted) portfolio income using the annual returns of a portfolio from 1991 to 2020. The returns are organized in three different sequences:

1) Chronological (actual) order;
2) Highest returns first;
3) Lowest returns first;



Despite the fact that all three sequences generate the same ENDING portfolio value, they do NOT generate the same income. In fact, sequence 2 generates over 6 times as much lifetime income as sequence 3.

Even if the investor knew with perfect certainty that their portfolio would earn an average return of 10% with 2.2% inflation, they still would be facing a significant risk: the average income from a $100k portfolio could range anywhere from $2,700 to $16,700.

Could you do the analysis for sequence 3 with a 40% decrease in spending until returns reverted to the mean? Would be curious to see if that helps mitigate the income risk.

NEVERMIND: The data I seek is inherent in line 3. 50% haircut for many, many years. Ouch. So even if you reduce spending in year 1-10, it really doesn't help recover. It just keeps you from going completely broke. That is moderately terrifying.

[marcopolo]

Here is the simple (not great in practice) way to eliminate all SOR risk: If withdrawals are proportional to portfolio size, there can be no sequence of return issue. The commutative property of multiplication applies and the sequence of returns is immaterial. So a fixed percent of portfolio withdrawal removes all SOR risk.

A percentage-based withdrawal strategy does not remove sequence of returns risk. It just moves the impact of the risk from the terminal value to the amount of income withdrawn.

Take a look at what happens to the real (inflation-adjusted) portfolio income using the annual returns of a portfolio from 1991 to 2020. The returns are organized in three different sequences:

1) Chronological (actual) order;
2) Highest returns first;
3) Lowest returns first;



Despite the fact that all three sequences generate the same ENDING portfolio value, they do NOT generate the same income. In fact, sequence 2 generates over 6 times as much lifetime income as sequence 3.

Even if the investor knew with perfect certainty that their portfolio would earn an average return of 10% with 2.2% inflation, they still would be facing a significant risk: the average income from a $100k portfolio could range anywhere from $2,700 to $16,700.

Nicely done. You have moved the discussion away from sequence of risk to other portfolio risks (which you continue to call SOR, though I do not know why, other than obfuscate). Which truly exist. Income generation is a risk, but just because you put a label on the top that says "SORR" does not make it a sequence of return question.

I am not sure that is not a SORR. The drop in income happens precisely because of the sequence of returns.
The only thing you are changing is how that risk is absorbed.
In constant-dollar approach you absorb it by running out of money before the planning horizon.
In constant-percentage approach you absorb it by taking lower withdrawals in many years.

Both of those were necessary because you got hit with a poor SOR.

[patrick013]

I'm still stuck on a strategic allocation.

A basic 3 year bond ladder where each year represents one year
of expenses. 3 years being the time most market crashes would
fully recover and capital gains would be available again at
average or expected levels. If risk aversion is more important
make it a 5 year or longer bond ladder. Replenish the ladder
when stock prices recover from SOR.

There hasn't been a 20 year stagnant market since before 1900
while the longest stagnant market in more modern times has been
~10 years. Where prices took that long to recover from previous
levels for the market portfolio index.

You shouldn't have to reduce spending with a bond ladder covering
expenses during SOR market crashes.

[David Jay]

I'm still stuck on a strategic allocation.

A basic 3 year bond ladder where each year represents one year
of expenses. 3 years being the time most market crashes would
fully recover and capital gains would be available again at
average or expected levels. If risk aversion is more important
make it a 5 year or longer bond ladder. Replenish the ladder
when stock prices recover from SOR.

There hasn't been a 20 year stagnant market since before 1900
while the longest stagnant market in more modern times has been
~10 years. Where prices took that long to recover from previous
levels for the market portfolio index.

You shouldn't have to reduce spending with a bond ladder covering
expenses during SOR market crashes.

This is a common fallacy. SORR is not about asset allocation (other than the marginal reduction in volatility from holding more bonds). It is about withdrawing larger percentages of one’s portfolio when the market is down. A poor sequence of returns will deplete a portfolio regardless if one is withdrawing from bonds or stocks. See the graph below, note that no asset allocation is described:


I address this more fully here: viewtopic.php?t=315102

[corn18]

I took a quick look at the impact of AA on the actual, worst and best SOR. I used returns from 1994-2011. Looks like adding more FI reduces the magnitude of the income reduction.

For worst case run:

60/40 Min = $2,505 = 50% reduction
100/0 Min = $1,468 = 71% reduction
0/100 Min = $4,035 = 19% reduction

The really scary part is that it takes 16-17 YEARS to get back to the original withdrawal value. YIKES! Anyone thinking they can just spend less in down years is going to be spending less for a really looooooonnnnnng time.

[Wrench]

I have laid out over several recent threads that Sequence of Return (SOR) risk has two components: Portfolio volatility and relatively level withdrawals. If there is no portfolio volatility, there can be no SOR issue. If there are no withdrawals (or deposits, as there is SOR impact for those in accumulation), there can be no SOR issue. Both must be present in order for sequence of return issues to exist. If either is missing then the commutative property controls and sequence does not matter.

Much as been publicized about reducing volatility. I myself utilized a "bond tent" in early retirement because I had relatively thin safety margins and sought to minimize portfolio volatility in the early years of retirement. But I have not seen a published evaluation looking at the withdrawal side:

Here is the simple (not great in practice) way to eliminate all SOR risk: If withdrawals are proportional to portfolio size, there can be no sequence of return issue. The commutative property of multiplication applies and the sequence of returns is immaterial. So a fixed percent of portfolio withdrawal removes all SOR risk.

Examples with fixed, 5% of portfolio balance annual withdrawal:

Sequence 1 - Early poor performance, 3 down years(-20%), followed by 27 up years (+7%).
Note: the 5% withdrawal subtracts from the annual percentage of portfolio change - i.e. down years are down 25% (-20%-5%) and up years are up 2% (7%-5%).

Starting Portfolio Balance * .75³ * 1.02²⁷ = Ending portfolio balance

Sequence 2 - Late poor performance, 27 up years (+7%), followed by 3 down years (-20%)

Starting Portfolio Balance * 1.02²⁷ * .75³ = Ending portfolio balance

Anyone with a knowledge of basic math will recognize that (.75³ * 1.02²⁷) = (1.02²⁷ * .75³)

Again, I want to state for the record that this is not a recommended withdrawal strategy for the typical retiree, it is an inductive evaluation of Sequence of Return. But intuitively, this would suggest that reducing withdrawals in down years and increasing withdrawals in up years would reduce SOR impact.

Thank you for pointing out that "If there is no portfolio volatility, there can be no SOR issue". I can think of four ways then to eliminate SOR, though they are only really practical for those at or near traditional retirement age (not for FIRE folks):
1. Social security
2. Single premium income annuity (SPIA)
3. Stable value funds with fixed guaranteed interest rate.
4. A pension.
None of these are risk-free of course, and #3 and #4 may not be available to many. But they DO eliminate SOR risk. I would suggest that some combination of these with a fraction of one's portfolio to provide an income floor would reduce the risk of SOR sufficiently in the balance of the portfolio so one should be able to sleep well at night. It does come at the cost of working longer, reducing potential returns, and for #2, losing control of the investment. Two and maybe three out of the four also do not have inflation adjustments so real income will decrease for those with time. These disadvantages may make these approaches unacceptable to some (many?), though it happens to work for me.

Wrench

[corn18]

I do take comfort that the annual returns for the stock market have never looked like the worst or best case. They look kindof choppy, which helps mitigate SORR. None of the best/worst returns look like the S&P actual returns. This is a good thing. Might they in the future? No clue.

S&P Returns



60/40 SORR returns (can you figure out which line is actual, best, worst?)



100/0 SORR returns



0/100 SORR returns



One cool thing about these charts is just pick a starting point on the actual line and shift that to the initial withdrawal value. That will show you what would happen if you started in different years.

[Ben Mathew]

I am not sure that is not a SORR. The drop in income happens precisely because of the sequence of returns.
The only thing you are changing is how that risk is absorbed.
In constant-dollar approach you absorb it by running out of money before the planning horizon.
In constant-percentage approach you absorb it by taking lower withdrawals in many years.

Both of those were necessary because you got hit with a poor SOR.

I too have interpreted SORR to include income withdrawals, not just terminal balance.

If SORR is defined solely on terminal balance, amortization based withdrawal (ABW) guarantees that the portfolio will be depleted down to a predetermined terminal balance. So, like the fixed percentage withdrawal proposed in the OP, ABW would eliminate SORR on terminal balance (but not SORR on total withdrawals.)

[Ben Mathew]

Again, I want to state for the record that this is not a recommended withdrawal strategy for the typical retiree, it is an inductive evaluation of Sequence of Return. But intuitively, this would suggest that reducing withdrawals in down years and increasing withdrawals in up years would reduce SOR impact.

Agree with your conclusion that percentage based withdrawal strategies reduce SORR. Amortization based withdrawal (ABW) is basically percentage based, which is why it does pretty well in terms of SORR. Unlike the fixed percentage withdrawal described in the OP, the ABW withdrawal percentage is not constant. But the math still carries through:

final balance = initial balance * (1+r1)(1-w1)(1+r2)(1-w2).....(1+r30)(1-w30)

where wi is percentage withdrawal in year i.

Sequence of returns doesn't matter for final balance even if the wi are not the same.

(There will still be SORR over income withdrawals. This can't be avoided. But it can be minimized, and ABW strategies do a good job of that.)

[vineviz]

Nicely done. You have moved the discussion away from sequence of risk to other portfolio risks (which you continue to call SOR, though I do not know why, other than obfuscate). Which truly exist. Income generation is a risk, but just because you put a label on the top that says "SORR" does not make it a sequence of return question.

If you're going to discuss sequence of return risk, the least you should do is make some effort to understand it.

Sequence of return risk is nothing more or less than the risk that an unfavorable sequence of returns will negatively impact the investor's ability to achieve their goal.

In the the three paths I plotted, only the sequence (i.e. the order) of the returns differed. The average returns were the same, the volatility of returns was the same, the withdrawal strategy (i.e. percentage of portfolio) was the same.

The only variable is sequence.

That makes what I illustrated sequence of return risk.

You may have assumed that sequence of returns risk only refers to the impact of the sequence on the longevity of the portfolio or its terminal value. That's a common assumption, but it is mistaken.

[vineviz]

NEVERMIND: The data I seek is inherent in line 3. 50% haircut for many, many years. Ouch. So even if you reduce spending in year 1-10, it really doesn't help recover. It just keeps you from going completely broke. That is moderately terrifying.

Keep in mind that the illustration I provided upthread was stylized: I showed the absolute best and absolute worst possible sequence of those particular return. In real life, even a "bad" sequence of returns would have no chance of being as bad as the worst case scenario I showed.

[David Jay]

Nicely done. You have moved the discussion away from sequence of risk to other portfolio risks (which you continue to call SOR, though I do not know why, other than obfuscate). Which truly exist. Income generation is a risk, but just because you put a label on the top that says "SORR" does not make it a sequence of return question.

If you're going to discuss sequence of return risk, the least you should do is make some effort to understand it.

Sequence of return risk is nothing more or less than the risk that an unfavorable sequence of returns will negatively impact the investor's ability to achieve their goal.

In the the three paths I plotted, only the sequence (i.e. the order) of the returns differed. The average returns were the same, the volatility of returns was the same, the withdrawal strategy (i.e. percentage of portfolio) was the same.

The only variable is sequence.

That makes what I illustrated sequence of return risk.

You may have assumed that sequence of returns risk only refers to the impact of the sequence on the longevity of the portfolio or its terminal value. That's a common assumption, but it is mistaken.

OK, we will have to agree to disagree on our respective definitions (kind of like the “diversification” discussion a ways back).

All the best.

[patrick013]

You shouldn't have to reduce spending with a bond ladder covering
expenses during SOR market crashes.

This is a common fallacy. SORR is not about asset allocation (other than the marginal reduction in volatility from holding more bonds). It is about withdrawing larger percentages of one’s portfolio when the market is down. A poor sequence of returns will deplete a portfolio regardless if one is withdrawing from bonds or stocks.

The only way I can think of which avoids SOR account depletion is maintaining a
bond ladder (CD) where all withdrawals are made at par from matured bonds or
CD's target dated for that purpose. It's a terrible thing having to withdraw from
an account where 30-40% loss has occured no doubt. So individual target dated
bonds can be used until stocks recover. TBM can still be used for other bonds
not target dated. So in that regard the model has/could be changed.

[aj76er]

You shouldn't have to reduce spending with a bond ladder covering
expenses during SOR market crashes.

This is a common fallacy. SORR is not about asset allocation (other than the marginal reduction in volatility from holding more bonds). It is about withdrawing larger percentages of one’s portfolio when the market is down. A poor sequence of returns will deplete a portfolio regardless if one is withdrawing from bonds or stocks.

The only way I can think of which avoids SOR account depletion is maintaining a
bond ladder (CD) where all withdrawals are made at par from matured bonds or
CD's target dated for that purpose. It's a terrible thing having to withdraw from
an account where 30-40% loss has occured no doubt. So individual target dated
bonds can be used until stocks recover. TBM can still be used for other bonds
not target dated. So in that regard the model has/could be changed.

If you keep a constant percentage in rest of portfolio, then this is essentially the bond-tent idea.

However, unless the bonds are TIPs or IBonds you still have inflation risk. Today, you can build a TIPs ladder, but you must adjust for the negative yield (since you'll get less back at maturity). And IBonds have purchase limit issues.

Not a lot of good solutions to SORR aside from just being really darn rich, unfortunately.

[patrick013]

The only way I can think of which avoids SOR account depletion is maintaining a
bond ladder (CD) where all withdrawals are made at par from matured bonds or
CD's target dated for that purpose. It's a terrible thing having to withdraw from
an account where 30-40% loss has occured no doubt. So individual target dated
bonds can be used until stocks recover. TBM can still be used for other bonds
not target dated. So in that regard the model has/could be changed.

If you keep a constant percentage in rest of portfolio, then this is essentially the bond-tent idea.

However, unless the bonds are TIPs or IBonds you still have inflation risk. Today, you can build a TIPs ladder, but you must adjust for the negative yield (since you'll get less back at maturity). And IBonds have purchase limit issues.

Not a lot of good solutions to SORR aside from just being really darn rich, unfortunately.

Bond-tent sounds fine to me. With a 3 year bond tent I think most people
could still maintain a 50-50 AA or even a 75-25 stock/bond AA.

[Schlabba]

I'm still stuck on a strategic allocation.

A basic 3 year bond ladder where each year represents one year
of expenses. 3 years being the time most market crashes would
fully recover and capital gains would be available again at
average or expected levels. If risk aversion is more important
make it a 5 year or longer bond ladder. Replenish the ladder
when stock prices recover from SOR.

There hasn't been a 20 year stagnant market since before 1900
while the longest stagnant market in more modern times has been
~10 years. Where prices took that long to recover from previous
levels for the market portfolio index.

You shouldn't have to reduce spending with a bond ladder covering
expenses during SOR market crashes.

This is a common fallacy. SORR is not about asset allocation (other than the marginal reduction in volatility from holding more bonds). It is about withdrawing larger percentages of one’s portfolio when the market is down. A poor sequence of returns will deplete a portfolio regardless if one is withdrawing from bonds or stocks. See the graph below, note that no asset allocation is described:


I address this more fully here: viewtopic.php?t=315102

SORR is not about asset allocation? But aren't portfolios like the Permanent Portfolio or the All-Weather Portfolio designed for not running out of money?

[David Jay]

I'm still stuck on a strategic allocation.

A basic 3 year bond ladder where each year represents one year
of expenses. 3 years being the time most market crashes would
fully recover and capital gains would be available again at
average or expected levels. If risk aversion is more important
make it a 5 year or longer bond ladder. Replenish the ladder
when stock prices recover from SOR.

There hasn't been a 20 year stagnant market since before 1900
while the longest stagnant market in more modern times has been
~10 years. Where prices took that long to recover from previous
levels for the market portfolio index.

You shouldn't have to reduce spending with a bond ladder covering
expenses during SOR market crashes.

This is a common fallacy. SORR is not about asset allocation (other than the marginal reduction in volatility from holding more bonds). It is about withdrawing larger percentages of one’s portfolio when the market is down. A poor sequence of returns will deplete a portfolio regardless if one is withdrawing from bonds or stocks. See the graph below, note that no asset allocation is described:


I address this more fully here: viewtopic.php?t=315102

SORR is not about asset allocation? But aren't portfolios like the Permanent Portfolio or the All-Weather Portfolio designed for not running out of money?

(running out of money) != (sequence of return risk)

This is one of the challenges, we are approaching the point on this forum of characterizing every retirement risk as “sequence of return” risk.

Sequence of Return risk refers to only one thing - what happens if “bad years” come early and “good years” come late.