## The current annuity factor

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
Topic Author
bobcat2
Posts: 5568
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

### The current annuity factor

Allison Schrager, who writes the weekly finance newsletter Known Unknowns for pension geeks like yours truly, has just written her initial column for Bloomberg on retirement planning. Here's a key portion of that column.
You might have encountered a guideline that you can spend 4% of your savings each year. But really the amount you can spend is dependent on interest rates and inflation, and at the current low rates that protect you from inflation, which have even dipped negative, your money doesn’t go as far. ...

There are few hard and fast rules when it comes to retirement finance, but one is this: if you want to see how much you can spend each year, divide your wealth by 32. That’s the current annuity factor, a number based on inflation-adjusted interest rates that helps you figure out how much \$1 of spending will cost over a prospective 30 years of retirement.

Real interest rates, which protect you from inflation, have fallen in recent years, making it more expensive to finance future spending — at today’s negative rates, ensuring you have \$1 to spend in 30 years costs \$1.01 today. That change in real interest rates has also driven up the annuity factor by 13% since January 2020.

Think about it his way: Suppose you had \$500,000 in January 2020 when the annuity factor was 28. That meant you could afford to spend \$17,500 a year in retirement. By May 2021, if you invested all your money in the stock market, you’d have \$646,000, a 30% increase. But your spending capacity only increased 14%, to \$20,000 because the annuity factor jumped to 32.
Link to article - https://www.bloomberg.com/opinion/artic ... -you-think

The annuity factor for 'n' periods at a periodic yield of 'r' is calculated as:

AF(n,r) = (1 - (1 + r)-n ) / r
Note that when r is zero then PV=FV=30 for 30 years

So the currrent slightly negative real interest rates result in an annuity factor of 32 for a 30 year period. Or as Schrager puts it, you need \$1.01 today to receive \$1.00 in thirty years. And of course most people who were 17 months from retirement at the beginning of last year were not 100% stocks.

BobK
Last edited by bobcat2 on Mon May 24, 2021 7:49 pm, edited 1 time in total.
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Kenkat
Posts: 7350
Joined: Thu Mar 01, 2007 11:18 am
Location: Cincinnati, OH

### Re: The current annuity factor

So 3% is the new 4% then. Great.
grabiner
Posts: 29905
Joined: Tue Feb 20, 2007 11:58 pm
Location: Columbia, MD

### Re: The current annuity factor

The 4% rule was always based on inflation-adjusted spending. And it didn't assume an all-TIPS portfolio (which would have an annuity factor of 32); a balanced portfolio is likely to outperform inflation by enough that you can spend more from it.

That said, the current projected returns from a balanced portfolio are probably also lower now than they were in the past, with negative TIPS yields, and nominal yields less than expected inflation. Therefore, the 4% withdrawal rate may be less safe than it was in the past.
David Grabiner
RubyTuesday
Posts: 775
Joined: Fri Oct 19, 2012 11:24 am

### Re: The current annuity factor

Am I understanding this correctly?

Assume you want to fund 40 year retirement with TIPs. Would you use 20 year yield because duration of retirement is 20, or 40 year rate (which doesn’t exist)?

If you use a 20 year duration, the 20 year real yield is -0.25%.

You get an Annuity Factor of

AF = (1 - (1 + r)^(-n))) / r where n = 40, r = -0.25%
AF ~= 42
Or 2.4% withdrawal
“Doing nothing is better than being busy doing nothing.” – Lao Tzu
grabiner
Posts: 29905
Joined: Tue Feb 20, 2007 11:58 pm
Location: Columbia, MD

### Re: The current annuity factor

RubyTuesday wrote: Mon May 24, 2021 8:53 pm Am I understanding this correctly?

Assume you want to fund 40 year retirement with TIPs. Would you use 20 year yield because duration of retirement is 20, or 40 year rate (which doesn’t exist)?
You would use the middle of retirement.

You can fund a 30-year retirement with a TIPS ladder; that ladder would have a duration of 15 years, so the 15-year rate would be close to the average rate of return on your TIPS.

For 40 years, you could not quite guarantee the retirement with TIPS, but you could come close, buying new TIPS when your 30-year TIPS mature 30 years from now. Thus the duration of 20 years makes sense.
David Grabiner
nisiprius
Posts: 43755
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

### Re: The current annuity factor

I'm about 80% sure I understand this... let me state it as if I did, in hope of correction if I am mistaken.

"Annuity" has too many meanings, and in this article the word "annuity" is being used in a legitimate way that is different from the way I usually use it.

Usually I use "annuity" to mean "life annuity," a series of payments continuing for the rest of someone's life--that is to say for a variable and uncertain period of time.

In the strict sense, "annuity" simply means any regular series of payments, and that's how it's being used here.

She is using the word "annuity" to mean "a series of payments continuing for exactly thirty years."

This goes back to the days when books of math tables had forty-page sections devoted to "the present value of an annuity."

Her "annuity factor" corresponds to the total number of dollars you would get from a inflation-adjusted 30-year MYGA, if such a thing existed, and if the insurance company invested 100% in TIPS and took no profit... or something like that.

Actually, it's not even clear to me what interest rate her chart is based on--that is to say, how many years' term is assumed.

Is it literally calculating the cost of a ladder of TIPS, purchased today, in which the amount of each issue purchased is cleverly calculated so that for every year over the next thirty years, the sum of the total number of real dollars, from coupon payments plus the repayment of principal from maturing bonds, is equal every year?

Notice that the words "longevity" and "life expectancy" do not appear in the article or in bobcat2's formula.

It does not mean that the safe withdrawal rate from a 60/40 portfolio is going to be 1/32.

As a practical consideration I don't even know how you act on this information, other than trying to time the market in choosing your retirement year.

It probably bears a decent proportional correspondence to the price you would need to pay for an inflation-adjusted SPIA--if such things still existed. Actually such an SPIA could pay more, because it has access to a source of income not accounted for in the "annuity factor:" mortality credits from participants living less than thirty years, and since life expectancy at age 65 is a good deal less than thirty years, the collective number for a pool of annuitants would be a good deal higher than the number for an individual drawing income for exactly thirty years.

In any case, on the face of it we are looking at fluctuations on that chart that are relatively small amounts of uncertainty compared to the a) the uncertainty of longevity, and b) the uncertainty of future return in a portfolio with even a conservative stock allocation.

Last edited by nisiprius on Tue May 25, 2021 6:19 am, edited 1 time in total.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
grok87
Posts: 9615
Joined: Tue Feb 27, 2007 9:00 pm

### Re: The current annuity factor

bobcat2 wrote: Mon May 24, 2021 7:41 pm Allison Schrager, who writes the weekly finance newsletter Known Unknowns for pension geeks like yours truly, has just written her initial column for Bloomberg on retirement planning. Here's a key portion of that column.
You might have encountered a guideline that you can spend 4% of your savings each year. But really the amount you can spend is dependent on interest rates and inflation, and at the current low rates that protect you from inflation, which have even dipped negative, your money doesn’t go as far. ...

There are few hard and fast rules when it comes to retirement finance, but one is this: if you want to see how much you can spend each year, divide your wealth by 32. That’s the current annuity factor, a number based on inflation-adjusted interest rates that helps you figure out how much \$1 of spending will cost over a prospective 30 years of retirement.

Real interest rates, which protect you from inflation, have fallen in recent years, making it more expensive to finance future spending — at today’s negative rates, ensuring you have \$1 to spend in 30 years costs \$1.01 today. That change in real interest rates has also driven up the annuity factor by 13% since January 2020.

Think about it his way: Suppose you had \$500,000 in January 2020 when the annuity factor was 28. That meant you could afford to spend \$17,500 a year in retirement. By May 2021, if you invested all your money in the stock market, you’d have \$646,000, a 30% increase. But your spending capacity only increased 14%, to \$20,000 because the annuity factor jumped to 32.
Link to article - https://www.bloomberg.com/opinion/artic ... -you-think

The annuity factor for 'n' periods at a periodic yield of 'r' is calculated as:

AF(n,r) = (1 - (1 + r)-n ) / r
Note that when r is zero then PV=FV=30 for 30 years

So the currrent slightly negative real interest rates result in an annuity factor of 32 for a 30 year period. Or as Schrager puts it, you need \$1.01 today to receive \$1.00 in thirty years. And of course most people who were 17 months from retirement at the beginning of last year were not 100% stocks.

BobK
thanks for posting Bob. very interesting. I think for clarity, i might suggest your formula to read:

AF(n,r) = [1 - (1 + r)^(-n) ]/ r

Here is the table i get using your formula:
• n -0.45% 0% 0.45%
5 5.07 5.00 4.93
10 10.25 10.00 9.76
15 15.55 15.00 14.47
20 20.98 20.00 19.09
25 26.52 25.00 23.59
30 32.20 30.00 28.00
RIP Mr. Bogle.
Grt2bOutdoors
Posts: 23795
Joined: Thu Apr 05, 2007 8:20 pm
Location: New York

### Re: The current annuity factor

Kenkat wrote: Mon May 24, 2021 7:48 pm So 3% is the new 4% then. Great.
The interesting thing is 25/32 is a rate of 3.125. For those who’s longevity factor based on family health issues is more or less in the 25 year bucket, 4 percent may continue to be fine. Those who have 30-40 year retirements should have been using a lower annuity factor to begin with. You don’t have to withdraw from your account on an inflation adjusted basis each year either. It would be interesting to see how many retirees on the forum are each year withdrawing the previous year’s withdrawal plus inflation. As others have previously posted, if you see the balance declining more quickly you make adjustments to spend less and preserve what you have.
"One should invest based on their need, ability and willingness to take risk - Larry Swedroe" Asking Portfolio Questions
Topic Author
bobcat2
Posts: 5568
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

### Re: The current annuity factor

grok87 wrote: Tue May 25, 2021 6:05 am
bobcat2 wrote: Mon May 24, 2021 7:41 pm

The annuity factor for 'n' periods at a periodic yield of 'r' is calculated as:
AF(n,r) = (1 - (1 + r)-n )/ r

BobK
thanks for posting Bob. very interesting. I think for clarity, i might suggest your formula to read:

AF(n,r) = [1 - (1 + r)^(-n) ]/ r
I agree.

Another way that's cleaner than what I originally wrote is
AF(n,r) = [1 - (1/(1 + r)^n )]/r

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
HappyJack
Posts: 269
Joined: Thu Jan 10, 2019 7:45 am

### Re: The current annuity factor

Bob
Would it he possible for you to illustrate this formula with some hypothetical values illustrating what the math represents.
Topic Author
bobcat2
Posts: 5568
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

### Re: The current annuity factor

This calculation is telling you how much a fixed time annuity costs. As such it's a useful metric for how expensive retirement income will be over your retirement horizon. Schrager is using 30 years and using real rather than nominal dollars.
An annuity table is a tool that simplifies the calculation of the present value of an annuity. Also referred to as a “present value table,” an annuity table contains the present value interest factor of an annuity (PVIFA), which you then multiply by your recurring payment amount to get the present value of your annuity.
In the generic case Schrager is using, the recurring payment is \$1.

When real interest rates are low retirement is expensive, unless your entire portfolio is in equity.

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
grok87
Posts: 9615
Joined: Tue Feb 27, 2007 9:00 pm

### Re: The current annuity factor

HappyJack wrote: Tue May 25, 2021 9:16 am Bob
Would it he possible for you to illustrate this formula with some hypothetical values illustrating what the math represents.
here's the table
• n -0.45% 0% 0.45%
5 5.07 5.00 4.93
10 10.25 10.00 9.76
15 15.55 15.00 14.47
20 20.98 20.00 19.09
25 26.52 25.00 23.59
30 32.20 30.00 28.00
for example at current real interest rates, with a 25 year horizon you would need 26.52x in a tips ladder for every dollar of retirement spending needs.

so if you need \$10k a year then you need \$265.2k in a tips ladder
RIP Mr. Bogle.
Kenkat
Posts: 7350
Joined: Thu Mar 01, 2007 11:18 am
Location: Cincinnati, OH

### Re: The current annuity factor

Grt2bOutdoors wrote: Tue May 25, 2021 7:02 am
Kenkat wrote: Mon May 24, 2021 7:48 pm So 3% is the new 4% then. Great.
The interesting thing is 25/32 is a rate of 3.125. For those who’s longevity factor based on family health issues is more or less in the 25 year bucket, 4 percent may continue to be fine. Those who have 30-40 year retirements should have been using a lower annuity factor to begin with. You don’t have to withdraw from your account on an inflation adjusted basis each year either. It would be interesting to see how many retirees on the forum are each year withdrawing the previous year’s withdrawal plus inflation. As others have previously posted, if you see the balance declining more quickly you make adjustments to spend less and preserve what you have.
I would think you are correct that very few people set their withdraw at 4%, adjust it for inflation each year and that’s it come what may. It is probably better as a planning number than an execution number.

In my situation, if/when I retire early, I may need/choose to draw down my portfolio at a rate of 5-6% for a few years until things such as pensions and social security kick in, at which point my draw will be closer to 0-1% which should put me in good shape.
nisiprius
Posts: 43755
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

### Re: The current annuity factor

bobcat2 wrote: Tue May 25, 2021 9:20 am...When real interest rates are low retirement is expensive, unless your entire portfolio is in equity...
?????

First, I don't see how "equity" can be taken into account in this methodology at all. You know the future real payouts from a TIPS bond with near-certainty, but not from equities.

Second, there is a way to increase income without taking more risk... or rather by reducing the financial effect of longevity risk. The 30 year number is an attempt, and not a very good one, to allow for longevity by crude brute force: picking a single, fixed, conservative number and hoping you won't outlive it. 30 years is considerably more than life expectancy at age 65. Yet at the same time many of us can name people in our circle of acquaintances who are more than 95 years old--even men who are more than 95 years old.

If you are willing to become part of a risk pool, you can take advantage of "mortality credits" that are available to annuitants in such a pool. That is, in a pool of annuitants it is possible for everyone to withdraw on the basis of average remaining life expectancy, which is more like 20 years than 30. That creates a significant improvement in the numbers.

Actually, I thought that was what "annuity factor" was going to mean.

An immediate annuity website is showing me that \$100,000 will buy a 65-year-old female a life annuity with a starting payment of \$330/month and a 3% compound annual increase. Since the Fed targets 2% inflation, a 3% compound annual increase for inflation isn't a crazy planning number. That works out to 3.96% per year, with is about 1.25X the "1/32" = 3⅛% number in the article. And it is for life, with no 30-year limit (balanced by the likelihood of not paying out for a full 30 years).

So if you are willing to pool risk, you can multiply the "annuity factor" by something I will call an "actuarial longevity factor," which I define as the improvement in monthly income obtainable by in a group life annuity, over the number for a fixed 30-year period. And that is something in the ballpark of 1.25.

In other words, 1/32 is the pessimistic worst of both worlds. It is not the best you can do, because you can increase it in two completely different ways: 1) by taking on more investment risk than a 100% TIPS ladder, or 2) taking advantage of mortality credits by buying an insurance product that lets payouts be based on group average life expectancy. And yet at the same time it is not good enough, because it doesn't allow for living past age 95.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
DaufuskieNate
Posts: 437
Joined: Wed May 28, 2014 11:53 am

### Re: The current annuity factor

nisiprius wrote: Tue May 25, 2021 10:36 am I don't see how "equity" can be taken into account in this methodology at all.
If by methodology we are referring to the formula and not a guaranteed annuity in the literal sense, then the formula is just another way of expressing the PMT function. In this sense, a historical or projected real equity return can be plugged into the formula and used in a variable withdrawal regime such as VPW or ABW.
nisiprius
Posts: 43755
Joined: Thu Jul 26, 2007 9:33 am
Location: The terrestrial, globular, planetary hunk of matter, flattened at the poles, is my abode.--O. Henry

### Re: The current annuity factor

DaufuskieNate wrote: Tue May 25, 2021 11:18 am
nisiprius wrote: Tue May 25, 2021 10:36 am I don't see how "equity" can be taken into account in this methodology at all.
If by methodology we are referring to the formula and not a guaranteed annuity in the literal sense, then the formula is just another way of expressing the PMT function. In this sense, a historical or projected real equity return can be plugged into the formula and used in a variable withdrawal regime such as VPW or ABW.
Except that we have the actual future numbers for a TIPS ladder purchased today, and we don't for equities.

The whole point of the article is that it (claims to) present a "hard and fast rule."
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
nedsaid
Posts: 14747
Joined: Fri Nov 23, 2012 12:33 pm

### Re: The current annuity factor

nisiprius wrote: Tue May 25, 2021 10:36 am
bobcat2 wrote: Tue May 25, 2021 9:20 am...When real interest rates are low retirement is expensive, unless your entire portfolio is in equity...
?????
Let me take a stab at this. I don't think Bob is advocating for 100% equity portfolios in retirement, I think what he is saying that with very low interest rates that people are taking more risk in their portfolios. People assume, incorrectly, that stocks will steadily have higher returns than bonds. We know that it is very likely that stocks will outperform bonds in the future, what we don't know is when that excess return will show up. Just think of the folks with stock heavy portfolios who retired in 1929, or 1973, or 2000, or 2008, just before a very nasty bear market. It is called the sequence of returns problem. I think Bob is saying, in a backhanded sort of way that people are fooling themselves about the risks they are taking. Of course, I can't speak for Bob.

I would like to ask Bob, and I hope that he responds, how the negative real returns from TIPS are figuring into retirement planning. What is Dr. Merton saying about this and how does this affect the construction of the Dimensional Fund Advisors Target Date Retirement funds? As far as I can tell, not much has changed at DFA.

For new readers, the DFA Target Date Funds get to be very heavy with TIPS as one approaches retirement. For example, the DFA Target Date Retirement 2025 fund has Global stocks at 35%, Global bonds at 4%, and TIPS at 61%. When I see negative real returns for both nominal and inflation protected bonds, I go YIKES! My guess is that such a portfolio might create a 1% to 2% real return after inflation. In a crisis, TIPS can be amazingly volatile.
A fool and his money are good for business.
Topic Author
bobcat2
Posts: 5568
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

### Re: The current annuity factor

Hi nisi,

First of all this is not my methodology, it's a common methodology actuaries use. And an important point that is being made here is that retirement is expensive when real interest rates are low. This is something that is ignored when the '4% rule' is used.

The only way you can get around the extra retirement expense of low real interest rates is to be all equity. A very risky proposition for a retiree not contemplating becoming a possible former retiree. One of Schrager's points was that even though the stock market is way up since the end of 2019, retirees are not that much better off, because real interest rates have fallen, thus offsetting much of the equity gains. The '4% rule' completely fails to supply this warning signal.

The 4% rule is simply a bad rule. Better to use the funded ratio, or apply the RMD rule to all your assets dedicated to producing retirement income, or even the annuity factor. All these rules, unlike the 4% rule, at least take account of where you are now - not where you thought you'd be today several years ago.

The 4% advocates point out that you don't strictly follow the rule, and cut back spending if portfolio returns head south. But the point of prudent retirement planning is to minimize the times and amounts you have to cut spending back. All these simple rules do a much better job of that than the '4% rule'.

All three of these rules give guidance on how much to cut back, after bad returns. The '4%' rule says your guess is as good as mine as to how far to cut back.

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
nedsaid
Posts: 14747
Joined: Fri Nov 23, 2012 12:33 pm

### Re: The current annuity factor

Okay Bob. Could you address my question on TIPS?

Just to clarify my own position, I like TIPS but the negative real returns make me a bit nervous about them. Earlier this year, I did increase modestly my position in TIPS and might do so again. Also to clarify, TIPS were volatile during the 2008-2009 crisis and again in 2020 during the Covid-19 bear market but each time did rebound smartly and the volatility was short lived. I am certainly not anti-TIPS at all.

A fool and his money are good for business.
David Jay
Posts: 11054
Joined: Mon Mar 30, 2015 5:54 am
Location: Michigan

### Re: The current annuity factor

bobcat2 wrote: Tue May 25, 2021 11:54 amThe only way you can get around the extra retirement expense of low real interest rates is to be all equity.
Why do you keep repeating that phrase? It is most certainly not necessary to be "all equity" to receive the benefit of equity growth. How about 20/80? 30/70?
Prediction is very difficult, especially about the future - Niels Bohr | To get the "risk premium", you really do have to take the risk - nisiprius
TN_Boy
Posts: 2265
Joined: Sat Jan 17, 2009 12:51 pm

### Re: The current annuity factor

bobcat2 wrote: Tue May 25, 2021 11:54 am Hi nisi,

First of all this is not my methodology, it's a common methodology actuaries use. And an important point that is being made here is that retirement is expensive when real interest rates are low. This is something that is ignored when the '4% rule' is used.

The only way you can get around the extra retirement expense of low real interest rates is to be all equity. A very risky proposition for a retiree not contemplating becoming a possible former retiree. One of Schrager's points was that even though the stock market is way up since the end of 2019, retirees are not that much better off, because real interest rates have fallen, thus offsetting much of the equity gains. The '4% rule' completely fails to supply this warning signal.

The 4% rule is simply a bad rule. Better to use the funded ratio, or apply the RMD rule to all your assets dedicated to producing retirement income, or even the annuity factor. All these rules, unlike the 4% rule, at least take account of where you are now - not where you thought you'd be today several years ago.

The 4% advocates point out that you don't strictly follow the rule, and cut back spending if portfolio returns head south. But the point of prudent retirement planning is to minimize the times and amounts you have to cut spending back. All these simple rules do a much better job of that than the '4% rule'.

All three of these rules give guidance on how much to cut back, after bad returns. The '4%' rule says your guess is as good as mine as to how far to cut back.

BobK
Well, my conservative portfolio (about 50-50) is up over 13% since the end of 2019 (after a fine 2019 return of 15%) so I'm not quite seeing Schrager's point. I feel better off .......

I'm not following the "only way is to be all equity." I don't understand why it is all or nothing. I thought that primary determinate of portfolio growth has always been equity returns, so any decent chunk of equity will drive returns. It's great when bonds are yielding well above inflation, but low real returns on bonds are hardly unique to 2021.

The 4% "rule" certainly has flaws, but the unmodified RMD rule is awful -- you get to spend all your money in your mid 70s and beyond -- so much for enjoying the early healthier years of retirement with travel and such. I would prefer some other variable spending approach to RMD calculations.
GoneCamping
Posts: 69
Joined: Mon Mar 01, 2021 6:45 pm

### Re: The current annuity factor

bobcat2 wrote: Tue May 25, 2021 11:54 am Hi nisi,

The 4% rule is simply a bad rule. Better to use the funded ratio, or apply the RMD rule to all your assets dedicated to producing retirement income, or even the annuity factor. All these rules, unlike the 4% rule, at least take account of where you are now - not where you thought you'd be today several years ago.
This part, about where you are now, is there an annuity table that reflects this for today's low/negative interest rates? I can only find ones that have 1% as the lowest, in which case the annuity factor is 25.8 for 30 years, yielding a significantly higher (24%) wd rate of 3.875%. So getting only a 1% return on a portfolio gets us back pretty close to the old standard 4% rule using the annuity factor.

It seems to me this is just another way, and a very conservative one at that, of arriving at a safer and more current 4% rule, somewhere between 3-4% instead. And in the current low interest climate, it happens to be 3.125%.
Topic Author
bobcat2
Posts: 5568
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

### Re: The current annuity factor

nedsaid wrote: Tue May 25, 2021 11:46 am I would like to ask Bob, and I hope that he responds, how the negative real returns from TIPS are figuring into retirement planning. What is Dr. Merton saying about this ...
Negative real interest rates are bad news, and not just regarding TIPS. I don't think in finance it was ever contemplated that there would be an extended period where real interest rates were zero or negative. For instance, I have never seen TVM example calculations using negative interest rates. Just this morning I was looking at tables with calculated annuity factors. I saw several tables, but the lowest interest rate was 1%.

Another example, present value is often called discounted present value. The two terms are treated as equivalent. But when real interest rates are negative, appreciated present value is the appropriate term. (Today's value is worth more than next year's value, which in turn is worth more than values farther in the future.)

If you are in the lowest 2/3's of the wealth distribution at retirement, this doesn't make much difference. Your primary income source in retirement will be SS in all likelihood. If you are in the top 3% of the wealth distribution, this won't make much difference to your income in retirement. For the remaining 30%, the high middle wealth group, this is a retirement income problem with no easy solution that I am aware of.

BobK

Corrected spelling error.
Last edited by bobcat2 on Tue May 25, 2021 1:14 pm, edited 1 time in total.
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
nedsaid
Posts: 14747
Joined: Fri Nov 23, 2012 12:33 pm

### Re: The current annuity factor

bobcat2 wrote: Tue May 25, 2021 12:35 pm
nedsaid wrote: Tue May 25, 2021 11:46 am I would like to ask Bob, and I hope that he responds, how the negative real returns from TIPS are figuring into retirement planning. What is Dr. Merton saying about this ...
Negative real interest rates are bad news, and not just regarding TIPS. I don't think in finance it was ever contemplated that there would be an extended period where real interest rates were zero or negative. For instance, I have never seen TVM example calculations using negative interest rates. Just this morning I was looking at tables with calculated annuity factors. I saw several tables, but the lowest interest rate was 1%.

Another example, present value is often called discounted present value. The two terms are treated as equivalent. But when real interest rates are negative, appreciated present value is the appropriate term. (Today's value is worth more than next year's value, which in term is worth more than values farther in the future.)

If you are in the lowest 2/3's of the wealth distribution at retirement, this doesn't make much difference. Your primary income source in retirement will be SS in all likelihood. If you are in the top 3% of the wealth distribution, this won't make much difference to your income in retirement. For the remaining 30%, the high middle wealth group, this is a retirement income problem with no easy solution that I am aware of.

BobK
Thanks Bob for your thoughtful response. Sometimes you have to settle for an imperfect solution and TIPS are an example of that. If inflation continues to tick up, TIPS will fare better than nominal bonds but still won't provide 100% purchasing power protection. Not perfect, but better than the alternative. Despite all of this, I nibbled on TIPS earlier this year and might add to them again.

I keep looking at the US Treasury Yield Curve and it still looks okay. So far, the bond market is not anticipating a prolonged increase in the inflation rate as the yield curve is still well behaved. My guess, not being a bond analyst, is that the markets believe that most of the recent rise in inflation is transitory, such things as supply chain bottlenecks and temporary shortages.

Anywho, I am glad that I am not the only one out there who is puzzled by negative real interest rates and what to do about it.
A fool and his money are good for business.
GoneCamping
Posts: 69
Joined: Mon Mar 01, 2021 6:45 pm

### Re: The current annuity factor

bobcat2 wrote: Tue May 25, 2021 12:35 pm
nedsaid wrote: Tue May 25, 2021 11:46 am I would like to ask Bob, and I hope that he responds, how the negative real returns from TIPS are figuring into retirement planning. What is Dr. Merton saying about this ...
Negative real interest rates are bad news, and not just regarding TIPS. I don't think in finance it was ever contemplated that there would be an extended period where real interest rates were zero or negative. For instance, I have never seen TVM example calculations using negative interest rates. Just this morning I was looking at tables with calculated annuity factors. I saw several tables, but the lowest interest rate was 1%.

Another example, present value is often called discounted present value. The two terms are treated as equivalent. But when real interest rates are negative, appreciated present value is the appropriate term. (Today's value is worth more than next year's value, which in term is worth more than values farther in the future.)

If you are in the lowest 2/3's of the wealth distribution at retirement, this doesn't make much difference. Your primary income source in retirement will be SS in all likelihood. If you are in the top 3% of the wealth distribution, this won't make much difference to your income in retirement. For the remaining 30%, the high middle wealth group, this is a retirement income problem with no easy solution that I am aware of.

BobK
But is it? Isn't it just a drag on the FI portion of a portfolio? So, on average, a drag on the 40-60% of a portfolio reliant on interest rates? Again, using the annuity factor table, a 1% rate of return on a portfolio pushes the SWR back to 3.875%, meaning in a 50/50 portfolio one need only realize 2% on the equity side to see that 24% bump in SWR from 3.125% to 3.875%.

It does mean needing more exposure to equities perhaps but this nothing new for retirees, it's just now that its a little worse than it's been but it's been bad with low interest rates for a long time now.
Topic Author
bobcat2
Posts: 5568
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

### Re: The current annuity factor

GoneCamping wrote: Tue May 25, 2021 12:57 pm It does mean needing more exposure to equities perhaps but this nothing new for retirees, it's just now that its a little worse than it's been but it's been bad with low interest rates for a long time now.
Yes, but until 2019 it was generally considered an oddity that would straighten itself out once the unemployment hangover from the Great Recession worked its way out. We got to full employment by early 2019 (using any reasonable definition of full employment) and interest rates didn't budge. We now now that this is not a transitory phenomenon, but a LT problem with no solution in sight.

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Topic Author
bobcat2
Posts: 5568
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

### Re: The current annuity factor

If you are 75% fixed income - low real interest rates are hurting you.
If you are 60% fixed income - low real interest rates are hurting you.
If you are 30% fixed income - low real interest rates are hurting you.
If you are 20% or less fixed income in retirement - you are taking a lot of risk.

At retirement Joe has a million dollar portfolio at retirement. His portfolio is 60% bonds and 40% equity. If real interest rates are about 3%, which is about what they averaged from the mid 80s thru about 2001, Joe gets 18,000 per year in real interest. At zero or less real rates that \$18,000 is gone. That's a problem for Joe.

Notice that the '4% rule' doesn't care. Joe takes out \$40,000 in the first year regardless of whether the \$18,000 is there or not.

BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
GoneCamping
Posts: 69
Joined: Mon Mar 01, 2021 6:45 pm

### Re: The current annuity factor

I'm coming at it more from the angle of the first post, which is relative to the SWR and 4% "rule" and how the low/negative interest rates impact that.

That's not to say it's not "hurting" someone but it's situational; there's a difference between hurting someone and hurting someone's portfolio IMO. If someone has planned for a comfortable retirement based on a 3%-4% WR it is still reasonable to think they have a very good chance at a successful for ~30 years. To say that the current rate environment is hurting them may or may not be true but if they don't have to alter their spending and simply see less portfolio growth, that's not so bad.

It would be wonderful to get back to some sense of normalcy WRT interest rates and have the FI portion of our portfolios generate interest at least keeping pace with inflation if not even providing a little growth. Since I've contemplated retirement, that's simply never been the case. I've read a lot about the 4% rule being too aggressive now and that a safer bet is closer to 3% and this thread is aligned with that thinking. I appreciate your insights here and providing yet another tool for us. I'm not disagreeing, rather I just guess I'm conditioned to it and it's nothing new really so I'd already considered it in my planning.
AlwaysLearningMore
Posts: 235
Joined: Sun Jul 26, 2020 2:29 pm

### Re: The current annuity factor

If you are 75% fixed income - low real interest rates are hurting you.
If you are 60% fixed income - low real interest rates are hurting you.
If you are 30% fixed income - low real interest rates are hurting you.
If you are 20% or less fixed income in retirement - you are taking a lot of risk.

At retirement Joe has a million dollar portfolio at retirement. His portfolio is 60% bonds and 40% equity. If real interest rates are about 3%, which is about what they averaged from the mid 80s thru about 2001, Joe gets 18,000 per year in real interest. At zero or less real rates that \$18,000 is gone. That's a problem for Joe.

Notice that the '4% rule' doesn't care. Joe takes out \$40,000 in the first year regardless of whether the \$18,000 is there or not.

BobK
If Joe and his wife Joanne had been accumulating EE bonds over the years for each of them (and also perhaps through a trust for one or both of them) and at retirement began redeeming those bonds in succession (after 20 year each), then they'd be enjoying the one-time Treasury resent and thus a 3.53% return. They'd have a 20-year period certain payout. With that foundation Joanne and Joe could arrange the balance of their portfolio to see them through retirement.

And since years ago Joanne suggested that they also invest in I Bonds for an element of liability matching, they're definitely in decent financial shape.
Last edited by AlwaysLearningMore on Tue May 25, 2021 2:33 pm, edited 1 time in total.
Retirement is best when you have a lot to live on, and a lot to live for.
tibbitts
Posts: 13957
Joined: Tue Feb 27, 2007 6:50 pm

### Re: The current annuity factor

GoneCamping wrote: Tue May 25, 2021 12:26 pm It seems to me this is just another way, and a very conservative one at that, of arriving at a safer and more current 4% rule, somewhere between 3-4% instead. And in the current low interest climate, it happens to be 3.125%.
Except that the 4% rule was never the 4% rule for global equities. So you have to make that additional reduction, the math for which I'll let someone else figure out.
nedsaid
Posts: 14747
Joined: Fri Nov 23, 2012 12:33 pm

### Re: The current annuity factor

tibbitts wrote: Tue May 25, 2021 2:16 pm
GoneCamping wrote: Tue May 25, 2021 12:26 pm It seems to me this is just another way, and a very conservative one at that, of arriving at a safer and more current 4% rule, somewhere between 3-4% instead. And in the current low interest climate, it happens to be 3.125%.
Except that the 4% rule was never the 4% rule for global equities. So you have to make that additional reduction, the math for which I'll let someone else figure out.
I have joked about the Zero fund portfolio and now it seems we are heading for a Zero withdrawal rate in retirement. The only reason to take money out is for Required Minimum Distributions at age 72 and afterwards. We might be back to working until you can't work anymore and then moving in with the kids.

Low interest rates have complicated retirement planning. Retirees might have to take more risk by owning more stocks than they would like and to really watch their spending. "Safe" bonds might reduce portfolio volatility but are also delivering negative real returns. Sort of like your mom telling you to sit up straight, eat your spinach, and to do your homework from school. It isn't what we want to hear but it is a message we all need.

If I could get real returns above inflation of 3% from TIPS, probably 40% or more of my portfolio would be in them. I would be maybe 40% stocks. There was a day when bonds gave you 6% to 8% returns and now we are looking at 1% to 2% returns. With inflation, bonds are almost guaranteed now to lose purchasing power over time. So we might be back to the 65% stock/35% bond portfolio that John Bogle said was good for most investors.

What hurts even more is that the Alternative Investments, which were sort of an alternative to bonds, have mostly been pretty disappointing. Many threads on this topic.

It certainly isn't hopeless but we do have to temper our expectations.
A fool and his money are good for business.
grok87
Posts: 9615
Joined: Tue Feb 27, 2007 9:00 pm

### Re: The current annuity factor

grabiner wrote: Mon May 24, 2021 8:07 pm The 4% rule was always based on inflation-adjusted spending. And it didn't assume an all-TIPS portfolio (which would have an annuity factor of 32); a balanced portfolio is likely to outperform inflation by enough that you can spend more from it.

That said, the current projected returns from a balanced portfolio are probably also lower now than they were in the past, with negative TIPS yields, and nominal yields less than expected inflation. Therefore, the 4% withdrawal rate may be less safe than it was in the past.
Agree.

I think one way to frame this is to ask: what is the expected real return of the balanced (say 60/40) portfolio?
Say it's 5% for stocks and 0% for bonds right now. so that would be an expected real return of 3%. So maybe 3% is the new Safe Withdrawal rate.

cheers,
grok
RIP Mr. Bogle.
#Cruncher
Posts: 3222
Joined: Fri May 14, 2010 2:33 am
Location: New York City
Contact:

### Re: The current annuity factor

nisiprius wrote: Tue May 25, 2021 5:48 am... it's not even clear to me what interest rate her chart is based on ... Is it literally calculating the cost of a ladder of TIPS, purchased today, in which the amount of each issue purchased is cleverly calculated so that for every year over the next thirty years, the sum of the total number of real dollars, from coupon payments plus the repayment of principal from maturing bonds, is equal every year?
The Bloomberg article doesn't say how the "annuity factor" is calculated. Underneath the graph it simply says "Source: Bloomberg", which is not very helpful! The article could be using the cost of of a 30-year TIPS ladder divided by the annual constant dollar proceeds. By coincidence I get 31.9 (the 2021 value in the article's graph) if I use the default ladder from my TIPS Ladder Builder Excel workbook with prices from today's WSJ TIPS Quotes.
31.9 = 958159 / 30000

Code: Select all

`````` 5/25/2021 base date                        Mult  Nbr     Cost  Principal
5/25/2021 quote date                  Sum    30  651   958,159   749,986
Interest                        150,032
Combined                        900,017
Matures    Coupon      Yield     CUSIP``````

Code: Select all

`````` 4/15/2022   0.125%   (3.330%)   912828X39     1   19    21,309    20,661
4/15/2023   0.625%   (2.784%)   9128284H0     1   19    21,589    20,229
4/15/2024   0.500%   (2.445%)   9128286N5     1   19    21,727    19,923
4/15/2025   0.125%   (2.169%)   912828ZJ2     1   20    22,399    20,477
7/15/2026   0.125%   (1.925%)   912828S50     1   19    23,304    20,962
7/15/2027   0.375%   (1.630%)   9128282L3     1   19    23,239    20,541
7/15/2028   0.750%   (1.386%)   912828Y38     1   19    23,293    20,017
7/15/2029   0.250%   (1.185%)   9128287D6     1   20    23,242    20,677
7/15/2030   0.125%   (1.024%)   912828ZZ6     1   20    22,914    20,629
1/15/2031   0.125%   (0.910%)   91282CBF7     1   21    23,570    21,334
4/15/2032   3.375%   (0.888%)   912810FQ6     5   82   182,294   122,171
2/15/2040   2.125%   (0.339%)   912810QF8     4   86   155,982   105,224
2/15/2041   2.125%   (0.280%)   912810QP6     1   22    39,690    26,567
2/15/2042   0.750%   (0.179%)   912810QV3     1   24    33,659    28,089
2/15/2043   0.625%   (0.134%)   912810RA8     1   25    33,622    28,757
2/15/2044   1.375%   (0.135%)   912810RF7     1   25    38,359    28,368
2/15/2045   0.750%   (0.082%)   912810RL4     1   25    33,731    28,076
2/15/2046   1.000%   (0.078%)   912810RR1     1   26    36,915    29,019
2/15/2047   0.875%   (0.074%)   912810RW0     1   27    36,934    29,580
2/15/2048   1.000%   (0.075%)   912810SB5     1   27    37,441    28,956
2/15/2049   1.000%   (0.071%)   912810SG4     1   28    38,335    29,427
2/15/2050   0.250%   (0.058%)   912810SM1     1   29    32,507    29,830
2/15/2051   0.125%   (0.052%)   912810SV1     1   30    32,102    30,473``````
But I suspect this is just a coincidence. There are several ways to build a 30-year TIPS ladder especially to handle the gaps when no TIPS mature. Also I'm using prices from May 25 and the graph says it is based on May 13 of each year.

The article may be calculating the "annuity factor" with the simple formula given in the original post:
AF(n,r) = (1 - (1 + r) ^ -n ) / r (I've inserted the exponentiation symbol, "^", which was left out.)

This is the same as the formula for the Present Value of an Annuity of \$1 (PVA\$1) which works as long as "r" is not zero. It can also be determined with the Excel PV function
PVA\$1 = -PV(r, n, 1, 0, 0) (which works even if r = zero)

The article's interactive graph shows the result for every year 2011 - 2021. Using this and Excel's RATE function we can determine what is the corresponding discount rate. For example, as shown in the last row below, a rate of -0.39% is needed to get a PVA\$1 of 31.9.
-0.39% = RATE(30, 1, -31.9, 0, 0)
31.9 = (1 - (1 - 0.39%) ^ -30) / -0.39%
31.9 = -PV(-0.39%, 30, 1, 0, 0)

Code: Select all

``````                          ------ Constant Maturity Yield ------
Year   PVA\$1    Rate        5       7       10      20      30
2011    24.8    1.27%     (0.29)   0.34    0.79    1.47    1.78
2012    29.1    0.20%     (1.16)  (0.77)  (0.28)   0.54    0.76
2013    29.4    0.13%     (1.19)  (0.72)  (0.41)   0.30    0.69
2014    26.8    0.74%     (0.27)   0.30    0.45    0.90    1.15
2015    27.0    0.69%     (0.10)   0.31    0.41    0.81    1.04
2016    28.2    0.40%     (0.30)  (0.15)   0.13    0.55    0.79
2017    27.1    0.67%      0.10    0.32    0.49    0.82    1.01
2018    26.3    0.87%      0.71    0.82    0.82    0.88    0.94
2019    26.7    0.77%      0.45    0.49    0.55    0.74    0.92
2020    30.8   (0.17%)    (0.40)  (0.43)  (0.43)  (0.25)  (0.08)
2021    31.9   (0.39%)    (1.81)  (1.18)  (0.85)  (0.26)   0.03``````
For comparison, I'm showing the May 13th constant maturity real rates for 2021 and each prior year back to 2011. The computed Rate seems roughly (very roughly!) the same as the 20 year rate.
grok87
Posts: 9615
Joined: Tue Feb 27, 2007 9:00 pm

### Re: The current annuity factor

RIP Mr. Bogle.
vineviz
Posts: 10262
Joined: Tue May 15, 2018 1:55 pm

### Re: The current annuity factor

grok87 wrote: Tue May 25, 2021 4:40 pm
grabiner wrote: Mon May 24, 2021 8:07 pm The 4% rule was always based on inflation-adjusted spending. And it didn't assume an all-TIPS portfolio (which would have an annuity factor of 32); a balanced portfolio is likely to outperform inflation by enough that you can spend more from it.

That said, the current projected returns from a balanced portfolio are probably also lower now than they were in the past, with negative TIPS yields, and nominal yields less than expected inflation. Therefore, the 4% withdrawal rate may be less safe than it was in the past.
Agree.

I think one way to frame this is to ask: what is the expected real return of the balanced (say 60/40) portfolio?
Say it's 5% for stocks and 0% for bonds right now. so that would be an expected real return of 3%. So maybe 3% is the new Safe Withdrawal rate.
The expected real rate of return is not equal to the SWR.

To get from the return to the SWR you need to account for the length of retirement (ie the number of periods), the volatility in f returns (to get from the arithmetic mean return to geometric mean return, or compound growth rate), as well as some provision for poor sequence of return (how much bad luck will you prepare to experience).
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch
Topic Author
bobcat2
Posts: 5568
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

### Re: The current annuity factor

nedsaid wrote: Tue May 25, 2021 11:46 am I would like to ask Bob, and I hope that he responds, how the negative real returns from TIPS are figuring into retirement planning. What is Dr. Merton saying about this and how does this affect the construction of the Dimensional Fund Advisors Target Date Retirement funds?
nedsaid wrote: Tue May 25, 2021 11:59 amJust wondering what Dr. Merton, other academics, and Bob have to say about this [low real interest rates].
Hi Ned,
You do realize that Allison Schrager and Robert Merton were the two member team who put together the DFA Target Date Retirement funds? And Allison's column is what this thread is based on.

I subscribe to her weekly finance letter, Known Unknowns, and emailed Allison about two months asking essentially your question. She didn't respond. Why don't you ask her your questions about low interest rates by emailing her at her new Bloomberg email address.

To contact the author of this story:
Allison Schrager at aschrager4@bloomberg.net

You could start by saying how much you enjoyed her first Bloomberg column.

BobK

PS - To the extent possible my TIPS holdings are duration matched to my income targets. In my IRA are enough duration matched TIPS etf holdings to cover my RMD. While holding TIPS without a liability matching strategy is a good portfolio diversifier, it doesn't protect against inflation very well, because changes in the real interest rate can more than offset the inflation protection.
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
grabiner
Posts: 29905
Joined: Tue Feb 20, 2007 11:58 pm
Location: Columbia, MD

### Re: The current annuity factor

grok87 wrote: Tue May 25, 2021 4:40 pm
grabiner wrote: Mon May 24, 2021 8:07 pm The 4% rule was always based on inflation-adjusted spending. And it didn't assume an all-TIPS portfolio (which would have an annuity factor of 32); a balanced portfolio is likely to outperform inflation by enough that you can spend more from it.

That said, the current projected returns from a balanced portfolio are probably also lower now than they were in the past, with negative TIPS yields, and nominal yields less than expected inflation. Therefore, the 4% withdrawal rate may be less safe than it was in the past.
Agree.

I think one way to frame this is to ask: what is the expected real return of the balanced (say 60/40) portfolio?
Say it's 5% for stocks and 0% for bonds right now. so that would be an expected real return of 3%. So maybe 3% is the new Safe Withdrawal rate.
The correct model for the safe withdrawal rate isn't that simple. A portfolio with a 3% real return has a 50% chance of sustaining 3% withdrawals forever. However, you want more than a 50% chance, and you also don't care about the forever. You can model the returns of the portfolio (say as a model with a mean and standard deviation), and compute what withdrawal rate will have a 90% chance of lasting 30 years. Lowering the mean and keeping the same standard deviation will reduce the safe withdrawal rate.
David Grabiner
nedsaid
Posts: 14747
Joined: Fri Nov 23, 2012 12:33 pm

### Re: The current annuity factor

bobcat2 wrote: Tue May 25, 2021 5:42 pm
nedsaid wrote: Tue May 25, 2021 11:46 am I would like to ask Bob, and I hope that he responds, how the negative real returns from TIPS are figuring into retirement planning. What is Dr. Merton saying about this and how does this affect the construction of the Dimensional Fund Advisors Target Date Retirement funds?
nedsaid wrote: Tue May 25, 2021 11:59 amJust wondering what Dr. Merton, other academics, and Bob have to say about this [low real interest rates].
Hi Ned,
You do realize that Allison Schrager and Robert Merton were the two member team who put together the DFA Target Date Retirement funds? And Allison's column is what this thread is based on.

I subscribe to her weekly finance letter, Known Unknowns, and emailed Allison about two months asking essentially your question. She didn't respond. Why don't you ask her your questions about low interest rates by emailing her at her new Bloomberg email address.

To contact the author of this story:
Allison Schrager at aschrager4@bloomberg.net

You could start by saying how much you enjoyed her first Bloomberg column.

BobK

PS - To the extent possible my TIPS holdings are duration matched to my income targets. In my IRA are enough duration matched TIPS etf holdings to cover my RMD. While holding TIPS without a liability matching strategy is a good portfolio diversifier, it doesn't protect against inflation very well, because changes in the real interest rate can more than offset the inflation protection.
Hi Bob:

I am aware that Dr. Merton was involved with constructing the DFA Target Date Retirement Funds, I didn't know about Allison Schrager. The construction of the funds haven't changed so I assume that their thinking has not changed. I suppose TIPS are least dirty shirt in the laundry hamper, not perfect but the best solution available.

I will read her article more thoroughly and I will contact her. Thanks.

Edit: I have done both, I am awaiting her response.

I found her article posted at the Manhattan Institute in case you run up against your free article limit at Bloomberg.

https://www.manhattan-institute.org/ret ... -you-think
A fool and his money are good for business.
nedsaid
Posts: 14747
Joined: Fri Nov 23, 2012 12:33 pm

### Re: The current annuity factor

Another possible, but imperfect solution would be to take a bit more risk on the bond side. Add Corporates, Emerging Market Bonds, High Yield Corporates, and Investment Grade International Bonds to TIPS and a US Total Bond Market Index. I am sure that Larry Swedroe and others would shriek in terror at this suggestion. I noticed that American Century added a Preferred Stock and a Convertible Bond ETF to my managed account there.

So instead of going simply with stocks vs. bonds, do a stocks vs. stock/bond hybrids vs. bonds portfolio. I would count High Yield Bonds, Preferred Stock, Convertible Bonds, and perhaps Emerging Markets Bonds in the stock/bond hybrid category. I know this violates what the purists would recommend but extreme conditions require more creative solutions. Pretty much cross your fingers and hope it all works. It is reaching for yield a bit and taking on a bit of equity risk in your bond portfolio but somehow we have to get bonds and stock/bond hybrids back into real return category. It might be a bridge too far but it is worth a try.

What I have been doing is having my retirement portfolio a bit stock heavy at my age. I am at 63%-64% stocks right now instead of the 58% or so that Vanguard would recommend. I know this is the equivalent of doing 56 mph in a 55 mph speed zone but I was born to be mild.
Like a true nature child
We were born
Born to be wild
We can climbed so high
I never wanna die
Born to be wild
Born to be wild

Source: Musixmatch
Songwriters: Mars Bonfire
Born to Be Wild lyrics © Mca Music Ltd., Universal Music Publishing Canada
[Content in excess of fair use removed by moderator oldcomputerguy, see Quoting outside material]
A fool and his money are good for business.
Topic Author
bobcat2
Posts: 5568
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

### Re: The current annuity factor

There are some solutions I can suggest for the low real interest rate problem, but for the most part they aren't very exciting.

1) Save more per year.
2) Work more years.
3) Take out a reverse mortgage. A safe retirement product that is enhanced, rather than hurt, by low interest rates.
4) Immediate life annuities are a safe product that are hurt less by low interest rates than bonds.
5) Deferred life annuities, aka longevity insurance, are more attractive than immediate life annuities because they are hurt less by low interest rates than immediate life annuities.
6) Edge up the allocation to stocks, but be sure to diversify broadly & keep expense ratios low. (Hardly need to tell BHs this.)
7) Delay taking Social Security.
8) Check into delaying a DB pension. Sometimes delay of a pension can be about as beneficial as delaying Social Security.
9) A suggestion I heard from Richard Thaler. Let people purchase a little extra Social Security. This would be cheaper than commercial life annuities because there is so little overhead and no profit off the top.

Even taking up on all the above, low real interest rates are still a problem.

BobK
Last edited by bobcat2 on Wed May 26, 2021 6:11 am, edited 1 time in total.
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
grok87
Posts: 9615
Joined: Tue Feb 27, 2007 9:00 pm

### Re: The current annuity factor

grabiner wrote: Tue May 25, 2021 7:53 pm
grok87 wrote: Tue May 25, 2021 4:40 pm
grabiner wrote: Mon May 24, 2021 8:07 pm The 4% rule was always based on inflation-adjusted spending. And it didn't assume an all-TIPS portfolio (which would have an annuity factor of 32); a balanced portfolio is likely to outperform inflation by enough that you can spend more from it.

That said, the current projected returns from a balanced portfolio are probably also lower now than they were in the past, with negative TIPS yields, and nominal yields less than expected inflation. Therefore, the 4% withdrawal rate may be less safe than it was in the past.
Agree.

I think one way to frame this is to ask: what is the expected real return of the balanced (say 60/40) portfolio?
Say it's 5% for stocks and 0% for bonds right now. so that would be an expected real return of 3%. So maybe 3% is the new Safe Withdrawal rate.
The correct model for the safe withdrawal rate isn't that simple. A portfolio with a 3% real return has a 50% chance of sustaining 3% withdrawals forever. However, you want more than a 50% chance, and you also don't care about the forever. You can model the returns of the portfolio (say as a model with a mean and standard deviation), and compute what withdrawal rate will have a 90% chance of lasting 30 years. Lowering the mean and keeping the same standard deviation will reduce the safe withdrawal rate.
THanks David great points.

So has anyone done this analysis?

cheers,
grok
RIP Mr. Bogle.
nedsaid
Posts: 14747
Joined: Fri Nov 23, 2012 12:33 pm

### Re: The current annuity factor

bobcat2 wrote: Tue May 25, 2021 10:34 pm There are some solutions I can suggest for the low real interest rate problem, but for the most part they aren't very exciting.

1) Save more per year.
2) Work more years.
3) Take out a reverse mortgage. A safe retirement product that is enhanced, rather than hurt, by low interest rates.
4) Immediate life annuities are a safe product that are hurt less by low interest rates than bonds.
5) Deferred life annuities, aka longevity insurance, are more attractive than immediate life annuities because they are hurt less by low interest rates than immediate life annuities.
6) Edge up the allocation to stocks, but be sure to diversify broadly & keep expense ratios low. (Hardly need to tell BHs this.)
7) Delay taking Social Security.
8) Check into delaying a DB pension. Sometimes delay of a pension can be about as beneficial as delaying Social Security.
9) A suggestion I heard from Richard Thaler. Let people purchase a little extra Social Security. This would be cheaper than commercial life annuities because there is so little overhead and no profit off the top.

Even taking up on all the above, low real interest rates are still a problem.

BobK
Bob, thanks a lot. This is what I asked for and is very actionable. The doggoned markets again did something most of us did not anticipate, low or even negative real interest rates. This forced retirees and near retirees to consider higher stock allocations than they would like. Lots of strategies to deal with stock market volatility like the various 60/40, 50/50, 40/60 or even 30/70 balanced portfolios; buckets of money; various liability matching strategies have all been adversely affected. I long for the return of 6% bond yields coupled with low inflation and TIPS with 3% real interest rates, not sure we will see that again in our lifetimes.
A fool and his money are good for business.
grok87
Posts: 9615
Joined: Tue Feb 27, 2007 9:00 pm

### Re: The current annuity factor

AlwaysLearningMore wrote: Tue May 25, 2021 1:58 pm

If you are 75% fixed income - low real interest rates are hurting you.
If you are 60% fixed income - low real interest rates are hurting you.
If you are 30% fixed income - low real interest rates are hurting you.
If you are 20% or less fixed income in retirement - you are taking a lot of risk.

At retirement Joe has a million dollar portfolio at retirement. His portfolio is 60% bonds and 40% equity. If real interest rates are about 3%, which is about what they averaged from the mid 80s thru about 2001, Joe gets 18,000 per year in real interest. At zero or less real rates that \$18,000 is gone. That's a problem for Joe.

Notice that the '4% rule' doesn't care. Joe takes out \$40,000 in the first year regardless of whether the \$18,000 is there or not.

BobK
If Joe and his wife Joanne had been accumulating EE bonds over the years for each of them (and also perhaps through a trust for one or both of them) and at retirement began redeeming those bonds in succession (after 20 year each), then they'd be enjoying the one-time Treasury resent and thus a 3.53% return. They'd have a 20-year period certain payout. With that foundation Joanne and Joe could arrange the balance of their portfolio to see them through retirement.

And since years ago Joanne suggested that they also invest in I Bonds for an element of liability matching, they're definitely in decent financial shape.
have you done the trust thing? i've always thought it was too much trouble. but the 3.53% is looking awfully good. we've been maxing out on ibonds and EE bonds for a while now i.e. 40k total per year.
RIP Mr. Bogle.
#Cruncher
Posts: 3222
Joined: Fri May 14, 2010 2:33 am
Location: New York City
Contact:

### Re: The current annuity factor

#Cruncher wrote: Tue May 25, 2021 4:46 pm
nisiprius wrote: Tue May 25, 2021 5:48 am... it's not even clear to me what interest rate her chart is based on ...
The Bloomberg article doesn't say how the "annuity factor" is calculated. Underneath the graph it simply says "Source: Bloomberg", which is not very helpful! ...
I contacted the author and she replied,
Allison Schrager wrote:It is the present discounted value of \$1 a year, for 30 years using the current TIPS curve, and going back 10 years. (underline added)
So the "current annuity factor" of 32 in the article (rounded from 31.9 in the graph) is not based on a single value of "r" and the formula,
AF(n, r) = (1 - (1 + r) ^ -n ) / r, assumed in the original post.

Rather, it is apparently the sum of the present values of \$1 discounted with 30 separate rates. In her reply the author didn't say how she determined "the current TIPS curve" so I attempted to do so myself using the 5/13/2021 constant maturity rates for 5, 10, 20, & 30 years of -1.81, -0.85, -0.26, and +0.03 respectively. I extrapolated for years 1-4, and interpolated for years 6-9, 11-19, and 21-29. As shown at the bottom of the following table, I came up with the same 31.9 "annuity factor" for 2021!

Code: Select all

``Year     Rate      Diff      PV\$1``

Code: Select all

``````   1   (2.578%)             1.026  = 1 / (1 - 2.578%)
2   (2.386%)   0.192%    1.049  = 1 / (1 - 2.386%) ^ 2
3   (2.194%)   0.192%    1.069  etc.
4   (2.002%)   0.192%    1.084
5   (1.810%)   0.192%    1.096

6   (1.618%)   0.192%    1.103
7   (1.426%)   0.192%    1.106
8   (1.234%)   0.192%    1.104
9   (1.042%)   0.192%    1.099
10   (0.850%)   0.192%    1.089

11   (0.791%)   0.059%    1.091
12   (0.732%)   0.059%    1.092
13   (0.673%)   0.059%    1.092
14   (0.614%)   0.059%    1.090
15   (0.555%)   0.059%    1.087
16   (0.496%)   0.059%    1.083
17   (0.437%)   0.059%    1.077
18   (0.378%)   0.059%    1.071
19   (0.319%)   0.059%    1.063
20   (0.260%)   0.059%    1.053

21   (0.231%)   0.029%    1.050
22   (0.202%)   0.029%    1.045
23   (0.173%)   0.029%    1.041
24   (0.144%)   0.029%    1.035
25   (0.115%)   0.029%    1.029
26   (0.086%)   0.029%    1.023
27   (0.057%)   0.029%    1.016
28   (0.028%)   0.029%    1.008
29    0.001%    0.029%    1.000
30    0.030%    0.029%    0.991  = 1 / (1 + 0.030%) ^ 30
------
Sum                       31.862``````
I repeated the calculation for years 2011-2020 and got results pretty close to those from the article's graph. (The 5, 10, 20, & 30 year constant maturity rates I used are listed near the bottom of my previous post.)

Code: Select all

``````         My   Article   Differ
Year    Calc    Graph     ence
2011    24.9     24.8     0.1
2012    28.6     29.1    (0.5)
2013    29.2     29.4    (0.2)
2014    26.6     26.8    (0.2)
2015    26.9     27.0    (0.1)
2016    27.9     28.2    (0.3)
2017    26.8     27.1    (0.3)
2018    26.3     26.3    (0.0)
2019    26.8     26.7     0.1
2020    31.1     30.8     0.3
2021    31.9     31.9    (0.0)``````
grok87
Posts: 9615
Joined: Tue Feb 27, 2007 9:00 pm

### Re: The current annuity factor

#Cruncher wrote: Sat May 29, 2021 6:49 am
#Cruncher wrote: Tue May 25, 2021 4:46 pm
nisiprius wrote: Tue May 25, 2021 5:48 am... it's not even clear to me what interest rate her chart is based on ...
The Bloomberg article doesn't say how the "annuity factor" is calculated. Underneath the graph it simply says "Source: Bloomberg", which is not very helpful! ...
I contacted the author and she replied,
Allison Schrager wrote:It is the present discounted value of \$1 a year, for 30 years using the current TIPS curve, and going back 10 years. (underline added)
So the "current annuity factor" of 32 in the article (rounded from 31.9 in the graph) is not based on a single value of "r" and the formula,
AF(n, r) = (1 - (1 + r) ^ -n ) / r, assumed in the original post.

Rather, it is apparently the sum of the present values of \$1 discounted with 30 separate rates. In her reply the author didn't say how she determined "the current TIPS curve" so I attempted to do so myself using the 5/13/2021 constant maturity rates for 5, 10, 20, & 30 years of -1.81, -0.85, -0.26, and +0.03 respectively. I extrapolated for years 1-4, and interpolated for years 6-9, 11-19, and 21-29. As shown at the bottom of the following table, I came up with the same 31.9 "annuity factor" for 2021!

Code: Select all

``Year     Rate      Diff      PV\$1``

Code: Select all

``````   1   (2.578%)             1.026  = 1 / (1 - 2.578%)
2   (2.386%)   0.192%    1.049  = 1 / (1 - 2.386%) ^ 2
3   (2.194%)   0.192%    1.069  etc.
4   (2.002%)   0.192%    1.084
5   (1.810%)   0.192%    1.096

6   (1.618%)   0.192%    1.103
7   (1.426%)   0.192%    1.106
8   (1.234%)   0.192%    1.104
9   (1.042%)   0.192%    1.099
10   (0.850%)   0.192%    1.089

11   (0.791%)   0.059%    1.091
12   (0.732%)   0.059%    1.092
13   (0.673%)   0.059%    1.092
14   (0.614%)   0.059%    1.090
15   (0.555%)   0.059%    1.087
16   (0.496%)   0.059%    1.083
17   (0.437%)   0.059%    1.077
18   (0.378%)   0.059%    1.071
19   (0.319%)   0.059%    1.063
20   (0.260%)   0.059%    1.053

21   (0.231%)   0.029%    1.050
22   (0.202%)   0.029%    1.045
23   (0.173%)   0.029%    1.041
24   (0.144%)   0.029%    1.035
25   (0.115%)   0.029%    1.029
26   (0.086%)   0.029%    1.023
27   (0.057%)   0.029%    1.016
28   (0.028%)   0.029%    1.008
29    0.001%    0.029%    1.000
30    0.030%    0.029%    0.991  = 1 / (1 + 0.030%) ^ 30
------
Sum                       31.862``````
I repeated the calculation for years 2011-2020 and got results pretty close to those from the article's graph. (The 5, 10, 20, & 30 year constant maturity rates I used are listed near the bottom of my previous post.)

Code: Select all

``````         My   Article   Differ
Year    Calc    Graph     ence
2011    24.9     24.8     0.1
2012    28.6     29.1    (0.5)
2013    29.2     29.4    (0.2)
2014    26.6     26.8    (0.2)
2015    26.9     27.0    (0.1)
2016    27.9     28.2    (0.3)
2017    26.8     27.1    (0.3)
2018    26.3     26.3    (0.0)
2019    26.8     26.7     0.1
2020    31.1     30.8     0.3
2021    31.9     31.9    (0.0)``````
Well done #Cruncher.
IMHO this method used by the author would be conservative, i.e. produce annuity factors that err on the high side. THis is because the curve is being constructed generally using on-the run securities (i think the 20 year would be the exception). if the actual off-the run securities were used for say the 2,3 year or 7,8 year tips spot rates then the real yields would likely be higher and the annuity factors lower.

as one example, interpolation produces a yield of -1.234% for the 8 year tip whereas the WSJ has it as -1.145%
cheers,
grok
RIP Mr. Bogle.
Topic Author
bobcat2
Posts: 5568
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

### Re: The current annuity factor

I don't think Schrager was using her calculation as a suggested withdrawal rate as many on this thread have inferred. Instead she was showing that last year's falling interest rates were offsetting much of last year's equity gains for retirees and near retirees. Surely, she is not expecting retirees to make this complicated calculation every year.

The typical way the annuity factor is used in retirement calculations is somewhat different from what Schrager is doing and is known as the life expectancy withdrawal rate. The formula for the withdrawal amount is rewritten to become a product of the annuity factor based withdrawal rate times the portfolio value in each retirement year.

Withdrawal Amount = r/[1-(1+r)^-n] x (portfolio value in current year) – Not initial portfolio value at retirement!

Where n is life expectancy for your current age and for r I would use the rate for TIPS at .5n - the duration of the withdrawals.

At age 65 n will be less than 30, even if you use a joint life table. For a couple using a standard joint life table this calculation is probably fairly accurate. Conservative retirees, including couples, may want to extend life expectancy values in standard tables by one to three years. Or, you could look at a mortality table and pick a length of time where the probability of being alive is low, e.g., only a 25% chance of being alive this far into the future.

But a single retiree can have a life expectancy significantly different from the value in a standard life table. If an individual believes his or her life expectancy is significantly different than the life expectancy at their age in standard life tables, they should adjust the life expectancy value. There are several web sites you can use to estimate your specific life expectancy. Otherwise for a long lived individual this withdrawal strategy may be too aggressive but too conservative for someone with severe health problems.

While you could use the TIPS rate for every year, I doubt that makes much difference other than to make the calculations much more complicated. We are not aiming for perfection here - just something relatively simple and better than the 4% rule. (Truly a low bar.)

What does make a big difference is using 30 years at age 65, as Schrager does in the article, rather than life expectancy. That is what is making a withdrawal strategy based on this method so conservative - not how the real interest rate is calculated. Because at age 65 life expectancy will be significantly less than 30. (For a single male it's probably about 19). It makes little sense to construct an "annuity factor" for retirement withdrawal rates and then ignore life expectancy and use instead an arbitrary number of years such as 30 at age 65.

To repeat a couple of important points. Set n equal to life expectancy at your age, not some arbitrary value such as 30 years at age 65. And as you age continue to use the ever shorter life expectancy values - not arbitrary values such as 25 at age 70.

Lastly, I doubt very much if Schrager was intending for people to use her formula as a retirement withdrawal rate strategy starting at age 65 with n = 30. For what she was doing in the article she needed a number - not a life expectancy for a single male at a particular age, or the life expectancy for a single female at a particular age, or the the joint life expectancy of a couple at particular ages. Schrager picked the number 30.

BobK
Last edited by bobcat2 on Mon May 31, 2021 3:27 pm, edited 2 times in total.
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
Topic Author
bobcat2
Posts: 5568
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

### Re: The current annuity factor

In her weekly financial news letter, Known Unknowns, Allison Schrager succinctly describes what her initial Bloomberg article covering annuity factors was demonstrating. It wasn't about how to construct retirement withdrawal rates going forward. It was instead showing that today's retirees, and near retirees, are not as well off as they think they are.
Early reports indicate an increase in early retirement since the pandemic. One reason is that the stock market is up 30%, which makes people feel they are closer to their retirement goals.

BUT your account balance is not the only number you need to worry about. After all, you save money to spend it – and how much you can spend depends on real interest rates. This is especially important lately with rising inflation fears.

Now we’ve been hearing a lot about rising rates, but what gets less attention is that real rates haven’t moved up, they’ve even fallen a bit. The whole TIPS curve is negative. Which tells us a lot about inflation expectations and the value of inflation insurance.

In any case, I used the Bloomberg terminal(!!!) to calculate annuity factors (yes, I wrote about annuity factors) over the last 10 years, and retirement has become a lot more expensive as real rates fell. It became even more expensive in the last year.

So even if the market is up, retirees have a lot less than they think they do – at least if they want protection from inflation and the market.
BobK
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
#Cruncher
Posts: 3222
Joined: Fri May 14, 2010 2:33 am
Location: New York City
Contact:

### Re: The current annuity factor

bobcat2 wrote: Sat May 29, 2021 10:44 am I don't think Schrager was using her calculation as a suggested withdrawal rate as many on this thread have inferred.
It sure seems like that's what she meant. In the article
Allison Schrager wrote:There are few hard and fast rules when it comes to retirement finance, but one is this: if you want to see how much you can spend each year, divide your wealth by 32.
bobcat2 in same post wrote:Surely, she is not expecting retirees to make this complicated calculation every year.
Agreed. But for anyone interested, it can be estimated fairly easily as follows:
• Select All, Copy, and Paste [1] the following at cell A1 of a blank Excel sheet:

Code: Select all

``````Term	Yield	Chg / Yr
0	=2*B3-B4	=(B3-B2)/(A3-A2)
5	-1.81	=(B4-B3)/(A4-A3)
10	-0.85	=(B5-B4)/(A5-A4)
20	-0.26	=(B6-B5)/(A6-A5)
30	0.03	0
Year	Rate	PV
1	=(VLOOKUP(A8,\$A\$2:\$C\$6,2,TRUE)+(A8-VLOOKUP(A8,\$A\$2:\$C\$6,1,TRUE))*VLOOKUP(A8,\$A\$2:\$C\$6,3,TRUE))/100	=1/(1+B8)^A8
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
Sum		=SUM(C8:C37)``````
• Copy cells B8:C9 down to row 37.
• Enter the the four constant maturity TIPS rates for 5, 10, 20, and 30 years for the current date in cells B3:B6. (Omit the 7-year rate.)
• Read the "annuity factor" in cell C38.
bobcat2 in same post wrote:The formula for the withdrawal amount is ...
Withdrawal Amount = r/[1-(1+r)^-n] x (portfolio value in current year) – Not initial portfolio value at retirement!
Where n is life expectancy for your current age and r is the rate for TIPS maturing in the nth year.
At first I thought this method exposed one to much interest rate risk since to implement it, one would buy a single long term TIPS maturing after a number of years equal to life expectancy. But after working through an example, I see that a change in interest rates causes two partially offsetting results. If yields go up, the value of the TIPS will go down, but the new withdrawal rate will go up; and vice-versa. Since the withdrawal amount is the product of the two, this makes it vary less than I expected. Here's the example:
• Covers the eleven years 2011 - 2021 of the graph in the article.
• Uses the joint life expectancies for a man/woman couple both age 59 in 2011 from the SSA 2017 Period Life Table as computed with my Longevity Estimator.
• Rate interpolated between the 20 and 30 year constant maturity TIPS rates as shown in my first post.
• An initial \$1,000,000 portfolio balance.

Code: Select all

``````             Life   ----- TIPS Yields -----   Withdraw
Year  Age  Expect    20 Yr   30 Yr   Interp       Rate    Balance  Withdraw
2011   59   29.62    1.47%   1.78%   1.768%     4.366%  1,000,000    43,661
2012   60   28.71    0.54%   0.76%   0.732%     3.874%  1,304,604    50,545 [2]
2013   61   27.81    0.30%   0.69%   0.605%     3.917%  1,308,186    51,247
2014   62   26.91    0.90%   1.15%   1.073%     4.298%  1,116,542    47,989
2015   63   26.02    0.81%   1.04%   0.948%     4.355%  1,115,003    48,559
2016   64   25.13    0.55%   0.79%   0.673%     4.339%  1,152,699    50,012
2017   65   24.25    0.82%   1.01%   0.901%     4.609%  1,051,229    48,451
2018   66   23.37    0.88%   0.94%   0.900%     4.764%  1,011,935    48,209
2019   67   22.50    0.74%   0.92%   0.785%     4.866%    997,576    48,541
2020   68   21.64   (0.25%) (0.08%) (0.222%)    4.506%  1,187,007    53,484
2021   69   20.78   (0.26%)  0.03%  (0.237%)    4.689%  1,134,582    53,199
Avg                                                                 49,445``````
For comparison I repeated the example assuming the reverse of the 20 and 30 year TIPS rates 2011-2021. I.e., instead of falling from 1.47% and 1.78% in 2011 to -0.26% and 0.03% in 2021, they start at -0.26% and 0.03% in 2011 and rise to 1.47% and 1.78% in 2021.

Code: Select all

``````             Life   ----- TIPS Yields -----   Withdraw
Year  Age  Expect    20 Yr   30 Yr   Interp       Rate    Balance  Withdraw
2011   59   29.62   (0.26%)  0.03%   0.019%     3.386%  1,000,000    33,859
2012   60   28.71   (0.25%) (0.08%) (0.102%)    3.431%  1,000,363    34,319
2013   61   27.81    0.74%   0.92%   0.881%     4.070%    735,823    29,947
2014   62   26.91    0.88%   0.94%   0.921%     4.213%    704,400    29,675
2015   63   26.02    0.82%   1.01%   0.934%     4.347%    678,687    29,503
2016   64   25.13    0.55%   0.79%   0.673%     4.339%    699,148    30,334
2017   65   24.25    0.81%   1.04%   0.908%     4.613%    636,537    29,362
2018   66   23.37    0.90%   1.15%   0.984%     4.811%    601,985    28,961
2019   67   22.50    0.30%   0.69%   0.398%     4.655%    659,234    30,687
2020   68   21.64    0.54%   0.76%   0.576%     4.928%    607,388    29,934
2021   69   20.78    1.47%   1.78%   1.494%     5.634%    481,457    27,123
Avg                                                                 30,337``````
This causes the withdrawal amounts to be much less. But this is to be expected. The withdrawal amounts primarily depend on the initial rates. The same thing happens with the "TIPS Curve" method used in the article and estimated in my second post. Both methods show that the amount you can withdraw is less when current TIPS yields are low.

Code: Select all

``````                             Actual  Reversed
Rates     Rates
------  --------
Using method above           49,400    30,300  (11 year average)
Using "TIPS Curve" method    40,200    31,300  (1,000,000 / 24.9 and 31.9)``````
1. If you have trouble pasting, try "Paste Special" and "Text".
2. Example calculation of withdrawal rate and balance for 2012:
3.874% = 0.00732 / (1 - 1.00732 ^ -28.71)
1,304,604 = (1000000 - 43661) * 1.01768 ^ 29.62 / 1.00732 ^ 28.62
Topic Author
bobcat2
Posts: 5568
Joined: Tue Feb 20, 2007 3:27 pm
Location: just barely Outside the Beltway

### Re: The current annuity factor

It amazes me that there are so many adherents to the 4% rule for retirement withdrawal rates. It is a bad rule for many reasons, including one that is obvious.

It bases inflation adjusted withdrawals throughout retirement on the level of assets at the beginning of retirement. This could only work well if all the assets are liability matched with real bonds. However, nearly everyone has volatile risky assets included in their retirement portfolio. It is almost a certainty that such a rule will either result in unspent assets, if stocks perform well, or result in overspending, if stocks perform poorly. In other words, any sound withdrawal strategy for a portfolio that includes volatile assets (such as stocks) must calculate the withdrawal rate for each year based on the portfolio asset level in that year – not the initial asset level at the beginning of retirement, and then adjusted for inflation over time.

There are many articles criticizing the 4% rule that are readily available, but I am going to focus on three. The first is by Nobel laureate William Sharpe et al. and focuses on the weaknesses of the 4% rule. A key quote.
This rule and its variants finance a constant, non-volatile spending plan using a risky, volatile investment strategy. As a result, retirees accumulate unspent surpluses when markets outperform and face spending shortfalls when markets underperform.
Link to The 4% Rule – At What Price?
https://web.stanford.edu/~wfsharpe/retecon/4percent.pdf

The other two papers are by Wei Sun and Anthony Webb and published by the Center for Retirement Research at Boston College.

Should Households Base Asset Decumulation Strategies on Required Minimum Distribution Tables?
and
Can Retirees Base Wealth Withdrawals on the IRS’ Required Minimum Distributions?

The first of the above two papers compares the efficacy of four rule of thumb withdrawal rates to a theoretically optimal withdrawal rate.
The four rule of thumb withdrawal rate strategies are –
1.) Spend only interest and dividends
2.) Life expectancy withdrawal rate (uses the annuity factor)
3.) fixed percentage of initial wealth each period in real terms (the 4% rule and its variants)
4.) RMD rule

The above life expectancy rule is Withdrawal Amount = r/[1-(1+r)^-n] x (portfolio value in current year)
Where n is life expectancy for your current age and for r, I would use the rate for TIPS at .5n, the duration of a real fixed term immediate annuity of fixed term n. This, of course, doesn't mean that you should purchase a real fixed term immediate annuity. It is simply a method to calculate your portfolio withdrawal rate.

Here are their main conclusions.
When deciding how rapidly to decumulate their wealth, households will likely fall back on rules of thumb. We show that two of the rules of thumb that households might plausibly adopt -- spending the interest and dividends while preserving the capital, and consuming a fixed 4 percent of initial wealth – can be highly sub-optimal. A strategy of using the RMD tables often performs better, but still represents a substantial departure from optimality.

… The RMD strategy is sometimes outperformed by a strategy of spending down over the household’s life expectancy. But, as mentioned previously, the effectiveness of this strategy is highly sensitive to the coefficient of risk aversion and proportion of pre-annuitized wealth.
The second paper by Sun and Webb considers a fifth rule of thumb strategy.
5.) Use RMD withdrawal rate plus dividends and interest.

A criticism of the RMD rule is that it somewhat restricts spending in the early years of retirement when the elderly are typically more active. The RMD rule can be adjusted by adding dividends and interest to the portfolio withdrawal amount. Such a strategy would likely result in bigger withdrawals in early retirement relative to late retirement, but that is a spending plan many retirees prefer. Since most people retire before age 70, the authors have included a table in the appendix with calculated RMD rates starting at age 65.

Sun and Webb conclude the second paper with the following.
Rather than attempt the complex calculations necessary to arrive at an optimal strategy for drawing down and spending their retirement savings, retirees rely on easy-to-follow rules of thumb such as the 4-percent rule advocated by some financial planners. This brief suggests that the IRS’ Required Minimum Distribution rules may be a viable alternative. For financial and practical reasons, the effectiveness of the alternative RMD strategy compares favorably to traditional rules of thumb. And a modified RMD strategy does even better.

Two more observations about the 4% rule compared to the RMD and life expectancy rules.
1.) A complaint sometimes made of rules based on each year’s level of assets, is that the withdrawals will vary from year to year as volatile assets move up and down. That’s true. But don’t blame the messenger! If you don’t want withdrawal amounts fluctuating over the years, lower the allocation to volatile assets.
2.) Adherents to the 4% rule claim that you need to be flexible when applying the rule. But flexibility turns out to be guessing how to adjust the rule when assets are either significantly higher or lower than was previously expected for a given year. Flexible guessing isn’t much of a strategy. Better to rely on a dynamic rule that adjusts automatically, such as one of the RMD rules or the life expectancy rule.

While the life expectancy rule and the RMD rules are more robust than the 4% rule, all withdrawal rate rules of thumb have deficiencies. A close to optimal portfolio withdrawal rate is affected by many things including the amount of Social Security and db pension benefits, the distribution of portfolio assets between regular and tax advantaged accounts, how risk averse the members of the household are, and the composition of the household, e.g., a couple or the survivor.

Milevsky and Huang consider some of the most important of these issues in their paper,
Spending Retirement on Planet Vulcan. Here is a key take-away.
The main point of our study can be summarized in one sentence: The optimal portfolio withdrawal rate (PWR) depends on longevity risk aversion and the level of pre-existing pension income. The larger the amount of the pre-existing pension income, the greater the optimal consumption rate and the greater the PWR.

The pension acts primarily as a buffer and allows the retiree to consume more from discretionary wealth. Even at high levels of longevity risk aversion, the risk of living a long life does not “worry” retirees too much because they have pension income to fall back on should that chance (i.e., a long life) materialize. We believe that this insight is absent from most of the popular media discussion (and practitioner implementation) of optimal spending rates. If a potential client has substantial income from a DB pension or Social Security, she can afford to withdraw more—percentagewise—than her neighbor, who is relying entirely on his investment portfolio to finance his retirement income needs.
https://www.soa.org/globalassets/assets ... levsky.pdf

In summary, the best withdrawal rate strategy is to use a sound financial planning software such as MaxiFi to calculate your portfolio withdrawal rate. Such a tool needs to take account of SS & db pension benefits, the distribution of portfolio assets between regular accounts and tax advantaged accounts, the composition of the household, and be able to at least take some account of the household’s risk aversion. I realize most people won’t do that. So, if you are going to use a rule of thumb, don’t use the 4% rule or one of its variants, or the spend only dividends and interest rule. Instead use the life expectancy rule or one of the RMD rules. And informally take account whether you have a relatively large amount of SS & pension income relative to your portfolio, or a small amount and make an adjustment to the pwr up or down. Also take account how longevity risk averse you are. If you are using the life expectancy rule - raise your life expectancy if you are are worried about outliving your money. If you are using RMD and are worried about outliving your money stick closer to the RMD, rather than the RMD plus dividends and interest.

BobK
Last edited by bobcat2 on Mon May 31, 2021 5:55 pm, edited 1 time in total.
In finance risk is defined as uncertainty that is consequential (nontrivial). | The two main methods of dealing with financial risk are the matching of assets to goals & diversifying.
grok87
Posts: 9615
Joined: Tue Feb 27, 2007 9:00 pm

### Re: The current annuity factor

#Cruncher wrote: Mon May 31, 2021 3:33 pm
bobcat2 wrote: Sat May 29, 2021 10:44 am I don't think Schrager was using her calculation as a suggested withdrawal rate as many on this thread have inferred.
It sure seems like that's what she meant. In the article
Allison Schrager wrote:There are few hard and fast rules when it comes to retirement finance, but one is this: if you want to see how much you can spend each year, divide your wealth by 32.
I agree with #Cruncher
RIP Mr. Bogle.