Funds used in the 4% rule

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Gemini1962
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Funds used in the 4% rule

Post by Gemini1962 »

Does anybody know the full make up of the funds used when the 4% rule was calculated. I am in the drawdown phase and I keep a few years in cash in case there's a crash in the market. But the rest of my portfolio is in index funds, I don't have any bonds as I'd rather keep cash (even though it is subject to inflation). I was just wondering if the 4% rule relies on being 100% invested.
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Re: Funds used in the 4% rule

Post by FactualFran »

Studies that use historical returns have tended to use returns of asset classes rather than returns of funds. The historical returns of asset classes is more extensive. A Stock, Bond, Bills, and Inflation yearbook is a widely used source of historical return data for asset classes, such as: large-cap stocks, small-cap, stocks, long-term corporate bonds, long-term government bonds, and Treasury bills.

The 4% rule is about withdrawals made from a portfolio. The withdrawals come 100% from the portfolio. A way to include cash in a portfolio of asset classes is to have Treasury bills in the portfolio.
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arcticpineapplecorp.
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Re: Funds used in the 4% rule

Post by arcticpineapplecorp. »

Gemini1962 wrote: Sat May 27, 2023 3:20 pm Does anybody know the full make up of the funds used when the 4% rule was calculated. I am in the drawdown phase and I keep a few years in cash in case there's a crash in the market. But the rest of my portfolio is in index funds, I don't have any bonds as I'd rather keep cash (even though it is subject to inflation). I was just wondering if the 4% rule relies on being 100% invested.
100% invested like in stocks?

gosh no. I mean the Trinity study did look at the impact on withdrawal survival rates if you'd held 100% stocks down to 0% stocks (this looked at stocks and bonds, but for present day if you're earning 5% on your cash which you should be, that's around the historical returns for bonds so now cash could act similarly in returns to bonds, but if interest rates get down to lower levels, cash earning little could prove unwise, depending upon what percentage of your overall portfolio that represents). Click on the link to the trinity study to see how the different allocations affected portfolio survival over different time periods.

or do you mean 100% invested in stocks and bonds? It's probably not uncommon for people to have some cash for emergencies, so I'm sure most people aren't 100% invested in stocks and bonds (except for livesoft :wink: ). But the rest of the portfolio (stocks and bonds) would be used to determine the withdrawal rate, etc. Especially if you only have 3 years in cash (don't know the exact amount, you only said "a few"). Then you likely would have the other 27 years of retirement (or more) in stocks and/or bonds, depending upon your preference.

By the way, i assume you hold the cash in cash of a market crash so you don't have to sell stock. Have you thought about what happens if the recovery takes more than a few years? Stocks bottom in March 2009 took until March 2012 to recover fully. That's 3 years, not 2. Just sayin,don't know how much cash you have because you said "a few years". Of course a 50/50 portfolio would have recovered I believe by some time in 2010 which shows you how more conservative portfolios can recover faster. If you're holding like 99.9% of your money in stock and 0.1% in cash, you could be in for a shock if we experience a lost decade again, etc.

Does that help?
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000
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Re: Funds used in the 4% rule

Post by 000 »

IIRC achieved fund returns, expenses, and taxes were not considered. Another strike against using the 4% "rule" as an actual planning tool.

Also I believe the bonds used were Long Term Corporates, the very part of the bond market most different from cash.

Of course the 4% rule didn't work at all in many other countries.... but there's another thread on that subject somewhere here.
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Re: Funds used in the 4% rule

Post by nisiprius »

I was 99% certain, and have now verified that in the 1996 "Trinity" study,
The Standard & Poor’s 500 index was used to represent stocks, and long-term, high-grade corporate bonds were used to represent bonds. (All stock, bond, and inflation data were from "Stocks, Bonds, Bills, and Inflation, 1996 Yearbook," Ibbotson Associates, 1996).
The source cited is the source of an enormous percentage of the data used in older studies. If the starting date is 1926, it's usually Ibbotson.

It's almost never real-world mutual funds because most of them don't go far enough back.
Last edited by nisiprius on Sat May 27, 2023 9:14 pm, edited 1 time in total.
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Re: Funds used in the 4% rule

Post by nisiprius »

Gemini1962 wrote: Sat May 27, 2023 3:20 pm ...I was just wondering if the 4% rule relies on being 100% invested...
These tools and simulations are nowhere near accurate enough to fuss about but, yes, it does.

You can experiment using tools like the Vanguard Retirement Nest Egg Calculator which in fact does not quite support a withdrawal rate as high as 4%.

You will find, for example, that in their simulator, 4% withdrawals over 30 years from 50/50 stocks/bonds had a 92% success rate.

If you change it to 50% stocks, 50% cash, the success rate drops to 88%.
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.
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tre3sori
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Re: Funds used in the 4% rule

Post by tre3sori »

Gemini1962 wrote: Sat May 27, 2023 3:20 pm I was just wondering if the 4% rule relies on being 100% invested.
You may also want to look at this somewhat related thread where the 4% rule is challenged:
viewtopic.php?t=393123

On the other hand there are also others (Kitces for example) that say, that with variable withdrawals a higher withdrawal rate is sustainable (at least for the US retiree), especially if your basic needs are covered by social security: Morningstar The Long View: Michael Kitces - How Higher Yields Affect Asset Allocation and Retirement Planning https://www.youtube.com/watch?v=touHZMqDJiw

I myself rather err on the safe side with a withdrawal rate of less than 2% p.a. over the last 10 years (well, I also invest for my heirs I guess :wink:).
The information provided is intended to be entertaining. It is not to be construed as professional advice. Use it at your own risk.
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Re: Funds used in the 4% rule

Post by doobiedoo »

Gemini1962 wrote: Sat May 27, 2023 3:20 pm Does anybody know the full make up of the funds used when the 4% rule was calculated. I am in the drawdown phase and I keep a few years in cash in case there's a crash in the market. But the rest of my portfolio is in index funds, I don't have any bonds as I'd rather keep cash (even though it is subject to inflation). I was just wondering if the 4% rule relies on being 100% invested.
William Bengen's 4% SWD study was based on 50/50 AA [Asset Allocation] and a 30-year retirement.
https://www.forbes.com/advisor/retireme ... etirement/

Subsequent studies often use a 60/40 AA.
https://newacademyoffinance.com/ideal-s ... awal-rule/
StillGoing
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Re: Funds used in the 4% rule

Post by StillGoing »

Gemini1962 wrote: Sat May 27, 2023 3:20 pm Does anybody know the full make up of the funds used when the 4% rule was calculated. I am in the drawdown phase and I keep a few years in cash in case there's a crash in the market. But the rest of my portfolio is in index funds, I don't have any bonds as I'd rather keep cash (even though it is subject to inflation). I was just wondering if the 4% rule relies on being 100% invested.
I note that you appear to be based in the UK (as am I) where the '4% rule' translates to something more like a '3% to 3.5% rule' (see https://www.2020financial.co.uk/pension ... alculator/ for a useful UK historical data based calculator). You'll also see in that calculator the effect of adding cash (actually the returns on 3 month bills) compared to using bonds (which are, at 15-20 years, quite long duration) - historically, the worst cases in the UK were improved by holding cash (this is because there were periods where the performance of long bonds was awful). For example using the calculator, with 60% stocks and 40% bonds, the MSWR was 2.9%, while with 60% stocks and 40% cash, the MSWR was 3.6% (although the amount of money left in the better cases was less with cash). In other words, providing some care is taken to get a reasonable interest rate, holding cash is not a dreadful strategy

FWIW, my own portfolio has a target of 60% of the fixed income in cash (including fixed rate cash accounts of up to 2 year duration - with rates of 5% currently available, that is not too shoddy although still -3% real!) with the remaining part in bonds.

cheers
StillGoing
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Re: Funds used in the 4% rule

Post by Mors »

I would also argue that for your basic needs an inflation adjusted immediate annuity is appropriate.
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Re: Funds used in the 4% rule

Post by Valuethinker »

StillGoing wrote: Sun May 28, 2023 4:21 am
Gemini1962 wrote: Sat May 27, 2023 3:20 pm Does anybody know the full make up of the funds used when the 4% rule was calculated. I am in the drawdown phase and I keep a few years in cash in case there's a crash in the market. But the rest of my portfolio is in index funds, I don't have any bonds as I'd rather keep cash (even though it is subject to inflation). I was just wondering if the 4% rule relies on being 100% invested.
I note that you appear to be based in the UK (as am I) where the '4% rule' translates to something more like a '3% to 3.5% rule' (see https://www.2020financial.co.uk/pension ... alculator/ for a useful UK historical data based calculator). You'll also see in that calculator the effect of adding cash (actually the returns on 3 month bills) compared to using bonds (which are, at 15-20 years, quite long duration) - historically, the worst cases in the UK were improved by holding cash (this is because there were periods where the performance of long bonds was awful). For example using the calculator, with 60% stocks and 40% bonds, the MSWR was 2.9%, while with 60% stocks and 40% cash, the MSWR was 3.6% (although the amount of money left in the better cases was less with cash). In other words, providing some care is taken to get a reasonable interest rate, holding cash is not a dreadful strategy

FWIW, my own portfolio has a target of 60% of the fixed income in cash (including fixed rate cash accounts of up to 2 year duration - with rates of 5% currently available, that is not too shoddy although still -3% real!) with the remaining part in bonds.

cheers
StillGoing
Thank you for pointing this out.
I note that you appear to be based in the UK (as am I) where the '4% rule' translates to something more like a '3% to 3.5% rule' (
It's really important for readers here to understand that difference. That the "4% rule" was based on stock returns of what is almost the best performance of a stock market we have in the data. There's no guarantee the majority of our funds will be invested in the next US-like stock market.

Inflation-adjusted annuities are available in the UK and should be considered. Most pensioners reject them because of their high cost in terms of immediate income relative to a straight annuity. But unless you are annuitizing quite late in life, that's a dangerous strategy.

The low level of the UK Basic State Pension v other countries makes getting this aspect of retirement planning right particularly tricky - large risk transfer from the state onto the individual. "Pension Freedom" compounded the problem because people are not good at managing lump sums. The Australian example should have warned us of that, conversely I do understand the issue that George Osborne was confronting ie that for most people, annuities were bad value.
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Re: Funds used in the 4% rule

Post by Parkinglotracer »

How much interest are you getting on your cash? Vanguard mm fund is paying 5%. I don’t like to let my cash loaf - lots of places you can get CDs even paying more right thru vanguard brokerage - click on buying bonds or CDs and see what’s there.
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Re: Funds used in the 4% rule

Post by ivk5 »

Mors wrote: Mon Jun 12, 2023 1:02 pm I would also argue that for your basic needs an inflation adjusted immediate annuity is appropriate.
Is this actionable? Where do you find such an annuity these days in UK (or US)?
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Re: Funds used in the 4% rule

Post by StillGoing »

ivk5 wrote: Tue Jun 13, 2023 4:19 am
Mors wrote: Mon Jun 12, 2023 1:02 pm I would also argue that for your basic needs an inflation adjusted immediate annuity is appropriate.
Is this actionable? Where do you find such an annuity these days in UK (or US)?
Yes - they are readily available in the UK (for example, current payout rates for a single life RPI annuity are available at https://www.hl.co.uk/retirement/annuiti ... -buy-rates and quotes from https://www.moneyhelper.org.uk/en/pensi ... -annuities (amongst other places, my understanding is that IFA are able to get better rates than these general ones).

Given rates at 65yo of 4.5% (single life) and about 3.7% for a joint life with 50% benefits, these are attractive compared to historical SWR (as mentioned by valuethinker in a post a few above this one).

However, they are not currently available in the US.

cheers
StillGoing
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Re: Funds used in the 4% rule

Post by Valuethinker »

StillGoing wrote: Tue Jun 13, 2023 4:33 am
ivk5 wrote: Tue Jun 13, 2023 4:19 am
Mors wrote: Mon Jun 12, 2023 1:02 pm I would also argue that for your basic needs an inflation adjusted immediate annuity is appropriate.
Is this actionable? Where do you find such an annuity these days in UK (or US)?
Yes - they are readily available in the UK (for example, current payout rates for a single life RPI annuity are available at https://www.hl.co.uk/retirement/annuiti ... -buy-rates and quotes from https://www.moneyhelper.org.uk/en/pensi ... -annuities (amongst other places, my understanding is that IFA are able to get better rates than these general ones).

Given rates at 65yo of 4.5% (single life) and about 3.7% for a joint life with 50% benefits, these are attractive compared to historical SWR (as mentioned by valuethinker in a post a few above this one).

However, they are not currently available in the US.

cheers
StillGoing
Thank you.

Generals always "fight the last war" (allegedly) so a long period of inflation below expectations probably tilted retirees towards fixed annuities. That has become a very painful bet (w inflation running at 10% ish).

Given the volatility of UK gilt prices recently, annuities look like an even better idea. Particularly if there is a need to draw down more than say 2.5-3.0% of capital each year (inflation adjusted).
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Re: Funds used in the 4% rule

Post by NearlyRetired »

I would also point out, IIRC, that the withdrawal rate was for all withdrawals from the portfolio - so that rate will also need to include any portfolio charges you may incur. So for UK investors as StillGoing pointed out, the SWR is more like 3-3.5%, you would need to reduce that by portfolio charges to determine how much "you" get to see (e.g. if your portfolio and platform charges come to 0.5% then your withdrawal will be 2.5-3%)
To err is to be human, to really mess up, use a computer
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Re: Funds used in the 4% rule

Post by StillGoing »

NearlyRetired wrote: Tue Jun 13, 2023 10:32 am I would also point out, IIRC, that the withdrawal rate was for all withdrawals from the portfolio - so that rate will also need to include any portfolio charges you may incur. So for UK investors as StillGoing pointed out, the SWR is more like 3-3.5%, you would need to reduce that by portfolio charges to determine how much "you" get to see (e.g. if your portfolio and platform charges come to 0.5% then your withdrawal will be 2.5-3%)
The 'nice' thing about fees (if anything about fees can ever be described as 'nice') is that they have less effect than a simple subtraction. Very roughly, subtract about half the fee rate from the SWR (see https://www.kitces.com/blog/the-impact- ... wal-rates/). In other words, in this case, the 0.5% fee would end up reducing the SWR to about 2.75%-3.25%. The better news, is that, redoing Kitces work, the reduction for the UK is a little bit less at about 0.35*(fee rate)

cheers
StillGoing
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Re: Funds used in the 4% rule

Post by StillGoing »

Valuethinker wrote: Tue Jun 13, 2023 7:56 am
StillGoing wrote: Tue Jun 13, 2023 4:33 am
ivk5 wrote: Tue Jun 13, 2023 4:19 am
Mors wrote: Mon Jun 12, 2023 1:02 pm I would also argue that for your basic needs an inflation adjusted immediate annuity is appropriate.
Is this actionable? Where do you find such an annuity these days in UK (or US)?
Yes - they are readily available in the UK (for example, current payout rates for a single life RPI annuity are available at https://www.hl.co.uk/retirement/annuiti ... -buy-rates and quotes from https://www.moneyhelper.org.uk/en/pensi ... -annuities (amongst other places, my understanding is that IFA are able to get better rates than these general ones).

Given rates at 65yo of 4.5% (single life) and about 3.7% for a joint life with 50% benefits, these are attractive compared to historical SWR (as mentioned by valuethinker in a post a few above this one).

However, they are not currently available in the US.

cheers
StillGoing
Thank you.

Generals always "fight the last war" (allegedly) so a long period of inflation below expectations probably tilted retirees towards fixed annuities. That has become a very painful bet (w inflation running at 10% ish).

Given the volatility of UK gilt prices recently, annuities look like an even better idea. Particularly if there is a need to draw down more than say 2.5-3.0% of capital each year (inflation adjusted).
You're right - anyone who bought a level annuity in 2000 (with a payout rate of about 7.0% for a 65yo) would have seen the income to 2020 fall by 'only' a third (inflation averaged about 2%), while it has fallen to about 56% of the original 'real' rate since then (i.e. about 4% in real terms). An inflation linked annuity at the time would have had a payout rate of about 5%* and would still be paying out 5% after a period of largely benign inflation.

cheers
StillGoing

* The rates are based on my own calculations using gender neutral mortalities from 2018 and gilts rates (nominal and inflation linked) from 2000. Uncertainties are likely to be of the order of 50 b.p.
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Re: Funds used in the 4% rule

Post by Valuethinker »

StillGoing wrote: Tue Jun 13, 2023 12:11 pm
Valuethinker wrote: Tue Jun 13, 2023 7:56 am
StillGoing wrote: Tue Jun 13, 2023 4:33 am
ivk5 wrote: Tue Jun 13, 2023 4:19 am
Mors wrote: Mon Jun 12, 2023 1:02 pm I would also argue that for your basic needs an inflation adjusted immediate annuity is appropriate.
Is this actionable? Where do you find such an annuity these days in UK (or US)?
Yes - they are readily available in the UK (for example, current payout rates for a single life RPI annuity are available at https://www.hl.co.uk/retirement/annuiti ... -buy-rates and quotes from https://www.moneyhelper.org.uk/en/pensi ... -annuities (amongst other places, my understanding is that IFA are able to get better rates than these general ones).

Given rates at 65yo of 4.5% (single life) and about 3.7% for a joint life with 50% benefits, these are attractive compared to historical SWR (as mentioned by valuethinker in a post a few above this one).

However, they are not currently available in the US.

cheers
StillGoing
Thank you.

Generals always "fight the last war" (allegedly) so a long period of inflation below expectations probably tilted retirees towards fixed annuities. That has become a very painful bet (w inflation running at 10% ish).

Given the volatility of UK gilt prices recently, annuities look like an even better idea. Particularly if there is a need to draw down more than say 2.5-3.0% of capital each year (inflation adjusted).
You're right - anyone who bought a level annuity in 2000 (with a payout rate of about 7.0% for a 65yo) would have seen the income to 2020 fall by 'only' a third (inflation averaged about 2%), while it has fallen to about 56% of the original 'real' rate since then (i.e. about 4% in real terms). An inflation linked annuity at the time would have had a payout rate of about 5%* and would still be paying out 5% after a period of largely benign inflation.

cheers
StillGoing

* The rates are based on my own calculations using gender neutral mortalities from 2018 and gilts rates (nominal and inflation linked) from 2000. Uncertainties are likely to be of the order of 50 b.p.
Your numbers are interesting to me because when I last checked this (before the ill-fated Truss/ Kwartung budget & its effect on gilt yields*) about 18 months ago, I think Index-linked annuities were running at about 2% and level annuities at about 4%? i.e. a doubling of income if one accepted the inflation risk.

Humans, and especially your average potential retiree, are bad at estimating these sorts of risks & understanding what their future selves will think. I saw City (ie finance) people make bad decisions in these regards (but if you retired from the City in the last 10 years or so, you likely had a lot of housing wealth and you could trade down).

* gilt yields are now back to where they were at the time of that Budget. However we don't know the true counterfactual, which is where they would be if there had not been that Budget. My belief (which I cannot prove) is that it shook credit markets, and coupled with other types of political instability that have gone on, has pushed gilt yields (nominal) up by 0.5-1.5%.
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Re: Funds used in the 4% rule

Post by StillGoing »

Valuethinker wrote: Tue Jun 13, 2023 12:34 pm
StillGoing wrote: Tue Jun 13, 2023 12:11 pm
Valuethinker wrote: Tue Jun 13, 2023 7:56 am
StillGoing wrote: Tue Jun 13, 2023 4:33 am
ivk5 wrote: Tue Jun 13, 2023 4:19 am

Is this actionable? Where do you find such an annuity these days in UK (or US)?
Yes - they are readily available in the UK (for example, current payout rates for a single life RPI annuity are available at https://www.hl.co.uk/retirement/annuiti ... -buy-rates and quotes from https://www.moneyhelper.org.uk/en/pensi ... -annuities (amongst other places, my understanding is that IFA are able to get better rates than these general ones).

Given rates at 65yo of 4.5% (single life) and about 3.7% for a joint life with 50% benefits, these are attractive compared to historical SWR (as mentioned by valuethinker in a post a few above this one).

However, they are not currently available in the US.

cheers
StillGoing
Thank you.

Generals always "fight the last war" (allegedly) so a long period of inflation below expectations probably tilted retirees towards fixed annuities. That has become a very painful bet (w inflation running at 10% ish).

Given the volatility of UK gilt prices recently, annuities look like an even better idea. Particularly if there is a need to draw down more than say 2.5-3.0% of capital each year (inflation adjusted).
You're right - anyone who bought a level annuity in 2000 (with a payout rate of about 7.0% for a 65yo) would have seen the income to 2020 fall by 'only' a third (inflation averaged about 2%), while it has fallen to about 56% of the original 'real' rate since then (i.e. about 4% in real terms). An inflation linked annuity at the time would have had a payout rate of about 5%* and would still be paying out 5% after a period of largely benign inflation.

cheers
StillGoing

* The rates are based on my own calculations using gender neutral mortalities from 2018 and gilts rates (nominal and inflation linked) from 2000. Uncertainties are likely to be of the order of 50 b.p.
Your numbers are interesting to me because when I last checked this (before the ill-fated Truss/ Kwartung budget & its effect on gilt yields*) about 18 months ago, I think Index-linked annuities were running at about 2% and level annuities at about 4%? i.e. a doubling of income if one accepted the inflation risk.

Humans, and especially your average potential retiree, are bad at estimating these sorts of risks & understanding what their future selves will think. I saw City (ie finance) people make bad decisions in these regards (but if you retired from the City in the last 10 years or so, you likely had a lot of housing wealth and you could trade down).

* gilt yields are now back to where they were at the time of that Budget. However we don't know the true counterfactual, which is where they would be if there had not been that Budget. My belief (which I cannot prove) is that it shook credit markets, and coupled with other types of political instability that have gone on, has pushed gilt yields (nominal) up by 0.5-1.5%.
While I don't routinely collect data on joint inflation linked annuities, I do have a list of single life payout rates for inflation linked annuities going back a couple of years (all from https://www.hl.co.uk/retirement/annuiti ... -buy-rates),

UK Single life, inflation linked annuity payout rates

Code: Select all

	60	65	70	75
July 2021	2.1	2.8	3.7	5.0
May 2022	2.5	3.2	4.2	5.5
Oct 2022	3.6	4.5	5.4	6.7
Jun 2023	3.6	4.5	5.4	6.7
Where you can see that we are indeed back to where we were in October 2022 - I think the difference is that after the mini-budget, 6-9 months worth of interest rate increases were packed into a fortnight.

I know we're going OT quite a bit (but it is relevant to planning a retirement, since the use of a baseline of guaranteed inflation linked income means that requiring inflation linked withdrawals from the portfolio becomes less important).

To look at joint life rates (since I don't have actual ones for the older dates), two tables will suffice

The first is the actuarially fair (i.e., no fees) annuity payout rate for a single life annuity at various real interest rates and ages (assuming ONS life tables from 2022 and gender neutral - these will not be the same as the mortality tables used by the insurance companies)

Code: Select all

		Real Interest rate (%)
Age     -2      -1.5    -1      -0.5    0       0.5     1       1.5     2
60      2.8     3.0     3.3     3.6     3.8     4.1     4.4     4.7     5.0
65      3.6     3.8     4.1     4.4     4.6     4.9     5.2     5.5     5.8
70      4.7     4.9     5.2     5.5     5.8     6.1     6.4     6.7     7.0
75      6.3     6.6     6.9     7.2     7.5     7.8     8.1     8.4     8.7
80      8.8     9.1     9.4     9.7     10.0    10.3    10.6    10.9    11.3
85      12.8    13.1    13.4    13.7    14.0    14.3    14.6    14.9    15.2
And for a joint life annuity with 100% survivor benefits with annuitant and beneficiary being the same age

Code: Select all

		Real interest rate (%)
Age        -2      -1.5    -1      -0.5    0       0.5     1       1.5     2
60      2.2     2.4     2.7     2.9     3.2     3.4     3.7     4.0     4.3
65      2.8     3.0     3.3     3.5     3.8     4.0     4.3     4.6     4.8
70      3.6     3.8     4.1     4.3     4.6     4.8     5.1     5.4     5.7
75      4.8     5.0     5.3     5.5     5.8     6.0     6.3     6.6     6.9
80      6.6     6.8     7.1     7.3     7.6     7.9     8.1     8.4     8.7
85      9.3     9.6     9.8     10.1    10.4    10.6    10.9    11.2    11.5
So, for the single life annuity at 65 in June 2023, we have an actual payout rate of 4.5%, whereas the actuarially fair rate should be about 5.2% (assuming yield of 1% for 15-20 year gilt maturities), i.e., implying fees of about 13.5% - applying the same process to the joint annuity would give about 0.865*4.3=3.8% (not too far off the current payout rate on moneyhelper). Using this for July 2021, would give 0.865*2.8=2.4% for joint life (i.e., not far off your recollection).

cheers
StillGoing
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