Safe Withdrawal Rates: Does it matter if the bond component is short, intermediate, or long?

[StillGoing]

A conversation a few months back (viewtopic.php?p=7322789#p7322789) which looked, in passing, at the differences between the safe withdrawal rates (SWR) produced using different data sets (e.g., SBBI, macrohistory.net, and Shiller) concluded that, after stock allocation, bond maturity was a key aspect. The macrohistory.net dataset ostensibly contains returns from T-bills and bonds with maturities close to 20 years, SBBI returns from T-bills, intermediate (~5 year) and long (~20 year) bonds, while the monthly version of Shiller contains returns from 10 year treasuries (at least since 1950s, e.g., see viewtopic.php?p=6131409#p6131409 and a few posts beyond). In this thread, the effect of bond fund maturity or duration (I’ve tended to use the word ‘duration’, although see following post) on SWR will be explored a bit further (at least to my own satisfaction!).

Using asset returns from the Simba dataset (https://www.bogleheads.org/wiki/Simba%2 ... preadsheet, rev22c) a 30 year retirement with an asset allocation of 50% stocks and 50% fixed income was modelled with annual rebalancing and constant inflation adjusted withdrawals taken at the beginning of each year. Fixed income (FI) ‘funds’ of four different maturities/durations were used, T-bills, short term treasuries (STT), total bond market (TBM), and long term treasuries (LTT). Note that, if I understand the Simba spreadsheet correctly, for TBM, before 1976 the returns were for US treasuries only, while post-1976 they were for all investment grade bonds.

The safe withdrawal rate (SWR), i.e., the maximum initial withdrawal expressed as a percentage of the initial portfolio value (%IPV) that ensured the portfolio was not exhausted before 30 years had elapsed, is plotted for each of the FI funds as a function of retirement start year in the following figure.



As is well known in these parts, the SWR varied considerably from retirement to retirement ranging from a minimum of below 4% in the mid-1960s, to a maximum of over 10% in the early 1980s. While it is a bit difficult to see the different behaviour of the various FI funds, it is clear that in some periods (e.g., late 1970s onwards) longer duration FI resulted in the highest SWR, while in other periods (e.g., late 19th and early 20th century) T-bills gave the highest SWR. Of course, it is important to note that it would not have been possible at the beginning of a particular retirement to know what duration FI would have subsequently provided the best outcome.

A clearer picture of the behaviour with time can be gained from the following graph where (upper panel) the highest SWR from the four FI funds and (lower panel) which FI fund produced the highest SWR are plotted as a function of retirement start year.



The results in lower panel illustrate how the highest SWR was delivered by different duration FI at different times. For example, longer duration FI was dominant in the periods from 1920 to 1940 and for 1980 onwards, while bills were dominant from approximately 1880 to 1910.

The following table shows the percentage of retirements using FI of a particular duration led to the highest SWR for the entire data set (‘all SWR’) and for a subset of the data where the best SWR was less than, an arbitrarily chosen, 5% (labelled as ‘SWR<5’). Therefore, SWR<5 represents the poorest historical retirements. Note: Rounding may mean that the numbers do not add up to 100.

Code: Select all

Percentage of retirements that produced highest SWR by FI fund				
	Bills	STT	TBM	LTT
All SWR	31	25	11	33
SWR<5	41	33	11	15

For the all SWR case, FI at the shorter end of duration (T-bills or STT) resulted in the highest SWR slightly more often (56% compared to 44%) than those at the longer end (TBM or LTT). However, for the subset of data where SWR<5% (i.e., the worst historical cases), using shorter duration FI produced the highest SWR in just under 75% of cases.

By way of contrast, the FI fund that produced the lowest SWR by retirement start year are presented in the following table in a similar form as the previous table.

Code: Select all

Percentage of retirements that produced worst SWR by FI fund				
	Bills	STT	TBM	LTT
All SWR	40	0	23	37
SWR<5	19	0	19	63

For the all SWR case, longer duration FI led to the lowest SWR in 60% of cases, while for the subset where SWR<5% (note that the highest SWR was used rather than the lowest to ensure that the same subset of retirements were selected as previously), longer duration FI led to the worst SWR in about 80% of cases. It is interesting to note that while using STT led to the highest SWR in, depending on the subset of data, 25% to 33% of retirements it never led to the lowest SWR.

While the future is unknowable, the historical evidence would suggest that, in poor retirements, short term treasuries tended to be a better choice in terms of SWR than the intermediate maturity bonds in total bond market or long term treasuries.

cheers
StillGoing

edit: Title as per McQ's suggestion

[StillGoing]

In this post, we'll have a look at maturity/duration.

The weighted effective maturity (WEM) of a bond fund depends on the maturities of the bonds that are in the fund and the relative value of the holdings (noting that the latter will change with changes in yields). For example, the long term treasury index/fund (LTT/VLGSX/Bloomberg Barclays US Treasury Long) contains all US treasuries of 10 year maturity or greater and, as of September 2023, has a WEM of just under 23 years. However, this would not have necessarily been the case historically since the WEM will depend on the portfolio of bonds meeting the 10 year or more maturity criterion. For example (see https://www.treasurydirect.gov/research ... ine/bonds/), 30 year bonds were not issued until 1977 (replacing the 25 year bonds that were issued from 1974) so the WEM in early 1970s would probably have been much lower than it is now, although bonds with maturities greater than 30 years had been issued in the 1950s and 1960s (see https://libertystreeteconomics.newyorkf ... 7-to-1965/) that would, in the early 1970s, have had maturities greater than 10 years. According to the same source, “Following the cessation of bond issuance, the average maturity of marketable Treasury debt declined from 5⅓ years in mid-1965 to 2⅔ years in mid-1975” with average maturity then reaching 6 years by 1989 which would, consequently, change the WEM of the Treasury portion of TBM.

I note that the chart referred to in that article doesn’t show up in either Safari or Firefox – does anyone have a source for available maturities (on a very quick read I think, Hall et al, “US Federal Debt 1776 -1960: Quantities and Prices”, http://www.tomsargent.com/research/US_F ... t_Data.pdf and accompanying data set appears to be a strong candidate – has anyone worked with that dataset or any alternatives)? I also note McQ’s comprehensive discussions at viewtopic.php?t=353607 and in the papers cited in that thread.

The duration of a bond that pays a coupon is always less than its maturity and depends on the coupon rate (the higher the coupon, the lower the duration) and yield (the higher the yield, the lower the duration). For example, the duration of the LTT (VLGSX) fund is currently just under 16 years compared to the maturity of 23 years.

While I cannot find a timeline of duration for the relevant indices or funds (does anyone have one?), the following graph shows the duration of three funds simulated in the rather excellent and useful Bogleheads bond fund simulator (see viewtopic.php?t=179425) using the par yield curves of treasuries from 1962 onwards held by FRED (https://fred.stlouisfed.org/categories/115) that roughly correspond to LTT (notated as 30-10, where ‘30’ indicates the longest maturity held, and ‘10’ the maturity when bonds are sold), TBM (approximated as 10-3), and STT (3-1).



The graph indicates that for the longest duration simulated fund (LTT), the weighted duration changed by about 8 years from peak to trough with, as expected, the minimum occurring when yields were highest at the beginning of the 1980s. There are two reasons for the decrease in duration, firstly the duration of the individual bonds decreases with increasing yield, which is further enhanced by the higher coupons of newly issued bonds and, secondly, the bonds with the longest maturity undergo a greater decline in price and hence the weighting shifts to bonds with earlier maturities and hence results in a decrease in duration. The recent rise in yields has led to a fall in duration (note that data are plotted to end of 2022) and well as price. The difference between the maximum and minimum duration is smaller for the intermediate (TBM) and short bond funds (STT).

So, two outcomes are:
1) The duration of a given fund is not constant
2) While the qualitative description of the duration for a bond fund holds, in other words, at any given instant short term funds have the lowest duration and long term funds the highest, the relative values of the duration may change.

cheers
StillGoing

[dcabler]

Longinvest's bond fund simulator includes weighted duration. Data from this spreadsheet is used by the Simba spreadsheet.

Thread and links here: viewtopic.php?f=10&t=179425

Cheers

[alluringreality]

While I cannot find a timeline of duration for the relevant indices or funds (does anyone have one?)

This was posted fairly recently for the aggregate index.
viewtopic.php?p=7367129#p7367129

[StillGoing]

While I cannot find a timeline of duration for the relevant indices or funds (does anyone have one?)

This was posted fairly recently for the aggregate index.
viewtopic.php?p=7367129#p7367129

That's great, thank you

cheers
StillGoing

[StillGoing]

Longinvest's bond fund simulator includes weighted duration. Data from this spreadsheet is used by the Simba spreadsheet.

Thread and links here: viewtopic.php?f=10&t=179425

Cheers

I was hoping to find historical, rather than simulated, values of maturity/duration, but thanks

StillGoing

[McQ]

Stillgoing—thanks as always for your excellent analytic work on SWR topics.

In this post, I will argue that your inputs in this thread can’t support the weight of the analysis. Pushback welcome.

The basic problem is the comparative youth of some of the familiar bond instruments we have today in the US. None of them actually existed in 1871; and some are much younger than that. Of course there were both short and long-term fixed instruments available in 1871, and for long term US bonds, a record back to 1790, per the Hall et al. data. And Shiller and Jorda et al. can cobble together simulacra of what exists today and call it a series.

But SWR is the most practical of subjects, and simulated series that are perfectly fine for academic work may not be suitable.

Here is my critique:

1. A T-bill is an arbitrarily short-dated instrument (30 or 90 days in most accounts) that may be continually rolled over, backed by the full faith and credit of the Treasury. These don’t exist before 1929 (history in Garbade: https://www.google.com/books/edition/Bi ... frontcover There are short-dated issues before then, but they weren’t continually issued in a standard maturity, and weren’t always backed by full faith and credit (one part of Shiller’s short term series uses commercial paper issued by haberdashers).

2. Short-term Treasuries: same problem, but much later resolution, in the 1970s. Before then, short bonds were issued from time to time, and long bonds got close to maturity from time to time, but there was no regular issue of, say, a 2- or 3- year bond.

3. Total bond market. No such index exists before 1973. I made a stab at putting together one back to 1900, but it’s got simulated elements, and is in the shop waiting for improvements. See this paper for more historical notes on bonds by maturity by period: https://papers.ssrn.com/sol3/papers.cfm ... id=3947293

4. Long term treasuries: here the record is much better than the others, going back to 1790, but with gaps. From about 1865 to 1917 standard yield histories exclude Treasuries because they were collateral for bank currency issuance, with depressed yields (see Sydney Homer’s History of Interest Rates, a book I think you will greatly enjoy if not already on your shelf, with UK as well as US coverage). After 1917 a pretty good LTT series can be put together, and after 1926, the SBBI series can be used (for a vetting of the SBBI long bond series, see https://papers.ssrn.com/sol3/papers.cfm ... id=3740190).

5. “Intermediate” Treasuries—a 5 year maturity that today would fall in between Short and Intermediate Bloomberg indexes—is good back through 1934, but simulated back to 1926 from yield curves. Parts of this SBBI series are funky—as when an illiquid 50-year bond in the last five years of its life, with a bid-ask spread of multiple points, is used for a year. The bond used for 1972 does not exist. Etc.

I would believe post-1934 comparative SWR analyses for T-bills, 5-year, and 20-year Treasuries; and a 50-50 weight of the last two would reasonably simulate a Total Treasury Bond fund. The long corporate series in the SBBI is problematic, see the reference in #4 above, and shouldn't be included; thus, not a TBM index.

But, in my judgment, earlier data are only suitable for academic work.

PS: suggested thread retitle for max readership (use compose pen on the OP):
"Safe Withdrawal Rates: Does it matter if the bond component is short, intermediate, or long?"

[L84SUPR]

If I am reading the first two charts correctly, TBM is never the best, often second best, and rarely the worst. That makes TBM the best "set it and forget it" option. Within five years of retirement add your favorite cash equivalent to taste.

Am I wrong?

[dcabler]

If I am reading the first two charts correctly, TBM is never the best, often second best, and rarely the worst. That makes TBM the best "set it and forget it" option. Within five years of retirement add your favorite cash equivalent to taste.

Am I wrong?

Yes and if he had added it, ITT (Intermediate Term Treasuries) would likely have a similar outcome. I came to that conclusion during my accumulation days when it appeared that STT treasuries did best during the inflation runup of the 70's as interest rates rose and LTT did best during the inflation rundown starting in the 80's as interest rates dropped - putting intermediate term treasuries in the middle. Another reason people call out for bond funds with intermediate duration is that, at least when yield curves aren't inverted, you often get a substantial yield increase just moving from short to intermediate and significantly less increase moving from intermediate to long.

Now this is about SWR - something I'm not a fan of but which definitely makes the math easier for comparative analysis.

Cheers

[StillGoing]

Stillgoing—thanks as always for your excellent analytic work on SWR topics.

In this post, I will argue that your inputs in this thread can’t support the weight of the analysis. Pushback welcome.

The basic problem is the comparative youth of some of the familiar bond instruments we have today in the US. None of them actually existed in 1871; and some are much younger than that. Of course there were both short and long-term fixed instruments available in 1871, and for long term US bonds, a record back to 1790, per the Hall et al. data. And Shiller and Jorda et al. can cobble together simulacra of what exists today and call it a series.

But SWR is the most practical of subjects, and simulated series that are perfectly fine for academic work may not be suitable.

McQ, thank you for your welcome critique - while I was familiar with some of your sources, your 200+ page discussion of SBBI data had eluded me (there's a read for the long winter nights!). At some point I was actually going to implement the outputs of your pre-1973 analysis.

One of the reasons I chose to do this particular bit of analysis with the Simba dataset is that it is, in my view, one of the most carefully and clearly put together series (and has more durations available), but as you say suffers from the limitations of available data.

For example, I note that for the Long Term Treasury (LTT) series returns are sourced from

Post 2010: VLGSX (admiral)
1973-2009: Bloomberg Barclays US Treasury Long TR USD
1962-1973: The output from the Bogleheads Bond fund simulator (BBFS) where bonds from 30 to 10 years were held with returns derived from end of month par yields drawn from FRED (https://fred.stlouisfed.org/categories/115)
1942-1961: The output from BBFS with par yields drawn from Coleman et al. (1993)
pre-1942: The output from BBFS with par yields drawn from a very sparse data set of commercial and, from 1919 onwards, long term US bonds

So, I concede that the pre-1942 data may be of limited value in terms of any precise assessment of returns at different durations. However, for post-1942 data the sources are at least a bit clearer and for that period (looking back to my earlier figures) there are three regimes - 1942-1970 where shorter term funds performed best, post-1980 where long-term fund performed best, and a transition period between the two.

One of the reasons I've been looking at the bond fund simulator (I've now implemented it as a program in octave rather than a spreadsheet) is because I want to try to estimate the returns for shorter term bond funds for the UK (the '20 year' maturities in the Jorda et al. dataset being somewhat longer than those typically used). There's good data going back to 1970 (Bank of England) and (so far) rather sparse data going back somewhat further.

cheers
StillGoing

ps I'll think about changing the title of the thread as you suggested

[StillGoing]

Stillgoing—thanks as always for your excellent analytic work on SWR topics.

In this post, I will argue that your inputs in this thread can’t support the weight of the analysis. Pushback welcome.

[snip]

But SWR is the most practical of subjects, and simulated series that are perfectly fine for academic work may not be suitable.

Hi McQ,

Just a few thoughts in mild pushback!

While the returns for the different duration bond 'funds' in the simba spreadsheet are, pre-1970s, simulated/estimated from sources of varying quality and detail, the behaviour of such funds to broad changes in interest rate/yield regimes are going to be broadly correct, e.g., the NAV of short term funds will not change much with changes in interest rates, while that of a longer term fund will. Consequently the effect of changes in interest rate regimes (e.g. the post-1980s gradual fall in interest rates) on SWR will also broadly reflected - i.e. the details might be missed, but the general responses will not.

This is one reason in the analysis, that while I calculated the SWR at four different durations, most of the discussion concentrated on 'shorter term' (i.e., T-bills and STT) and 'longer term' (i.e., TBM and LTT) and why I think that looking at the behaviour when the SWR was relatively low was also instructive since one possible reason for low SWR is poor bond performance (the other, of course, being poor stock performance!) and duration has a strong effect on performance. I think four categories of duration is probably the absolute sensible maximum that the spectrum of bond returns can be divided into.

So, from an 'engineering' perspective (while I was educated as a physicist, I spent most of my career as an engineering academic), provided the duration of the bonds included in the Simba database are qualitatively correct (i.e. short bonds have a shorter duration than long bonds - I have no reason to believe otherwise) then the outcomes from the analysis can provide some practical indicators - one of which is that shorter term bonds tended to provide a higher SWR when the SWR was relatively low - that result is also true post-1942 (although I note the the percentages are different - e.g. 'T-bills' never gave the best SWR - see tables added below). I would agree that stating the outcome more definitely than that would be unreasonable, even more so since existing bond funds will vary in maturity with the subset of bonds (and the weighting of the individual holdings) that meet the appropriate filter.

cheers
StillGoing

Edit: Added tables of post-1942 results.

Percentage of retirements using FI of a particular duration that led to the highest SWR for the entire data set (‘all SWR’) and for a subset of the data where the best SWR was less than, an arbitrarily chosen, 5% (labelled as ‘SWR<5’)

Code: Select all

Bond duration that gave highest SWR				
	Bills	STT	TBM	LTT
All SWR	0	53	20	27
SWR<5	0	75	25	0

Code: Select all

Bond duration that gave lowest SWR				
	Bills	STT	TBM	LTT
All SWR	47	0	0	53
SWR<5	17	0	0	83

So, post 1942 neither TBM nor STT gave the worst result, while STT gave the best outcome on more occasions than TBM.

[Alpha4]

Stillgoing—thanks as always for your excellent analytic work on SWR topics.

In this post, I will argue that your inputs in this thread can’t support the weight of the analysis. Pushback welcome.

The basic problem is the comparative youth of some of the familiar bond instruments we have today in the US. None of them actually existed in 1871; and some are much younger than that. Of course there were both short and long-term fixed instruments available in 1871, and for long term US bonds, a record back to 1790, per the Hall et al. data. And Shiller and Jorda et al. can cobble together simulacra of what exists today and call it a series.

But SWR is the most practical of subjects, and simulated series that are perfectly fine for academic work may not be suitable.

McQ, thank you for your welcome critique - while I was familiar with some of your sources, your 200+ page discussion of SBBI data had eluded me (there's a read for the long winter nights!). At some point I was actually going to implement the outputs of your pre-1973 analysis.

One of the reasons I chose to do this particular bit of analysis with the Simba dataset is that it is, in my view, one of the most carefully and clearly put together series (and has more durations available), but as you say suffers from the limitations of available data.

For example, I note that for the Long Term Treasury (LTT) series returns are sourced from

Post 2010: VLGSX (admiral)
1973-2009: Bloomberg Barclays US Treasury Long TR USD
1962-1973: The output from the Bogleheads Bond fund simulator (BBFS) where bonds from 30 to 10 years were held with returns derived from end of month par yields drawn from FRED (https://fred.stlouisfed.org/categories/115)
1942-1961: The output from BBFS with par yields drawn from Coleman et al. (1993)
pre-1942: The output from BBFS with par yields drawn from a very sparse data set of commercial and, from 1919 onwards, long term US bonds

So, I concede that the pre-1942 data may be of limited value in terms of any precise assessment of returns at different durations. However, for post-1942 data the sources are at least a bit clearer and for that period (looking back to my earlier figures) there are three regimes - 1942-1970 where shorter term funds performed best, post-1980 where long-term fund performed best, and a transition period between the two.

One of the reasons I've been looking at the bond fund simulator (I've now implemented it as a program in octave rather than a spreadsheet) is because I want to try to estimate the returns for shorter term bond funds for the UK (the '20 year' maturities in the Jorda et al. dataset being somewhat longer than those typically used). There's good data going back to 1970 (Bank of England) and (so far) rather sparse data going back somewhat further.

cheers
StillGoing

ps I'll think about changing the title of the thread as you suggested

Even the pre-1942 government bond return data in the simulator is reasonably good--albeit IMO more as a simulation of a blend of a long-term bond and a cash equivalent since for much of the 1871-1942 period bonds with an IT maturity didn't really exist in neat laddered tranches that mature some every year like they are issued today--and will (please see my PM) get even more accurate still with the Jan 2024 annual update. Also, McQ has annual returns (albeit as Jan average to Jan average rather than Dec 31 to Dec 31st like the Simba spreadsheet has) for IT government bonds and LT government bonds back to 1919 or 1920 in his papers on SSRN. Underlying bond price data is available for free in the C&FC/B&QR on Fraser if you wish to compile your own index. Be warned, though, that true "IT" government bonds didn't really exist until the late 1930s/early 1940s on a consistent basis (and most of those were aged longer-term Treasuries; as per McQ's post actual IT at issue Treasuries weren't regularly issued until around 1971 or 1972; there were 5-year Treasury notes from 1932 onward but they were tax-free; taxable 5-year Treasury notes didn't start being issued until mid-1941). Also bear in mind that a, say Treasury bond with 7 years remaining could fall above/below its call price and thus become a longer/shorter term bond overnight if rates changed (before the late 1970s or early 1980s almost all US Treasury bonds had both a call date and a maturity date; a bond was assumed to mature at its maturity date if it was trading at oir below par and at its call date if it was trading above par) and would thus suddenly become more/less volatile in price as it moved from being an IT bond to a longer term one and back again.

Regarding UK government debt/gilts - I could swore that by the late 1940s/early 1950s there were shorter-term bonds available than just consols (perpetuals) or even 20-year bonds; I don't recall where I saw it but IIRC it was a paper from the Bank of England in the late 1950s that had lists of all gilts outstanding and it would show intermediate-term debt with names like "4% Exchequer Stock of 1965" or " 4 and 1/2% Exchequer Stock of 1967". In any event, presumably FRED had to get their 10-year bond yield data for the UK (see https://fred.stlouisfed.org/series/IRLTLT01GBM156N ) from either the IMF/BIS/OECD which I guess would in turn have gotten it directly from either The Bank of England or from Her Majesty's Exchequer (i.e. the UK Treasury Department or equivalent thereof)....unless they are just calling a 20-year bond yield a "10-year" bond yield here (which is what, say, GFD does for its UK "10-year government bond yield" series until the 1970s).

[StillGoing]

Stillgoing—thanks as always for your excellent analytic work on SWR topics.

In this post, I will argue that your inputs in this thread can’t support the weight of the analysis. Pushback welcome.

The basic problem is the comparative youth of some of the familiar bond instruments we have today in the US. None of them actually existed in 1871; and some are much younger than that. Of course there were both short and long-term fixed instruments available in 1871, and for long term US bonds, a record back to 1790, per the Hall et al. data. And Shiller and Jorda et al. can cobble together simulacra of what exists today and call it a series.

But SWR is the most practical of subjects, and simulated series that are perfectly fine for academic work may not be suitable.

McQ, thank you for your welcome critique - while I was familiar with some of your sources, your 200+ page discussion of SBBI data had eluded me (there's a read for the long winter nights!). At some point I was actually going to implement the outputs of your pre-1973 analysis.

One of the reasons I chose to do this particular bit of analysis with the Simba dataset is that it is, in my view, one of the most carefully and clearly put together series (and has more durations available), but as you say suffers from the limitations of available data.

For example, I note that for the Long Term Treasury (LTT) series returns are sourced from

Post 2010: VLGSX (admiral)
1973-2009: Bloomberg Barclays US Treasury Long TR USD
1962-1973: The output from the Bogleheads Bond fund simulator (BBFS) where bonds from 30 to 10 years were held with returns derived from end of month par yields drawn from FRED (https://fred.stlouisfed.org/categories/115)
1942-1961: The output from BBFS with par yields drawn from Coleman et al. (1993)
pre-1942: The output from BBFS with par yields drawn from a very sparse data set of commercial and, from 1919 onwards, long term US bonds

So, I concede that the pre-1942 data may be of limited value in terms of any precise assessment of returns at different durations. However, for post-1942 data the sources are at least a bit clearer and for that period (looking back to my earlier figures) there are three regimes - 1942-1970 where shorter term funds performed best, post-1980 where long-term fund performed best, and a transition period between the two.

One of the reasons I've been looking at the bond fund simulator (I've now implemented it as a program in octave rather than a spreadsheet) is because I want to try to estimate the returns for shorter term bond funds for the UK (the '20 year' maturities in the Jorda et al. dataset being somewhat longer than those typically used). There's good data going back to 1970 (Bank of England) and (so far) rather sparse data going back somewhat further.

cheers
StillGoing

ps I'll think about changing the title of the thread as you suggested

Even the pre-1942 government bond return data in the simulator is reasonably good--albeit IMO more as a simulation of a blend of a long-term bond and a cash equivalent since for much of the 1871-1942 period bonds with an IT maturity didn't really exist in neat laddered tranches that mature some every year like they are issued today--and will (please see my PM) get even more accurate still with the Jan 2024 annual update. Also, McQ has annual returns (albeit as Jan average to Jan average rather than Dec 31 to Dec 31st like the Simba spreadsheet has) for IT government bonds and LT government bonds back to 1919 or 1920 in his papers on SSRN. Underlying bond price data is available for free in the C&FC/B&QR on Fraser if you wish to compile your own index. Be warned, though, that true "IT" government bonds didn't really exist until the late 1930s/early 1940s on a consistent basis (and most of those were aged longer-term Treasuries; as per McQ's post actual IT at issue Treasuries weren't regularly issued until around 1971 or 1972; there were 5-year Treasury notes from 1932 onward but they were tax-free; taxable 5-year Treasury notes didn't start being issued until mid-1941). Also bear in mind that a, say Treasury bond with 7 years remaining could fall above/below its call price and thus become a longer/shorter term bond overnight if rates changed (before the late 1970s or early 1980s almost all US Treasury bonds had both a call date and a maturity date; a bond was assumed to mature at its maturity date if it was trading at oir below par and at its call date if it was trading above par) and would thus suddenly become more/less volatile in price as it moved from being an IT bond to a longer term one and back again.

Regarding UK government debt/gilts - I could swore that by the late 1940s/early 1950s there were shorter-term bonds available than just consols (perpetuals) or even 20-year bonds; I don't recall where I saw it but IIRC it was a paper from the Bank of England in the late 1950s that had lists of all gilts outstanding and it would show intermediate-term debt with names like "4% Exchequer Stock of 1965" or " 4 and 1/2% Exchequer Stock of 1967". In any event, presumably FRED had to get their 10-year bond yield data for the UK (see https://fred.stlouisfed.org/series/IRLTLT01GBM156N ) from either the IMF/BIS/OECD which I guess would in turn have gotten it directly from either The Bank of England or from Her Majesty's Exchequer (i.e. the UK Treasury Department or equivalent thereof)....unless they are just calling a 20-year bond yield a "10-year" bond yield here (which is what, say, GFD does for its UK "10-year government bond yield" series until the 1970s).

Thanks for this - I need a bit of time to digest some of this info.

Apart from the BoE yield curves (https://www.bankofengland.co.uk/statistics/yield-curves) which go back to 1970 (and I note are spot yields rather than par) and macrohistory.net, the other UK data I've found so far are in 'a millenium of macroeconomic data for the UK' (https://www.bankofengland.co.uk/statist ... h-datasets) which appears to have T-bills from 1923, yield on 10 year securities from 1929 (which is spliced from various sources - indicated in the spreadsheet), consols (from 19th century) and better quality data from 1945 onwards.

cheers
StillGoing

[McQ]

Stillgoing—thanks as always for your excellent analytic work on SWR topics.

In this post, I will argue that your inputs in this thread can’t support the weight of the analysis. Pushback welcome.

[snip]

But SWR is the most practical of subjects, and simulated series that are perfectly fine for academic work may not be suitable.

Hi McQ,

Just a few thoughts in mild pushback!

While the returns for the different duration bond 'funds' in the simba spreadsheet are, pre-1970s, simulated/estimated from sources of varying quality and detail, the behaviour of such funds to broad changes in interest rate/yield regimes are going to be broadly correct, e.g., the NAV of short term funds will not change much with changes in interest rates, while that of a longer term fund will. Consequently the effect of changes in interest rate regimes (e.g. the post-1980s gradual fall in interest rates) on SWR will also broadly reflected - i.e. the details might be missed, but the general responses will not.

This is one reason in the analysis, that while I calculated the SWR at four different durations, most of the discussion concentrated on 'shorter term' (i.e., T-bills and STT) and 'longer term' (i.e., TBM and LTT) and why I think that looking at the behaviour when the SWR was relatively low was also instructive since one possible reason for low SWR is poor bond performance (the other, of course, being poor stock performance!) and duration has a strong effect on performance. I think four categories of duration is probably the absolute sensible maximum that the spectrum of bond returns can be divided into.

So, from an 'engineering' perspective (while I was educated as a physicist, I spent most of my career as an engineering academic), provided the duration of the bonds included in the Simba database are qualitatively correct (i.e. short bonds have a shorter duration than long bonds - I have no reason to believe otherwise) then the outcomes from the analysis can provide some practical indicators - one of which is that shorter term bonds tended to provide a higher SWR when the SWR was relatively low - that result is also true post-1942 (although I note the the percentages are different - e.g. 'T-bills' never gave the best SWR - see tables added below). I would agree that stating the outcome more definitely than that would be unreasonable, even more so since existing bond funds will vary in maturity with the subset of bonds (and the weighting of the individual holdings) that meet the appropriate filter.

cheers
StillGoing

Edit: Added tables of post-1942 results.

Percentage of retirements using FI of a particular duration that led to the highest SWR for the entire data set (‘all SWR’) and for a subset of the data where the best SWR was less than, an arbitrarily chosen, 5% (labelled as ‘SWR<5’)

Code: Select all

Bond duration that gave highest SWR				
	Bills	STT	TBM	LTT
All SWR	0	53	20	27
SWR<5	0	75	25	0

Code: Select all

Bond duration that gave lowest SWR				
	Bills	STT	TBM	LTT
All SWR	47	0	0	53
SWR<5	17	0	0	83

So, post 1942 neither TBM nor STT gave the worst result, while STT gave the best outcome on more occasions than TBM.

Pushback acknowledged! To be clear, I like the analysis (effect of different bond duration on SWR) and respect the effort. I just wanted you to know that some of the inputs are more sketchy than might have appeared.

There’s a tendency among Bogleheads to accept “what Shiller did” or “the peer-reviewed macrohistory.net database” as rock solid and comparable to the vast and diverse bond instruments available today. I don’t believe that to be wise. The older the data, the messier.

It was also rewarding for me to assemble on one page all my issues with the different bond series you put together.
You can definitely push back harder on my skepticism about “yield-curve-interpolated returns.” It is certainly a respectable academic procedure; and maybe it doesn’t make as much difference as I fear, relative to observations of actual bond prices.

On the long paper you mentioned, half of it is Appendices. What happened was that this paper was the last in a series where data collection consumed three or four years. Since I was about done, I threw into this last bond paper everything that was still in the drawer or piled on the desk. The Appendix titles of broader applicability, in case of interest, are:

• A Brief Tutorial on How US Bond Markets Changed over the 20th Century
...
• Issues Concerning Older Yield Averages Published by Moody’s and Standard & Poor’s
• Additional Findings for the Fallen Angels and Distressed Bonds in the Sample
• The Ontology of Moody’s Rating Grades
• How a Yield Spread Might Fail to Translate into an Earned Premium

https://papers.ssrn.com/sol3/papers.cfm ... id=3740190

[StillGoing]

If I am reading the first two charts correctly, TBM is never the best, often second best, and rarely the worst. That makes TBM the best "set it and forget it" option. Within five years of retirement add your favorite cash equivalent to taste.

Am I wrong?

Yes and if he had added it, ITT (Intermediate Term Treasuries) would likely have a similar outcome. I came to that conclusion during my accumulation days when it appeared that STT treasuries did best during the inflation runup of the 70's as interest rates rose and LTT did best during the inflation rundown starting in the 80's as interest rates dropped - putting intermediate term treasuries in the middle. Another reason people call out for bond funds with intermediate duration is that, at least when yield curves aren't inverted, you often get a substantial yield increase just moving from short to intermediate and significantly less increase moving from intermediate to long.

Now this is about SWR - something I'm not a fan of but which definitely makes the math easier for comparative analysis.

Cheers

You're right ITT would have come out similar (in the Simba spreadsheet, pre-1973 the data are quite similar). My own reading the data (particularly with the removal of the pre-1942 period where the data were less sound) is that either STT or TBM/ITT would have been a good choice with the statistics slightly favouring STT. The clear outcome is that T-bills and LTT are unlikely to be suitable for a set and forget approach.

cheers
StillGoing

[grabiner]

The safe withdrawal rate (SWR), i.e., the maximum initial withdrawal expressed as a percentage of the initial portfolio value (%IPV) that ensured the portfolio was not exhausted before 30 years had elapsed, is plotted for each of the FI funds as a function of retirement start year in the following figure.



As is well known in these parts, the SWR varied considerably from retirement to retirement ranging from a minimum of below 4% in the mid-1960s, to a maximum of over 10% in the early 1980s. While it is a bit difficult to see the different behaviour of the various FI funds, it is clear that in some periods (e.g., late 1970s onwards) longer duration FI resulted in the highest SWR, while in other periods (e.g., late 19th and early 20th century) T-bills gave the highest SWR. Of course, it is important to note that it would not have been possible at the beginning of a particular retirement to know what duration FI would have subsequently provided the best outcome.

What this suggests is a risk effect. Using long-term bonds with the same stock percentage increases withdrawals in rising markets, and decreases them in falling markets. The same thing would happen if you compared portfolios with identical stock and bond funds, but varied the stock percentage slightly.

A possible alternative to consider is adjusting the stock percentage and bond type at the same time; is 50% stocks and 50% short-term bonds better or worse than 45% stocks and 55% long-term bonds?

[typical.investor]

The safe withdrawal rate (SWR), i.e., the maximum initial withdrawal expressed as a percentage of the initial portfolio value (%IPV) that ensured the portfolio was not exhausted before 30 years had elapsed, is plotted for each of the FI funds as a function of retirement start year in the following figure.



As is well known in these parts, the SWR varied considerably from retirement to retirement ranging from a minimum of below 4% in the mid-1960s, to a maximum of over 10% in the early 1980s. While it is a bit difficult to see the different behaviour of the various FI funds, it is clear that in some periods (e.g., late 1970s onwards) longer duration FI resulted in the highest SWR, while in other periods (e.g., late 19th and early 20th century) T-bills gave the highest SWR. Of course, it is important to note that it would not have been possible at the beginning of a particular retirement to know what duration FI would have subsequently provided the best outcome.

What this suggests is a risk effect. Using long-term bonds with the same stock percentage increases withdrawals in rising markets, and decreases them in falling markets. The same thing would happen if you compared portfolios with identical stock and bond funds, but varied the stock percentage slightly.

Do you mean LLT decrease returns in falling equity markets?

If so, I'm going to disagree here (knowing that disagreeing with grabiner has never gone well for me - wish me luck).

Personally, I can't conclude this is market risk.

1950-1965 CAGR
Stocks 15.58% (13.45% real)
LTT 0.93% (-0.94% real)
STT 2.69% (0.80% real)

What explains the performance of LTT here? Inflation ran about 2%.

Well, we had yield curve control 1942 to 1951, and longer dated maturities had capital losses when it was lifted.

And until '79 when Volker came in, rates were set to boost employment. What was found though that actually setting rates to affect stable pricing actually benefitted the goal of maximally sustainable employment.

And the treasuries we have today are not callable. If rates drop, having a NAV boost instead of the bond being called isn't a trivial effect I think. Rather it give LTT a better mechanism to offset equity risk.

I don't know Fed policy going forward, but a backtest without consideration of how rates were being set doesn't seem so informative and I don't think really indicative of risk. Fed risk perhaps. Under current conditions, I'd expect LTT to offset equity risk

A possible alternative to consider is adjusting the stock percentage and bond type at the same time; is 50% stocks and 50% short-term bonds better or worse than 45% stocks and 55% long-term bonds?

No, quibbles here. Anyway, if grabiner and I have different view on fixed income - ignore me.

I just have a difficult time as seeing say 1929 being informative. Sure it's a yard stick measure but economic policy has changed and Bernanke's study of 1929 informed his response.

I'm not convinced I can infer a pattern from the past because I have absolutely no ability to predict future economic policy which I suspect may be one of the largest explanatory factors for returns on bonds.

https://libertystreeteconomics.newyorkf ... the-1940s/
https://www.chicagofed.org/publications ... ves/2021/2
https://www.stlouisfed.org/publications ... ht-us-much

[StillGoing]

The safe withdrawal rate (SWR), i.e., the maximum initial withdrawal expressed as a percentage of the initial portfolio value (%IPV) that ensured the portfolio was not exhausted before 30 years had elapsed, is plotted for each of the FI funds as a function of retirement start year in the following figure.



As is well known in these parts, the SWR varied considerably from retirement to retirement ranging from a minimum of below 4% in the mid-1960s, to a maximum of over 10% in the early 1980s. While it is a bit difficult to see the different behaviour of the various FI funds, it is clear that in some periods (e.g., late 1970s onwards) longer duration FI resulted in the highest SWR, while in other periods (e.g., late 19th and early 20th century) T-bills gave the highest SWR. Of course, it is important to note that it would not have been possible at the beginning of a particular retirement to know what duration FI would have subsequently provided the best outcome.

What this suggests is a risk effect. Using long-term bonds with the same stock percentage increases withdrawals in rising markets, and decreases them in falling markets. The same thing would happen if you compared portfolios with identical stock and bond funds, but varied the stock percentage slightly.

A possible alternative to consider is adjusting the stock percentage and bond type at the same time; is 50% stocks and 50% short-term bonds better or worse than 45% stocks and 55% long-term bonds?

A very quick initial reply... the volatility of LTT is likely to be much larger than that of STT, so where risk is defined as volatility, then you may be right Although, a second question is then whether this then translates into a larger portfolio volatility since the returns from the bonds are not necessarily correlated with those from stocks.

However, it does raise the important point that risk is usually thought of as being largely controlled by the stock allocation with bonds comprising the 'risk free' part of the portfolio with little consideration as to exactly what that means.

cheers
StillGoing

[StillGoing]

The safe withdrawal rate (SWR), i.e., the maximum initial withdrawal expressed as a percentage of the initial portfolio value (%IPV) that ensured the portfolio was not exhausted before 30 years had elapsed, is plotted for each of the FI funds as a function of retirement start year in the following figure.



As is well known in these parts, the SWR varied considerably from retirement to retirement ranging from a minimum of below 4% in the mid-1960s, to a maximum of over 10% in the early 1980s. While it is a bit difficult to see the different behaviour of the various FI funds, it is clear that in some periods (e.g., late 1970s onwards) longer duration FI resulted in the highest SWR, while in other periods (e.g., late 19th and early 20th century) T-bills gave the highest SWR. Of course, it is important to note that it would not have been possible at the beginning of a particular retirement to know what duration FI would have subsequently provided the best outcome.

What this suggests is a risk effect. Using long-term bonds with the same stock percentage increases withdrawals in rising markets, and decreases them in falling markets. The same thing would happen if you compared portfolios with identical stock and bond funds, but varied the stock percentage slightly.

Do you mean LLT decrease returns in falling equity markets?

If so, I'm going to disagree here (knowing that disagreeing with grabiner has never gone well for me - wish me luck).

Personally, I can't conclude this is market risk.

1950-1965 CAGR
Stocks 15.58% (13.45% real)
LTT 0.93% (-0.94% real)
STT 2.69% (0.80% real)

What explains the performance of LTT here? Inflation ran about 2%.

Well, we had yield curve control 1942 to 1951, and longer dated maturities had capital losses when it was lifted.

And until '79 when Volker came in, rates were set to boost employment. What was found though that actually setting rates to affect stable pricing actually benefitted the goal of maximally sustainable employment.

And the treasuries we have today are not callable. If rates drop, having a NAV boost instead of the bond being called isn't a trivial effect I think. Rather it give LTT a better mechanism to offset equity risk.

I don't know Fed policy going forward, but a backtest without consideration of how rates were being set doesn't seem so informative and I don't think really indicative of risk. Fed risk perhaps. Under current conditions, I'd expect LTT to offset equity risk

A possible alternative to consider is adjusting the stock percentage and bond type at the same time; is 50% stocks and 50% short-term bonds better or worse than 45% stocks and 55% long-term bonds?

No, quibbles here. Anyway, if grabiner and I have different view on fixed income - ignore me.

I just have a difficult time as seeing say 1929 being informative. Sure it's a yard stick measure but economic policy has changed and Bernanke's study of 1929 informed his response.

I'm not convinced I can infer a pattern from the past because I have absolutely no ability to predict future economic policy which I suspect may be one of the largest explanatory factors for returns on bonds.

https://libertystreeteconomics.newyorkf ... the-1940s/
https://www.chicagofed.org/publications ... ves/2021/2
https://www.stlouisfed.org/publications ... ht-us-much

A quick few initial thoughts...

Along with McQ's comments above (and Alpha4), it is clear that the US bond market today is quite different to how it was 100 years ago not only in terms of policy, as you state, but also implementation (i.e., the number of new issues, callable bonds etc.).

However, I am convinced that bond duration must play a part regardless of policy since shorter term bonds will tend to have a lower average return and a lower volatility than longer term bonds, which would imply that looking at historical values with different durations is at least indicative if not predictive. In terms of SWR studies (but not percentage of portfolio approaches), volatility and, consequently, sequence of returns is crucial to the outcome as can be seen from the outcomes.

The standard 'advice' given around here suggesting intermediate durations for buy and hold bond funds then, for a given value of 'intermediate', steers a middle course between the two extreme values. The results here are consistent with that advice without determining what intermediate means beyond a duration of somewhere between about 2-8 years. That is probably good enough!

cheers
StillGoing

[dcabler]

Along with McQ's comments above (and Alpha4), it is clear that the US bond market today is quite different to how it was 100 years ago not only in terms of policy, as you state, but also implementation (i.e., the number of new issues, callable bonds etc.).

Not only was the bond market different, but of course bond funds also didn't exist. And I don't know if any active bond traders back in the day were creating rolling ladders that resemble what bond funds do today in any way. Over time, I've come to think of it as a bit strange that we've taken something that was designed to create an income stream (actual bonds) and turned it into a returns vehicle (bond funds).

Cheers

[typical.investor]

A quick few initial thoughts...

Along with McQ's comments above (and Alpha4), it is clear that the US bond market today is quite different to how it was 100 years ago not only in terms of policy, as you state, but also implementation (i.e., the number of new issues, callable bonds etc.).

However, I am convinced that bond duration must play a part regardless of policy since shorter term bonds will tend to have a lower average return and a lower volatility than longer term bonds, which would imply that looking at historical values with different durations is at least indicative if not predictive. In terms of SWR studies (but not percentage of portfolio approaches), volatility and, consequently, sequence of returns is crucial to the outcome as can be seen from the outcomes.

The standard 'advice' given around here suggesting intermediate durations for buy and hold bond funds then, for a given value of 'intermediate', steers a middle course between the two extreme values. The results here are consistent with that advice without determining what intermediate means beyond a duration of somewhere between about 2-8 years. That is probably good enough!

cheers
StillGoing

Fair enough and probably good enough.

I don't like it though because one does increase interest rate risk when duration is significantly shorter than investment horizon. In that sense, a ladder of long term treasuries would produce higher yields without incurring sequence of return risks.

[seajay]

LTT have a tendency to shorter term inverse correlate with stocks, mid term correlate.
50/50 TSM/LTT is broadly more volatile than 50/50 TSM/TBill, as a measure of the standard deviation in 30 year MaxWR% will tend to indicate, and as your graphs also indicate (higher highs, lower lows in 30 year MaxWR%).

Equalize the volatility, comparing the likes of 50/50 TSM/TBill with thirds TSM/LTT/Gold such that the standard deviation in 30 year MaxWR% are more aligned, as are the charts highest/lowest, and they'll still be misalignment in the actual outcomes (worst cases for each will occur at different times). By blending both 50/50 (or whatever), each of the individual worst cases will be uplifted, less bad. Maybe of the order 41/25/17/17 TSM/TBill/LTT/Gold. Substitute the 25/17/17 TBill/LTT/Gold with TBM ... likely to similar effect (of the order 40/60 TSM/TBM).

While the future is unknowable, the historical evidence would suggest that, in poor retirements, short term treasuries tended to be a better choice in terms of SWR than the intermediate maturity bonds in total bond market or long term treasuries.

Not if you, In Larry Swedroe's terminology, shift some of the bond risk over to the stock side, 50/50 TSM/TBill instead of 40/60 TSM/TBM or suchlike.

[StillGoing]

Along with McQ's comments above (and Alpha4), it is clear that the US bond market today is quite different to how it was 100 years ago not only in terms of policy, as you state, but also implementation (i.e., the number of new issues, callable bonds etc.).

Not only was the bond market different, but of course bond funds also didn't exist. And I don't know if any active bond traders back in the day were creating rolling ladders that resemble what bond funds do today in any way. Over time, I've come to think of it as a bit strange that we've taken something that was designed to create an income stream (actual bonds) and turned it into a returns vehicle (bond funds).

Cheers

I wonder that too. As an example, my father's retirement portfolio in the 1980s (not entirely ancient history) had individual bonds in it that provided a fixed income stream (albeit the rates were somewhat higher at that time). I think the recentish interest in bond ladders, particularly with TIPS, is a recognition that what they can provide is known income whether nominal or inflation adjusted. Otherwise, bond funds appear to be considered as a way of controlling the volatility of stocks or to avoid withdrawals when the stock market is down.

I think that rolling down the yield curve, adjusting duration, etc. have been known to active traders for some time, but I'm not knowledgeable enough to known for how long.

cheers
StillGoing

[StillGoing]

A quick few initial thoughts...

Along with McQ's comments above (and Alpha4), it is clear that the US bond market today is quite different to how it was 100 years ago not only in terms of policy, as you state, but also implementation (i.e., the number of new issues, callable bonds etc.).

However, I am convinced that bond duration must play a part regardless of policy since shorter term bonds will tend to have a lower average return and a lower volatility than longer term bonds, which would imply that looking at historical values with different durations is at least indicative if not predictive. In terms of SWR studies (but not percentage of portfolio approaches), volatility and, consequently, sequence of returns is crucial to the outcome as can be seen from the outcomes.

The standard 'advice' given around here suggesting intermediate durations for buy and hold bond funds then, for a given value of 'intermediate', steers a middle course between the two extreme values. The results here are consistent with that advice without determining what intermediate means beyond a duration of somewhere between about 2-8 years. That is probably good enough!

cheers
StillGoing

Fair enough and probably good enough.

I don't like it though because one does increase interest rate risk when duration is significantly shorter than investment horizon. In that sense, a ladder of long term treasuries would produce higher yields without incurring sequence of return risks.

However, I also think that your comments on historical conditions for bonds (and, by extension, to stocks) have some validity. The conditions that produced historical outcomes are unlikely to be repeated in exactly the same way again. However, it is probable that at some stage in the future
1) Bond yields will trend downwards over an extended period and long term bonds will do better than short term.
2) Bond yields will trend upwards over an extended period and short term bonds will do better than long term.
3) Bond yields will stay level for an extended period and which set of bonds then do best will depend on whether the yield curve is inverted or not.

How often those conditions will occur is impossible to predict.

There is a thread that discusses the bond duration glide path (viewtopic.php?t=318412) - but as far as I can remember, I don't think there was any backtesting (while backtesting might not predict the future, it at least allows us to see what would have happened in the past).

cheers
StillGoing

[dbr]

However, I also think that your comments on historical conditions for bonds (and, by extension, to stocks) have some validity. The conditions that produced historical outcomes are unlikely to be repeated in exactly the same way again. However, it is probable that at some stage in the future
1) Bond yields will trend downwards over an extended period and long term bonds will do better than short term.
2) Bond yields will trend upwards over an extended period and short term bonds will do better than long term.
3) Bond yields will stay level for an extended period and which set of bonds then do best will depend on whether the yield curve is inverted or not.

How often those conditions will occur is impossible to predict.

Keeping in mind that both the shape and the level of the yield curve changes all the time: https://stockcharts.com/freecharts/yieldcurve.php

[seajay]

I wonder that too. As an example, my father's retirement portfolio in the 1980s (not entirely ancient history) had individual bonds in it that provided a fixed income stream (albeit the rates were somewhat higher at that time). I think the recentish interest in bond ladders, particularly with TIPS, is a recognition that what they can provide is known income whether nominal or inflation adjusted. Otherwise, bond funds appear to be considered as a way of controlling the volatility of stocks or to avoid withdrawals when the stock market is down.

Here in the UK a individual TIPS bond (Index Linked Gilt treasury bond) has the price appreciation element exempt from tax, you only pay tax on the yield. Buy such a bond with a low coupon yield, such as 0.125% https://www.yieldgimp.com/index-linked-gilt-yields and the taxable interest element is near small enough to be irrelevant, most of the return arises out of price increase (inflation). Ideal for holding in a general (taxable) account. Hold a bond fund instead, and the tax efficiencies are lost. Assuming a 20% taxation rate and 4% of tax free requires a 5% taxable to compare equally.

Things are not as new as you may opine, the three fund for example, has evidence of being proposed back in the mid 1960's for instance viewtopic.php?p=7444951#p7444951

[StillGoing]

However, I also think that your comments on historical conditions for bonds (and, by extension, to stocks) have some validity. The conditions that produced historical outcomes are unlikely to be repeated in exactly the same way again. However, it is probable that at some stage in the future
1) Bond yields will trend downwards over an extended period and long term bonds will do better than short term.
2) Bond yields will trend upwards over an extended period and short term bonds will do better than long term.
3) Bond yields will stay level for an extended period and which set of bonds then do best will depend on whether the yield curve is inverted or not.

How often those conditions will occur is impossible to predict.

Keeping in mind that both the shape and the level of the yield curve changes all the time: https://stockcharts.com/freecharts/yieldcurve.php

Of course, but there are long-term trends too... e.g., the long run of declining bond yields from the 1980s until the last few years(?).

cheers
StillGoing

[StillGoing]

I wonder that too. As an example, my father's retirement portfolio in the 1980s (not entirely ancient history) had individual bonds in it that provided a fixed income stream (albeit the rates were somewhat higher at that time). I think the recentish interest in bond ladders, particularly with TIPS, is a recognition that what they can provide is known income whether nominal or inflation adjusted. Otherwise, bond funds appear to be considered as a way of controlling the volatility of stocks or to avoid withdrawals when the stock market is down.

Here in the UK a individual TIPS bond (Index Linked Gilt treasury bond) has the price appreciation element exempt from tax, you only pay tax on the yield. Buy such a bond with a low coupon yield, such as 0.125% https://www.yieldgimp.com/index-linked-gilt-yields and the taxable interest element is near small enough to be irrelevant, most of the return arises out of price increase (inflation). Ideal for holding in a general (taxable) account. Hold a bond fund instead, and the tax efficiencies are lost. Assuming a 20% taxation rate and 4% of tax free requires a 5% taxable to compare equally.

Things are not as new as you may opine, the three fund for example, has evidence of being proposed back in the mid 1960's for instance viewtopic.php?p=7444951#p7444951

Indeed - I hold a few, low coupon, index linked gilts to bridge the gap to my OH's state pension should I keel over beforehand (since, in those circumstances, my DB pension will be halved). One of the (minor) problems with the recent increases in gilt yields is that coupons (for both nominal and index linked gilts) will be getting larger again.

I'm not sure I've expressed an opinion on when the three fund portfolio started, but the link you provided is certainly interesting.

cheers
StillGoing

[FactualFran]

Do you mean LLT decrease returns in falling equity markets?

The topic is safe withdrawal rate (SWR), "i.e., the maximum initial withdrawal expressed as a percentage of the initial portfolio value (%IPV) that ensured the portfolio was not exhausted before 30 years had elapsed". The topic is not total return.

The total return does not depend on the sequence of returns. The safe withdrawal rate depends on the sequence of returns, this is known as sequence of returns risk. Long Term bonds tend to have a higher variance in the period, leading to a lower maximum initial withdrawal percent.

[typical.investor]

Do you mean LLT decrease returns in falling equity markets?

The topic is safe withdrawal rate (SWR), "i.e., the maximum initial withdrawal expressed as a percentage of the initial portfolio value (%IPV) that ensured the portfolio was not exhausted before 30 years had elapsed". The topic is not total return.

The total return does not depend on the sequence of returns. The safe withdrawal rate depends on the sequence of returns, this is known as sequence of returns risk. Long Term bonds tend to have a higher variance in the period, leading to a lower maximum initial withdrawal percent.

Yes, but no.

I believe long term bonds can have the same low variance as Tbills and also the higher return of duration. Look, if we want to optimize withdrawals, then let's do so. Intermediate bond funds are for convenience.

Your assumption is that to use long term bonds, that you may have to sell it after a NAV loss which would increase SOR risk. I question the assumption.

Optimal would be to have a ladder of longer term bonds set to mature when you need money. So I don't see the returns of LTT and effects of portfolio failure as being a function of risk as much as a function of how you held them.

[Alpha4]

The safe withdrawal rate (SWR), i.e., the maximum initial withdrawal expressed as a percentage of the initial portfolio value (%IPV) that ensured the portfolio was not exhausted before 30 years had elapsed, is plotted for each of the FI funds as a function of retirement start year in the following figure.



As is well known in these parts, the SWR varied considerably from retirement to retirement ranging from a minimum of below 4% in the mid-1960s, to a maximum of over 10% in the early 1980s. While it is a bit difficult to see the different behaviour of the various FI funds, it is clear that in some periods (e.g., late 1970s onwards) longer duration FI resulted in the highest SWR, while in other periods (e.g., late 19th and early 20th century) T-bills gave the highest SWR. Of course, it is important to note that it would not have been possible at the beginning of a particular retirement to know what duration FI would have subsequently provided the best outcome.

What this suggests is a risk effect. Using long-term bonds with the same stock percentage increases withdrawals in rising markets, and decreases them in falling markets. The same thing would happen if you compared portfolios with identical stock and bond funds, but varied the stock percentage slightly.

And the treasuries we have today are not callable. If rates drop, having a NAV boost instead of the bond being called isn't a trivial effect I think. Rather it give LTT a better mechanism to offset equity risk.

I have seen this posted on Bogleheads (that callability of Treasuries somehow was a major factor in LTT returns--especially in the bond bear market of 1947-1981) quite a few times and yet I don't recall anyone ever pushing back hard against it.

Here are the facts: Yes, most (albeit not all) Treasuries issued before 1984 or 1985 did indeed have a provision to call them in early if the issuer (the US treasury) so desired. However.

1. For virtually all Treasury bonds issued from the mid-1920s onward the earliest possible call date only arrived one, two, three, four, or five years before the actual maturity date. This was most unlike corporate bonds during this period (1925 or 1926 on to the 1970s) where there was either no call protection at all (i.e. the call price would be set at something like 102 or 105 when par was 100....but the bond was theoretically callable even immediately after issue had the issuer chosen to do so) or--on corporate bonds from the early or mid-1940s onward--they generally had a period of call protection for a few years after issue but after that they could be called, generally at a call price that steadily declined to par over the next 5-10 years or so. For a corporate bond with a maturity of 30 years (which was fairly standard by the late 1930s) this might mean that it was callable at 102 or 103 from its fourth or fifth year since issue and by its tenth or twelfth of thirteenth year it would've been callable at par; if rates fell enough such a bond essentially could become a short term or IT bond as soon as the call protection period (if any) was up and it would quite likely be called at some point. For a 30-year Treasury bond, on the other hand, even if rates fell enough to make it callable (which certainly was the case from, say, 1932 to 1946) the only thing that happened was it became a bond that was callable in 25 years (i.e. it would effectively mature in 25 years) rather than maturing in 30...which is a lot smaller change than going from being a long-term bond to being a potentially virtually short-term bond (due to becoming under the gun for being called) the minute rates fell. Indeed, this is why during the 1930s and 1920s very few callable corporate bonds rose much above their call prices at all whereas some long Treasuries rallied to prices of 110 (or even 115, 117, or 118) during the 1940s.

2. From 1947 or 1948 onward (i.e. during virtually all of the bond bear market from 1947 to late 1981) callability became almost a non-issue for Treasuries and corporates alike; no issuer would call a bond paying a coupon of, say, 2.75% when it would have to replace it/refund it with a new one paying, say, 3.75%.

There were a few calls of corporate bonds during this period but most of these were either issuers locking in a longer time frame in return for perhaps a slightly higher interest rate or at worst the same rate (i.e. refunding a bond with, say, 19 years left into one with 40 years left), or else medium to slightly low grade or "just above junk" quality issuers refunding higher much rated debt issued (in the 1930s or early 1940s) when their credit was absolutely junk and they had had to issue bonds at five or six or seven percent or greater rates (when investment-grade credits could borrow at 2.75, 2.875, or 3.00 percent)

IIRC the few Treasuries that were called in the late 1940s or early 1950s were almost all issues that had less then ten years until maturity anyhow....IOW they would not have been in a long bond index to begin with. After the early 1950s--certainly after the mid 1950s--and until 1983 or so I don't think many if any Treasuries were called; why would Uncle Sam call in a bond at a lower rate only to have to refund it at a much higher rate?

[StillGoing]

Stillgoing—thanks as always for your excellent analytic work on SWR topics.

In this post, I will argue that your inputs in this thread can’t support the weight of the analysis. Pushback welcome.

[snip]

But SWR is the most practical of subjects, and simulated series that are perfectly fine for academic work may not be suitable.

Hi McQ,

Just a few thoughts in mild pushback!

While the returns for the different duration bond 'funds' in the simba spreadsheet are, pre-1970s, simulated/estimated from sources of varying quality and detail, the behaviour of such funds to broad changes in interest rate/yield regimes are going to be broadly correct, e.g., the NAV of short term funds will not change much with changes in interest rates, while that of a longer term fund will. Consequently the effect of changes in interest rate regimes (e.g. the post-1980s gradual fall in interest rates) on SWR will also broadly reflected - i.e. the details might be missed, but the general responses will not.

This is one reason in the analysis, that while I calculated the SWR at four different durations, most of the discussion concentrated on 'shorter term' (i.e., T-bills and STT) and 'longer term' (i.e., TBM and LTT) and why I think that looking at the behaviour when the SWR was relatively low was also instructive since one possible reason for low SWR is poor bond performance (the other, of course, being poor stock performance!) and duration has a strong effect on performance. I think four categories of duration is probably the absolute sensible maximum that the spectrum of bond returns can be divided into.

So, from an 'engineering' perspective (while I was educated as a physicist, I spent most of my career as an engineering academic), provided the duration of the bonds included in the Simba database are qualitatively correct (i.e. short bonds have a shorter duration than long bonds - I have no reason to believe otherwise) then the outcomes from the analysis can provide some practical indicators - one of which is that shorter term bonds tended to provide a higher SWR when the SWR was relatively low - that result is also true post-1942 (although I note the the percentages are different - e.g. 'T-bills' never gave the best SWR - see tables added below). I would agree that stating the outcome more definitely than that would be unreasonable, even more so since existing bond funds will vary in maturity with the subset of bonds (and the weighting of the individual holdings) that meet the appropriate filter.

cheers
StillGoing

Edit: Added tables of post-1942 results.

Percentage of retirements using FI of a particular duration that led to the highest SWR for the entire data set (‘all SWR’) and for a subset of the data where the best SWR was less than, an arbitrarily chosen, 5% (labelled as ‘SWR<5’)

Code: Select all

Bond duration that gave highest SWR				
	Bills	STT	TBM	LTT
All SWR	0	53	20	27
SWR<5	0	75	25	0

Code: Select all

Bond duration that gave lowest SWR				
	Bills	STT	TBM	LTT
All SWR	47	0	0	53
SWR<5	17	0	0	83

So, post 1942 neither TBM nor STT gave the worst result, while STT gave the best outcome on more occasions than TBM.

Pushback acknowledged! To be clear, I like the analysis (effect of different bond duration on SWR) and respect the effort. I just wanted you to know that some of the inputs are more sketchy than might have appeared.

There’s a tendency among Bogleheads to accept “what Shiller did” or “the peer-reviewed macrohistory.net database” as rock solid and comparable to the vast and diverse bond instruments available today. I don’t believe that to be wise. The older the data, the messier.

It was also rewarding for me to assemble on one page all my issues with the different bond series you put together.
You can definitely push back harder on my skepticism about “yield-curve-interpolated returns.” It is certainly a respectable academic procedure; and maybe it doesn’t make as much difference as I fear, relative to observations of actual bond prices.

On the long paper you mentioned, half of it is Appendices. What happened was that this paper was the last in a series where data collection consumed three or four years. Since I was about done, I threw into this last bond paper everything that was still in the drawer or piled on the desk. The Appendix titles of broader applicability, in case of interest, are:

• A Brief Tutorial on How US Bond Markets Changed over the 20th Century
...
• Issues Concerning Older Yield Averages Published by Moody’s and Standard & Poor’s
• Additional Findings for the Fallen Angels and Distressed Bonds in the Sample
• The Ontology of Moody’s Rating Grades
• How a Yield Spread Might Fail to Translate into an Earned Premium

https://papers.ssrn.com/sol3/papers.cfm ... id=3740190

Thanks for this - I've had a read through some of the paper - there's a lot of interesting stuff to get my head round!

You're right about the problems with the data bases - you've already written (here on the forum and at SSRN) about some of the problems with Shiller, SBBI, and others. Jorda et al (macrohistory.net) tend to use existing databases although they do splice different sources and the durations associated with each series are not necessarily constant and those for bond yields are not always related with those for bond returns.

For example, for the US, bond returns are

1870–1926 Total return on a basket of central government bonds around 10-year maturity. Calculated from prices of individual bonds in the Commercial and Financial Chronicle, various issues.
1927–1928 Total return on 10-year government bonds, price changes imputed from yields. Source: Aswath Damodaran database (http://pages.stern.nyu.edu/~adamodar/ New_Home_Page/datafile/histretSP.html).
1929–2015 Total return on US long-term government bonds, from Barclays (2016).

I note that post-1929, the Barclay's source uses "For the bond index, the CRSP has used software which selects the bond that is closest to a 20-year bond in each month."

Their yields are derived from
Short term: From www.measuringworth.com/datasets/interestrates/
Long-term
1871-1939 Shiller 10 year government rate
1940-1953 From Schmelzing, P. (2020). Eight centuries of global real interest rates, R-G, and the ‘suprasecular’ decline, 1311-2018. Bank of England Staff Working Paper No. 845.
1954-2020 International Monetary Fund, International Financial Statistics (IFS). Data reports “Economic indicators (IFS)”, Section “Interest rates”, Series “Government Bonds, percent per Anum”.

I've never been interested/motivated enough to compare the yield series with others (e.g. FRED) to see if I could work out exactly what bonds they referred to.

As for the basics of converting yields to prices, I note that, if my understanding is correct, there are several different yields

yield to maturity for a given bond with a given coupon and price. The spreadsheet price function, can be used to determine the price (I've done this for individual bonds when buying them) or the function yield, which does the opposite (converts price to yield) - these appear to get close enough for practical purposes.

par yields - which is the yield to maturity for a bond at par (and are the yields quoted by FRED for US bonds)

zero coupon (spot) yields - which is the yield to maturity for a zero coupon bond (and are the yields quoted by the Bank of England, see https://www.bankofengland.co.uk/statist ... d-concepts)

Using prices then, where available, makes a lot of sense!

cheers
StillGoing

[typical.investor]

The safe withdrawal rate (SWR), i.e., the maximum initial withdrawal expressed as a percentage of the initial portfolio value (%IPV) that ensured the portfolio was not exhausted before 30 years had elapsed, is plotted for each of the FI funds as a function of retirement start year in the following figure.



As is well known in these parts, the SWR varied considerably from retirement to retirement ranging from a minimum of below 4% in the mid-1960s, to a maximum of over 10% in the early 1980s. While it is a bit difficult to see the different behaviour of the various FI funds, it is clear that in some periods (e.g., late 1970s onwards) longer duration FI resulted in the highest SWR, while in other periods (e.g., late 19th and early 20th century) T-bills gave the highest SWR. Of course, it is important to note that it would not have been possible at the beginning of a particular retirement to know what duration FI would have subsequently provided the best outcome.

What this suggests is a risk effect. Using long-term bonds with the same stock percentage increases withdrawals in rising markets, and decreases them in falling markets. The same thing would happen if you compared portfolios with identical stock and bond funds, but varied the stock percentage slightly.

And the treasuries we have today are not callable. If rates drop, having a NAV boost instead of the bond being called isn't a trivial effect I think. Rather it give LTT a better mechanism to offset equity risk.

I have seen this posted on Bogleheads (that callability of Treasuries somehow was a major factor in LTT returns--especially in the bond bear market of 1947-1981) quite a few times and yet I don't recall anyone ever pushing back hard against it.

Here are the facts: Yes, most (albeit not all) Treasuries issued before 1984 or 1985 did indeed have a provision to call them in early if the issuer (the US treasury) so desired. However.

1. For virtually all Treasury bonds issued from the mid-1920s onward the earliest possible call date only arrived one, two, three, four, or five years before the actual maturity date. This was most unlike corporate bonds during this period (1925 or 1926 on to the 1970s) where there was either no call protection at all (i.e. the call price would be set at something like 102 or 105 when par was 100....but the bond was theoretically callable even immediately after issue had the issuer chosen to do so) or--on corporate bonds from the early or mid-1940s onward--they generally had a period of call protection for a few years after issue but after that they could be called, generally at a call price that steadily declined to par over the next 5-10 years or so. For a corporate bond with a maturity of 30 years (which was fairly standard by the late 1930s) this might mean that it was callable at 102 or 103 from its fourth or fifth year since issue and by its tenth or twelfth of thirteenth year it would've been callable at par; if rates fell enough such a bond essentially could become a short term or IT bond as soon as the call protection period (if any) was up and it would quite likely be called at some point. For a 30-year Treasury bond, on the other hand, even if rates fell enough to make it callable (which certainly was the case from, say, 1932 to 1946) the only thing that happened was it became a bond that was callable in 25 years (i.e. it would effectively mature in 25 years) rather than maturing in 30...which is a lot smaller change than going from being a long-term bond to being a potentially virtually short-term bond (due to becoming under the gun for being called) the minute rates fell. Indeed, this is why during the 1930s and 1920s very few callable corporate bonds rose much above their call prices at all whereas some long Treasuries rallied to prices of 110 (or even 115, 117, or 118) during the 1940s.

Ok, relative to corporate bond there is less of an effect. Still, given a thumbnail approximation of a 1% gain for every year of duration with a 1% fall in interest, losing 5% NAV appreciation for a 1% drop in rates (or 10% NAV loss with a 2% drop - what would trigger a call) doesn't seem insignificant. Also, you'd lose roll yield.

2. From 1947 or 1948 onward (i.e. during virtually all of the bond bear market from 1947 to late 1981) callability became almost a non-issue for Treasuries and corporates alike; no issuer would call a bond paying a coupon of, say, 2.75% when it would have to replace it/refund it with a new one paying, say, 3.75%.

There were a few calls of corporate bonds during this period but most of these were either issuers locking in a longer time frame in return for perhaps a slightly higher interest rate or at worst the same rate (i.e. refunding a bond with, say, 19 years left into one with 40 years left), or else medium to slightly low grade or "just above junk" quality issuers refunding higher much rated debt issued (in the 1930s or early 1940s) when their credit was absolutely junk and they had had to issue bonds at five or six or seven percent or greater rates (when investment-grade credits could borrow at 2.75, 2.875, or 3.00 percent)

That's perhaps true, but still I'd argue that yield control from 1942 to 1951 hurt any LTT issued in that time since they would suffer capital losses as long rate rose to a more natural level.

Also, it wasn't until 1985 that 30 year uncallable became quite regular issuances.

IIRC the few Treasuries that were called in the late 1940s or early 1950s were almost all issues that had less then ten years until maturity anyhow....IOW they would not have been in a long bond index to begin with.

Vanguard LTT now holds 11.40% in 5-10 year maturities. So not only would they be affected, but also probably the 10-20 year maturities which would see 5 years less of NAV gains than you'd expect for that level of rate drop.

After the early 1950s--certainly after the mid 1950s--and until 1983 or so I don't think many if any Treasuries were called; why would Uncle Sam call in a bond at a lower rate only to have to refund it at a much higher rate?

Sure. Nothing to call but LTT would have suffered NAV loss as yield control came off. And that effect (previous suppression of bond yield) was perhaps large enough so that nothing needed to be called. It doesn't mean though that previous policy actions have no bearing on the return or that returns from the era should be expected to be similar today.

Anyway, the presumption I question is why would one use a fund if choosing LTT. We know volatility is too great to spend from a fund with a 20 year duration. We know a portfolio has less interest rate risk with the fixed income duration closer matches the investment horizon.

So why not either use a ladder, or adjust duration as the investment horizon shortens if using a fund.

I don't know, I'm 13.2 years duration two years into retirement which is a little shorter than Vanguard's 15.7 year duration on their long term fund and I don't believe my sequence of return risk is a problem. Cash flows are such that there is little chance I'll be selling bonds that have NAV loss from rate hikes. Some of that is a maturing ladder, and some is a low withdrawal rate due to legacy needs.

I have trouble holding intermediates of 5-6 years duration I know I am not going to use for a decade or two. I guess they are a convenience package.

[StillGoing]

Just to push the data a little more, up to now I have only used a single bond fund (STT, TBM, etc.). What happens if we use two bond funds simultaneously instead? One example of this would be the 'barbell' approach where short term fixed income (Bills or STT) is held simultaneously with long term.

Scenario as before, 50% stocks, 50% allocation to fixed income that is now divided 50/50 between two funds (so the overall allocation is 50% stocks, 25% BondFundA and 25% BondFundB) with annual rebalancing and annual withdrawals taken at the start of each year over a 30 year retirement. Only Simba returns data from 1942 onwards have been used for reasons discussed earlier in the thread.

The following table shows percentage of historical retirements where holding the fund or fund combination obtained the given rank (from 1st, i.e. highest SWR to 10th, i.e. lowest SWR - there are 10 ranks because there are 10 combinations of one or two funds). The Maximum Safe withdrawal Rate (MSWR, i.e., the withdrawal rate that led to no historical failures) is also shown (I have rounded this to 1 decimal place since there is no justification to quote this more precisely). Since there are just over 50 retirements, the percentages have a resolution of about 2 percentage points and rounding may mean that the numbers in rows and columns do not add up to 100.

Code: Select all

		Rank (1=highest SWR, 10=lowest SWR)									
		MSWR	1	2	3	4	5	6	7	8	9	10
Bills		4.1	0	0	10	16	4	16	0	6	2	47
STT		4.3	53	0	10	4	4	6	20	4	0	0
TBM		4.1	20	0	20	31	0	29	0	0	0	0
LTT		3.8	27	0	0	2	0	8	6	2	2	53
Bills/STT	4.2	0	29	10	8	6	0	6	8	33	0
Bills/TBM	4.2	0	0	0	8	45	10	12	24	2	0
Bills/LTT	4.0	0	0	0	0	18	6	4	41	31	0
STT/TBM		4.2	0	41	22	10	10	18	0	0	0	0
STT/LTT		4.0	0	2	20	14	12	8	45	0	0	0
TBM/LTT		4.0	0	27	10	8	2	0	8	16	29	0

There are a few things to note:
1) Only the single funds led to the outcomes being in the best and worst ranks (the percentages are the same as presented upthread).
2) While STT was was ranked first more often than TBM, it also had marginally more outcomes in the bottom half (ranks 6-10).
3) Combining bills with STT or TBM made the ranking outcomes worse than holding STT or TBM alone.
4) Combining bills with LTT improved the worst performing retirements, but resulted in more than 80% of retirements falling in ranks 6-10.
5) Combining STT with LTT resulted in middle ranked outcomes, but more than 50% of retirements were still in the bottom half.
6) Combining STT and TBM led to fewer occasions where the retirements ranked 6-10 than any other combination.
7) With the exception of holding LTT alone, the values of MSWR were within 30 basis points of each other (4.0 to 4.3%). Given the nature of the data, this is may be close to the order of the errors.

I haven't presented the statistics for SWR<5% since the number of retirements is then too small for meaningful statistics to be obtained with 10 fund combinations (it was marginal enough with 4).

cheers
StillGoing

[typical.investor]

Just to push the data a little more, up to now I have only used a single bond fund (STT, TBM, etc.). What happens if we use two bond funds simultaneously instead? One example of this would be the 'barbell' approach where short term fixed income (Bills or STT) is held simultaneously with long term.

Scenario as before, 50% stocks, 50% allocation to fixed income that is now divided 50/50 between two funds (so the overall allocation is 50% stocks, 25% BondFundA and 25% BondFundB) with annual rebalancing and annual withdrawals taken at the start of each year over a 30 year retirement. Only Simba returns data from 1942 onwards have been used for reasons discussed earlier in the thread.

The following table shows percentage of historical retirements where holding the fund or fund combination obtained the given rank (from 1st, i.e. highest SWR to 10th, i.e. lowest SWR - there are 10 ranks because there are 10 combinations of one or two funds). The Maximum Safe withdrawal Rate (MSWR, i.e., the withdrawal rate that led to no historical failures) is also shown (I have rounded this to 1 decimal place since there is no justification to quote this more precisely). Since there are just over 50 retirements, the percentages have a resolution of about 2 percentage points and rounding may mean that the numbers in rows and columns do not add up to 100.

Code: Select all

		Rank (1=highest SWR, 10=lowest SWR)									
		MSWR	1	2	3	4	5	6	7	8	9	10
Bills		4.1	0	0	10	16	4	16	0	6	2	47
STT		4.3	53	0	10	4	4	6	20	4	0	0
TBM		4.1	20	0	20	31	0	29	0	0	0	0
LTT		3.8	27	0	0	2	0	8	6	2	2	53
Bills/STT	4.2	0	29	10	8	6	0	6	8	33	0
Bills/TBM	4.2	0	0	0	8	45	10	12	24	2	0
Bills/LTT	4.0	0	0	0	0	18	6	4	41	31	0
STT/TBM		4.2	0	41	22	10	10	18	0	0	0	0
STT/LTT		4.0	0	2	20	14	12	8	45	0	0	0
TBM/LTT		4.0	0	27	10	8	2	0	8	16	29	0

There are a few things to note:
1) Only the single funds led to the outcomes being in the best and worst ranks (the percentages are the same as presented upthread).
2) While STT was was ranked first more often than TBM, it also had marginally more outcomes in the bottom half (ranks 6-10).
3) Combining bills with STT or TBM made the ranking outcomes worse than holding STT or TBM alone.
4) Combining bills with LTT improved the worst performing retirements, but resulted in more than 80% of retirements falling in ranks 6-10.
5) Combining STT with LTT resulted in middle ranked outcomes, but more than 50% of retirements were still in the bottom half.
6) Combining STT and TBM led to fewer occasions where the retirements ranked 6-10 than any other combination.
7) With the exception of holding LTT alone, the values of MSWR were within 30 basis points of each other (4.0 to 4.3%). Given the nature of the data, this is may be close to the order of the errors.

I haven't presented the statistics for SWR<5% since the number of retirements is then too small for meaningful statistics to be obtained with 10 fund combinations (it was marginal enough with 4).

cheers
StillGoing

That's quite interesting and something to think about. Still, I think it's a bit unfair of a picture to duration or at least how I'd envision it optimally used.

Ideally I think, we'd want duration to more match investment horizon. For example, holding a LTT fund with a duration of 16 when you are starting a 30 or 40 year retirement is very different than when you have perhaps 10 years of retirement left. And in both those case, parts of your portfolio really have a 1, 2, 3 etc investment horizon as you have to spend them down.

As such, I'd expect STT with LTT to potentially do better, but only if we are reducing duration along the way. Perhaps a ladder of LTT that matured and were reinvested in STT would do the trick. Or perhaps a glide path of sorts if you were holding two funds.

To me, this data address the question of "what's the best fixed duration for retirement" and not "what's the best duration throughout retirement".

Don't get me wrong, I appreciate your work and find it useful to think about.

[FactualFran]

I believe long term bonds can have the same low variance as Tbills and also the higher return of duration. Look, if we want to optimize withdrawals, then let's do so. Intermediate bond funds are for convenience.

Your assumption is that to use long term bonds, that you may have to sell it after a NAV loss which would increase SOR risk. I question the assumption.

Optimal would be to have a ladder of longer term bonds set to mature when you need money. So I don't see the returns of LTT and effects of portfolio failure as being a function of risk as much as a function of how you held them.

Anyone can believe anything.

What was written in the opening post includes

Using asset returns from the Simba dataset (https://www.bogleheads.org/wiki/Simba%2 ... preadsheet, rev22c) a 30 year retirement with an asset allocation of 50% stocks and 50% fixed income was modelled with annual rebalancing and constant inflation adjusted withdrawals taken at the beginning of each year.

I did not make an assumption; I have done calculations using the modelling described in opening post. Using a fixed income ladder rather than published returns is not what this topic is about. Anyone who is interested in the results of using a fixed income ladder can gather the historical data, do the detailed calculations, and post results of the calculations.

[typical.investor]

I believe long term bonds can have the same low variance as Tbills and also the higher return of duration. Look, if we want to optimize withdrawals, then let's do so. Intermediate bond funds are for convenience.

Your assumption is that to use long term bonds, that you may have to sell it after a NAV loss which would increase SOR risk. I question the assumption.

Optimal would be to have a ladder of longer term bonds set to mature when you need money. So I don't see the returns of LTT and effects of portfolio failure as being a function of risk as much as a function of how you held them.

Anyone can believe anything.

What was written in the opening post includes

Using asset returns from the Simba dataset (https://www.bogleheads.org/wiki/Simba%2 ... preadsheet, rev22c) a 30 year retirement with an asset allocation of 50% stocks and 50% fixed income was modelled with annual rebalancing and constant inflation adjusted withdrawals taken at the beginning of each year.

I did not make an assumption; I have done calculations using the modelling described in opening post. Using a fixed income ladder rather than published returns is not what this topic is about. Anyone who is interested in the results of using a fixed income ladder can gather the historical data, do the detailed calculations, and post results of the calculations.

Well, the topic is "Safe Withdrawal Rates: Does it matter if the bond component is short, intermediate, or long?".

I'd argue that a laddered bond component is still a bond component and fits under the topic.

If yield and volatility (due to duration) are the critical aspects influencing SOR and the SWR, it's difficult to see how discussion of a ladder doesn't fit.

Does "component" really imply only a fund and not a ladder? Given a standard definition of "a part or element of a larger whole", it's difficult to see how using a ladder doesn't fit.

Now if you change the topic to "Safe Withdrawal Rates: Does it matter if the bond fund is short, intermediate, or long?", then yeah I guess maybe I agree with your definition of the topic.

[StillGoing]

Do you mean LLT decrease returns in falling equity markets?

The topic is safe withdrawal rate (SWR), "i.e., the maximum initial withdrawal expressed as a percentage of the initial portfolio value (%IPV) that ensured the portfolio was not exhausted before 30 years had elapsed". The topic is not total return.

The total return does not depend on the sequence of returns. The safe withdrawal rate depends on the sequence of returns, this is known as sequence of returns risk. Long Term bonds tend to have a higher variance in the period, leading to a lower maximum initial withdrawal percent.

Yes, but no.

I believe long term bonds can have the same low variance as Tbills and also the higher return of duration. Look, if we want to optimize withdrawals, then let's do so. Intermediate bond funds are for convenience.

Your assumption is that to use long term bonds, that you may have to sell it after a NAV loss which would increase SOR risk. I question the assumption.

Optimal would be to have a ladder of longer term bonds set to mature when you need money. So I don't see the returns of LTT and effects of portfolio failure as being a function of risk as much as a function of how you held them.

Expanding on your last point in particular, I think there are a several broad ways of handling fixed income in retirement (there may be others):

1) Hold a selection of one or bond funds, withdraw and rebalance between stocks and bonds in such a way as to maintain constant proportions, i.e. the two/three fund portfolio.

2) Hold a bond fund or individual bonds and take the natural yield as income. In times when interest rates are high, holding individual bonds may make a lot of sense. No rebalancing, but unless bonds of very long maturity are bought, then new ones will need to be bought when the old ones mature.

3) Construct a ladder of bonds maturing at required intervals. Probably no rebalancing, although one way rebalancing from stocks to bonds might be interesting (I've not seen any analysis of that - does anyone know of any work out there?). A special case of this approach is the purchase of an annuity.

The duration can be changed with time in 1), while 3) can be mimicked by holding combinations of bond funds and will lead to declining maturity and, hence, duration. I note that strictly speaking, a ladder is actually matching maturity and not duration.

You'll be pleased to know that having got my code to the stage where I can mix the different bond funds (as I did a post or two ago), it is then not too much of a leap to change the mix through the retirement to approximately match life expectancy - it is on my to do list and I'll post here when I've done.

With the ladder, in the context of SWR, a TIPS ladder is easy enough to model provided the ladder is the same length as the planning horizon since the payout rate can be calculated using the pmt function and the consequent portfolio withdrawal rate determined. For example, assuming a target SWR of 4%, assuming TIP yields are 1.5% and a 30 year ladder, then the payout rate is 4.1%. Assuming a $1m portfolio, using half the portfolio to construct the ladder will then provide an income of $20500, with the residual portfolio required to provide the remaining $19500, i.e. a withdrawal rate of 3.9%. For more extensive results with TIPS ladders of various lengths, see https://papers.ssrn.com/sol3/papers.cfm ... id=4256534. Of course, there are longevity risks if the retiree survives after the ladder has expired, but from a practical perspective this is little different to the potential for outliving a portfolio (except it is a known quantity rather than stochastic).

I have not seen any work with nominal ladders (again, I'd be interested if someone has a reference), although there is a fair amount of work with nominal annuities (which, as mentioned, can be considered a special case of a ladder) - the outcomes are critically dependent on the payout rate (e.g. see https://papers.ssrn.com/sol3/papers.cfm ... id=4289339) and some recent discussion from viewtopic.php?p=7457956#p7457956 onwards (I note that with yields around 4.5%, a 30 year nominal ladder would have a payout rate of about 5.9%).

From the perspective of the topic, I originally envisaged dealing with the first approach (i.e., the 2 or 3 fund portfolio) here, although that includes looking at a glide path in duration, with, I think, the key distinguishing feature being the two way rebalancing.

cheers
StillGoing

[McQ]

All: I discovered another source of intermediate Treasury returns that may be more appropriate than the SBBI (is a 5-year bond held until it is a 4-year bond what most of us think of as “intermediate” duration?)

You need to find a library with S&P’s “Security Price Index Record,” a paperback series issued annually (or maybe quarterly), from the early 1940s on, I believe. In the 1966 issue, way in the back, after page 200, you will see both a yield and a price series for IT (the price series is manufactured to express the impact of the yield change in standardized form (set coupon and average maturity). Price series facilitates total return calculations.

Intermediate here means more than 6 but less than 9 years to maturity, closer to the modern usage.

Data back to 1919. Tax exempt issues separated from taxable. Indexes for long and short maturities too.

BTW, StillGoing, and apologies if you already knew of it, but the US equivalent of the Bank of England spreadsheet (i.e., a cornucopia) is Monetary and Banking Statistics, two book length compilations 1914-41 and 1941-1970, available at https://fraser.stlouisfed.org/, along with 5-year follow-ups until about 2000. No end of yield data.

[seajay]

Do you mean LLT decrease returns in falling equity markets?

The topic is safe withdrawal rate (SWR), "i.e., the maximum initial withdrawal expressed as a percentage of the initial portfolio value (%IPV) that ensured the portfolio was not exhausted before 30 years had elapsed". The topic is not total return.

The total return does not depend on the sequence of returns. The safe withdrawal rate depends on the sequence of returns, this is known as sequence of returns risk. Long Term bonds tend to have a higher variance in the period, leading to a lower maximum initial withdrawal percent.

Some stocks are more bond-like and some bonds are more stock-like

If you shift bond risk totally over to the stock side, 75/25 TSM/hard cash, then historically compared to 50/50 TSM/TBM ...



and there were points that had a lower SWR. However with hard cash you have the option to drop that into deposits (interest) as/when interest rates are relatively high, which in the above chart at least would have fixed the 1960/70's cases, as interest rates during those 30 year periods were relatively high.

Hard cash/T-Bills have better capacity to potentially reduce bad sequence of returns risk.

Long Term bonds tend to have a higher variance in the period, leading to a lower maximum initial withdrawal percent.

But more like-for-like might be ... more in long term bonds, less in stock versus more in stock, less in short term bonds ... comparisons?

[StillGoing]

All: I discovered another source of intermediate Treasury returns that may be more appropriate than the SBBI (is a 5-year bond held until it is a 4-year bond what most of us think of as “intermediate” duration?)

You need to find a library with S&P’s “Security Price Index Record,” a paperback series issued annually (or maybe quarterly), from the early 1940s on, I believe. In the 1966 issue, way in the back, after page 200, you will see both a yield and a price series for IT (the price series is manufactured to express the impact of the yield change in standardized form (set coupon and average maturity). Price series facilitates total return calculations.

Intermediate here means more than 6 but less than 9 years to maturity, closer to the modern usage.

Data back to 1919. Tax exempt issues separated from taxable. Indexes for long and short maturities too.

BTW, StillGoing, and apologies if you already knew of it, but the US equivalent of the Bank of England spreadsheet (i.e., a cornucopia) is Monetary and Banking Statistics, two book length compilations 1914-41 and 1941-1970, available at https://fraser.stlouisfed.org/, along with 5-year follow-ups until about 2000. No end of yield data.

Thanks for the link to Banking and Monetary statistics - I've had a quick look through and there is certainly appears to be more information for the pre-1942 period than is currently present on the NBER tab in the bond simulator (and, hence, in the Simba spreadsheet). As far as I can see the relevant UK data in that source is limited to 3-month bills, but I can compare that with what is in other sources (and monthly is useful for calculating returns). I think I will concentrate my energies on mining this and the other UK datasets since there are plenty of people (e.g., you and alpha4 amongst others) working on US bond data.

cheers
StillGoing

[StillGoing]

As promised above, I've now run some simulations with a bond duration glidepath rather than fixed duration.

In order to do so, I have had to make a few assumptions:

Fund duration in years:

Code: Select all

Bills	0.25
STT	2.0
TBM	7.0
LTT	15.0

Historically, the fund durations would have been dependent on both the group of bonds/notes/bills that matched the selection criteria for the particular fund and the yields/maturities. In the absence of actual data, these are probably good enough estimates.

The following table then contains the target duration which is based on the median unisex life expectancy (LE) for a retiree at 65 found on page 119 of McClung. The allocation to each of the bond funds required to match the target duration assuming the fund durations in the first table is then indicated.

Code: Select all

		Holding (%)			
Year	LE	Bills	STT	TBM	LTT
1	19	0.0	0.0	0.0	100.0
2	18	0.0	0.0	0.0	100.0
3	17	0.0	0.0	0.0	100.0
4	16	0.0	0.0	0.0	100.0
5	16	0.0	0.0	0.0	100.0
6	15	0.0	0.0	0.0	100.0
7	14	0.0	0.0	12.5	87.5
8	14	0.0	0.0	12.5	87.5
9	13	0.0	0.0	25.0	75.0
10	12	0.0	0.0	37.5	62.5
11	12	0.0	0.0	37.5	62.5
12	11	0.0	0.0	50.0	50.0
13	10	0.0	0.0	62.5	37.5
14	10	0.0	0.0	62.5	37.5
15	9	0.0	0.0	75.0	25.0
16	9	0.0	0.0	75.0	25.0
17	8	0.0	0.0	87.5	12.5
18	8	0.0	0.0	87.5	12.5
19	7	0.0	0.0	100.0	0.0
20	7	0.0	0.0	100.0	0.0
21	6	0.0	20.0	80.0	0.0
22	6	0.0	20.0	80.0	0.0
23	6	0.0	20.0	80.0	0.0
24	5	0.0	40.0	60.0	0.0
25	5	0.0	40.0	60.0	0.0
26	5	0.0	40.0	60.0	0.0
27	4	0.0	60.0	40.0	0.0
28	4	0.0	60.0	40.0	0.0
29	4	0.0	60.0	40.0	0.0
30	3	0.0	80.0	20.0	0.0

So, for this set of assumptions the retiree would hold 100% LTT for the first 6 years, the proportion of which would decline until year 19 when TBM only would be held, for the remaining years to the end of the 30 year planning horizon, the propotion of STT would gradually be increased.

In the following table, the results by rank for the now 11 different bond fund combinations (the 10 constant duration combos already tested plus the new glidepath) for the same conditions as previously (i.e., 50% stock, 50% fixed income, 30 year planning horizon, post-1942 data only). I've added an additional column, labelled weighted rank, for which low values indicate better performance and high values worse.

Code: Select all

		Rank (1=highest SWR, 11=lowest SWR)								Weighted
		MSWR	1	2	3	4	5	6	7	8	9	10	11	Rank
Bills		4.1	0	0	10	16	4	16	0	6	2	0	47	7.9
STT		4.3	53	0	6	6	6	2	4	20	4	0	0	3.5
TBM		4.1	14	6	14	20	18	29	0	0	0	0	0	4.1
LTT		3.8	27	0	0	0	2	8	2	6	0	8	47	7.4
Bills/STT	4.2	0	29	10	8	6	0	4	4	10	29	0	5.9
Bills/TBM	4.2	0	0	0	8	43	8	10	6	25	0	0	6.4
Bills/LTT	4.0	0	0	0	0	0	18	6	41	20	16	0	8.1
STT/TBM		4.2	0	37	24	12	2	8	18	0	0	0	0	3.7
STT/LTT		4.0	0	2	2	24	14	12	47	0	0	0	0	5.7
TBM/LTT		4.0	0	4	31	6	6	0	8	10	35	0	0	6.1
GlideA		3.8	6	22	4	2	0	0	2	8	4	47	6	7.2

So, how did this glide in duration perform compared to fixed duration approaches?
1) It had the second lowest MSWR (when looking at the second decimal place it just did better than LTT)
2) At 7.2, it had the 4th highest weighted rank (i.e. was 4th worst on this basis) because although 34% of historical retirements ranked in the top half, it also appeared in the lowest two ranks in more than 50% of historical retirements (this was better than LTT).

An explanation for this poor performance is that it may result from poor returns with LTT (i.e., rising yields) in the first 12 years or so after retirement when it was the dominant fixed income allocation (i.e. the glide path didn't necessarily ameliorate poor sequence of return early on).

I note that tweaking the assumptions will make little difference to the outcomes (e.g., changing the life expectancy sequence or the durations of the longer term funds by a year or two), although making larger changes could do so.

cheers
StillGoing

[typical.investor]

Wow, fantastic work again.

What language is your code? Do you share it?

The glided path looks way too long to me.

100% LTT for the first six years is asking for trouble.

Year 1 spending should not come out of 15 year duration fund. And year 30 spending is coming out of a 3 year duration.

It seems too long. I believe your glide path optimizes for spending all your money at end-of-life. I don't believe it is optimizing for a sequence of 30 withdrawals.

And again, don't get me wrong, I appreciate your hard work on this.

[Florida Orange]

It matters in that the duration should match your investment horizon or anticipated withdrawal timeframe.

[typical.investor]

As promised above, I've now run some simulations with a bond duration glidepath rather than fixed duration.

Thanks for your hard work.

In order to do so, I have had to make a few assumptions:

Fund duration in years:

Code: Select all

Bills	0.25
STT	2.0
TBM	7.0
LTT	15.0

Historically, the fund durations would have been dependent on both the group of bonds/notes/bills that matched the selection criteria for the particular fund and the yields/maturities. In the absence of actual data, these are probably good enough estimates.

Fair enough.

The following table then contains the target duration which is based on the median unisex life expectancy (LE) for a retiree at 65 found on page 119 of McClung. The allocation to each of the bond funds required to match the target duration assuming the fund durations in the first table is then indicated.

Code: Select all

		Holding (%)			
Year	LE	Bills	STT	TBM	LTT
1	19	0.0	0.0	0.0	100.0
2	18	0.0	0.0	0.0	100.0
3	17	0.0	0.0	0.0	100.0
4	16	0.0	0.0	0.0	100.0
5	16	0.0	0.0	0.0	100.0
6	15	0.0	0.0	0.0	100.0
7	14	0.0	0.0	12.5	87.5
8	14	0.0	0.0	12.5	87.5
9	13	0.0	0.0	25.0	75.0
10	12	0.0	0.0	37.5	62.5
11	12	0.0	0.0	37.5	62.5
12	11	0.0	0.0	50.0	50.0
13	10	0.0	0.0	62.5	37.5
14	10	0.0	0.0	62.5	37.5
15	9	0.0	0.0	75.0	25.0
16	9	0.0	0.0	75.0	25.0
17	8	0.0	0.0	87.5	12.5
18	8	0.0	0.0	87.5	12.5
19	7	0.0	0.0	100.0	0.0
20	7	0.0	0.0	100.0	0.0
21	6	0.0	20.0	80.0	0.0
22	6	0.0	20.0	80.0	0.0
23	6	0.0	20.0	80.0	0.0
24	5	0.0	40.0	60.0	0.0
25	5	0.0	40.0	60.0	0.0
26	5	0.0	40.0	60.0	0.0
27	4	0.0	60.0	40.0	0.0
28	4	0.0	60.0	40.0	0.0
29	4	0.0	60.0	40.0	0.0
30	3	0.0	80.0	20.0	0.0

So, for this set of assumptions the retiree would hold 100% LTT for the first 6 years, the proportion of which would decline until year 19 when TBM only would be held, for the remaining years to the end of the 30 year planning horizon, the propotion of STT would gradually be increased.

As I mentioned, it's too long. Typically, you'd take 15 as the portfolio duration and reduce it by half a year for each year. If you want to do life expectancy, that's fine but you'd have to divide it by two I think. The reason is that otherwise you will be optimizing for spending all your money end of life. Even if you have 19 years to live as above, you still have bills to pay in 1,2,3, etc years. That will reduce the portfolio duration.

Vineviz (a poster here) was big on this technique. He believed you could use two bond ETFS, one long and one short and pair them to match the remaining duration (again that's horizon divided by two). I protested that it still leaves your vulnerable to SORR risk because an early rise in long rates would see you spend the 2 year holdings and need to not only replenish them, but add to them to reduce the duration and you could only do that from depreciated long bonds --ie. the jump from 15 to 2 duration year was too great.

Your portfolio has a duration of 9.3. Vineviz's had a duration of 7.75.

If I look at a glide path starting with 7.0% Bills, 23% STT, 47% TBM, and LTT 23% and start reducing LTT after 8 years (because with seven years left to break even, doesn't that seem a good time to move to a 7 year bond) for a year of spending, the portfolio duration will be only 4.23.

In the following table, the results by rank for the now 11 different bond fund combinations (the 10 constant duration combos already tested plus the new glidepath) for the same conditions as previously (i.e., 50% stock, 50% fixed income, 30 year planning horizon, post-1942 data only). I've added an additional column, labelled weighted rank, for which low values indicate better performance and high values worse.

Code: Select all

		Rank (1=highest SWR, 11=lowest SWR)								Weighted
		MSWR	1	2	3	4	5	6	7	8	9	10	11	Rank
Bills		4.1	0	0	10	16	4	16	0	6	2	0	47	7.9
STT		4.3	53	0	6	6	6	2	4	20	4	0	0	3.5
TBM		4.1	14	6	14	20	18	29	0	0	0	0	0	4.1
LTT		3.8	27	0	0	0	2	8	2	6	0	8	47	7.4
Bills/STT	4.2	0	29	10	8	6	0	4	4	10	29	0	5.9
Bills/TBM	4.2	0	0	0	8	43	8	10	6	25	0	0	6.4
Bills/LTT	4.0	0	0	0	0	0	18	6	41	20	16	0	8.1
STT/TBM	4.2	0	37	24	12	2	8	18	0	0	0	0	3.7
STT/LTT	4.0	0	2	2	24	14	12	47	0	0	0	0	5.7
TBM/LTT	4.0	0	4	31	6	6	0	8	10	35	0	0	6.1
GlideA	3.8	6	22	4	2	0	0	2	8	4	47	6	7.2

So, how did this glide in duration perform compared to fixed duration approaches?
1) It had the second lowest MSWR (when looking at the second decimal place it just did better than LTT)
2) At 7.2, it had the 4th highest weighted rank (i.e. was 4th worst on this basis) because although 34% of historical retirements ranked in the top half, it also appeared in the lowest two ranks in more than 50% of historical retirements (this was better than LTT).

An explanation for this poor performance is that it may result from poor returns with LTT (i.e., rising yields) in the first 12 years or so after retirement when it was the dominant fixed income allocation (i.e. the glide path didn't necessarily ameliorate poor sequence of return early on).

I note that tweaking the assumptions will make little difference to the outcomes (e.g., changing the life expectancy sequence or the durations of the longer term funds by a year or two), although making larger changes could do so.

cheers
StillGoing

Based on those results, it seems as if a duration of between 2 and 4.5 is best. I'm curious how my glide path with a 4.23 duration would work. At 30% Bills and STT, you should have a fair amount for spending in rate hikes. And I think the 23% LTT might offset equity risk.

Sure STT do look that best a 2 based on your results, but I am curious shortening duration as we go along can improve that.

Can you share your code or can I give you a glide path to test? And I wonder if it would have more of an effect for longer (early) retirements.

[StillGoing]

Wow, fantastic work again.

What language is your code? Do you share it?

The glided path looks way too long to me.

100% LTT for the first six years is asking for trouble.

Year 1 spending should not come out of 15 year duration fund. And year 30 spending is coming out of a 3 year duration.

It seems too long. I believe your glide path optimizes for spending all your money at end-of-life. I don't believe it is optimizing for a sequence of 30 withdrawals.

And again, don't get me wrong, I appreciate your hard work on this.

My code is written in octave and, while I am happy to share it, it needs a lot of tidying to become useable (it is not well documented and has some very overloaded variables and idiosyncratic features - I'm definitely a hacker not a software engineer) - I fully intend to do this at some stage when (if?) I ever finish doing major tweaks.

I agree with you, I realised as I was posting that matching the duration to life expectancy was not right - however, I thought I'd post it anyway with a small edit - I changed the name from Glide to GlideA allowing me some future wriggle room!

Here are the results for a much better test, where GlideB uses a duration of half the LE, i.e. it starts with a duration of 9.5 years and allocations of 68.75% and 31.25% to TBM and LTT, respectively and ends after 30 years with a duration of 1.5 years and allocations of 71% and 29% to STT and Bills, respectively.

Code: Select all

			Rank (1=highest SWR, 11=lowest SWR)							Weighted
		MSWR	1	2	3	4	5	6	7	8	9	10	11	Rank
Bills		4.1	0	0	10	14	4	2	16	0	8	0	47	8.1
STT		4.3	51	2	6	4	8	2	4	20	4	0	0	3.6
TBM		4.1	12	8	14	27	10	18	12	0	0	0	0	4.2
LTT		3.8	27	0	0	0	2	4	4	6	2	4	51	7.5
Bills/STT	4.2	0	29	6	6	12	0	2	4	8	33	0	6.1
Bills/TBM	4.2	0	0	0	8	24	24	8	12	25	0	0	6.7
Bills/LTT	4.0	0	0	0	0	2	16	6	8	37	31	0	8.6
STT/TBM		4.2	0	27	33	12	4	6	18	0	0	0	0	3.8
STT/LTT		4.0	0	2	20	12	4	12	6	45	0	0	0	6.0
TBM/LTT		4.0	0	25	8	6	8	0	4	4	16	29	0	6.3
GlideB		4.1	10	6	4	12	24	18	22	2	0	2	2	5.1

Shortening the duration during the glide has distinctly improved the outcomes. For example, the weighted rank was now 4th after STT, TBM, and STT/TBM.

A 30 year ladder constructed of bonds with a flat yield curve with 0% yield will have a weighted maturity of 15 years (i.e. half the length of the ladder). For positive yields (and withdrawals at the start of each year), the weighted maturity at the outset will be less than this. For example, at 1%, the initial weighted maturity would be 14.3 years, at 2% 13.5 years, etc. It is also noteworthy that for higher return values, the weighted maturity initially falls at a rate of less than 0.5 year per year. For non-zero yields and where the yield curve is rising, the duration will be less than the weighted maturity.

I think the ladder approach would give higher allocations to LTT for the first few years than GlideB as described above.

cheers
StillGoing

Edit: The allocations in GlideB (i.e. using half the value of life expectancy as the target duration) are as follows:

Code: Select all

Year	Bills	STT	TBM	LTT
1	0.00	0.00	68.75	31.25
2	0.00	0.00	75.00	25.00
3	0.00	0.00	81.25	18.75
4	0.00	0.00	87.50	12.50
5	0.00	0.00	87.50	12.50
6	0.00	0.00	93.75	6.25
7	0.00	0.00	100.00	0.00
8	0.00	0.00	100.00	0.00
9	0.00	10.00	90.00	0.00
10	0.00	20.00	80.00	0.00
11	0.00	20.00	80.00	0.00
12	0.00	30.00	70.00	0.00
13	0.00	40.00	60.00	0.00
14	0.00	40.00	60.00	0.00
15	0.00	50.00	50.00	0.00
16	0.00	50.00	50.00	0.00
17	0.00	60.00	40.00	0.00
18	0.00	60.00	40.00	0.00
19	0.00	70.00	30.00	0.00
20	0.00	70.00	30.00	0.00
21	0.00	80.00	20.00	0.00
22	0.00	80.00	20.00	0.00
23	0.00	80.00	20.00	0.00
24	0.00	90.00	10.00	0.00
25	0.00	90.00	10.00	0.00
26	0.00	90.00	10.00	0.00
27	0.00	100.00	0.00	0.00
28	0.00	100.00	0.00	0.00
29	0.00	100.00	0.00	0.00
30	28.57	71.43	0.00	0.00

[StillGoing]

As promised above, I've now run some simulations with a bond duration glidepath rather than fixed duration.

Thanks for your hard work.

[...]

Based on those results, it seems as if a duration of between 2 and 4.5 is best. I'm curious how my glide path with a 4.23 duration would work. At 30% Bills and STT, you should have a fair amount for spending in rate hikes. And I think the 23% LTT might offset equity risk.

Sure STT do look that best a 2 based on your results, but I am curious shortening duration as we go along can improve that.

Can you share your code or can I give you a glide path to test? And I wonder if it would have more of an effect for longer (early) retirements.

As mentioned above, my code is probably not in a fit state to be shared, but I am happy to run specific examples. I've currently assumed that only two funds are ever held at the same time, but the code is flexible enough to accommodate any set of allocations between the 4 funds (Bills, STT, TBM, and LTT). If you post the glide path as a table as I did earlier (without the LE column), i.e.,

Code: Select all

		Holding (%)			
Year	LE	Bills	STT	TBM	LTT
1	19	0.0	0.0	0.0	100.0
2	18	0.0	0.0	0.0	100.0

then it should be easy enough to run.

This is interesting stuff since I've seen a lot of people suggest duration matching but not seen anything in the way of backtesting (unless someone knows of a report/paper or a post here on Bogleheads). Of course, the usual limitations of historical backtesting apply (and using only post-1942 data does limit the number of retirement cases )!

cheers
StillGoing

[typical.investor]

If you post the glide path as a table as I did earlier (without the LE column), i.e.,

Code: Select all

		Holding (%)			
Year	LE	Bills	STT	TBM	LTT
1	19	0.0	0.0	0.0	100.0
2	18	0.0	0.0	0.0	100.0

then it should be easy enough to run.

Would it be possible to test this?

I think it will test the effect of laddering funds well.

I don't know GlideB's exact path, but I bet the overall portfolio duration is around 7 years.

This (can we call it GlideC?) path has a overall portfolio duration of 4.68 years and the weighed maturity falls at 0.32/year once it starts falling in year 10.

The STT/TBM portfolio has overall portfolio duration of 4.5 years, so let see if it can do better than that. If not, then the glide path is not helping.

Bills/TBM has a portfolio duration of about 3.6 and good MSWR, but ultimately a poor weighted rank. Maybe (GlideC?) ends with too short a duration? Bills seem to hurt weighted rank. (GlideC?) is certainly shorter than GlideB's ending.

Anyway, 68.75% and 31.25% to TBM and LTT for GlideB seems too high of a start. Where do the first 6 years of spending come from? You would have to be spending out of a depreciated fund if rates rose which is a loss of 7% for TBM and 15% for LTT per each 1% rise.

It'll be interesting to see what the data says. I hope you can run it.

Code: Select all

YEAR	MM  	STT  	 TM  	  LTT  	Pdur	Tdur	Dred
1	7%	23%	47%	23%	7.22	14.5	0
2	7%	23%	47%	23%	7.22	14	0.00
3	7%	23%	47%	23%	7.22	13.5	0.00
4	7%	23%	47%	23%	7.22	13	0.00
5	7%	23%	47%	23%	7.22	12.5	0.00
6	7%	23%	47%	23%	7.22	12	0.00
7	7%	23%	47%	23%	7.22	11.5	0.00
8	7%	23%	47%	23%	7.22	11	0.00
9	7%	23%	47%	23%	7.22	10.5	0.00
10	7%	25%	48%	20%	6.88	10	0.34
11	7%	26%	50%	17%	6.59	9.5	0.29
12	7%	28%	51%	14%	6.25	9	0.34
13	7%	29%	53%	11%	5.96	8.5	0.29
14	7%	31%	54%	8%	5.62	8	0.34
15	7%	31%	58%	4%	5.30	7.5	0.32
16	7%	31%	62%	0%	4.98	7	0.32
17	7%	38%	55%	0%	4.63	6.5	0.35
18	7%	45%	48%	0%	4.28	6	0.35
19	7%	52%	41%	0%	3.93	5.5	0.35
20	7%	59%	34%	0%	3.58	5	0.35
21	7%	66%	27%	0%	3.23	4.5	0.35
22	7%	73%	20%	0%	2.88	4	0.35
23	7%	80%	13%	0%	2.53	3.5	0.35
24	7%	86%	7%	0%	2.23	3	0.30
25	7%	93%	0%	0%	1.88	2.5	0.35
26	20%	80%	0%	0%	1.65	2	0.23
27	40%	60%	0%	0%	1.30	1.5	0.35
28	60%	40%	0%	0%	0.95	1	0.35
29	80%	20%	0%	0%	0.60	0.5	0.35
30	100%	0%	0%	0%	0.25	0	0.35
					4.68	7.25	0.32

Pdur is the portfolio duration
Tdur would Vineviz's target duration when blending a long and short fund to match duration
Dred is the duration reduction from the previous year. Vineviz's method used 0.5 years.

Let me know if you want it posted with Pdud, Tdur and Dred removed.

[StillGoing]

If you post the glide path as a table as I did earlier (without the LE column), i.e.,

Code: Select all

		Holding (%)			
Year	LE	Bills	STT	TBM	LTT
1	19	0.0	0.0	0.0	100.0
2	18	0.0	0.0	0.0	100.0

then it should be easy enough to run.

Would it be possible to test this?

I think it will test the effect of laddering funds well.

I don't know GlideB's exact path, but I bet the overall portfolio duration is around 7 years.

This (can we call it GlideC?) path has a overall portfolio duration of 4.68 years and the weighed maturity falls at 0.32/year once it starts falling in year 10.

The STT/TBM portfolio has overall portfolio duration of 4.5 years, so let see if it can do better than that. If not, then the glide path is not helping.

Bills/TBM has a portfolio duration of about 3.6 and good MSWR, but ultimately a poor weighted rank. Maybe (GlideC?) ends with too short a duration? Bills seem to hurt weighted rank. (GlideC?) is certainly shorter than GlideB's ending.

Anyway, 68.75% and 31.25% to TBM and LTT for GlideB seems too high of a start. Where do the first 6 years of spending come from? You would have to be spending out of a depreciated fund if rates rose which is a loss of 7% for TBM and 15% for LTT per each 1% rise.

It'll be interesting to see what the data says. I hope you can run it.

Code: Select all

YEAR	MM  	STT  	 TM  	  LTT  	Pdur	Tdur	Dred
1	7%	23%	47%	23%	7.22	14.5	0
2	7%	23%	47%	23%	7.22	14	0.00
3	7%	23%	47%	23%	7.22	13.5	0.00
4	7%	23%	47%	23%	7.22	13	0.00
5	7%	23%	47%	23%	7.22	12.5	0.00
6	7%	23%	47%	23%	7.22	12	0.00
7	7%	23%	47%	23%	7.22	11.5	0.00
8	7%	23%	47%	23%	7.22	11	0.00
9	7%	23%	47%	23%	7.22	10.5	0.00
10	7%	25%	48%	20%	6.88	10	0.34
11	7%	26%	50%	17%	6.59	9.5	0.29
12	7%	28%	51%	14%	6.25	9	0.34
13	7%	29%	53%	11%	5.96	8.5	0.29
14	7%	31%	54%	8%	5.62	8	0.34
15	7%	31%	58%	4%	5.30	7.5	0.32
16	7%	31%	62%	0%	4.98	7	0.32
17	7%	38%	55%	0%	4.63	6.5	0.35
18	7%	45%	48%	0%	4.28	6	0.35
19	7%	52%	41%	0%	3.93	5.5	0.35
20	7%	59%	34%	0%	3.58	5	0.35
21	7%	66%	27%	0%	3.23	4.5	0.35
22	7%	73%	20%	0%	2.88	4	0.35
23	7%	80%	13%	0%	2.53	3.5	0.35
24	7%	86%	7%	0%	2.23	3	0.30
25	7%	93%	0%	0%	1.88	2.5	0.35
26	20%	80%	0%	0%	1.65	2	0.23
27	40%	60%	0%	0%	1.30	1.5	0.35
28	60%	40%	0%	0%	0.95	1	0.35
29	80%	20%	0%	0%	0.60	0.5	0.35
30	100%	0%	0%	0%	0.25	0	0.35
					4.68	7.25	0.32

Pdur is the portfolio duration
Tdur would Vineviz's target duration when blending a long and short fund to match duration
Dred is the duration reduction from the previous year. Vineviz's method used 0.5 years.

Let me know if you want it posted with Pdud, Tdur and Dred removed.

Thank you for providing this. Here are the results for glideC - i.e., the set of allocations you posted above

Code: Select all

			Rank (1=highest SWR, 11=lowest SWR)							Weighted
		MSWR	1	2	3	4	5	6	7	8	9	10	11	Rank
Bills		4.1	0	0	10	16	4	0	16	0	6	2	47	8.1
STT		4.3	53	0	6	6	6	2	4	20	4	0	0	3.5
TBM		4.1	20	0	20	31	0	24	6	0	0	0	0	3.9
LTT		3.8	27	0	0	0	2	4	4	6	2	2	53	7.5
Bills/STT	4.2	0	29	10	4	10	0	0	6	8	33	0	6.0
Bills/TBM	4.2	0	0	0	8	31	16	8	12	24	2	0	6.6
Bills/LTT	4.0	0	0	0	0	4	14	6	4	41	31	0	8.6
STT/TBM		4.2	0	35	25	12	4	6	18	0	0	0	0	3.7
STT/LTT		4.0	0	2	20	14	4	10	6	45	0	0	0	6.0
TBM/LTT		4.0	0	25	10	6	6	0	2	6	16	29	0	6.3
GlideC		4.1	0	8	0	4	29	25	31	2	0	0	0	5.7

Interestingly, the ranking for GlideC are clustered in the middle, there were few occasions when it was ranked in the bottom 4 ranks, but there also few occasions when it was ranked in the top 4. Overall, it still lies 4th by weighted rank, with a slightly worse score than with GlideB.

I'll edit my earlier post to include the allocations for the whole of GlideB, but the chief difference is that while it starts with a higher allocation to LTT (31.25% compared to 23% for GlideC), there is no allocation to LTT after Year 6 and no allocation to bills until Year 30. Apart from the start and end periods, GlideB is largely a glide from TBM to STT.

I'm not quite sure on the rationale for the portfolio duration, Pdur in GlideC. I can see that Pdur is initially half of the target ladder duration, Tdur but the reason for values after that is not clear to me (except, as you stated, that the Pdur drops by roughly 0.3-0.35 each time). I note that Tdur is implicitly assuming a flat yield curve with a yield of 0% (under those circumstances, the allocation to each rung in the ladder is equal and the duration is the same as the maturity).

From the data it would appear that holding STT, TBM, or a 50/50 mix of STT/TBM provided the best outcomes for the post-1942 historical period with glides B and C coming 4th. I don't think the quality of the data (at least prior to the early 1960s) enable any more detailed 'optimisation'.

cheers
StillGoing

[typical.investor]

Thank you for providing this. Here are the results for glideC - i.e., the set of allocations you posted above

Code: Select all

			Rank (1=highest SWR, 11=lowest SWR)							Weighted
		MSWR	1	2	3	4	5	6	7	8	9	10	11	Rank
Bills		4.1	0	0	10	16	4	0	16	0	6	2	47	8.1
STT		4.3	53	0	6	6	6	2	4	20	4	0	0	3.5
TBM		4.1	20	0	20	31	0	24	6	0	0	0	0	3.9
LTT		3.8	27	0	0	0	2	4	4	6	2	2	53	7.5
Bills/STT	4.2	0	29	10	4	10	0	0	6	8	33	0	6.0
Bills/TBM	4.2	0	0	0	8	31	16	8	12	24	2	0	6.6
Bills/LTT	4.0	0	0	0	0	4	14	6	4	41	31	0	8.6
STT/TBM		4.2	0	35	25	12	4	6	18	0	0	0	0	3.7
STT/LTT		4.0	0	2	20	14	4	10	6	45	0	0	0	6.0
TBM/LTT		4.0	0	25	10	6	6	0	2	6	16	29	0	6.3
GlideB		4.1	10	6	4	12	24	18	22	2	0	2	2	5.1
GlideC		4.1	0	8	0	4	29	25	31	2	0	0	0	5.7

Interestingly, the ranking for GlideC are clustered in the middle, there were few occasions when it was ranked in the bottom 4 ranks, but there also few occasions when it was ranked in the top 4. Overall, it still lies 4th by weighted rank, with a slightly worse score than with GlideB.

One question, why is Weighted Rank important? I understand what it is, but not how to interpret it. For example, can I assume that the average SWR for Bills/STT is higher than Bills/TBM because the rank is higher?

I mean STT has nearly 25% of its returns worse than TBM.

I'm not quite sure on the rationale for the portfolio duration, Pdur in GlideC. I can see that Pdur is initially half of the target ladder duration, Tdur but the reason for values after that is not clear to me (except, as you stated, that the Pdur drops by roughly 0.3-0.35 each time). I note that Tdur is implicitly assuming a flat yield curve with a yield of 0% (under those circumstances, the allocation to each rung in the ladder is equal and the duration is the same as the maturity).

First, Tdur is shown merely to represent the thinking here on Bogleheads about using two bond funds (one short, one long) to achieve portfolio immunization to minimize interest rate risk (ie. having to reinvest at lower rates when your duration is shorter than your horizon). The methodology simply took investment horizon divided by two (to account for each years spending).

As for Pdur, it's an attempt to mimic individual bonds to the extent possible. I don't have a precise mathematical definition worked out and at some point maybe will have enough of a concept to try.

The original premise was if I had 7% in Bills, that I could plan to spend 1/30th (3.33%) of the portfolio for a couple of years before a two year 'matured'. Similarly, 23% in STT gave 7 years before TBM would mature, and 50% in TBM gives 15 years of LTT. So that's the logic behind starting with about 7% Bills, 23% STT, 50% TBM 20% LTT.

Anyway, can you test another one? Glide C was 4.68 years and this is 3.75. So I think it should test between STT (2 years) and STT/TBM (4.5 years).

I realized probably a benefit of Glide B is the sooner and steeper reduction in LTT. Perhaps this might be steeper. I realized that probably on a rate hike, you would be rebalancing back into LTT because they'd dropped so much. I could reduce it at a faster pace but overall it's a little shorter than STT/TBM now and to me would be an interesting comparison to see if we can move Glide C to the left. I view the lack of tails as a win. Intuitively I think one component of risk is a wider disparity in expected returns. STT is the winner except for that.

(Glide D)

Code: Select all

 YEAR	MM  	STT  	 TM  	  LTT  	Pdur
1	7%	23%	50%	20%	6.98
2	7%	26%	48%	19%	6.75
3	7%	29%	46%	18%	6.52
4	7%	32%	44%	17%	6.29
5	7%	35%	42%	16%	6.06
6	7%	38%	40%	15%	5.83
7	7%	41%	38%	14%	5.60
8	7%	44%	36%	13%	5.37
9	7%	47%	34%	12%	5.14
10	7%	50%	32%	11%	4.91
11	7%	53%	30%	10%	4.68
12	7%	56%	28%	9%	4.45
13	7%	59%	26%	8%	4.22
14	7%	62%	24%	7%	3.99
15	7%	65%	22%	6%	3.76
16	7%	68%	20%	5%	3.53
17	7%	71%	18%	4%	3.30
18	7%	74%	16%	3%	3.07
19	7%	77%	14%	2%	2.84
20	7%	80%	12%	1%	2.61
21	7%	83%	10%	0%	2.38
22	7%	85%	8%	0%	2.28
23	10%	84%	6%	0%	2.13
24	14%	82%	4%	0%	1.96
25	17%	81%	2%	0%	1.80
26	20%	80%	0%	0%	1.65
27	25%	75%	0%	0%	1.56
28	33%	67%	0%	0%	1.42
29	50%	50%	0%	0%	1.13
30	100%	0%	0%	0%	0.25
					3.75