A bond duration glide path for retirement investing

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BrooklynInvest
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Re: A bond duration glide path for retirement investing

Post by BrooklynInvest »

spdoublebass wrote: Thu Aug 04, 2022 11:37 am
BrooklynInvest wrote: Thu Aug 04, 2022 11:06 am Someone please correct me -

Let's pretend I'm 60, just retired and I expect to live to 90 (glossing over the obvious problem for now.) The midpoint is 15 years. This "duration matching" thing implies I should have zero rate risk in my bonds when I'm 75? Why?

Assuming I maintained a 60-40 allocation in my portfolio, at 75 I'm now 60% stocks and 40 cash. I've got 15 years of 40% of my money doing roughly nothing for me before I kick the bucket. How is this beneficial? I'm still 60% in stocks so my portfolio still has volatility. I've just removed interest rate risk and, importantly, almost all of the bond income for some reason. My equity beta is still .6, I may have international exposure and currency risk etc. etc.

I can see this methodology in rare instances when, say, I'm a corporation with a balloon payment on something on a specific date AND the volatility of my fixed income portfolio needs to track to zero as that date looms, but as a tool for individual retirement, massively overweighting cash to remove one specific risk among many seems odd to me.
At 75 you'd then have a 7.5 year duration. I'm not following what you are saying.
I'm using the midpoint of my retirement years as my investment horizon - the point at which my duration becomes zero, no? I realize at best it's a fudge. Or is it a different point? But my question really is why am I removing rate risk while maintaining other portfolio risks?
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Re: A bond duration glide path for retirement investing

Post by BrooklynInvest »

hudson wrote: Thu Aug 04, 2022 11:41 am
BrooklynInvest wrote: Thu Aug 04, 2022 11:06 am Someone please correct me -

Let's pretend I'm 60, just retired and I expect to live to 90 (glossing over the obvious problem for now.) The midpoint is 15 years. This "duration matching" thing implies I should have zero rate risk in my bonds when I'm 75? Why?

Assuming I maintained a 60-40 allocation in my portfolio, at 75 I'm now 60% stocks and 40 cash. I've got 15 years of 40% of my money doing roughly nothing for me before I kick the bucket. How is this beneficial? I'm still 60% in stocks so my portfolio still has volatility. I've just removed interest rate risk and, importantly, almost all of the bond income for some reason. My equity beta is still .6, I may have international exposure and currency risk etc. etc.

I can see this methodology in rare instances when, say, I'm a corporation with a balloon payment on something on a specific date AND the volatility of my fixed income portfolio needs to track to zero as that date looms, but as a tool for individual retirement, massively overweighting cash to remove one specific risk among many seems odd to me.
Are you using "cash" and "bonds" as equivalents?
I don't think that vineviz ever recommended that anyone go all cash for the fixed income part of their holdings.
He might have recommended duration matched TIPS.
Entirely possible I've misconstrued but how am I getting to zero duration without cash? Short term bonds will lower my duration to be sure, but - if I'm understanding correctly - I have to get to zero duration.
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Re: A bond duration glide path for retirement investing

Post by vineviz »

BrooklynInvest wrote: Thu Aug 04, 2022 12:26 pm I'm using the midpoint of my retirement years as my investment horizon - the point at which my duration becomes zero, no? I realize at best it's a fudge. Or is it a different point? But my question really is why am I removing rate risk while maintaining other portfolio risks?
You want to use the midpoint of your REMAINING retirement years as the duration you're targeting.

When you have 30 more years of retirement, your investment horizon and your target duration are roughly 15 years.

When you have 20 more years of retirement, your investment horizon and your target duration are roughly 10 years.

When you have 10 more years of retirement, your investment horizon and your target duration are roughly 5 years.

And so on.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch
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Re: A bond duration glide path for retirement investing

Post by hudson »

BrooklynInvest wrote: Thu Aug 04, 2022 12:27 pm
hudson wrote: Thu Aug 04, 2022 11:41 am
BrooklynInvest wrote: Thu Aug 04, 2022 11:06 am Someone please correct me -

Let's pretend I'm 60, just retired and I expect to live to 90 (glossing over the obvious problem for now.) The midpoint is 15 years. This "duration matching" thing implies I should have zero rate risk in my bonds when I'm 75? Why?

Assuming I maintained a 60-40 allocation in my portfolio, at 75 I'm now 60% stocks and 40 cash. I've got 15 years of 40% of my money doing roughly nothing for me before I kick the bucket. How is this beneficial? I'm still 60% in stocks so my portfolio still has volatility. I've just removed interest rate risk and, importantly, almost all of the bond income for some reason. My equity beta is still .6, I may have international exposure and currency risk etc. etc.

I can see this methodology in rare instances when, say, I'm a corporation with a balloon payment on something on a specific date AND the volatility of my fixed income portfolio needs to track to zero as that date looms, but as a tool for individual retirement, massively overweighting cash to remove one specific risk among many seems odd to me.
Are you using "cash" and "bonds" as equivalents?
I don't think that vineviz ever recommended that anyone go all cash for the fixed income part of their holdings.
He might have recommended duration matched TIPS.
Entirely possible I've misconstrued but how am I getting to zero duration without cash? Short term bonds will lower my duration to be sure, but - if I'm understanding correctly - I have to get to zero duration.
I'm 74. At 76 when intermediate CDs mature, I'm going to do a form of duration matching.
My plan will cover from ages 76 to 96. That's 20 years; if I divide by 2, the average duration would be 10 years.
I'm thinking my holdings will be made up of half nominal treasuries and half TIPS...again with an average duration of 10 years.
Will my duration ever be zero? No, If I make it to 96, I'm thinking that I won't go under 5 years average duration. I haven't really thought that through.
Will my plan work for you? Most likely not. My plan is customized for my unique situation.
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Re: A bond duration glide path for retirement investing

Post by Wrench »

hudson wrote: Thu Aug 04, 2022 1:15 pm
BrooklynInvest wrote: Thu Aug 04, 2022 12:27 pm
hudson wrote: Thu Aug 04, 2022 11:41 am
BrooklynInvest wrote: Thu Aug 04, 2022 11:06 am Someone please correct me -

Let's pretend I'm 60, just retired and I expect to live to 90 (glossing over the obvious problem for now.) The midpoint is 15 years. This "duration matching" thing implies I should have zero rate risk in my bonds when I'm 75? Why?

Assuming I maintained a 60-40 allocation in my portfolio, at 75 I'm now 60% stocks and 40 cash. I've got 15 years of 40% of my money doing roughly nothing for me before I kick the bucket. How is this beneficial? I'm still 60% in stocks so my portfolio still has volatility. I've just removed interest rate risk and, importantly, almost all of the bond income for some reason. My equity beta is still .6, I may have international exposure and currency risk etc. etc.

I can see this methodology in rare instances when, say, I'm a corporation with a balloon payment on something on a specific date AND the volatility of my fixed income portfolio needs to track to zero as that date looms, but as a tool for individual retirement, massively overweighting cash to remove one specific risk among many seems odd to me.
Are you using "cash" and "bonds" as equivalents?
I don't think that vineviz ever recommended that anyone go all cash for the fixed income part of their holdings.
He might have recommended duration matched TIPS.
Entirely possible I've misconstrued but how am I getting to zero duration without cash? Short term bonds will lower my duration to be sure, but - if I'm understanding correctly - I have to get to zero duration.
I'm 74. At 76 when intermediate CDs mature, I'm going to do a form of duration matching.
My plan will cover from ages 76 to 96. That's 20 years; if I divide by 2, the average duration would be 10 years.
I'm thinking my holdings will be made up of half nominal treasuries and half TIPS...again with an average duration of 10 years.
Will my duration ever be zero? No, If I make it to 96, I'm thinking that I won't go under 5 years average duration. I haven't really thought that through.
Will my plan work for you? Most likely not. My plan is customized for my unique situation.
For shorter terms, why not just use a CD/bond ladder? Pretty easily done for 20 years. If you want higher returns, you could use corporate bonds for some of the rungs. If you plan to spend the proceeds when each rung matures, STRIPS make it really straightforward if the money is in a tax deferred account. (If not, you have to deal with phantom income for tax purposes). Duration matching makes sense for much longer durations, but it seems to me to be more complicated than a simple bond ladder for shorter terms.

Wrench
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BrooklynInvest
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Re: A bond duration glide path for retirement investing

Post by BrooklynInvest »

vineviz wrote: Thu Aug 04, 2022 12:42 pm
BrooklynInvest wrote: Thu Aug 04, 2022 12:26 pm I'm using the midpoint of my retirement years as my investment horizon - the point at which my duration becomes zero, no? I realize at best it's a fudge. Or is it a different point? But my question really is why am I removing rate risk while maintaining other portfolio risks?
You want to use the midpoint of your REMAINING retirement years as the duration you're targeting.

When you have 30 more years of retirement, your investment horizon and your target duration are roughly 15 years.

When you have 20 more years of retirement, your investment horizon and your target duration are roughly 10 years.

When you have 10 more years of retirement, your investment horizon and your target duration are roughly 5 years.

And so on.
Ahhhh. So using Total Bond Market as a proxy, I'd need to more than double my current bond duration at retirement in order to bring it down a year for every two years of retirement? My duration is zero (cash) at 90, not 75 because the target moves as long as I'm still breathing.

I get being more conservative in general as I age. It's just not clear how isolating this one risk does it, especially since I'm dialing my rate risk wayyyy up before I'm bringing it down each year.
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Re: A bond duration glide path for retirement investing

Post by vineviz »

BrooklynInvest wrote: Thu Aug 04, 2022 1:53 pm Ahhhh. So using Total Bond Market as a proxy, I'd need to more than double my current bond duration at retirement in order to bring it down a year for every two years of retirement? My duration is zero (cash) at 90, not 75 because the target moves as long as I'm still breathing.
Almost.

Remember that if you live to age 90, your life expectancy won't be zero at that point. For instance, a 90-year female in excellent health has a 50% chance of living to age 95 and a 10% chance of living to age 101.


BrooklynInvest wrote: Thu Aug 04, 2022 1:53 pm I get being more conservative in general as I age. It's just not clear how isolating this one risk does it, especially since I'm dialing my rate risk wayyyy up before I'm bringing it down each year.
Keeping your duration matched to your investment horizon dials your interest rate risk DOWN, not up.

An investor starting a 30 year retirement with TBM has "wayyyy" more interest rate risk than if they started retirement with a long-term bond fund.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch
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Re: A bond duration glide path for retirement investing

Post by hudson »

Wrench wrote: Thu Aug 04, 2022 1:42 pm
hudson wrote: Thu Aug 04, 2022 1:15 pm
BrooklynInvest wrote: Thu Aug 04, 2022 12:27 pm
hudson wrote: Thu Aug 04, 2022 11:41 am
BrooklynInvest wrote: Thu Aug 04, 2022 11:06 am Someone please correct me -

Let's pretend I'm 60, just retired and I expect to live to 90 (glossing over the obvious problem for now.) The midpoint is 15 years. This "duration matching" thing implies I should have zero rate risk in my bonds when I'm 75? Why?

Assuming I maintained a 60-40 allocation in my portfolio, at 75 I'm now 60% stocks and 40 cash. I've got 15 years of 40% of my money doing roughly nothing for me before I kick the bucket. How is this beneficial? I'm still 60% in stocks so my portfolio still has volatility. I've just removed interest rate risk and, importantly, almost all of the bond income for some reason. My equity beta is still .6, I may have international exposure and currency risk etc. etc.

I can see this methodology in rare instances when, say, I'm a corporation with a balloon payment on something on a specific date AND the volatility of my fixed income portfolio needs to track to zero as that date looms, but as a tool for individual retirement, massively overweighting cash to remove one specific risk among many seems odd to me.
Are you using "cash" and "bonds" as equivalents?
I don't think that vineviz ever recommended that anyone go all cash for the fixed income part of their holdings.
He might have recommended duration matched TIPS.
Entirely possible I've misconstrued but how am I getting to zero duration without cash? Short term bonds will lower my duration to be sure, but - if I'm understanding correctly - I have to get to zero duration.
I'm 74. At 76 when intermediate CDs mature, I'm going to do a form of duration matching.
My plan will cover from ages 76 to 96. That's 20 years; if I divide by 2, the average duration would be 10 years.
I'm thinking my holdings will be made up of half nominal treasuries and half TIPS...again with an average duration of 10 years.
Will my duration ever be zero? No, If I make it to 96, I'm thinking that I won't go under 5 years average duration. I haven't really thought that through.
Will my plan work for you? Most likely not. My plan is customized for my unique situation.
For shorter terms, why not just use a CD/bond ladder? Pretty easily done for 20 years. If you want higher returns, you could use corporate bonds for some of the rungs. If you plan to spend the proceeds when each rung matures, STRIPS make it really straightforward if the money is in a tax deferred account. (If not, you have to deal with phantom income for tax purposes). Duration matching makes sense for much longer durations, but it seems to me to be more complicated than a simple bond ladder for shorter terms.

Wrench
Thanks Wrench!
I'm not doing the perfect glide path. My plan is not to adjust the average duration yearly. I may stay at a 10 year average duration. I haven't totally figured it out.

I never warmed up to ladders; I like to go 5 years minimum especially if I can get 3% or more nominal. Since I like the safest fixed income choices, that rules out corporate bonds, but there are times when they look tempting.

STRIPS...I need to do some research. I was going with regular nominal treasuries and TIPS...some in taxable; some not. I don't have a lot of tax advantaged space.
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Re: A bond duration glide path for retirement investing

Post by BrooklynInvest »

vineviz wrote: Thu Aug 04, 2022 2:01 pm
BrooklynInvest wrote: Thu Aug 04, 2022 1:53 pm Ahhhh. So using Total Bond Market as a proxy, I'd need to more than double my current bond duration at retirement in order to bring it down a year for every two years of retirement? My duration is zero (cash) at 90, not 75 because the target moves as long as I'm still breathing.
Almost.

Remember that if you live to age 90, your life expectancy won't be zero at that point. For instance, a 90-year female in excellent health has a 50% chance of living to age 95 and a 10% chance of living to age 101.


BrooklynInvest wrote: Thu Aug 04, 2022 1:53 pm I get being more conservative in general as I age. It's just not clear how isolating this one risk does it, especially since I'm dialing my rate risk wayyyy up before I'm bringing it down each year.
Keeping your duration matched to your investment horizon dials your interest rate risk DOWN, not up.

An investor starting a 30 year retirement with TBM has "wayyyy" more interest rate risk than if they started retirement with a long-term bond fund.
I'm in TBM. My duration is about 6 years. If I duration matched for a 30 year retirement that I just started my duration would be 15 years. More than double. I'm in effect taking on a considerable amount more rate risk than I have today, no?

Granted every two years it'd decline by a year but it'd take 18 years in this scenario to shave 9 years off my duration and bring it to that of TBM? Give or take.
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Re: A bond duration glide path for retirement investing

Post by vineviz »

BrooklynInvest wrote: Thu Aug 04, 2022 3:18 pm I'm in TBM. My duration is about 6 years. If I duration matched for a 30 year retirement that I just started my duration would be 15 years. More than double. I'm in effect taking on a considerable amount more rate risk than I have today, no?
No, it's the opposite.

With a 30 year retirement ahead of you, you have MORE interest risk with TBM than you would with Vanguard Long-Term Bond ETF (BLV).

Interest rate risk is a proportional to the difference between your investment horizon and your bonds' duration. Most people, including many professionals", don't understand this.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch
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Re: A bond duration glide path for retirement investing

Post by Nutmeg »

Jaylat wrote: Tue Apr 19, 2022 4:24 pm
vineviz wrote: Tue Apr 19, 2022 12:34 pm
Jaylat wrote: Tue Apr 19, 2022 12:07 pm
vineviz wrote: Tue Apr 19, 2022 10:12 am
Jaylat wrote: Tue Apr 19, 2022 9:18 am The other factor is that individuals are much less diversified than banks. Stuff happens – people get divorced, injured, lose jobs, their house burns down, unexpected kids, etc. Any of these events might require you to liquidate your investment portfolio.
All of those events (specifically, the probability-weighted value of them occurring) are inputs in determining the investment horizon as well, at least indirectly, the overall asset allocation.
Can you explain how this would work in real life? Here's how I would envision this kind of logical thought process:

"I expect to retire in 30 years, but I have a 15% chance of getting a divorce in year 10, plus a 5% chance of my house burning down in year 20, plus a 30% chance of getting run over by a truck in year 25, resulting in a debilitating spinal injury."
That's one way to do it, but I suspect this approach will appeal to only to the overly analytical. I'm definitely try not to be dogmatic about being overly precise, since financial planning inherently involves working with a great deal of uncertainty. But I do think most people who are actively managing their personal finances have a pretty good idea about whether most of their future portfolio-funded consumption lies in the next five years or is more like 10+ years away.
I was actually joking. :happy

But the bigger point is that people are not like banks. They don't have clearly defined liabilities that can be known with certainty.

I find it ironic (and more than a bit worrysome) that you are touting LTT, which are extremely volatile, as a way of eliminating interest rate risk. As I've shown many times above, this is not the case in real life. I am worried that an unsuspecting investor will follow this advice and get burned.

It's very nice of you to engage like this, but as I've said before I don't think we will come to agreement.
I have read this thread and others several times because I am trying to help my relatives match assets and liabilities. This quote stood out:
But the bigger point is that people are not like banks. They don't have clearly defined liabilities that can be known with certainty.
In this case, my relatives do have clearly defined liabilities (other than not knowing how long they will live.) At ages 84 and 90, the couple’s liabilities are $7,000 per month greater than their income due to the costs of a private room in a SNF for the older spouse. I have purchased a Treasury ladder for the next year and plan to buy 52-week Treasury bills every three months to cover that three-month extra cost.

What I am trying to understand now, from both a theoretical and a practical perspective, is how to invest the funds outside the ladder (about four years’ worth to make up the monthly income shortfall) to minimize risk while maximizing income. The couple highly values the benefits of a private room, even if this means the younger spouse will have less money.

I proposed investing most of the funds outside the one-year ladder in a bond fund with a longer duration, such as the Fidelity ST Treasury Bond Fund with a duration of 2.59 years, but a family member is concerned that the fund value will decline as interest rates rise, causing the younger spouse to worry. The alternative I see would be to construct a longer-term ladder now by buying Treasuries in the secondary market and holding them to maturity,

I am posting here, in a theory discussion, because I truly want to understand the reasons for making a particular choice. I probably should write a separate post for a different sub-forum, but am writing to ask the experts here:

How should we invest funds beyond one year to correspond with known liabilities, preserve principal, and maximize yield given the first two conditions?
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Re: A bond duration glide path for retirement investing

Post by vineviz »

Nutmeg wrote: Fri Aug 05, 2022 5:19 pm
What I am trying to understand now, from both a theoretical and a practical perspective, is how to invest the funds outside the ladder (about four years’ worth to make up the monthly income shortfall) to minimize risk while maximizing income. The couple highly values the benefits of a private room, even if this means the younger spouse will have less money.
A lot depends on how much life expectancy you want (or are able) to plan for. For my example below, I'm assuming that you want a plan that will cover them each to age 95. Whether that is optimistic or pessimistic I'll leave up to you.

If you are comfortable buying 52-week nominal Treasuries, then I presume you'd be equally comfortable buying individual TIPS as well? If so, "from both a theoretical and a practical perspective" it seems to me the indicated path is simply to buy a ladder of about 10-11 individual TIPS spread out evenly over the next decade or so (at either annual or biannual intervals).

You're avoiding both interest rate risk and inflation risk, and the "family member" is accommodated because no bonds will need to be sold. They'll just mature and the proceeds will be spent.

Otherwise, a short-term Treasury ladder should be paired with an intermediate-term bond bond (again, I prefer TIPS in this case but total bond market would be okay). Each year, peel off a bit of that bond fund to add a rung to the Treasury ladder. And when each Treasury note matures, spend it.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch
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Re: A bond duration glide path for retirement investing

Post by Nutmeg »

vineviz wrote: Fri Aug 05, 2022 5:58 pm
Nutmeg wrote: Fri Aug 05, 2022 5:19 pm
What I am trying to understand now, from both a theoretical and a practical perspective, is how to invest the funds outside the ladder (about four years’ worth to make up the monthly income shortfall) to minimize risk while maximizing income. The couple highly values the benefits of a private room, even if this means the younger spouse will have less money.
A lot depends on how much life expectancy you want (or are able) to plan for. For my example below, I'm assuming that you want a plan that will cover them each to age 95. Whether that is optimistic or pessimistic I'll leave up to you.

If you are comfortable buying 52-week nominal Treasuries, then I presume you'd be equally comfortable buying individual TIPS as well? If so, "from both a theoretical and a practical perspective" it seems to me the indicated path is simply to buy a ladder of about 10-11 individual TIPS spread out evenly over the next decade or so (at either annual or biannual intervals).

You're avoiding both interest rate risk and inflation risk, and the "family member" is accommodated because no bonds will need to be sold. They'll just mature and the proceeds will be spent.

Otherwise, a short-term Treasury ladder should be paired with an intermediate-term bond bond (again, I prefer TIPS in this case but total bond market would be okay). Each year, peel off a bit of that bond fund to add a rung to the Treasury ladder. And when each Treasury note matures, spend it.
Thanks very much! To be clear, the invested funds will last only about four years at this rate of spending. I hope to gain a better understanding of investing in individual TIPS before doing so, but am very grateful for your response!
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Re: A bond duration glide path for retirement investing

Post by international001 »

so if I follow rights and I have 5 years of life expectancy, I should split my $1M into 5 and buy:

$200k in 1 year bonds
$200k in 2 year bonds
$200k in 3 year bonds
$200k in 4 year bonds
$200k in 5 year bonds

what about the nominal value of the bond (the $200k you get every year upon maturity)?
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Re: A bond duration glide path for retirement investing

Post by rossington »

international001 wrote: Mon Aug 08, 2022 6:38 pm so if I follow rights and I have 5 years of life expectancy, I should split my $1M into 5 and buy:

$200k in 1 year bonds
$200k in 2 year bonds
$200k in 3 year bonds
$200k in 4 year bonds
$200k in 5 year bonds

what about the nominal value of the bond (the $200k you get every year upon maturity)?
This is somewhat of a loaded question but if you know you have a life expectancy of 5 years then yes and spend it all any way that is best!

Other than that if you want to spend 1M in roughly equivalent amounts over 5 years then yes to to that too.
what about the nominal value of the bond (the $200k you get every year upon maturity?
...all or part of the 200k would be needed each year because the interest only is obviously not going to cover your expenditures.
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Re: A bond duration glide path for retirement investing

Post by longinvest »

Because they're relevant to this thread, I'm copying here two posts I made on another thread. -- longinvest

First post:

I thought that this thread was about the YTM of a single bond fund, not about the YTM of a single declining-maturity bond (or trying to simulate one with bond funds).

I hadn't noticed that forum member Vineviz had changed the context to make a claim about a declining-duration bond portfolio composed two bond funds of non-declining average maturity.

So, I'll address his claim in that new context. Here's what that forum member Vineviz wrote:
vineviz wrote: Sat Sep 03, 2022 12:02 pm
Charles Joseph wrote: Sat Sep 03, 2022 11:41 am So does the average yield to maturity have no predictive value whatsoever?
That's not the right conclusion.

Average yield to maturity has a great deal of "predictive value" about future returns. The question, which goes back to your original question, is how to best take advantage of that YTM for your planning purposes.

The answer involves taking advantage of TWO pieces of information: the average YTM of the fund, and the average duration of the fund.

The YTM is an excellent predictor of the total return you can expect over an investment horizon equal to the bond's duration.

A complication with bond funds is that the duration remains relatively constant, because maturing bonds are sold/redeemed and new bonds are added, but the investor's investment horizon typically shrinks (as the time between now and the investment goals is reduced).

This doesn't change the truth of the prior statement, just informs you about how to take advantage of that truth. Specifically, it means you need some way of inducing the average duration of your bond portfolio to shrink at the same rate that your investment horizon is shrinking. That's the topic of another thread on bond duration glide paths.

If you keep your duration matched to your investment horizon, then your actual return will almost exactly match the initial averageYTM regardless of what happens to interest rates in the meantime.
Here's a counterexample to the claim that "If you keep your duration matched to your investment horizon, then your actual return will almost exactly match the initial average YTM regardless of what happens to interest rates in the meantime" when using a duration-managed portfolio.

To keep calculations simple, I'll only use zero-coupon Treasury bonds* and semestrial zero-coupon yields derived from FRED DGSX bond-equivalent par yields extracted from the Bond Fund Simulator.

* Using bonds with coupons would just require many more more calculations to get to the same conclusion.

The earliest 30-year yield, in FRED DGS30 goes back to February 15, 1977. As the Bond Fund Simulator only uses end-of-semester yields (June 30 and December 31), I'll start the simulation on June 30, 1977. I'll call this "1977.5" for 1977 and a half.

Note that data tables will be provided in a separate post so that readers can verify calculations.

Here's the setup. In mid-1977, an investor wants to invest enough money to get back exactly $10,000 thirty years later in mid-2007.

I'll compare the outcome of two scenarios:
  • SCENARIO 1: A single 30-year zero-coupon bond bought and held until maturity.
  • SCENARIO 2: A declining-duration managed bond portfolio composed of:
    • An extended-duration bond fund holding a single 30-year zero-coupon bond for one semester (6 months), selling it, and buying a new 30-year zero-coupon bond, repeating this every semester. The average duration of this bond fund goes down from 30 years to 29.5 years and back to 30 years every 6 months.
    • A very-short-duration bond fund holding a single 6-month zero-coupon bond until maturity (6 months), and reinvesting the money into a new 6-months zero-coupon bond every semester. The average duration of this bond fund goes down from 6-months to zero and back to 6 months every 6 months.
SCENARIO 1:

The semestrial zero-coupon yield on a 60-semester (that's 30 years) zero-coupon bond was 3.91436839493459% on June 30, 1977. In order to get $10,000 back in mid-2007, the investor pays $998.77 (rounded) to buy a 30-year zero-coupon bond with a $10,000 face value because ($998.77 X ((1 + 3.914368%) ^ 60)) = $10,000.

The investment fluctuates, but thirty years later, the bond pays back its $10,000 face value to the investor. The investor gets the desired $10,000 in mid-2007.

SCENARIO 2:

The investors uses two funds, an extended-duration one and a very-short-duration one. As each fund holds a single zero-coupon bond, our calculations are simplified. At the start of each semester, the duration of the first fund is 30 years (60 semesters), and the duration of the second fund is 6 months (1 semester). During the semester, the duration of each of the two funds is reduced by exactly 1 semester, like the single bond they hold. As the start of the next semester, their duration is reset to 60 and 1 semesters, respectively.

In the hope of getting back $10,000 60 semesters later, the investor invests $998.77 (rounded) into the extended-duration bond fund in mid-1977. This is because the fund has a 3.91436839493459% yield-to-maturity (YTM) and a 60-semester duration. The investor doesn't put any money into the very-short-duration bond fund at this time.

One semester later, just as the two bond funds reset their duration back to 30-year and 0.5 year, the investor sells part of the extended-duration fund to invest into the very-short-duration fund. The objective is for the overall portfolio to have a duration of 59 semesters (at the beginning of the semester). The proportion of the portfolio to leave in the extended-duration fund is: ((59 - 1) / (60 - 1)) = 98.3% (rounded), because ((98.3% X 60 semesters) + (1.7% X 1 semester)) = 59 semesters. At the end of the semester, the portfolio's duration is down to 58 semesters, just before the two bond funds reset their duration.

Every semester, the investor repeats the calculation and allocates the money appropriately between the two funds to follow the target declining duration. The generic formula for the weight of the extended-duration fund is: ((number of semesters until target maturity - 1) / (60 - 1)). (This would have resulted into 100% at the start of the scenario in mid-1977).

The portfolio fluctuates. In mid-2007, the investor gets back $8,423.46. The investor got -$1,576.54 less than desired. That's a significant -16% hole in the investor's planning.

COMPARISON

Here's a growth chart for the two scenarios. I called Scenario 1 "Single Bond" (blue) and Scenario 2 "Portfolio" (red).

Image

We see a significant divergence in returns between the zero-coupon bond and the duration-managed portfolio.

The interesting question is: Who was on the other side of the investor's trades?

Anyway, there it is. Scenario 2, above, is a counterexample, proving that the following claim is false in the context of a duration-managed bond portfolio:
vineviz wrote: Sat Sep 03, 2022 12:02 pm If you keep your duration matched to your investment horizon, then your actual return will almost exactly match the initial averageYTM regardless of what happens to interest rates in the meantime.
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Re: A bond duration glide path for retirement investing

Post by longinvest »

Second post:

As promised, here's the data.

I won't copy here a 60+ columns X 60+ row table for semestrial zero-coupon yields. Interested readers can simply download the Bond Fund Simulator spreadsheet (version 2.3), making sure that the "FRED DGSX" data set is selected (it's the default), to find the semestrial zero-coupon yields in the "Zero Coupon Yield" sheet.

Here's the simulation table. Returns are semestrial (not annual). The "Treasury Return" column contains the returns of the a single declining-duration zero-coupon 30-year Treasury held until maturity. The "Bond Return" column contains the returns of a bond fund containing a single 30-year zero-coupon bond replaced with a new one every semester. The "Cash Return" column contains the returns of a bond fund containing a single 6-month zero-coupon bond replaced with a new one every semester. The "Single Bond" column contains the value of the declining-duration single zero-coupon Treasury bond at the start of the semester. The "Portfolio" column contains the value of the duration-managed portfolio at the start of the semester. The "Bond" and "Cash" columns contain the values of the two internal holdings of the portfolio. The "Bond Ratio" and "Cash Ratio" column contain the target weight of the porfolio's internal holdings at the start of the semester to achieve the desired decline in duration.

Code: Select all

   Date     Treasury Return    Bond Return    Cash Return    Single Bond    Portfolio      Bond         Cash       Bond Ratio    Cash Ratio  
1977.5                -7.85%         -7.85%          2.86%        $998.77      $998.77      $998.77        $0.00       100.00%         0.00%
1978                  -4.87%         -4.56%          3.49%        $920.36      $920.36      $904.76       $15.60        98.31%         1.69%
1978.5                -1.50%         -2.07%          4.19%        $875.56      $879.67      $849.85       $29.82        96.61%         3.39%
1979                   2.44%          1.88%          5.29%        $862.44      $863.34      $819.44       $43.90        94.92%         5.08%
1979.5               -20.12%        -20.76%          4.70%        $883.47      $881.03      $821.30       $59.73        93.22%         6.78%
1980                   3.06%          4.73%          5.85%        $705.70      $713.31      $652.86       $60.45        91.53%         8.47%
1980.5               -27.19%        -30.01%          4.25%        $727.27      $747.72      $671.68       $76.04        89.83%        10.17%
1981                 -15.19%         -9.08%          6.93%        $529.51      $549.39      $484.21       $65.18        88.14%        11.86%
1981.5                -9.06%         -2.66%          7.44%        $449.09      $509.92      $440.78       $69.14        86.44%        13.56%
1982                   4.28%         -6.95%          6.47%        $408.41      $503.32      $426.55       $76.78        84.75%        15.25%
1982.5                86.72%         91.84%          7.07%        $425.90      $478.66      $397.53       $81.13        83.05%        16.95%
1983                  -8.08%        -10.24%          4.21%        $795.23      $849.51      $691.12      $158.38        81.36%        18.64%
1983.5               -13.05%        -21.70%          4.72%        $730.96      $785.39      $625.65      $159.74        79.66%        20.34%
1984                 -22.03%        -26.74%          4.87%        $635.57      $657.18      $512.38      $144.80        77.97%        22.03%
1984.5                52.12%         70.52%          5.60%        $495.54      $527.22      $402.12      $125.10        76.27%        23.73%
1985                  24.61%         28.46%          4.32%        $753.80      $817.78      $609.87      $207.91        74.58%        25.42%
1985.5                31.77%         49.82%          3.67%        $939.28    $1,000.34      $729.06      $271.28        72.88%        27.12%
1986                  79.96%         80.17%          3.72%      $1,237.70    $1,373.47      $977.72      $395.75        71.19%        28.81%
1986.5                -2.01%        -13.13%          3.11%      $2,227.32    $2,172.07    $1,509.40      $662.66        69.49%        30.51%
1987                 -14.52%        -20.28%          2.94%      $2,182.46    $1,994.47    $1,352.18      $642.29        67.80%        32.20%
1987.5                -4.17%         -8.22%          3.10%      $1,865.62    $1,739.09    $1,149.57      $589.52        66.10%        33.90%
1988                   6.14%         11.12%          3.24%      $1,787.85    $1,662.87    $1,071.00      $591.87        64.41%        35.59%
1988.5                 2.91%          9.51%          3.52%      $1,897.64    $1,801.13    $1,129.52      $671.61        62.71%        37.29%
1989                  23.10%         31.23%          4.34%      $1,952.80    $1,932.15    $1,178.94      $753.21        61.02%        38.98%
1989.5                 5.96%          2.77%          4.07%      $2,403.93    $2,333.01    $1,383.99      $949.02        59.32%        40.68%
1990                  -3.49%         -6.02%          3.94%      $2,547.19    $2,409.93    $1,388.77    $1,021.16        57.63%        42.37%
1990.5                 7.20%          0.42%          4.01%      $2,458.17    $2,366.52    $1,323.64    $1,042.87        55.93%        44.07%
1991                   1.41%         -0.41%          3.37%      $2,635.05    $2,413.92    $1,309.24    $1,104.68        54.24%        45.76%
1991.5                25.80%         17.46%          2.98%      $2,672.21    $2,445.67    $1,285.01    $1,160.66        52.54%        47.46%
1992                  -2.70%         -5.34%          2.00%      $3,361.73    $2,704.56    $1,375.20    $1,329.36        50.85%        49.15%
1992.5                11.31%         20.02%          1.89%      $3,270.92    $2,657.77    $1,306.36    $1,351.41        49.15%        50.85%
1993                  17.06%         28.50%          1.69%      $3,640.99    $2,944.80    $1,397.53    $1,547.27        47.46%        52.54%
1993.5                 1.86%         45.12%          1.61%      $4,262.14    $3,369.18    $1,541.83    $1,827.35        45.76%        54.24%
1994                 -13.00%        -26.64%          1.65%      $4,341.38    $4,094.28    $1,804.26    $2,290.02        44.07%        55.93%
1994.5                 0.28%          0.62%          2.42%      $3,777.17    $3,651.38    $1,547.20    $2,104.19        42.37%        57.63%
1995                  24.35%         35.86%          3.26%      $3,787.71    $3,711.81    $1,509.89    $2,201.92        40.68%        59.32%
1995.5                11.20%         27.48%          2.80%      $4,709.88    $4,324.92    $1,685.98    $2,638.93        38.98%        61.02%
1996                  -8.89%        -18.48%          2.59%      $5,237.44    $4,861.95    $1,812.93    $3,049.02        37.29%        62.71%
1996.5                 6.98%          8.59%          2.69%      $4,771.81    $4,605.68    $1,639.31    $2,966.37        35.59%        64.41%
1997                   2.89%         -2.38%          2.67%      $5,104.92    $4,826.07    $1,635.96    $3,190.12        33.90%        66.10%
1997.5                11.01%         35.10%          2.67%      $5,252.46    $4,872.14    $1,569.00    $3,303.15        32.20%        67.80%
1998                   5.61%         12.68%          2.73%      $5,830.72    $5,511.08    $1,681.35    $3,829.73        30.51%        69.49%
1998.5                 9.40%         19.74%          2.62%      $6,157.73    $5,828.67    $1,679.45    $4,149.22        28.81%        71.19%
1999                  -6.99%        -18.80%          2.28%      $6,736.61    $6,268.89    $1,700.04    $4,568.85        27.12%        72.88%
1999.5                -1.74%         -9.13%          2.52%      $6,265.67    $6,053.26    $1,538.97    $4,514.30        25.42%        74.58%
2000                   5.55%         21.30%          2.87%      $6,156.74    $6,026.55    $1,430.03    $4,596.52        23.73%        76.27%
2000.5                10.73%          5.76%          3.12%      $6,498.43    $6,463.07    $1,424.07    $5,039.00        22.03%        77.97%
2001                   2.16%         -6.27%          2.85%      $7,196.02    $6,702.01    $1,363.12    $5,338.89        20.34%        79.66%
2001.5                 5.98%         10.81%          1.82%      $7,351.76    $6,768.70    $1,261.96    $5,506.74        18.64%        81.36%
2002                   4.45%        -13.84%          0.92%      $7,791.54    $7,005.05    $1,187.30    $5,817.75        16.95%        83.05%
2002.5                 9.31%         19.02%          0.88%      $8,138.47    $6,893.93    $1,051.62    $5,842.32        15.25%        84.75%
2003                   3.48%          8.71%          0.62%      $8,895.98    $7,145.12      $968.83    $6,176.29        13.56%        86.44%
2003.5                -0.82%         -4.36%          0.49%      $9,205.59    $7,267.47      $862.24    $6,405.23        11.86%        88.14%
2004                  -0.38%          0.67%          0.51%      $9,130.23    $7,261.30      $738.44    $6,522.87        10.17%        89.83%
2004.5                 1.62%         26.22%          0.84%      $9,095.84    $7,299.54      $618.61    $6,680.94         8.47%        91.53%
2005                   0.61%         30.91%          1.30%      $9,243.15    $7,517.85      $509.68    $7,008.16         6.78%        93.22%
2005.5                 0.74%         -5.99%          1.67%      $9,299.41    $7,766.15      $394.89    $7,371.26         5.08%        94.92%
2006                   1.39%        -15.30%          2.19%      $9,368.64    $7,865.58      $266.63    $7,598.95         3.39%        96.61%
2006.5                 2.66%         13.12%          2.62%      $9,498.71    $7,990.82      $135.44    $7,855.38         1.69%        98.31%
2007                   2.55%         -6.82%          2.55%      $9,751.82    $8,214.40        $0.00    $8,214.40         0.00%       100.00%
2007.5                                                         $10,000.00    $8,423.46                                        
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Robot Monster
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Re: A bond duration glide path for retirement investing

Post by Robot Monster »

longinvest wrote: Sun Sep 04, 2022 4:13 pm COMPARISON

Here's a growth chart for the two scenarios. I called Scenario 1 "Single Bond" (blue) and Scenario 2 "Portfolio" (red).

Image

We see a significant divergence in returns between the zero-coupon bond and the duration-managed portfolio.
Nice work. I see that between 1977-1991 there is hardly any divergence, there are episodes of noteworthy divergence between 1991-2000ish, but the divergence really gets cooking thereafter -- monster divergence! Why is there dissimilar behavior between these three timespans?
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Re: A bond duration glide path for retirement investing

Post by vineviz »

longinvest wrote: Sun Sep 04, 2022 2:10 pm Here's a counterexample to the claim that "If you keep your duration matched to your investment horizon, then your actual return will almost exactly match the initial average YTM regardless of what happens to interest rates in the meantime" when using a duration-managed portfolio.
I appreciate the effort you expended to create your counterexample. It highlights a couple of factors that I, admittedly, didn't address.

One is that "almost exactly match" is clearly subjective. The counterexample illustrates a difference in annualized returns of 7.98% versus 7.37% over a 30 year holding period. I'd argue that is highly predictive, given everything that happened to interest rates and bond markets between 1977 and 2007, but will concede that a reasonable person might feel that "almost exactly match" is a stretched description of accuracy.

Additionally, there are some technical assumptions being made in deriving the proof that duration matching immunizes against interest rate risk.
Both are related to bond convexity, which is an additional measure of a bond's sensitivity to rate changes beyond duration. We often ignore convexity measures because, as a second derivative of price change, it usually plays a limited role in affecting returns.

But it plays role in the example that longinvest constructed, especially towards the end of the simulation (e.g. 2001 to 2007) when the two strategies diverge in returns. Why?

One is that although we can match the duration of a 5 year zero coupon bond with a combination of cash and a 30 year zero coupon bond, the convexity of those two portfolios is significantly different.

Another is that conventional estimations of duration and convexity involve an assumption that yield curves shift in a parallel manner.

In the last five years or so of the "counterexample", we witness two portfolios with similar durations but wildly different convexities AND the yield curve shifted in a non-parallel manner. For instance, by 2004 in the example we are trying to replicate a 3 year bond (aka "bullet" portfolio) with a combination of a 30 year bond and cash (aka "barbell" portfolio).

We can replicate the duration by doing that, but the convexities didn't match. As a result of that (and the particular history of non-parallel shifts in the yield curve during the recession>>expansion>>recession period of the 2000s), in 2004 the "true" 3 year yield was about 3.6% but the "replicated" yield was less than 2%

So we owe longinvest a debt by illustrating that maintaining duration ALONE is sometimes not sufficient to get the "almost exactly match" result we desire: using a combination of funds that, themselves, are similar in duration to our target is preferable.

In other words, if your target duration is 3 years it probably safer to use a combination of cash and a 5 year duration fund than to use a combination
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Re: A bond duration glide path for retirement investing

Post by vineviz »

Because longinvest has cross-posted the same comments in two threads, this is going to be messy.

In the orginaial thread, in addition to my own comments user petulant added some important commentary. I suggest reading their whole post, but here's the start.

petulant wrote: Mon Sep 05, 2022 8:28 am
Right. At a simpler level that a new reader might not grasp, longinvest's example is also tied to reinvestment risk, which is going to afflict all actual bond funds that invest in coupon-paying bonds and which can provide the intuitions for what's happening to the bond portfolio.
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Re: A bond duration glide path for retirement investing

Post by vineviz »

Robot Monster wrote: Mon Sep 05, 2022 10:47 am Nice work. I see that between 1977-1991 there is hardly any divergence, there are episodes of noteworthy divergence between 1991-2000ish, but the divergence really gets cooking thereafter -- monster divergence! Why is there dissimilar behavior between these three timespans?
See my earlier comments about convexity and yield curve shifts.

To further illustrate, here's the yield curve in 2004 (in blue) compared to the "yield curve" dictated by longinvest's decision to model the entire glide path using a combination of cash and 30-year duration bonds.

Image

During important points in the 2000s, when all the total return difference between the two strategies is generated, the "problem" is the decision to try to use a combination of 30-year duration bonds and cash to match what have by that time become very short duration liabilities. The image above shows the yield curve in 2004, when the investor would have been targeting a duration of a about 3 years or so.

That's a region of the yield curve that is very strongly concave, which means that the replicating barbell portfolio was "reinvesting" at a YTM that was 100-150 bps less than the actual target duration bond yield.

The so-called "counterexample" merely illustrates the wisdom of not taking a naively extreme approach to building the duration glide path. Their example illustrates the value of taking the useful (and common sense) step of avoiding extreme bets, such as employing a severe barbell to match a bullet liability.
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Re: A bond duration glide path for retirement investing

Post by dcabler »

vineviz wrote: Mon Sep 05, 2022 12:32 pm
Robot Monster wrote: Mon Sep 05, 2022 10:47 am Nice work. I see that between 1977-1991 there is hardly any divergence, there are episodes of noteworthy divergence between 1991-2000ish, but the divergence really gets cooking thereafter -- monster divergence! Why is there dissimilar behavior between these three timespans?
See my earlier comments about convexity and yield curve shifts.

To further illustrate, here's the yield curve in 2004 (in blue) compared to the "yield curve" dictated by longinvest's decision to model the entire glide path using a combination of cash and 30-year duration bonds.

Image

During important points in the 2000s, when all the total return difference between the two strategies is generated, the "problem" is the decision to try to use a combination of 30-year duration bonds and cash to match what have by that time become very short duration liabilities. The image above shows the yield curve in 2004, when the investor would have been targeting a duration of a about 3 years or so.

That's a region of the yield curve that is very strongly concave, which means that the replicating barbell portfolio was "reinvesting" at a YTM that was 100-150 bps less than the actual target duration bond yield.

The so-called "counterexample" merely illustrates the wisdom of not taking a naively extreme approach to building the duration glide path. Their example illustrates the value of taking the useful (and common sense) step of avoiding extreme bets, such as employing a severe barbell to match a bullet liability.
I always assumed most people would use a multistep approach. For example, starting first with something like EDV if doing this with nominal treasuries, then a combination of EDV/VGLT until the needed duration is less than VGLT's duration. Then VGLT/VGIT until the needed duration is less than VGIT's duration. Then VGIT/VGSH, then VGSH/(Cash or T-Bills or T-Bills fund). This would hug the curve a good deal better.
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Re: A bond duration glide path for retirement investing

Post by vineviz »

dcabler wrote: Mon Sep 05, 2022 7:04 pm I always assumed most people would use a multistep approach. For example, starting first with something like EDV if doing this with nominal treasuries, then a combination of EDV/VGLT until the needed duration is less than VGLT's duration. Then VGLT/VGIT until the needed duration is less than VGIT's duration. Then VGIT/VGSH, then VGSH/(Cash or T-Bills or T-Bills fund). This would hug the curve a good deal better.
This is certainly what I'd typically recommend.

Indeed, for a typical retiree at the start of retirement their investment horizon is probably in the range of 15-20 years store starting with a fund like Vanguard Long-Term Treasury ETF (VGLT), iShares Core 10+ Year USD Bond ETF (ILTB), or PIMCO 15+ Year US TIPS ETF (LTPZ) would be plenty of duration.
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Re: A bond duration glide path for retirement investing

Post by vineviz »

vineviz wrote: Mon Sep 05, 2022 7:48 pm
dcabler wrote: Mon Sep 05, 2022 7:04 pm I always assumed most people would use a multistep approach. For example, starting first with something like EDV if doing this with nominal treasuries, then a combination of EDV/VGLT until the needed duration is less than VGLT's duration. Then VGLT/VGIT until the needed duration is less than VGIT's duration. Then VGIT/VGSH, then VGSH/(Cash or T-Bills or T-Bills fund). This would hug the curve a good deal better.
This is certainly what I'd typically recommend.

Indeed, for a typical retiree at the start of retirement their investment horizon is probably in the range of 15-20 years store starting with a fund like Vanguard Long-Term Treasury ETF (VGLT), iShares Core 10+ Year USD Bond ETF (ILTB), or PIMCO 15+ Year US TIPS ETF (LTPZ) would be plenty of duration.
I want to mention a slightly different approach from the orginally proposed that can approximate a bond duration glide path while avoiding any need to perform any portfolio rebalancing during retirement. In fact derives some value from the avoidance of rebalancing. This approach might be easier to pass on to a family member or spouse who has no interest in actively managing the asset allocation.

Basically the idea is to start retirement with an allocation to three bond funds (long-term, intermediate-term, and short-term) instead of just two. In most cases about 50% of the bond allocation will be invested in the long-term fund, 25% in the intermediate-term fund, and 25% in the short-term fund.

Withdrawals are made from the long-term bond fund first and continue until that fund is depleted. Then withdrawals continue from the intermediate-term fund until that fund is depleted. Finally, withdrawals continue from the short-term fund until the end of the planned period.

Withdrawals can be calculated in several ways, but here are two:

1) The easiest way is with a simple 1/n (i.e. RMD) method, where n is the remaining number of annual withdrawals. For a 30 year planning horizon, the first withdrawal would be calculated as 1/3 = 3.33% of the current bond value. The second annual withdrawal would be 1/29 or 3.45%. And so on. This will introduce a bit of volatility in the withdrawal amount, but the advantage is that a simple calculator is all that's required.

2) A slightly more onerous calculation is the amortization (or ABW method), which requires a financial calculator or Excel. In Excel you'd use the PMT function.

Code: Select all

PMT(rate, nper, pv, [fv], [type])
rate is the weighted average yield of the bond funds minus the expected rate of inflation (to get income that adjusts to match the cost of living)*
nper is the number of remaining withdrawals
pv is the current total value of all the bond funds
fv is the desired bequest value (set to "0" to deplete the portfolio)
typce is set to 1 for withdrawals at the beginning of the year and 0 for withdrawals at the end of the year.

*A small additional adjustment to the "YIELD minus EXPECTED INFLATION" is required to account for the slope of the yield curve. This can be set at -0.25% as an approximation. So the final "rate" is "YIELD minus EXPECTED INFLATION minus 0.25%".

Again, this is an approximation but has the advantage of being set up once.
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Re: A bond duration glide path for retirement investing

Post by dcabler »

vineviz wrote: Tue Sep 13, 2022 4:16 pm
vineviz wrote: Mon Sep 05, 2022 7:48 pm
dcabler wrote: Mon Sep 05, 2022 7:04 pm I always assumed most people would use a multistep approach. For example, starting first with something like EDV if doing this with nominal treasuries, then a combination of EDV/VGLT until the needed duration is less than VGLT's duration. Then VGLT/VGIT until the needed duration is less than VGIT's duration. Then VGIT/VGSH, then VGSH/(Cash or T-Bills or T-Bills fund). This would hug the curve a good deal better.
This is certainly what I'd typically recommend.

Indeed, for a typical retiree at the start of retirement their investment horizon is probably in the range of 15-20 years store starting with a fund like Vanguard Long-Term Treasury ETF (VGLT), iShares Core 10+ Year USD Bond ETF (ILTB), or PIMCO 15+ Year US TIPS ETF (LTPZ) would be plenty of duration.
I want to mention a slightly different approach from the orginally proposed that can approximate a bond duration glide path while avoiding any need to perform any portfolio rebalancing during retirement. In fact derives some value from the avoidance of rebalancing. This approach might be easier to pass on to a family member or spouse who has no interest in actively managing the asset allocation.

Basically the idea is to start retirement with an allocation to three bond funds (long-term, intermediate-term, and short-term) instead of just two. In most cases about 50% of the bond allocation will be invested in the long-term fund, 25% in the intermediate-term fund, and 25% in the short-term fund.

Withdrawals are made from the long-term bond fund first and continue until that fund is depleted. Then withdrawals continue from the intermediate-term fund until that fund is depleted. Finally, withdrawals continue from the short-term fund until the end of the planned period.

Withdrawals can be calculated in several ways, but here are two:

1) The easiest way is with a simple 1/n (i.e. RMD) method, where n is the remaining number of annual withdrawals. For a 30 year planning horizon, the first withdrawal would be calculated as 1/3 = 3.33% of the current bond value. The second annual withdrawal would be 1/29 or 3.45%. And so on. This will introduce a bit of volatility in the withdrawal amount, but the advantage is that a simple calculator is all that's required.

2) A slightly more onerous calculation is the amortization (or ABW method), which requires a financial calculator or Excel. In Excel you'd use the PMT function.

Code: Select all

PMT(rate, nper, pv, [fv], [type])
rate is the weighted average yield of the bond funds minus the expected rate of inflation (to get income that adjusts to match the cost of living)*
nper is the number of remaining withdrawals
pv is the current total value of all the bond funds
fv is the desired bequest value (set to "0" to deplete the portfolio)
typce is set to 1 for withdrawals at the beginning of the year and 0 for withdrawals at the end of the year.

*A small additional adjustment to the "YIELD minus EXPECTED INFLATION" is required to account for the slope of the yield curve. This can be set at -0.25% as an approximation. So the final "rate" is "YIELD minus EXPECTED INFLATION minus 0.25%".

Again, this is an approximation but has the advantage of being set up once.
Good stuff. What I've set up is kind of similar, but only holding only one fund at a time. Move from VGLT(FNBGX) -> FUAMX -> FUMBX and for TIPs similarly starting with LTPZ -> SCHP -> STIP. PMT math would be as you showed above. The changeover happens when the remaining planning horizon is less than the duration of the bond fund currently in use.

Definitely want to look more at the 3 funds in parallel approach you describe above.

Cheers.
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Re: A bond duration glide path for retirement investing

Post by hoops777 »

Just curious, is now a good time to buy VGLT since it’s Nav has been decimated ?
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Re: A bond duration glide path for retirement investing

Post by vineviz »

hoops777 wrote: Tue Sep 13, 2022 5:46 pm Just curious, is now a good time to buy VGLT since it’s Nav has been decimated ?
I'd say that a good time to buy a bond fund is whenever you have money to invest and you need more bonds in your portfolio.

IMHO, making sudden and large moves in asset allocation or portfolio selection is usually unwise. But it is certainly true that everyone who was avoiding long-term bonds in 2020 because yields were low would seem to have less reason to avoid them now. :D
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Re: A bond duration glide path for retirement investing

Post by HappyJack »

vineviz wrote: Tue Sep 13, 2022 4:16 pm
vineviz wrote: Mon Sep 05, 2022 7:48 pm
dcabler wrote: Mon Sep 05, 2022 7:04 pm I always assumed most people would use a multistep approach. For example, starting first with something like EDV if doing this with nominal treasuries, then a combination of EDV/VGLT until the needed duration is less than VGLT's duration. Then VGLT/VGIT until the needed duration is less than VGIT's duration. Then VGIT/VGSH, then VGSH/(Cash or T-Bills or T-Bills fund). This would hug the curve a good deal better.
This is certainly what I'd typically recommend.

Indeed, for a typical retiree at the start of retirement their investment horizon is probably in the range of 15-20 years store starting with a fund like Vanguard Long-Term Treasury ETF (VGLT), iShares Core 10+ Year USD Bond ETF (ILTB), or PIMCO 15+ Year US TIPS ETF (LTPZ) would be plenty of duration.
I want to mention a slightly different approach from the orginally proposed that can approximate a bond duration glide path while avoiding any need to perform any portfolio rebalancing during retirement. In fact derives some value from the avoidance of rebalancing. This approach might be easier to pass on to a family member or spouse who has no interest in actively managing the asset allocation.

Basically the idea is to start retirement with an allocation to three bond funds (long-term, intermediate-term, and short-term) instead of just two. In most cases about 50% of the bond allocation will be invested in the long-term fund, 25% in the intermediate-term fund, and 25% in the short-term fund.

Withdrawals are made from the long-term bond fund first and continue until that fund is depleted. Then withdrawals continue from the intermediate-term fund until that fund is depleted. Finally, withdrawals continue from the short-term fund until the end of the planned period.

Withdrawals can be calculated in several ways, but here are two:

1) The easiest way is with a simple 1/n (i.e. RMD) method, where n is the remaining number of annual withdrawals. For a 30 year planning horizon, the first withdrawal would be calculated as 1/3 = 3.33% of the current bond value. The second annual withdrawal would be 1/29 or 3.45%. And so on. This will introduce a bit of volatility in the withdrawal amount, but the advantage is that a simple calculator is all that's required.

2) A slightly more onerous calculation is the amortization (or ABW method), which requires a financial calculator or Excel. In Excel you'd use the PMT function.

Code: Select all

PMT(rate, nper, pv, [fv], [type])
rate is the weighted average yield of the bond funds minus the expected rate of inflation (to get income that adjusts to match the cost of living)*
nper is the number of remaining withdrawals
pv is the current total value of all the bond funds
fv is the desired bequest value (set to "0" to deplete the portfolio)
typce is set to 1 for withdrawals at the beginning of the year and 0 for withdrawals at the end of the year.

*A small additional adjustment to the "YIELD minus EXPECTED INFLATION" is required to account for the slope of the yield curve. This can be set at -0.25% as an approximation. So the final "rate" is "YIELD minus EXPECTED INFLATION minus 0.25%".

Again, this is an approximation but has the advantage of being set up once.
Vince,
I am currently using LTPZ -VTIP, duration matched, for a 24 year retirement. This does involve rebalancing. What type of precision would I be sacrificing if I went to a three fund parallel approach and just spent off the longest duration fund and move down as you had noted above.
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Re: A bond duration glide path for retirement investing

Post by vineviz »

HappyJack wrote: Tue Sep 13, 2022 6:30 pm I am currently using LTPZ -VTIP, duration matched, for a 24 year retirement. This does involve rebalancing. What type of precision would I be sacrificing if I went to a three fund parallel approach and just spent off the longest duration fund and move down as you had noted above.
You might actually gain some benefit. Including a 3rd, intermediate-term fund (either from the start, as I just outlined, or as part of the glide path as initially described), helps maintain fidelity whenever your target duration is on a portion of the yield curve that is concave.

For instance the following graph shows a hypothetical real yield curve (similar, but not identical, to what we might have observed about a year ago) in blue. Duration, not maturity, is plotted on the x-axis.

The grey line shows the "yield curve" that could be replicated by using just VTIP and LTPZ. You can see, I hope, that because the yield curve is concave that the yield of the "synthetic" 2-fund portfolio shown by the grey line consistently was below the "synthetic" yield curve obtainable by using three funds (e.g. VTIP, SCHP, and LTPZ) as shown by the orange line.

Whenever you're bleeding two funds to get a duration target, it's better to use funds that are - themselves - relatively near the target duration on the yield curve if that makes any sense.

Image
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dcabler
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Re: A bond duration glide path for retirement investing

Post by dcabler »

HappyJack wrote: Tue Sep 13, 2022 6:30 pm
vineviz wrote: Tue Sep 13, 2022 4:16 pm
vineviz wrote: Mon Sep 05, 2022 7:48 pm
dcabler wrote: Mon Sep 05, 2022 7:04 pm I always assumed most people would use a multistep approach. For example, starting first with something like EDV if doing this with nominal treasuries, then a combination of EDV/VGLT until the needed duration is less than VGLT's duration. Then VGLT/VGIT until the needed duration is less than VGIT's duration. Then VGIT/VGSH, then VGSH/(Cash or T-Bills or T-Bills fund). This would hug the curve a good deal better.
This is certainly what I'd typically recommend.

Indeed, for a typical retiree at the start of retirement their investment horizon is probably in the range of 15-20 years store starting with a fund like Vanguard Long-Term Treasury ETF (VGLT), iShares Core 10+ Year USD Bond ETF (ILTB), or PIMCO 15+ Year US TIPS ETF (LTPZ) would be plenty of duration.
I want to mention a slightly different approach from the orginally proposed that can approximate a bond duration glide path while avoiding any need to perform any portfolio rebalancing during retirement. In fact derives some value from the avoidance of rebalancing. This approach might be easier to pass on to a family member or spouse who has no interest in actively managing the asset allocation.

Basically the idea is to start retirement with an allocation to three bond funds (long-term, intermediate-term, and short-term) instead of just two. In most cases about 50% of the bond allocation will be invested in the long-term fund, 25% in the intermediate-term fund, and 25% in the short-term fund.

Withdrawals are made from the long-term bond fund first and continue until that fund is depleted. Then withdrawals continue from the intermediate-term fund until that fund is depleted. Finally, withdrawals continue from the short-term fund until the end of the planned period.

Withdrawals can be calculated in several ways, but here are two:

1) The easiest way is with a simple 1/n (i.e. RMD) method, where n is the remaining number of annual withdrawals. For a 30 year planning horizon, the first withdrawal would be calculated as 1/3 = 3.33% of the current bond value. The second annual withdrawal would be 1/29 or 3.45%. And so on. This will introduce a bit of volatility in the withdrawal amount, but the advantage is that a simple calculator is all that's required.

2) A slightly more onerous calculation is the amortization (or ABW method), which requires a financial calculator or Excel. In Excel you'd use the PMT function.

Code: Select all

PMT(rate, nper, pv, [fv], [type])
rate is the weighted average yield of the bond funds minus the expected rate of inflation (to get income that adjusts to match the cost of living)*
nper is the number of remaining withdrawals
pv is the current total value of all the bond funds
fv is the desired bequest value (set to "0" to deplete the portfolio)
typce is set to 1 for withdrawals at the beginning of the year and 0 for withdrawals at the end of the year.

*A small additional adjustment to the "YIELD minus EXPECTED INFLATION" is required to account for the slope of the yield curve. This can be set at -0.25% as an approximation. So the final "rate" is "YIELD minus EXPECTED INFLATION minus 0.25%".

Again, this is an approximation but has the advantage of being set up once.
Vince,
I am currently using LTPZ -VTIP, duration matched, for a 24 year retirement. This does involve rebalancing. What type of precision would I be sacrificing if I went to a three fund parallel approach and just spent off the longest duration fund and move down as you had noted above.
If you used the PMT approach that vineviz described, you'd probably still be reasonably smooth. I did a quick and dirty couple of sims with nominal treasuries and 1/N withdrawals and looked at the volatility in real terms for a 30 year period starting in 1966 and another starting in 1984, using data from Simba's spreadsheet. Volatility was surprisingly low through the seventies but in both cases, once you hit the 80's, the withdrawals, even in real terms, increased rapidly while interest rates were dropping. Still, though, maybe not the worst "Plan B" for a spouse who might not be interested in this stuff.


Cheers.
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Re: A bond duration glide path for retirement investing

Post by dcabler »

vineviz wrote: Tue Sep 13, 2022 4:16 pm
2) A slightly more onerous calculation is the amortization (or ABW method), which requires a financial calculator or Excel. In Excel you'd use the PMT function.

Code: Select all

PMT(rate, nper, pv, [fv], [type])
rate is the weighted average yield of the bond funds minus the expected rate of inflation (to get income that adjusts to match the cost of living)*
nper is the number of remaining withdrawals
pv is the current total value of all the bond funds
fv is the desired bequest value (set to "0" to deplete the portfolio)
typce is set to 1 for withdrawals at the beginning of the year and 0 for withdrawals at the end of the year.

*A small additional adjustment to the "YIELD minus EXPECTED INFLATION" is required to account for the slope of the yield curve. This can be set at -0.25% as an approximation. So the final "rate" is "YIELD minus EXPECTED INFLATION minus 0.25%".

Again, this is an approximation but has the advantage of being set up once.
vineviz - this brings up a question I've had for a while regarding duration matching and withdrawing using the Excel PMT function, whether it's this method or one that's using rebalancing.

rate = weighted average of the bond funds minus expected rate of inflation

Regarding the portion of "rate" in the PMT function that's the "weighted average of the bond funds"
- Is it the weighted average of the bond fund mix that you have today for the current withdrawal period?
- Or, since you're calculating expected future returns, is it more correct to also look at the expected mix of bond funds for each future withdrawal period all the way out to the end and somehow take that into account when calculating "rate". If so, how exactly would you make that calculation?

cheers.
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Re: A bond duration glide path for retirement investing

Post by vineviz »

dcabler wrote: Wed Sep 14, 2022 4:36 am Regarding the portion of "rate" in the PMT function that's the "weighted average of the bond funds"
- Is it the weighted average of the bond fund mix that you have today for the current withdrawal period?
- Or, since you're calculating expected future returns, is it more correct to also look at the expected mix of bond funds for each future withdrawal period all the way out to the end and somehow take that into account when calculating "rate". If so, how exactly would you make that calculation?
It can be either one, and you shouldn't get a big variation in outcomes either way.

If you're recalculating PMT each period using an updated weighted average each time, that "yield curve adjustment factor" I mentioned above (i.e. go the -0.25% in my example) should do a reasonably good job of anticipating the fact that your mix of durations will be decreasing in the future. By the time you get most of the way through retirement, the growth rate assumption becomes less-and-less impactful anyway.

If you do a "one-time" set up with an initial payment that you intend to simply inflation adjust each period then you've got a little less certainty about the sustainability, but it still works surprisingly well.
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Re: A bond duration glide path for retirement investing

Post by HappyJack »

vineviz wrote: Tue Sep 13, 2022 7:10 pm
HappyJack wrote: Tue Sep 13, 2022 6:30 pm I am currently using LTPZ -VTIP, duration matched, for a 24 year retirement. This does involve rebalancing. What type of precision would I be sacrificing if I went to a three fund parallel approach and just spent off the longest duration fund and move down as you had noted above.
You might actually gain some benefit. Including a 3rd, intermediate-term fund (either from the start, as I just outlined, or as part of the glide path as initially described), helps maintain fidelity whenever your target duration is on a portion of the yield curve that is concave.

For instance the following graph shows a hypothetical real yield curve (similar, but not identical, to what we might have observed about a year ago) in blue. Duration, not maturity, is plotted on the x-axis.

The grey line shows the "yield curve" that could be replicated by using just VTIP and LTPZ. You can see, I hope, that because the yield curve is concave that the yield of the "synthetic" 2-fund portfolio shown by the grey line consistently was below the "synthetic" yield curve obtainable by using three funds (e.g. VTIP, SCHP, and LTPZ) as shown by the orange line.

Whenever you're bleeding two funds to get a duration target, it's better to use funds that are - themselves - relatively near the target duration on the yield curve if that makes any sense.

Image
Vineviz,
Thanks. Hmm.
1. Set the percentages 50% LTPZ, 25% (FIPDX or SCHP), 25% VTIP
2. Spend down from LTPZ until its depleted, then spend down FIPDX/SCHP ... down to VTIP
3. No rebalancing.
Seems simpler with a possible benefit since the yield curve is unknowable in the future.
Do I understand this correctly?
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Re: A bond duration glide path for retirement investing

Post by vineviz »

HappyJack wrote: Wed Sep 14, 2022 8:18 am Thanks. Hmm.
1. Set the percentages 50% LTPZ, 25% (FIPDX or SCHP), 25% VTIP
2. Spend down from LTPZ until its depleted, then spend down FIPDX/SCHP ... down to VTIP
3. No rebalancing.
Seems simpler with a possible benefit since the yield curve is unknowable in the future.
Do I understand this correctly?
Yep, that's exactly what I was suggesting.

Of course this is an approximation, and a lot of detailed analysis could probably produce a marginal improvement, but what you outline is incredibly simple and easily executable by a spouse or child who has no interest in portfolio management.
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Re: A bond duration glide path for retirement investing

Post by abuss368 »

vineviz wrote: Wed Sep 14, 2022 8:29 am
HappyJack wrote: Wed Sep 14, 2022 8:18 am Thanks. Hmm.
1. Set the percentages 50% LTPZ, 25% (FIPDX or SCHP), 25% VTIP
2. Spend down from LTPZ until its depleted, then spend down FIPDX/SCHP ... down to VTIP
3. No rebalancing.
Seems simpler with a possible benefit since the yield curve is unknowable in the future.
Do I understand this correctly?
Yep, that's exactly what I was suggesting.

Of course this is an approximation, and a lot of detailed analysis could probably produce a marginal improvement, but what you outline is incredibly simple and easily executable by a spouse or child who has no interest in portfolio management.
Hi Vince -

Do you often find a need for more than one bond fund in a portfolio?

Best
Tony
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Re: A bond duration glide path for retirement investing

Post by vineviz »

abuss368 wrote: Wed Sep 14, 2022 8:57 am Do you often find a need for more than one bond fund in a portfolio?
"Need" is a peculiar word.

It's certainly always possible to construct a portfolio that contains only one bond fund, and usually quite possible to get close to an ideal solution by holding only one bond fund at a time.

But because situations change over time (e.g. investment horizons get shorter or longer, tax brackets change, etc.) I think it's reasonable to expect that even people who hold only one bond fund at a time might need to change that fund as circumstances shift.
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Re: A bond duration glide path for retirement investing

Post by abuss368 »

vineviz wrote: Wed Sep 14, 2022 10:08 am
abuss368 wrote: Wed Sep 14, 2022 8:57 am Do you often find a need for more than one bond fund in a portfolio?
"Need" is a peculiar word.

It's certainly always possible to construct a portfolio that contains only one bond fund, and usually quite possible to get close to an ideal solution by holding only one bond fund at a time.

But because situations change over time (e.g. investment horizons get shorter or longer, tax brackets change, etc.) I think it's reasonable to expect that even people who hold only one bond fund at a time might need to change that fund as circumstances shift.
Hi Vince -

That is reasonable. Income levels can change. Tax brackets can change (taxable vs. tax exempt) as a result of higher or lower income and a change in tax laws. Investment horizons and goals can change.

Assuming if any of these changes would occur, you would evaluate the overall expected duration and structure the portfolio accordingly correct?

Best.
Tony
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Re: A bond duration glide path for retirement investing

Post by dcabler »

vineviz wrote: Wed Sep 14, 2022 8:29 am
HappyJack wrote: Wed Sep 14, 2022 8:18 am Thanks. Hmm.
1. Set the percentages 50% LTPZ, 25% (FIPDX or SCHP), 25% VTIP
2. Spend down from LTPZ until its depleted, then spend down FIPDX/SCHP ... down to VTIP
3. No rebalancing.
Seems simpler with a possible benefit since the yield curve is unknowable in the future.
Do I understand this correctly?
Yep, that's exactly what I was suggesting.

Of course this is an approximation, and a lot of detailed analysis could probably produce a marginal improvement, but what you outline is incredibly simple and easily executable by a spouse or child who has no interest in portfolio management.
Did a few Excel games on it. As you noted earlier in this part of the overall thread, some marginal improvements could be made.

- For the funds investors are most likely to use, for a 30 year horizon, the effective duration trajectory stays well below what the ideal duration glide path would be. Having the starting weight be higher for the longer duration bonds helps that quite a bit. That also has the potential to increase withdrawals as well. At least with 1/N easy withdrawals, you'll never match the ideal duration curve, but might wiggle above and below it.
- Perhaps adding an ultrashort fund to the mix would be beneficial as well, especially for the final years, but that might not matter to many investors by that point.

Anyway, I like this idea as a candidate for my own "Plan B" for my bond-income stream.

cheers.
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Re: A bond duration glide path for retirement investing

Post by HappyJack »

HappyJack wrote: Wed Sep 14, 2022 8:18 am
vineviz wrote: Tue Sep 13, 2022 7:10 pm
HappyJack wrote: Tue Sep 13, 2022 6:30 pm I am currently using LTPZ -VTIP, duration matched, for a 24 year retirement. This does involve rebalancing. What type of precision would I be sacrificing if I went to a three fund parallel approach and just spent off the longest duration fund and move down as you had noted above.
You might actually gain some benefit. Including a 3rd, intermediate-term fund (either from the start, as I just outlined, or as part of the glide path as initially described), helps maintain fidelity whenever your target duration is on a portion of the yield curve that is concave.

For instance the following graph shows a hypothetical real yield curve (similar, but not identical, to what we might have observed about a year ago) in blue. Duration, not maturity, is plotted on the x-axis.

The grey line shows the "yield curve" that could be replicated by using just VTIP and LTPZ. You can see, I hope, that because the yield curve is concave that the yield of the "synthetic" 2-fund portfolio shown by the grey line consistently was below the "synthetic" yield curve obtainable by using three funds (e.g. VTIP, SCHP, and LTPZ) as shown by the orange line.

Whenever you're bleeding two funds to get a duration target, it's better to use funds that are - themselves - relatively near the target duration on the yield curve if that makes any sense.

Image
Vineviz,
Thanks. Hmm.
1. Set the percentages 50% LTPZ, 25% (FIPDX or SCHP), 25% VTIP
2. Spend down from LTPZ until its depleted, then spend down FIPDX/SCHP ... down to VTIP
3. No rebalancing.
Seems simpler with a possible benefit since the yield curve is unknowable in the future.
Do I understand this correctly?
Currently, I am almost exactly 50/50 LTPZ and VTIP and duration matched for 24 year retirement. If I move FIPDX in there at 25% (taking it from VTIP), I would be set for withdrawals with the 1/n method and no rebalancing, and still on my Liability Matching path.

What would I be sacrificing with this move? Some precision for simplicity?
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Re: A bond duration glide path for retirement investing

Post by dcabler »

HappyJack wrote: Thu Sep 15, 2022 7:50 am
HappyJack wrote: Wed Sep 14, 2022 8:18 am
vineviz wrote: Tue Sep 13, 2022 7:10 pm
HappyJack wrote: Tue Sep 13, 2022 6:30 pm I am currently using LTPZ -VTIP, duration matched, for a 24 year retirement. This does involve rebalancing. What type of precision would I be sacrificing if I went to a three fund parallel approach and just spent off the longest duration fund and move down as you had noted above.
You might actually gain some benefit. Including a 3rd, intermediate-term fund (either from the start, as I just outlined, or as part of the glide path as initially described), helps maintain fidelity whenever your target duration is on a portion of the yield curve that is concave.

For instance the following graph shows a hypothetical real yield curve (similar, but not identical, to what we might have observed about a year ago) in blue. Duration, not maturity, is plotted on the x-axis.

The grey line shows the "yield curve" that could be replicated by using just VTIP and LTPZ. You can see, I hope, that because the yield curve is concave that the yield of the "synthetic" 2-fund portfolio shown by the grey line consistently was below the "synthetic" yield curve obtainable by using three funds (e.g. VTIP, SCHP, and LTPZ) as shown by the orange line.

Whenever you're bleeding two funds to get a duration target, it's better to use funds that are - themselves - relatively near the target duration on the yield curve if that makes any sense.

Image
Vineviz,
Thanks. Hmm.
1. Set the percentages 50% LTPZ, 25% (FIPDX or SCHP), 25% VTIP
2. Spend down from LTPZ until its depleted, then spend down FIPDX/SCHP ... down to VTIP
3. No rebalancing.
Seems simpler with a possible benefit since the yield curve is unknowable in the future.
Do I understand this correctly?
Currently, I am almost exactly 50/50 LTPZ and VTIP and duration matched for 24 year retirement. If I move FIPDX in there at 25% (taking it from VTIP), I would be set for withdrawals with the 1/n method and no rebalancing, and still on my Liability Matching path.

What would I be sacrificing with this move? Some precision for simplicity?
You'd be sacrificing withdrawal volatility for simplicity but that's mainly due to the 1/N withdrawals. 1/N does not pay attention to yields or portfolio growth rates. It might outpace the overall growth, resulting in a downward trajectory of withdrawals over time. Or it might withdraw less than the growth resulting in an upward trajectory of withdrawals over time. Or maybe some of both just resulting in large fluctuations in either direction over time...

The excel PMT function is the smoother option here for withdrawals. But you need to use "real yields" in the PMT function for withdrawals. And you should know that neither LTPZ at PIMCO nor FIPDX at Fidelity reports real yields. Of your 3 funds only VTIP does.

Fortunately #cruncher calculates real yields periodically on this thread. viewtopic.php?p=6754200#p6754200

If you're good with spreadsheets, I recommend downloading it yourself and understanding what he's doing. There's no guarantee that he'll always be there to update this. On the other hand, it's my opinion that once you're getting real rates and are savvy enough to use the PMT function, you're probably savvy enough to rebalance once per year for duration matching.

Cheers.
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Re: A bond duration glide path for retirement investing

Post by HappyJack »

Thanks dcabler and vineviz,
Would you say that this is a more accurate way to for the LMP to track the yield curve than a two fund barbell?
Also, for 24-27 year retirement, would a 50% LTPZ, 25% FIPDX, and 25% VTIP allottment with two years stable value or I bonds for the final two years would provide an accurate glide path?

Thanks again.
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vineviz
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Re: A bond duration glide path for retirement investing

Post by vineviz »

HappyJack wrote: Thu Sep 15, 2022 10:03 am Thanks dcabler and vineviz,
Would you say that this is a more accurate way to for the LMP to track the yield curve than a two fund barbell?
I don't think there's any doubt that using 3 funds (wisely chosen) will provide better duration and convexity protection than just using 2 funds. You wouldn't have to own all 3 funds all the time (e.g. starting with LTPZ+FIPDX and transitioning to FIPDX+VTIP would be fine).
HappyJack wrote: Thu Sep 15, 2022 10:03 am Also, for 24-27 year retirement, would a 50% LTPZ, 25% FIPDX, and 25% VTIP allottment with two years stable value or I bonds for the final two years would provide an accurate glide path?
I think that'd be fine, but honestly you could probably do nearly as well by leaving VTIP out altogether and just doing something like 50% LTPZ, 25% FIPDX, and 25% stable value. That'd be a good approximation and use 1/3 fewer funds.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch
Wrench
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Re: A bond duration glide path for retirement investing

Post by Wrench »

How would you adjust the percentages for shorter periods, say for an 85 year old with a 15 year window? Or an 80 year old with a 20 year planning window?

Wrench
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vineviz
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Re: A bond duration glide path for retirement investing

Post by vineviz »

Wrench wrote: Thu Sep 15, 2022 12:51 pm How would you adjust the percentages for shorter periods, say for an 85 year old with a 15 year window? Or an 80 year old with a 20 year planning window?
Good question.

The basic premise is to start the planning period with more of the allocation on the fund that matches your starting duration.

So if a 30 year period (i.e. 15 year duration) dictated a 50/25/25 split between long, intermediate, and short then. 20 year period (10 year duration) might start at 25/50/25 and a 15 year period (7.5 year duration) might start at 0/75/25. And so on.

Again, this is a simplifying approximation and I think avoiding unnecessary complexity while still getting less interest rate risk than you'd get by holding a single bond fund for the entire period has some merit.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch
HappyJack
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Re: A bond duration glide path for retirement investing

Post by HappyJack »

Vineviz,
I have used this formula for a two - fund duration match. What would be the formula for figuring the duration match if you use three funds?

(TD-DS) / (DL-DS) = % of Longest Duration fund
% of the shortest duration fund is: 1- % of the Longest Duration fund.
TD Target Duration of LMP
DL REAL Duration of longest Duration Fund
DS REAL Duration of shortest Duration Fund

Thanks again.
dcabler
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Re: A bond duration glide path for retirement investing

Post by dcabler »

HappyJack wrote: Thu Sep 15, 2022 4:23 pm Vineviz,
I have used this formula for a two - fund duration match. What would be the formula for figuring the duration match if you use three funds?

(TD-DS) / (DL-DS) = % of Longest Duration fund
% of the shortest duration fund is: 1- % of the Longest Duration fund.
TD Target Duration of LMP
DL REAL Duration of longest Duration Fund
DS REAL Duration of shortest Duration Fund

Thanks again.
It's the same formula. But you perform it in two steps.

For example, if you're using LTPZ and SCHP to start with, there will be a point where the amounts of each of those two are nonsensical, meaning it will require LTPZ to have a negative amount. That's because there's no combination of LTPZ and SCHP that can result in a duration that is less than SCHP's duration

At that point, SCHP becomes the longest duration fund and VTIP becomes the shortest duration fund and you continue onwards.

Again, you'll reach a point where one of the two funds (SCHP) requires a negative amount. At that point you can just freeze at VTIP and accept some volatility for the last few years, or swap in Ibonds, T-Bills, Stable value fund, etc...

Cheers.
Last edited by dcabler on Thu Sep 15, 2022 6:27 pm, edited 1 time in total.
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vineviz
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Re: A bond duration glide path for retirement investing

Post by vineviz »

dcabler wrote: Thu Sep 15, 2022 6:04 pm
HappyJack wrote: Thu Sep 15, 2022 4:23 pm Vineviz,
I have used this formula for a two - fund duration match. What would be the formula for figuring the duration match if you use three funds?

(TD-DS) / (DL-DS) = % of Longest Duration fund
% of the shortest duration fund is: 1- % of the Longest Duration fund.
TD Target Duration of LMP
DL REAL Duration of longest Duration Fund
DS REAL Duration of shortest Duration Fund

Thanks again.
It's the same formula. But you perform it in two steps.

For example, if you're using LTPZ and SCHP to start with, there will be a point where the amounts of each of those two are nonsensical, meaning it will require SCHP to have a negative amount. That's because there's no combination of LTPZ and SCHP that can result in a duration that is less than SCHP's duration

At that point, SCHP becomes the longest duration fund and VTIP becomes the shortest duration fund and you continue onwards.

Cheers.
Yep that's right.

If you set it up in Excel or Google Sheets you can use some functions like MAX, MIN, & IF to automate it.

So if we expand the above to include an intermediate-term fund

TD Target Duration of LMP
DL REAL Duration of longest Duration Fund
DM REAL Duration of intermediate Duration Fund
DS REAL Duration of shortest Duration Fund

Then the allocation (call it ALLOCATION1) to the long fund would be:

Code: Select all

=MIN(1,MAX(0,(TD-DM)/(DL-DM)))

Then the allocation (call it ALLOCATION2) to the intermediate fund would be:

Code: Select all

=IF(ALLOCATION1=0,MIN(1,MAX(0,(TD-DS)/(DM-DS))),1-ALLOCATION1)

And the allocation (call it ALLOCATION3) to the short fund would be:

Code: Select all

=1-ALLOCATION1-ALLOCATION2
Here's what it looks like in a spreadsheet.

https://docs.google.com/spreadsheets/d/ ... sp=sharing
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch
dcabler
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Re: A bond duration glide path for retirement investing

Post by dcabler »

vineviz wrote: Thu Sep 15, 2022 6:26 pm
dcabler wrote: Thu Sep 15, 2022 6:04 pm
HappyJack wrote: Thu Sep 15, 2022 4:23 pm Vineviz,
I have used this formula for a two - fund duration match. What would be the formula for figuring the duration match if you use three funds?

(TD-DS) / (DL-DS) = % of Longest Duration fund
% of the shortest duration fund is: 1- % of the Longest Duration fund.
TD Target Duration of LMP
DL REAL Duration of longest Duration Fund
DS REAL Duration of shortest Duration Fund

Thanks again.
It's the same formula. But you perform it in two steps.

For example, if you're using LTPZ and SCHP to start with, there will be a point where the amounts of each of those two are nonsensical, meaning it will require SCHP to have a negative amount. That's because there's no combination of LTPZ and SCHP that can result in a duration that is less than SCHP's duration

At that point, SCHP becomes the longest duration fund and VTIP becomes the shortest duration fund and you continue onwards.

Cheers.
Yep that's right.

If you set it up in Excel or Google Sheets you can use some functions like MAX, MIN, & IF to automate it.

So if we expand the above to include an intermediate-term fund

TD Target Duration of LMP
DL REAL Duration of longest Duration Fund
DM REAL Duration of intermediate Duration Fund
DS REAL Duration of shortest Duration Fund

Then the allocation (call it ALLOCATION1) to the long fund would be:

Code: Select all

=MIN(1,MAX(0,(TD-DM)/(DL-DM)))

Then the allocation (call it ALLOCATION2) to the intermediate fund would be:

Code: Select all

=IF(ALLOCATION1=0,MIN(1,MAX(0,(TD-DS)/(DM-DS))),1-ALLOCATION1)

And the allocation (call it ALLOCATION3) to the short fund would be:

Code: Select all

=1-ALLOCATION1-ALLOCATION2
Here's what it looks like in a spreadsheet.

https://docs.google.com/spreadsheets/d/ ... sp=sharing
Yup!

A couple of minor points if anybody's interested. LTPZ and SCHP report duration based on nominal returns instead of real returns. VTIP reports duration based on real returns. That said, the reported durations are in the rough ballpark anyway whether real or nominal. Again #cruncher's thread I mentioned upstream can come to the rescue if you want more accuracy as he reports both real yields (important if you're using PMT, not important if you're going with 1/N) and he reports real duration.

cheers.
HappyJack
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Re: A bond duration glide path for retirement investing

Post by HappyJack »

Thank you both
dcabler
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Re: A bond duration glide path for retirement investing

Post by dcabler »

vineviz wrote: Thu Sep 15, 2022 2:09 pm
Wrench wrote: Thu Sep 15, 2022 12:51 pm How would you adjust the percentages for shorter periods, say for an 85 year old with a 15 year window? Or an 80 year old with a 20 year planning window?
Good question.

The basic premise is to start the planning period with more of the allocation on the fund that matches your starting duration.

So if a 30 year period (i.e. 15 year duration) dictated a 50/25/25 split between long, intermediate, and short then. 20 year period (10 year duration) might start at 25/50/25 and a 15 year period (7.5 year duration) might start at 0/75/25. And so on.

Again, this is a simplifying approximation and I think avoiding unnecessary complexity while still getting less interest rate risk than you'd get by holding a single bond fund for the entire period has some merit.
Probably just because I haven't had enough coffee yet, but I can't quite figure out the pattern you have above for different splits, especially when you're splitting between 3 funds. Got a formula?

cheers.
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