Matching Bond Duration to Retirement Timeline Question

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Dink2018
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Matching Bond Duration to Retirement Timeline Question

Post by Dink2018 »

I agree with the general idea that I can't out predict the market or pick stocks etc.

So I'm all in on the total market funds and approach by Vanguard. But one thing sticks out to me...and that's the fact that I do know when I can start withdrawing from a retirement fund.

Let's say I'm 15 years from withdrawing from a retirement fund, why would I want short term bonds in there (which are IN Total Bond Marked BND), wouldn't it make sense and yield more to have bonds that match the 15 year duration (or use 15 years as the short end of my bond duration given I probably won't die at year one).

Buying bonds makes sense to dampen the volatility of a portfolio and have something to rebalance with, and they used to pay income...

I agree with the general premise that govt bonds are "risk free" in the sense that they'll print the money to make the payback.

I understand some of the basics of how interest rates impact nav but what I don't understand is that if you absolutely KNOW the timeline why would you buy short bonds in a tax sheltered place where you are confident you'll get back the principle and the coupon (I understand this isn't necessarily protection from inflation).

Anyone want to try to help me understand this better, so far the only reason I could come up with was this...

If I'm holding short term bonds and interest rates rise while equities crash I'll do better with rebalancing than if I was holding long term bonds and equities crash.

I found this guys videos really helpful to understand global market equities etc, he's basically advocating an equity position of global market cap etc. but says that the bond portion of a portfolio should be the highest quality govt bonds in your currency that match the duration needed. https://www.youtube.com/watch?v=gM4KEJQ_Z5U
000
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Re: Matching Bond Duration to Retirement Timeline Question

Post by 000 »

Some people here suggest that accumulators should hold long term bond funds and ease into intermediate as retirement approaches, which would imperfectly match the duration.

One could also start buying a ladder now of 15+ year bonds.

Note: this is not a recommendation to invest in bonds.
Last edited by 000 on Fri Aug 14, 2020 8:07 pm, edited 1 time in total.
MathIsMyWayr
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Re: Matching Bond Duration to Retirement Timeline Question

Post by MathIsMyWayr »

000 wrote: Fri Aug 14, 2020 7:57 pm Many people here suggest that accumulators should hold long term bond funds and ease into intermediate as retirement approaches, which would imperfectly match the duration.

One could also start buying a ladder now of 15+ year bonds.

Note: this is not a recommendation to invest in bonds.
Who are "many people here"?
000
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Re: Matching Bond Duration to Retirement Timeline Question

Post by 000 »

MathIsMyWayr wrote: Fri Aug 14, 2020 8:05 pm
000 wrote: Fri Aug 14, 2020 7:57 pm Many people here suggest that accumulators should hold long term bond funds and ease into intermediate as retirement approaches, which would imperfectly match the duration.

One could also start buying a ladder now of 15+ year bonds.

Note: this is not a recommendation to invest in bonds.
Who are "many people here"?
Sorry, meant "some". I will edit the post.
FishTaco
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Re: Matching Bond Duration to Retirement Timeline Question

Post by FishTaco »

I've read before that over longer periods of time, rolling purchases of a 5-year bond will approximate the return on rolling 30-year bond purchases. I'm not sure what my source of this was but a quick google came up with this link:

https://www.pimco.com/handlers/displayd ... d%2BfxA%3D

Disclosure: I didn't read the whole paper just the summary, but it seemed relevant.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by grabiner »

FishTaco wrote: Sat Aug 15, 2020 6:48 am I've read before that over longer periods of time, rolling purchases of a 5-year bond will approximate the return on rolling 30-year bond purchases.
There is a potential reason for this. Normally, you should get a higher expected return on a higher-risk investment, such as a long-term bond with inflation and interest-rate risk. But pension funds and insurance companies have long-term fixed-dollar liabilities; if an insurance company expects to pay $10M to people who die in 2050, it can minimize that risk by buying 30-year bonds which will be worth $10M in 2050. If there are two investments, each higher-risk to a different group of investors, they could well have the same expected return.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by dbr »

Dink2018 wrote: Fri Aug 14, 2020 6:38 pm

Let's say I'm 15 years from withdrawing from a retirement fund,

You mean you are 15 years from making your first withdrawals from your retirement assets. The timing of your withdrawals is continuous withdrawals over a (perhaps) thirty year period of time 15 to 45 years in the future.

I don't actually know what particular duration strategy for that can be constructed that would be meaningfully better than just holding intermediate duration bonds in perhaps a 60/40 stock/bond portfolio. I am not saying there isn't one just that I don't have the qualifications for that job. Note that as of now one half of that time span is further away in years than the longest bonds that are available.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by SantaClaraSurfer »

1. My answer may not be typical.
2. I am not an expert.

We are happy with our approach. Here's what we do:

a) Keep the standard Diversified Bond Index funds in our 401(k)s per our asset allocation. (ie. Vanguard TDF.)
b) For any Bonds / Savings Bonds outside of our tax deferred, make the Bond Duration match our retirement timeframe
c) Include I Bonds / EE Bonds in b) as a "first choice"

Rationale based on my situation (Married, Middle Aged, me 15-17 years from retirement, her 22+ years from retirement):

a) The Bond Index funds' role of stabilizing our 401(k)s is their most important function. Since our current plan is to defer any withdrawals from our 401(k)s until Required Minimum Distributions in 20-30 years, this makes sense. At that point, the Bond Index Funds will make up the larger part of our 401(k)s and their duration will be a great fit for their role in retirement. Since we have TDFs in our 401(k)s, we would have to modify that strategy in order to pick Bond Funds that weighted Long Term Bonds. That just doesn't make sense to me.

b) + c) We do have Long Term Bonds in Taxable with three components:

-In State, Municipal Long term Bond Fund Index. (Tax Free Bonds)
-EE Bond ladder. (Tax Deferred, Local Tax Free)
-I Bonds. (Tax Deferred, Local Tax Free)

The duration of these bonds matches our retirement horizon. The EE Bonds match the beginning of my RMDs and carry us into our late retirement. Building a position in I Bonds protects our overall portfolio from unexpected inflation and also protects our EE and Municipal Bonds along the way. The long term Municipal bonds match our retirement horizon, but give us flexibility with regards to our timeframe and taxation. We can use them along the way prior to RMDs kicking in, or keep them if that makes more sense.

None of this is chasing a return. I just don't see that as the function of any of these bond positions.

This approach allows us to use bonds for the role they are intended for (ballast, rebalancing, conservative intermediate and long term investing), and to match our retirement horizon.

I've been comfortable with this so far. Do I think I will look back in 15-25 years and be glad we did this, even given the current clamor about bonds? Yes.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by vineviz »

Dink2018 wrote: Fri Aug 14, 2020 6:38 pm I understand some of the basics of how interest rates impact nav but what I don't understand is that if you absolutely KNOW the timeline why would you buy short bonds in a tax sheltered place where you are confident you'll get back the principle and the coupon (I understand this isn't necessarily protection from inflation).
The short answer is that you should NOT do this.

The only reason to own bonds with a duration shorter than your investment time horizon is because you want to make a speculative bet on the future changes in bond prices. Market timing, in other words. There's no evidence that anyone can do this profitably, much less the typical individual investor. Furthermore, that bet comes with a higher cost (short-term bonds generally have lower real yields than long-term bonds) and higher risk (you are exposing your future consumption to more interest rate risk and inflation risk with a duration mismatch).

I could only guess about the reasons that so many investors make this unprofitable bet, but there are a number of well-known and prevalent behavioral biases and/or illogical belief that are plausible explanations. These include myopic loss aversion (the tendency to put too much weight on short-term losses despite a long-term goal horizon) and the fallacy of composition (the tendency to incorrectly assign characteristics of part of the portfolio to the whole portfolio).
"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: Matching Bond Duration to Retirement Timeline Question

Post by vineviz »

grabiner wrote: Sat Aug 15, 2020 9:44 am
FishTaco wrote: Sat Aug 15, 2020 6:48 am I've read before that over longer periods of time, rolling purchases of a 5-year bond will approximate the return on rolling 30-year bond purchases.
There is a potential reason for this. Normally, you should get a higher expected return on a higher-risk investment, such as a long-term bond with inflation and interest-rate risk. But pension funds and insurance companies have long-term fixed-dollar liabilities; if an insurance company expects to pay $10M to people who die in 2050, it can minimize that risk by buying 30-year bonds which will be worth $10M in 2050. If there are two investments, each higher-risk to a different group of investors, they could well have the same expected return.
The problem, of course, is that the premise ("rolling purchases of a 5-year bond will approximate the return on rolling 30-year bond purchases") isn't actually correct. The return on 30-year bonds has historically been significantly higher than the return on 5-year bonds (the PIMCO report is looking at duration-neutral strategies that apply leverage via swaps to equalized effective duration exposure).
"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: Matching Bond Duration to Retirement Timeline Question

Post by investor.saver1 »

I've wondered what the appropriate duration of bonds should be for an individual in retirement. I an not an expert!!!! For my portfolio, I've decided to target a blended duration of 5 years in each of the bond categories I hold (investment grade commercial bonds, treasuries, and TIPS). I came to this duration after reading Swedroe's book on bonds. Page 201 talks about taxable bond ladders and suggest a minimum term of 3 years and a maximum term of 5 years. He further says that "historical evidence for taxable bonds is that, on average, investors have not been rewarded for extending maturities beyond five years." I don't see a compelling reason to go longer term especially with the flat yield curves of today.
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Re: Matching Bond Duration to Retirement Timeline Question

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investor.saver1 wrote: Sun Aug 16, 2020 3:24 pmHe further says that "historical evidence for taxable bonds is that, on average, investors have not been rewarded for extending maturities beyond five years." I don't see a compelling reason to go longer term especially with the flat yield curves of today.
Swedroe’s analysis is often incorrect in this arena.

The yield on long-term bonds is almost always significantly higher than the yield on intermediate-term bonds (the yield on Vanguard Long-Term Bond ETF (BLV) is currently 100 bps higher than Vanguard Total Bond Market ETF (BND)), and for long term investors the former creates less interest rate risk than the latter.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by Steve Reading »

investor.saver1 wrote: Sun Aug 16, 2020 3:24 pm I've wondered what the appropriate duration of bonds should be for an individual in retirement. I an not an expert!!!! For my portfolio, I've decided to target a blended duration of 5 years in each of the bond categories I hold (investment grade commercial bonds, treasuries, and TIPS). I came to this duration after reading Swedroe's book on bonds. Page 201 talks about taxable bond ladders and suggest a minimum term of 3 years and a maximum term of 5 years. He further says that "historical evidence for taxable bonds is that, on average, investors have not been rewarded for extending maturities beyond five years." I don't see a compelling reason to go longer term especially with the flat yield curves of today.
No, what Swedroe refers to is that extending maturity increases your reward much slower than it increases duration and risk. So you get the "most bang for your duration buck" by going up to intermediate durations but then the incremental additional return slows down as you keep extending duration.

The piece Swedroe is missing is that the additional duration is actually a good thing for most. Provided you have a long investment horizon, using longer-term bonds is actually a free lunch. Lower investment risk with higher returns.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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Re: Matching Bond Duration to Retirement Timeline Question

Post by investor.saver1 »

Steve Reading wrote: Sun Aug 16, 2020 4:05 pm
investor.saver1 wrote: Sun Aug 16, 2020 3:24 pm I've wondered what the appropriate duration of bonds should be for an individual in retirement. I an not an expert!!!! For my portfolio, I've decided to target a blended duration of 5 years in each of the bond categories I hold (investment grade commercial bonds, treasuries, and TIPS). I came to this duration after reading Swedroe's book on bonds. Page 201 talks about taxable bond ladders and suggest a minimum term of 3 years and a maximum term of 5 years. He further says that "historical evidence for taxable bonds is that, on average, investors have not been rewarded for extending maturities beyond five years." I don't see a compelling reason to go longer term especially with the flat yield curves of today.
No, what Swedroe refers to is that extending maturity increases your reward much slower than it increases duration and risk. So you get the "most bang for your duration buck" by going up to intermediate durations but then the incremental additional return slows down as you keep extending duration.

The piece Swedroe is missing is that the additional duration is actually a good thing for most. Provided you have a long investment horizon, using longer-term bonds is actually a free lunch. Lower investment risk with higher returns.

Swedroe's position is "the longer the maturity, the greater the correlation of the fixed-income assets with equity assets. While you reduce reinvestment risk when you extend maturity, you increase price risk ... and the risk of the overall portfolio." He suggests extending maturities is prudent so long as you achieve "a minimum incremental yield for each additional year of maturity as compensation." His hurdle is "twenty basis points per annum." BLV has a duration of 16.25 years and an SEC of 2.17%. By comparison BND has a duration of 6.45 years and SEC of 1.15%. There's a 10 year difference in duration and only 1% difference in bond yield which isn't enough yield to justify the longer duration. I'm not expert in this. Hoping you can clarify. Ideal duration has been a huge question in my mind. I'm in retirement so maybe that clouds my judgement on this and am risk adverse. A 1% increase in yield is very close to being insignificant IMO.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by Steve Reading »

investor.saver1 wrote: Sun Aug 16, 2020 4:33 pm
Steve Reading wrote: Sun Aug 16, 2020 4:05 pm
investor.saver1 wrote: Sun Aug 16, 2020 3:24 pm I've wondered what the appropriate duration of bonds should be for an individual in retirement. I an not an expert!!!! For my portfolio, I've decided to target a blended duration of 5 years in each of the bond categories I hold (investment grade commercial bonds, treasuries, and TIPS). I came to this duration after reading Swedroe's book on bonds. Page 201 talks about taxable bond ladders and suggest a minimum term of 3 years and a maximum term of 5 years. He further says that "historical evidence for taxable bonds is that, on average, investors have not been rewarded for extending maturities beyond five years." I don't see a compelling reason to go longer term especially with the flat yield curves of today.
No, what Swedroe refers to is that extending maturity increases your reward much slower than it increases duration and risk. So you get the "most bang for your duration buck" by going up to intermediate durations but then the incremental additional return slows down as you keep extending duration.

The piece Swedroe is missing is that the additional duration is actually a good thing for most. Provided you have a long investment horizon, using longer-term bonds is actually a free lunch. Lower investment risk with higher returns.

Swedroe's position is "the longer the maturity, the greater the correlation of the fixed-income assets with equity assets. While you reduce reinvestment risk when you extend maturity, you increase price risk ... and the risk of the overall portfolio." He suggests extending maturities is prudent so long as you achieve "a minimum incremental yield for each additional year of maturity as compensation." His hurdle is "twenty basis points per annum." BLV has a duration of 16.25 years and an SEC of 2.17%. By comparison BND has a duration of 6.45 years and SEC of 1.15%. There's a 10 year difference in duration and only 1% difference in bond yield which isn't enough yield to justify the longer duration. I'm not expert in this. Hoping you can clarify. Ideal duration has been a huge question in my mind. I'm in retirement so maybe that clouds my judgement on this and am risk adverse. A 1% increase in yield is very close to being insignificant IMO.
First of all, I don't think the correlation statement is even true.

Secondly, everything you said is what I said before. The incremental return from extending duration tends to be much lower, as the duration is longer. So Swedroe would see BLV and BND just like you do. "BLV has a much higher duration, and price risk, for minimally better yield comparatively".

And like I said before, the issue is that the additional duration is a good thing for most. Vineviz has explained this to posters countless times so here's when he explained it to me:
viewtopic.php?p=4304007#p4304007

So BLV has two things going for it: It has a higher return and it will be less risky for you to hold, provided it matches your investment horizon (I don't know your age, so hard to say).
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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Re: Matching Bond Duration to Retirement Timeline Question

Post by investor.saver1 »

Steve Reading wrote: Sun Aug 16, 2020 4:45 pm
And like I said before, the issue is that the additional duration is a good thing for most. Vineviz has explained this to posters countless times so here's when he explained it to me:
viewtopic.php?p=4304007#p4304007

So BLV has two things going for it: It has a higher return and it will be less risky for you to hold, provided it matches your investment horizon (I don't know your age, so hard to say).
Thanks Steve Reading for the awesome link to vineviz's explanation of duration and bond investment wisdom. I learned more from your response and vineviz's discussion of duration than I've been able to dig out from any other source. Thank you!!!!!!!

So wife and I are 71 and in relatively good health. Our parents lived into their 90's. We're projecting being active into our mid 80's and perhaps beyond. I'm assuming if you were in our shoes you'd be investing long term. Let's say I'm correct and we have 10-15 more years on earth. Would you then target a blended duration of 10-15 years (a mix of long term and intermediate term) and as time goes by shorten the duration by weighting the intermediate term more heavily? What about TIPs? Are they the same as Commercial investment grade bonds? What about treasuries? Same duration?

Can't thank you enough for your thoughts. Would also greatly appreciate vinevis's thoughts if he/she is on the board?
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Re: Matching Bond Duration to Retirement Timeline Question

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investor.saver1 wrote: Sun Aug 16, 2020 7:15 pm
Steve Reading wrote: Sun Aug 16, 2020 4:45 pm
And like I said before, the issue is that the additional duration is a good thing for most. Vineviz has explained this to posters countless times so here's when he explained it to me:
viewtopic.php?p=4304007#p4304007

So BLV has two things going for it: It has a higher return and it will be less risky for you to hold, provided it matches your investment horizon (I don't know your age, so hard to say).
Thanks Steve Reading for the awesome link to vineviz's explanation of duration and bond investment wisdom. I learned more from your response and vineviz's discussion of duration than I've been able to dig out from any other source. Thank you!!!!!!!

So wife and I are 71 and in relatively good health. Our parents lived into their 90's. We're projecting being active into our mid 80's and perhaps beyond. I'm assuming if you were in our shoes you'd be investing long term. Let's say I'm correct and we have 10-15 more years on earth. Would you then target a blended duration of 10-15 years (a mix of long term and intermediate term) and as time goes by shorten the duration by weighting the intermediate term more heavily? What about TIPs? Are they the same as Commercial investment grade bonds? What about treasuries? Same duration?

Can't thank you enough for your thoughts. Would also greatly appreciate vinevis's thoughts if he/she is on the board?
If you are both 71, then there's a good chance you both (or even just one) will live into the 90s. So that's at least another 19 years of expenses. It would be best for your bond portfolio to target a duration of about half of that (so duration of around 9 years). It doesn't have to be exactly 9 years, but just roughly close counts (i.e. you don't want only 1 year bonds, you don't want only bonds with duration of 30 years either).

I would say in your case to use mostly Intermediate-term bonds. VBTLX/BND is a great choice. As you age, you could consider decreasing the duration but since intermediate bonds do tend to have a good bit yield over short-term bonds, I probably would just stay with VBTLX/BND. Yes, you'll start to take on some price risk on the bonds as you get further into retirement, but it's pretty modest and probably not something I would really worry much about.

If you use TIPs, you'd want to match that duration as well. Whether you use TIPs or not (and the proportion of TIPs vs BND) is a great question and depends on the rest of the portfolio as well as Social Security. Consider posting a portfolio question with more info here:
viewforum.php?f=1

In general, I think TIPs are fantastic and would say a good rule of thumb might be keeping half of your bond portfolio in nominal bonds (perhaps BND or even VTC if you'd like to take some more corporate bond risk), and half in an Intermediate-term TIPs fund (such as SCHP). But again, it's best to make a thread with your specific information above.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by vineviz »

investor.saver1 wrote: Sun Aug 16, 2020 4:33 pm
Swedroe's position is "the longer the maturity, the greater the correlation of the fixed-income assets with equity assets.
Steve Reading already pointed out that this position isn't consistent with the facts.
investor.saver1 wrote: Sun Aug 16, 2020 4:33 pmA 1% increase in yield is very close to being insignificant IMO.
As I'm sure you've already deduced, the good news is that extra yield comes with LOWER risk for investors with long-term investment goals: a win-win.

If it helps, don't think of its as a 1% increase in yield: think of it as nearly a doubling of yield to go from BND to BLV.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by investor.saver1 »

Steve Reading wrote: Sun Aug 16, 2020 8:12 pm

In general, I think TIPs are fantastic and would say a good rule of thumb might be keeping half of your bond portfolio in nominal bonds (perhaps BND or even VTC if you'd like to take some more corporate bond risk), and half in an Intermediate-term TIPs fund (such as SCHP). But again, it's best to make a thread with your specific information above.
Thanks a million Steve Reading for the valuable information. I think I'll work toward a 10 year duration and then shorten the duration as the years fly by. At some point in the future I'll be posting specific portfolio information as you suggest.

Again many many thanks!
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Re: Matching Bond Duration to Retirement Timeline Question

Post by investor.saver1 »

vineviz wrote: Sun Aug 16, 2020 8:28 pm
investor.saver1 wrote: Sun Aug 16, 2020 4:33 pm
Swedroe's position is "the longer the maturity, the greater the correlation of the fixed-income assets with equity assets.
Steve Reading already pointed out that this position isn't consistent with the facts.
investor.saver1 wrote: Sun Aug 16, 2020 4:33 pmA 1% increase in yield is very close to being insignificant IMO.
As I'm sure you've already deduced, the good news is that extra yield comes with LOWER risk for investors with long-term investment goals: a win-win.

If it helps, don't think of its as a 1% increase in yield: think of it as nearly a doubling of yield to go from BND to BLV.
Thank you very much Vineviz for your help! Over the next year, I'll be working toward a longer duration of approximately 10 years to take advantage of the extra yield and lower risk that you and Steve Reading have so clearly described. I am very appreciative. I've been searching for quite some time to find good information on matching bond duration to my portfolio time horizon. I think I'm finally there.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by Northern Flicker »

If you look at the mismatch of nominal bonds with real liabilities, the deviation increases as duration increases. Any theory about matching duration of a bond portfolio to long duration real liabilities that ignores this point is suspect.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by vineviz »

Northern Flicker wrote: Mon Aug 17, 2020 2:25 pm If you look at the mismatch of nominal bonds with real liabilities, the deviation increases as duration increases.
This isn’t the first time you’ve said something like this, but to my knowledge you’ve never offered either a direct proof or a source. I doubt you can produce either one, but if you can now might be a good time.
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Dink2018
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Re: Matching Bond Duration to Retirement Timeline Question

Post by Dink2018 »

vineviz wrote: Sun Aug 16, 2020 2:57 pm
Dink2018 wrote: Fri Aug 14, 2020 6:38 pm I understand some of the basics of how interest rates impact nav but what I don't understand is that if you absolutely KNOW the timeline why would you buy short bonds in a tax sheltered place where you are confident you'll get back the principle and the coupon (I understand this isn't necessarily protection from inflation).
The short answer is that you should NOT do this.

The only reason to own bonds with a duration shorter than your investment time horizon is because you want to make a speculative bet on the future changes in bond prices. Market timing, in other words. There's no evidence that anyone can do this profitably, much less the typical individual investor. Furthermore, that bet comes with a higher cost (short-term bonds generally have lower real yields than long-term bonds) and higher risk (you are exposing your future consumption to more interest rate risk and inflation risk with a duration mismatch).

I could only guess about the reasons that so many investors make this unprofitable bet, but there are a number of well-known and prevalent behavioral biases and/or illogical belief that are plausible explanations. These include myopic loss aversion (the tendency to put too much weight on short-term losses despite a long-term goal horizon) and the fallacy of composition (the tendency to incorrectly assign characteristics of part of the portfolio to the whole portfolio).
I appreciate your response, I'm not trying to be snarky, just learning.

So you are saying it would make sense to hold bonds that are a better match for duration in my retirement accounts than total bond market correct?
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Re: Matching Bond Duration to Retirement Timeline Question

Post by vineviz »

Dink2018 wrote: Mon Aug 17, 2020 3:31 pm So you are saying it would make sense to hold bonds that are a better match for duration in my retirement accounts than total bond market correct?
For sure, if you have access to a bond fund with long enough duration. Few 401k plans include a long term bond fund, but definitely an IRA would make this possible.
"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: Matching Bond Duration to Retirement Timeline Question

Post by Steve Reading »

Dink2018 wrote: Mon Aug 17, 2020 3:31 pm
vineviz wrote: Sun Aug 16, 2020 2:57 pm
Dink2018 wrote: Fri Aug 14, 2020 6:38 pm I understand some of the basics of how interest rates impact nav but what I don't understand is that if you absolutely KNOW the timeline why would you buy short bonds in a tax sheltered place where you are confident you'll get back the principle and the coupon (I understand this isn't necessarily protection from inflation).
The short answer is that you should NOT do this.

The only reason to own bonds with a duration shorter than your investment time horizon is because you want to make a speculative bet on the future changes in bond prices. Market timing, in other words. There's no evidence that anyone can do this profitably, much less the typical individual investor. Furthermore, that bet comes with a higher cost (short-term bonds generally have lower real yields than long-term bonds) and higher risk (you are exposing your future consumption to more interest rate risk and inflation risk with a duration mismatch).

I could only guess about the reasons that so many investors make this unprofitable bet, but there are a number of well-known and prevalent behavioral biases and/or illogical belief that are plausible explanations. These include myopic loss aversion (the tendency to put too much weight on short-term losses despite a long-term goal horizon) and the fallacy of composition (the tendency to incorrectly assign characteristics of part of the portfolio to the whole portfolio).
I appreciate your response, I'm not trying to be snarky, just learning.

So you are saying it would make sense to hold bonds that are a better match for duration in my retirement accounts than total bond market correct?
Yes, but it's really important to understand why that's the case. It's possible that you purchase a long-term bond fund, interest rates rise, say, 5% and your bond fund incurs a 50%+ loss. You might then ask "how the heck was this less risky?! I lost a ton of money!".

The answer is that, yes, your bond position might've lost 50%. But now it has a much higher yield than before (5% higher). So it will grow at a faster pace, recovering those losses. How long will it take to recover the losses? That is answered by the duration. If your bond fund has a 20 year duration, it will take 20 years for that recovery. But that's ok because you DO have a 20+ year horizon (that's why you picked it in the first place).

Just want to make sure that's clear.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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Re: Matching Bond Duration to Retirement Timeline Question

Post by Gufomel »

Northern Flicker wrote: Mon Aug 17, 2020 2:25 pm If you look at the mismatch of nominal bonds with real liabilities, the deviation increases as duration increases. Any theory about matching duration of a bond portfolio to long duration real liabilities that ignores this point is suspect.
Even if that’s true, wouldn’t the deviation increase even further by continuously rolling shorter-term nominal bonds that don’t match the duration of real liabilities?
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Re: Matching Bond Duration to Retirement Timeline Question

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Re: Matching Bond Duration to Retirement Timeline Question

Post by 1789 »

Steve Reading wrote: Mon Aug 17, 2020 3:44 pm
Dink2018 wrote: Mon Aug 17, 2020 3:31 pm
vineviz wrote: Sun Aug 16, 2020 2:57 pm
Dink2018 wrote: Fri Aug 14, 2020 6:38 pm I understand some of the basics of how interest rates impact nav but what I don't understand is that if you absolutely KNOW the timeline why would you buy short bonds in a tax sheltered place where you are confident you'll get back the principle and the coupon (I understand this isn't necessarily protection from inflation).
The short answer is that you should NOT do this.

The only reason to own bonds with a duration shorter than your investment time horizon is because you want to make a speculative bet on the future changes in bond prices. Market timing, in other words. There's no evidence that anyone can do this profitably, much less the typical individual investor. Furthermore, that bet comes with a higher cost (short-term bonds generally have lower real yields than long-term bonds) and higher risk (you are exposing your future consumption to more interest rate risk and inflation risk with a duration mismatch).

I could only guess about the reasons that so many investors make this unprofitable bet, but there are a number of well-known and prevalent behavioral biases and/or illogical belief that are plausible explanations. These include myopic loss aversion (the tendency to put too much weight on short-term losses despite a long-term goal horizon) and the fallacy of composition (the tendency to incorrectly assign characteristics of part of the portfolio to the whole portfolio).
I appreciate your response, I'm not trying to be snarky, just learning.

So you are saying it would make sense to hold bonds that are a better match for duration in my retirement accounts than total bond market correct?
Yes, but it's really important to understand why that's the case. It's possible that you purchase a long-term bond fund, interest rates rise, say, 5% and your bond fund incurs a 50%+ loss. You might then ask "how the heck was this less risky?! I lost a ton of money!".

The answer is that, yes, your bond position might've lost 50%. But now it has a much higher yield than before (5% higher). So it will grow at a faster pace, recovering those losses. How long will it take to recover the losses? That is answered by the duration. If your bond fund has a 20 year duration, it will take 20 years for that recovery. But that's ok because you DO have a 20+ year horizon (that's why you picked it in the first place).

Just want to make sure that's clear.
Steve

If i buy a long term bond fund (say for 100k) that matures in 25 years, and if interest rate goes up by 5% tomorrow isn't the yield locked in already since i purchased it before interest rate rise? So if the interest rate was 2% when i purchase, do i get coupon payments for 2% until the maturity date or i start getting 7% coupon payments after the increased rate until maturity?

I might be missing some basics here if you say latter is correct.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by vineviz »

1789 wrote: Mon Aug 17, 2020 4:08 pm If i buy a long term bond fund (say for 100k) that matures in 25 years, and if interest rate goes up by 5% tomorrow isn't the yield locked in already since i purchased it before interest rate rise? So if the interest rate was 2% when i purchase, do i get coupon payments for 2% until the maturity date or i start getting 7% coupon payments after the increased rate until maturity?
The 2% yield you were expecting when you first bought the bond was calculated assuming that yields won't change. Included in this assumption is the premise that your coupon payments will be reinvested in bonds that ALSO pay 2%.

If yields skyrocket to 5% tomorrow, the price of your bond will immediately fall BUT all your coupon payments will be reinvested at 5% instead of 2%. The higher return on the reinvestment will exactly make up for the initial drop in price at a point in time that corresponds to the duration of the bond.

The duration is less than the maturity (in the case let's say the duration of your 25 year bond is actually 20 years), so the easy way to conceptualize this is to state that for every $100 invested today at 2%, you expect to have 1.02^20 * $100= $148.60 on 8/17/2040.

No matter what happens to bond yields between now and then (up to 5%, down to -3%, whatever), if you reinvest your coupon payments in the same bond at whatever the prevailing yield is then your bond will always be worth $148.60 on that date. The path it takes to get there will depend on what happens in the meantime, but that value on that date is certain.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by Steve Reading »

1789 wrote: Mon Aug 17, 2020 4:08 pm
Steve Reading wrote: Mon Aug 17, 2020 3:44 pm
Dink2018 wrote: Mon Aug 17, 2020 3:31 pm
vineviz wrote: Sun Aug 16, 2020 2:57 pm
Dink2018 wrote: Fri Aug 14, 2020 6:38 pm I understand some of the basics of how interest rates impact nav but what I don't understand is that if you absolutely KNOW the timeline why would you buy short bonds in a tax sheltered place where you are confident you'll get back the principle and the coupon (I understand this isn't necessarily protection from inflation).
The short answer is that you should NOT do this.

The only reason to own bonds with a duration shorter than your investment time horizon is because you want to make a speculative bet on the future changes in bond prices. Market timing, in other words. There's no evidence that anyone can do this profitably, much less the typical individual investor. Furthermore, that bet comes with a higher cost (short-term bonds generally have lower real yields than long-term bonds) and higher risk (you are exposing your future consumption to more interest rate risk and inflation risk with a duration mismatch).

I could only guess about the reasons that so many investors make this unprofitable bet, but there are a number of well-known and prevalent behavioral biases and/or illogical belief that are plausible explanations. These include myopic loss aversion (the tendency to put too much weight on short-term losses despite a long-term goal horizon) and the fallacy of composition (the tendency to incorrectly assign characteristics of part of the portfolio to the whole portfolio).
I appreciate your response, I'm not trying to be snarky, just learning.

So you are saying it would make sense to hold bonds that are a better match for duration in my retirement accounts than total bond market correct?
Yes, but it's really important to understand why that's the case. It's possible that you purchase a long-term bond fund, interest rates rise, say, 5% and your bond fund incurs a 50%+ loss. You might then ask "how the heck was this less risky?! I lost a ton of money!".

The answer is that, yes, your bond position might've lost 50%. But now it has a much higher yield than before (5% higher). So it will grow at a faster pace, recovering those losses. How long will it take to recover the losses? That is answered by the duration. If your bond fund has a 20 year duration, it will take 20 years for that recovery. But that's ok because you DO have a 20+ year horizon (that's why you picked it in the first place).

Just want to make sure that's clear.
Steve

If i buy a long term bond fund (say for 100k) that matures in 25 years, and if interest rate goes up by 5% tomorrow isn't the yield locked in already since i purchased it before interest rate rise? So if the interest rate was 2% when i purchase, do i get coupon payments for 2% until the maturity date or i start getting 7% coupon payments after the increased rate until maturity?

I might be missing some basics here if you say latter is correct.
Ok, using some simple numbers. If you started at 100k and 2% yield and suddenly rates jump up to 7%, then your bond fund will drop to around 28K. It will continue to provide ~2K in dollars of yield a year (like before), but it's coming from an investment worth 28K (so it's around 7% yield).

These 2K will now be reinvested every year in the higher-yielding 7% bonds. So before, you had 100k growing at 2% but now you have 28K growing at 7% compound. How much time must pass for the latter to finally pass the former? Around X years, where X is the duration of the fund.

The above is a little more complicated because there are coupons and there is capital appreciation but it will be roughly correct.
"... so high a present discounted value of wealth, it is only prudent for him to put more into common stocks compared to his present tangible wealth, borrowing if necessary" - Paul Samuelson
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Re: Matching Bond Duration to Retirement Timeline Question

Post by 1789 »

vineviz wrote: Mon Aug 17, 2020 4:26 pm
1789 wrote: Mon Aug 17, 2020 4:08 pm If i buy a long term bond fund (say for 100k) that matures in 25 years, and if interest rate goes up by 5% tomorrow isn't the yield locked in already since i purchased it before interest rate rise? So if the interest rate was 2% when i purchase, do i get coupon payments for 2% until the maturity date or i start getting 7% coupon payments after the increased rate until maturity?
The 2% yield you were expecting when you first bought the bond was calculated assuming that yields won't change. Included in this assumption is the premise that your coupon payments will be reinvested in bonds that ALSO pay 2%.

If yields skyrocket to 5% tomorrow, the price of your bond will immediately fall BUT all your coupon payments will be reinvested at 5% instead of 2%. The higher return on the reinvestment will exactly make up for the initial drop in price at a point in time that corresponds to the duration of the bond.

The duration is less than the maturity (in the case let's say the duration of your 25 year bond is actually 20 years), so the easy way to conceptualize this is to state that for every $100 invested today at 2%, you expect to have 1.02^20 * $100= $148.60 on 8/17/2040.

No matter what happens to bond yields between now and then (up to 5%, down to -3%, whatever), if you reinvest your coupon payments in the same bond at whatever the prevailing yield is then your bond will always be worth $148.60 on that date. The path it takes to get there will depend on what happens in the meantime, but that value on that date is certain.
Vineviz

Thank you. As you can see i find it hard to process what bonds do and so i don't hold them until i completely understand. Your posts about bonds helped me to get a better understanding of whats going on. Thanks for explaining this.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by Northern Flicker »

Gufomel wrote: Mon Aug 17, 2020 3:50 pm
Northern Flicker wrote: Mon Aug 17, 2020 2:25 pm If you look at the mismatch of nominal bonds with real liabilities, the deviation increases as duration increases. Any theory about matching duration of a bond portfolio to long duration real liabilities that ignores this point is suspect.
Even if that’s true, wouldn’t the deviation increase even further by continuously rolling shorter-term nominal bonds that don’t match the duration of real liabilities?
In the 1970's, a rolling portfolio of t-bills had a positive real return. Long-term treasuries got crushed in real terms. I don't know (and nobody participating in this thread knows) whether short or long treasuries better match long duration real liabilities in the average case, but we have empirical evidence that long-duration nominal treasuries are a much worse match of long-duration real liabilities in the bad outcome scenarios.

I think a hypothetical 60-40 portfolio of the S&P500 and long-term treasuries lost about 15% of its spending power from 1967-1981.
Risk is not a guarantor of return.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by 1789 »

Steve Reading wrote: Mon Aug 17, 2020 4:36 pm
1789 wrote: Mon Aug 17, 2020 4:08 pm
Steve Reading wrote: Mon Aug 17, 2020 3:44 pm
Dink2018 wrote: Mon Aug 17, 2020 3:31 pm
vineviz wrote: Sun Aug 16, 2020 2:57 pm

The short answer is that you should NOT do this.

The only reason to own bonds with a duration shorter than your investment time horizon is because you want to make a speculative bet on the future changes in bond prices. Market timing, in other words. There's no evidence that anyone can do this profitably, much less the typical individual investor. Furthermore, that bet comes with a higher cost (short-term bonds generally have lower real yields than long-term bonds) and higher risk (you are exposing your future consumption to more interest rate risk and inflation risk with a duration mismatch).

I could only guess about the reasons that so many investors make this unprofitable bet, but there are a number of well-known and prevalent behavioral biases and/or illogical belief that are plausible explanations. These include myopic loss aversion (the tendency to put too much weight on short-term losses despite a long-term goal horizon) and the fallacy of composition (the tendency to incorrectly assign characteristics of part of the portfolio to the whole portfolio).
I appreciate your response, I'm not trying to be snarky, just learning.

So you are saying it would make sense to hold bonds that are a better match for duration in my retirement accounts than total bond market correct?
Yes, but it's really important to understand why that's the case. It's possible that you purchase a long-term bond fund, interest rates rise, say, 5% and your bond fund incurs a 50%+ loss. You might then ask "how the heck was this less risky?! I lost a ton of money!".

The answer is that, yes, your bond position might've lost 50%. But now it has a much higher yield than before (5% higher). So it will grow at a faster pace, recovering those losses. How long will it take to recover the losses? That is answered by the duration. If your bond fund has a 20 year duration, it will take 20 years for that recovery. But that's ok because you DO have a 20+ year horizon (that's why you picked it in the first place).

Just want to make sure that's clear.
Steve

If i buy a long term bond fund (say for 100k) that matures in 25 years, and if interest rate goes up by 5% tomorrow isn't the yield locked in already since i purchased it before interest rate rise? So if the interest rate was 2% when i purchase, do i get coupon payments for 2% until the maturity date or i start getting 7% coupon payments after the increased rate until maturity?

I might be missing some basics here if you say latter is correct.
Ok, using some simple numbers. If you started at 100k and 2% yield and suddenly rates jump up to 7%, then your bond fund will drop to around 28K. It will continue to provide ~2K in dollars of yield a year (like before), but it's coming from an investment worth 28K (so it's around 7% yield).

These 2K will now be reinvested every year in the higher-yielding 7% bonds. So before, you had 100k growing at 2% but now you have 28K growing at 7% compound. How much time must pass for the latter to finally pass the former? Around X years, where X is the duration of the fund.

The above is a little more complicated because there are coupons and there is capital appreciation but it will be roughly correct.
Steve

Thanks for illustrating this with an example. I am clear now. What is the catch then? I am 36. Let me ask you this way.

Why should I NOT own long term bond funds?
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Re: Matching Bond Duration to Retirement Timeline Question

Post by Steve Reading »

1789 wrote: Mon Aug 17, 2020 4:42 pm
Steve Reading wrote: Mon Aug 17, 2020 4:36 pm
1789 wrote: Mon Aug 17, 2020 4:08 pm
Steve Reading wrote: Mon Aug 17, 2020 3:44 pm
Dink2018 wrote: Mon Aug 17, 2020 3:31 pm

I appreciate your response, I'm not trying to be snarky, just learning.

So you are saying it would make sense to hold bonds that are a better match for duration in my retirement accounts than total bond market correct?
Yes, but it's really important to understand why that's the case. It's possible that you purchase a long-term bond fund, interest rates rise, say, 5% and your bond fund incurs a 50%+ loss. You might then ask "how the heck was this less risky?! I lost a ton of money!".

The answer is that, yes, your bond position might've lost 50%. But now it has a much higher yield than before (5% higher). So it will grow at a faster pace, recovering those losses. How long will it take to recover the losses? That is answered by the duration. If your bond fund has a 20 year duration, it will take 20 years for that recovery. But that's ok because you DO have a 20+ year horizon (that's why you picked it in the first place).

Just want to make sure that's clear.
Steve

If i buy a long term bond fund (say for 100k) that matures in 25 years, and if interest rate goes up by 5% tomorrow isn't the yield locked in already since i purchased it before interest rate rise? So if the interest rate was 2% when i purchase, do i get coupon payments for 2% until the maturity date or i start getting 7% coupon payments after the increased rate until maturity?

I might be missing some basics here if you say latter is correct.
Ok, using some simple numbers. If you started at 100k and 2% yield and suddenly rates jump up to 7%, then your bond fund will drop to around 28K. It will continue to provide ~2K in dollars of yield a year (like before), but it's coming from an investment worth 28K (so it's around 7% yield).

These 2K will now be reinvested every year in the higher-yielding 7% bonds. So before, you had 100k growing at 2% but now you have 28K growing at 7% compound. How much time must pass for the latter to finally pass the former? Around X years, where X is the duration of the fund.

The above is a little more complicated because there are coupons and there is capital appreciation but it will be roughly correct.
Steve

Thanks for illustrating this with an example. I am clear now. What is the catch then? I am 36. Let me ask you this way.

Why should I NOT own long term bond funds?
There's hardly a catch. Every investor needs to invest based on their circumstances. If you needed the money for next year, then you might place it in short-term bonds instead.
That said, as a 36 year old, it's likely you don't need to own much in bonds at all. Your income already acts like a very large fixed-income asset. You stand a better chance of having less risk and higher returns by having all invested in stocks.

I will say some want bonds for the stability component to their portfolio. Long-term bonds can drop, and quite a bit, and can do it along with stocks. Again, if you have the horizon, the bonds aren't problematic. But to the extent losses today are psychologically difficult to bear, then shorten the duration until they are OK with you. This is a normal trade-off between what is optimal and what you can stick to.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by vineviz »

Northern Flicker wrote: Mon Aug 17, 2020 4:41 pm
Gufomel wrote: Mon Aug 17, 2020 3:50 pm
Northern Flicker wrote: Mon Aug 17, 2020 2:25 pm If you look at the mismatch of nominal bonds with real liabilities, the deviation increases as duration increases. Any theory about matching duration of a bond portfolio to long duration real liabilities that ignores this point is suspect.
Even if that’s true, wouldn’t the deviation increase even further by continuously rolling shorter-term nominal bonds that don’t match the duration of real liabilities?
In the 1970's, a rolling portfolio of t-bills had a positive real return. Long-term treasuries got crushed in real terms.
Even making allowances for the subjective and arbitrary use of a word like “crushed”, this is a tremendous exaggeration. And more importantly, one anecdote.

I don't know (and nobody participating in this thread knows) whether short or long treasuries better match long duration real liabilities in the average case, but we have empirical evidence that long-duration nominal treasuries are a much worse match of long-duration real liabilities in the bad outcome scenarios.
Again, if you have this kind of empirical evidence I’d like to see it.

However, it’s easy to compare the base rate of success for a duration-matched strategy vs a rolling short-term strategy. I quickly went back to 1962 and found that a rolling 1-year Treasury strategy produced a negative real return over a 10 year period 33% more often than simply buying a 10 year bond.

Furthermore, this whole argument is a straw man attack to begin with. Unlike the 1960s, today investors can neutralize both interest rate risk AND inflation risk at the same time simply by allocating between duration-matched TIPS and/or nominal bonds depending on their needs.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by Northern Flicker »

Inflation peaked in 1981. If you bought a 10-year treasury 10 years prior to the end of that year on 1/1/1972, the yield was 5.95%. 6% would be a fairly good estimate for the yield on a 10-year zero coupon treasury strip bought at the start of 1972.

If we compound 6% for 10 years, a $100 initial principal turns into $179. When I use an online inflation calculator to see what a $100 basket of goods and services in 1972 would cost in 1981, I get $217.46. The bond had an 18% shortfall in real terms.

The 10-yr zero coupon bond initially has a duration of 10, and it shortens by 1 year every year it is held. Suppose you maintain constant duration by selling the zero coupon bond every year and buying a new 10-year zero coupon every year with no transaction cost. By standard bond arithmetic, the appreciation or depreciation of the bond you sell will approximately buy the new bond at the original face value but at the new rate, so this will not have much impact on return until you need to sell the last bond held in the final year (or at least value/mark it to market). There will be a slight deviation from the change in point on the yield curve by 1 year.

From 1980 to 1981, the 10-year rate went from 10.8% to 12.57%, or about a 177 bp increase. If you maintained a constant 10-year duration, that's another 17.7% hit less the 10.8% interest earned so about a 7% hit.

So 25% is a ballpark estimate of the loss in real terms of a 10-year duration treasury portfolio during the period. Reinvestment of coupon payments at higher rates would improve return but it would take a longer average maturity to maintain the 10-yr duration as well, resulting in a bigger interest rate hit to cover.

A rolling portfolio of 3-month t-bills had a positive real return over the period.

But it is actually incumbent upon the person making the claim that long-term nominal treasuries match long duration real liabilities to provide evidence that long-term nominal bonds provided a real return corresponding to the compound aggregate real yield over the period.
Last edited by Northern Flicker on Tue Aug 18, 2020 12:15 am, edited 2 times in total.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by Northern Flicker »

I wrote: From 1980 to 1981, the 10-year rate went from 10.8% to 12.57%, or about a 177 bp increase. If you maintained a constant 10-year duration, that's another 17.7% hit less the 10.8% interest earned so about a 7% hit.
In fact I accounted for the last year of interest twice since it was part of the original calculated return, so a 25% loss in real terms is probably too optimistic.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by Uncorrelated »

There are some reasons to vary bond duration over time, but they don't equate to duration matching.

if assume a world in which asset returns are i.i.d. and your utility function has certain nice properties, the optimal allocation bond allocation is constant. This has been shown in this paper, page 119.

If your utility function does not have those nice properties, the asset allocation can depend on time. However, matching the bond duration to time horizon cannot be the optimal solution, you would need a solution that responds to changed in net worth.

The above situation ignores human capital. When human capital taken into account, the optimal stock allocation for a young person is larger than for an old person. In general, the optimal bond duration depends on the optimal stock allocation, therefore it can be said that the optimal bond duration is higher for young persons. However, it is critical to understand that the optimal allocation does not depends on the time horizon, it only depends on the amount of remaining human capital. IIRC there are various papers that show that the bond allocation increases as the time horizon increase, but these papers actually show the effect of human capital, not time horizon.

Therefore we can conclude that, if market returns are i.i.d., bond duration is unrelated to time horizon.

We can also make other assumptions. For example, in Strategic asset allocation: Portfolio choice for long-term investors, by Campbell and Vireira, they show that if we assume a mean-reverting market and you have reasons to believe the market is currently in an equilibrium position, the optimal stock and bond allocation increases as the time horizon increases. However, it should be noted that when the mean-reverting market parameters are estimated on the time period 1952-1999, only a very small portion of bonds are chosen. In the time period 1983-1999, long term bonds dominate short term bonds. The conclusions appear to be dependent on the time horizon.

Additionally, it can be observed in chapter 4 that the stock allocation exhibits much stronger mean-reverting behavior than bonds. Therefore, we can argue that investors with long time horizons (that believe in mean-reverting markets) will see a larger impact in expected utility if they optimize their equity allocation instead of their bond allocation. Nothing in this paper suggests that the bond duration necessarily matches the investment horizon, or that the optimal bond duration decreases linearly as the time horizon decreases. It should also be noted that investors who believe in mean-reverting markets will see much higher expected utility if they employ market timing. (side note: I am working on such a system, but it is very difficult to beat a constant allocation out-of-sample. The probability of selecting an asset allocation based on the work of Campbell and Viceira that outperforms a constant allocation appears to be low. Proceed with extreme caution.).


Well then, are there no reasons where you should match the bond duration to investment horizon? If you have an infinitely high risk aversion and only nominal liabilities, then duration matching is the optimal strategy. The correct instrument for mere mortals in this situation is not a bond, but an annuity.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by vineviz »

Northern Flicker wrote: Mon Aug 17, 2020 7:11 pm
The 10-yr zero coupon bond initially has a duration of 10, and it shortens by 1 year every year it is held. Suppose you maintain constant duration by selling the zero coupon bond every year and buying a new 10-year zero coupon every year with no transaction cost.
Why would you do that? The point of duration matching is to match the duration of the liability, not maintain a constant duration.

And, as I keep repeating and you keep ignoring, the whole premise of your argument is dishonest: everyone acknowledges that using a nominal asset to match a real liability neutralizes one risk (interest rate risk) but does nothing to address other risks (e.g. inflation risk).

So, yes, if you pick a period of time like 1972 to 1981 where unexpected inflation was the highest in recent history then you've found an example of inflation risk. Congratulations.

But that doesn't advance the point you made earlier that I asked you to defend, which is that "if you look at the mismatch of nominal bonds with real liabilities, the deviation increases as duration increases". That's a general statement, and I've already illustrated that it's a false statement as such.
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Re: Matching Bond Duration to Retirement Timeline Question

Post by vineviz »

Uncorrelated wrote: Tue Aug 18, 2020 5:53 am if assume a world in which asset returns are i.i.d. and your utility function has certain nice properties, the optimal allocation bond allocation is constant. This has been shown in this paper, page 119.

If your utility function does not have those nice properties, the asset allocation can depend on time. However, matching the bond duration to time horizon cannot be the optimal solution, you would need a solution that responds to changed in net worth.

The above situation ignores human capital. When human capital taken into account, the optimal stock allocation for a young person is larger than for an old person. In general, the optimal bond duration depends on the optimal stock allocation, therefore it can be said that the optimal bond duration is higher for young persons. However, it is critical to understand that the optimal allocation does not depends on the time horizon, it only depends on the amount of remaining human capital. IIRC there are various papers that show that the bond allocation increases as the time horizon increase, but these papers actually show the effect of human capital, not time horizon.

Therefore we can conclude that, if market returns are i.i.d., bond duration is unrelated to time horizon.

In other words, you've assumed a world in which bond duration is unrelated to time horizon then used that assumption to conclude that bond duration is unrelated to time horizon.

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Re: Matching Bond Duration to Retirement Timeline Question

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vineviz wrote: Tue Aug 18, 2020 6:59 am
Uncorrelated wrote: Tue Aug 18, 2020 5:53 am if assume a world in which asset returns are i.i.d. and your utility function has certain nice properties, the optimal allocation bond allocation is constant. This has been shown in this paper, page 119.

If your utility function does not have those nice properties, the asset allocation can depend on time. However, matching the bond duration to time horizon cannot be the optimal solution, you would need a solution that responds to changed in net worth.

The above situation ignores human capital. When human capital taken into account, the optimal stock allocation for a young person is larger than for an old person. In general, the optimal bond duration depends on the optimal stock allocation, therefore it can be said that the optimal bond duration is higher for young persons. However, it is critical to understand that the optimal allocation does not depends on the time horizon, it only depends on the amount of remaining human capital. IIRC there are various papers that show that the bond allocation increases as the time horizon increase, but these papers actually show the effect of human capital, not time horizon.

Therefore we can conclude that, if market returns are i.i.d., bond duration is unrelated to time horizon.

In other words, you've assumed a world in which bond duration is unrelated to time horizon then used that assumption to conclude that bond duration is unrelated to time horizon.

Welcome to the Boglehead Museum of Circular Reasoning.
I did not assume a world where bond duration is unrelated to the time horizon. I assumed a world where market timing is impossible. If you believe in duration matching, then it appears you are a market timer. Most bogleheads appear to believe market timing is impossible, therefore duration matching wouldn't be an appropriate solution for them. Based on the work of Campbell and Viceira, I have also shown that duration matching isn't the optimal solution with other return assumptions such as mean reverting markets.

I'm wondering which set of assumptions mathematical methods you are using that result in the selection of a portfolio that includes duration matching, other than the hypothetical example with an infinite risk aversion.
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Re: Matching Bond Duration to Retirement Timeline Question

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Uncorrelated wrote: Tue Aug 18, 2020 7:17 am I did not assume a world where bond duration is unrelated to the time horizon.
Indeed, you did because you chose a utility function that includes this assumption.
Uncorrelated wrote: Tue Aug 18, 2020 7:17 amI assumed a world where market timing is impossible. If you believe in duration matching, then it appears you are a market timer.
You want to rethink this statement? It is nonsensical using any plausible definition of "market timing" since duration matching is the OPPOSITE or market timing.
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Re: Matching Bond Duration to Retirement Timeline Question

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vineviz wrote: Tue Aug 18, 2020 6:59 am Welcome to the Boglehead Museum of Circular Reasoning.
Haha don't be mean. The problem is that Uncorrelated has worked mostly (or only?) with dynamic stochastic optimizers. That means returns are i.i.d and how you got to a point has no effect on future returns.

So the bond asset is always rebalanced bonds with constant maturity. In fact, his optimizer does that too. I think this hides the strong inter-temporal hedging property of duration-matching (or at least, hides some of the inter-temporal hedging).

I've also said all of this and more before but probably my best explanation is here:
viewtopic.php?p=4978319#p4978319
Uncorrelated wrote: Tue Aug 18, 2020 7:17 am .
@Uncorrelated: It seems like you've brought this point back again. So clearly you have a lot of conviction and claimed repeatedly that your optimizer didn't back up duration-matching. I certainly could be wrong. But let me ask, have you ever ran an optimization with the following properties:

1) Investors have access to bonds with every duration, at any time. Such that the 65 year old can allocate to 30Y bonds, the 66 to 29Y bonds, etc, until the investor dies at 95 years old. You know, actual duration-matching.
2) Further, bond returns show the intertemporal hedging Campbell says. So if 2Y bonds suffer a 10% loss on year X, then you know for certain that 1Y bonds on year X+1 will produce a positive return of 11% (given that the initial 2Y bond return was 0% YTM).

If an optimizer, or any paper you've read, have the above properties and STILL don't show duration-matching as a thing, then I'll eat my words. Certainly I could be wrong, I'm only going off of intuition but I don't have an optimizer that can do the above (maybe some day :happy ).
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Re: Matching Bond Duration to Retirement Timeline Question

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Steve Reading wrote: Tue Aug 18, 2020 8:03 am
So the bond asset is always rebalanced bonds with constant maturity. In fact, his optimizer does that too. I think this hides the strong inter-temporal hedging property of duration-matching (or at least, hides some of the inter-temporal hedging).
I think you're correct that this partly explains that view. However, if you run the optimization under his assumptions and include annuities you get a result that favors annuities over short-term bonds. What is an annuity if not a perfectly duration-matched bond?

Additionally, it is very easy to underestimate the impact that the CRRA assumption has on the implied "optimal" solution. Maximizing expected utility using CRRA will, by definition, dictate a market-based approach. So when Uncorrelated says that under his assumptions investors "will see a larger impact in expected utility if they optimize their equity allocation instead of their bond allocation", my first thought is "yes, and???". 1) that flows from the assumption and 2) it doesn't address the question of which duration of bonds to hold.

There are undoubtedly some investors whose utility function is well-described as expected utility maximizing with CRRA or DRRA. It's definitely not ALL investors, and I think there is good evidence that it's not even most investors.
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Re: Matching Bond Duration to Retirement Timeline Question

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vineviz wrote: Tue Aug 18, 2020 9:20 am

Additionally, it is very easy to underestimate the impact that the CRRA assumption has on the implied "optimal" solution. Maximizing expected utility using CRRA will, by definition, dictate a market-based approach. So when Uncorrelated says that under his assumptions investors "will see a larger impact in expected utility if they optimize their equity allocation instead of their bond allocation", my first thought is "yes, and???". 1) that flows from the assumption and 2) it doesn't address the question of which duration of bonds to hold.
I don’t think I follow. Can you break down what you’re saying a little more? I’m not sure I understand why CRRA dictates a “market-based” approach or what that even means (bonds are also a “market” security).

FWIW, I like the CRRA assumption and think you can basically create any reasonable investor utility with it. You just need to create a piece-wise CRRA utility function. So you can say an investor is infinitely risk averse on the first 30k of consumption, has CRRA for 4 for anything between 30k and maybe 80k of consumption and then is infinitely risk averse on anything above that (for charity perhaps?).

I feel like that utility function matches well with many investors (certainly with me).

So I’m not sure it’s an issue with CRRA per se. You can add enough complexity to the utility function, all with CRRAs, as needed. But maybe I’m not understanding what your exact problem with CRRA is.
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Re: Matching Bond Duration to Retirement Timeline Question

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Steve Reading wrote: Tue Aug 18, 2020 9:41 am
I don’t think I follow. Can you break down what you’re saying a little more? I’m not sure I understand why CRRA dictates a “market-based” approach or what that even means (bonds are also a “market” security).
I cribbed the phrase from William Sharpe, so I'll let him explain:
In each of our prior examples, the optimal investment strategy was one in which income was exactly or almost a function of the total return on the market portfolio. In the previous chapter we called any such approach a market-based strategy, with the definition expanded slightly to require that income be a non-decreasing function of the total return on the market portfolio.

In our setting, to obtain maximum expected utility with any CRRA utility function requires the adoption of a market-based strategy. This may seem due to the fact that we have only two assets – the market portfolio and a risk-free asset. But it is a far more general result. The key ingredient is the necessity that in order to maximize expected utility, income must be a decreasing (or non-increasing) function of price per chance. And in our view of capital market equilibrium, price per chance is a decreasing function of the return on the market portfolio (that is, a portfolio in which all risky assets held in market proportions). It follows that anyone with a CRRA utility function wishing to maximize expected utility should adopt a market-based strategy.
The key is that utility under CRRA is entirely a function of total return (i.e. inter-temporal hedging demand is assumed to be zero).
Steve Reading wrote: Tue Aug 18, 2020 9:41 am FWIW, I like the CRRA assumption and think you can basically create any reasonable investor utility with it. You just need to create a piece-wise CRRA utility function. So you can say an investor is infinitely risk averse on the first 30k of consumption, has CRRA for 4 for anything between 30k and maybe 80k of consumption and then is infinitely risk averse on anything above that (for charity perhaps?).
The Sharpe link above does include a discussion of the kind of utility function you describe (he calls it a "kinked" function instead of a "piecewise" function). Personally, because a CRRA function is naturally continuous I don't prefer the term "piecewise CRRA" but it's descriptive enough that I think most people would clearly understand what you mean.

Image

Most of the academic literature suggests that a DRRA function (declining relative risk aversion) better describes most investors than a CRRA function, probably because it seems that people exhibit habit formation (i.e. once consumers become habituated to a certain level of consumption they experience disutility if that level of consumption is undermined).

This ultimately owes its origins to prospect theory from Kahneman and Tversky, and was solidified under Gul (1991) as "disappointment aversion". The idea is that once investors habituate to a certain expected level of consumption, they are experience a much stronger marginal disutility from small shortfalls relative to that expectation than they experience positive marginal utility from small surpluses.

There's a paper by Khanapure that generalizes both CRRA and DRRA as special cases of a broader function.

Image

The value θ represents the degree of disappointment aversion: if θ is zero, you get CRRA.

This is directly relevant to the question of duration matching, as I'm sure you've already deduced, duration matching is a strategy specifically aimed at reducing the risk of investor disappointment (at least relative to interest rates). Whatever portion of my wealth I choose to assign to a liability-matching strategy is essentially guaranteed to NOT produce less consumption than I expect it to. Therefore I can take a market-based approach (with the easier CRRA utility maximization approach) for the risky remainder of my portfolio (with a correspondingly lower numerical value for the RRA coefficient).
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Re: Matching Bond Duration to Retirement Timeline Question

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vineviz wrote: Tue Aug 18, 2020 7:34 am
Uncorrelated wrote: Tue Aug 18, 2020 7:17 am I did not assume a world where bond duration is unrelated to the time horizon.
Indeed, you did because you chose a utility function that includes this assumption.
Uncorrelated wrote: Tue Aug 18, 2020 7:17 amI assumed a world where market timing is impossible. If you believe in duration matching, then it appears you are a market timer.
You want to rethink this statement? It is nonsensical using any plausible definition of "market timing" since duration matching is the OPPOSITE or market timing.
The utility function isn't the problem here. My statements work for any utility function defined over a fixed time horizon.

Any strategy that is built on the assumption of market conditions that change over time is a market timing model. If you don't want to time the market, start with the assumption of i.i.d..
Steve Reading wrote: Tue Aug 18, 2020 8:03 am
vineviz wrote: Tue Aug 18, 2020 6:59 am Welcome to the Boglehead Museum of Circular Reasoning.
Haha don't be mean. The problem is that Uncorrelated has worked mostly (or only?) with dynamic stochastic optimizers. That means returns are i.i.d and how you got to a point has no effect on future returns.

So the bond asset is always rebalanced bonds with constant maturity. In fact, his optimizer does that too. I think this hides the strong inter-temporal hedging property of duration-matching (or at least, hides some of the inter-temporal hedging).

I've also said all of this and more before but probably my best explanation is here:
viewtopic.php?p=4978319#p4978319
Uncorrelated wrote: Tue Aug 18, 2020 7:17 am .
@Uncorrelated: It seems like you've brought this point back again. So clearly you have a lot of conviction and claimed repeatedly that your optimizer didn't back up duration-matching. I certainly could be wrong. But let me ask, have you ever ran an optimization with the following properties:

1) Investors have access to bonds with every duration, at any time. Such that the 65 year old can allocate to 30Y bonds, the 66 to 29Y bonds, etc, until the investor dies at 95 years old. You know, actual duration-matching.
2) Further, bond returns show the intertemporal hedging Campbell says. So if 2Y bonds suffer a 10% loss on year X, then you know for certain that 1Y bonds on year X+1 will produce a positive return of 11% (given that the initial 2Y bond return was 0% YTM).

If an optimizer, or any paper you've read, have the above properties and STILL don't show duration-matching as a thing, then I'll eat my words. Certainly I could be wrong, I'm only going off of intuition but I don't have an optimizer that can do the above (maybe some day :happy ).
1) That is a reverse lifecycle investing model. If we assume i.i.d. (lifecycle without i.i.d. is not yet solved?), then the optimal allocation must always be mean-variance optimal. It appears obvious that holding bonds to maturity is never optimal.

2) that is not wat Campbell says. Campbell says that if you have a 2Y bond and the short term interest rate decreases, then a 2Y bond will have higher expected return in the future. Whether the bonds are held to maturity isn't relevant for Campbell's argument, and indeed the mathematics in chapter 3 only consider constant maturity bonds.

It can be observed on page 94 on figure 4.2 (top pane, parameters estimated from 1892-1998) that rolled-long term bonds are more risky than bonds held to maturity. But in the bottom pane (1953-1999), he draws exactly the opposite conclusion and rolled T-bills are least risky. How's that for parameter estimation errors...

I'm not saying reducing bond duration as one ages is necessary a bad thing. My criticism is that Campbell never proves that the optimal bond duration is linear with investment horizon (it isn't). Campbell never proves that invest horizon is linear with age (it isn't). Campbell never proves that holding bonds to maturity is optimal. Vineviz never shows that, for investors with varying stock allocations, liability matching is necessary optimal (rather than, for example, a leveraged bond portfolio with the same duration). The liability matching argument requires you to assume those things, but it's far from obvious if and how they are true.
vineviz wrote: Tue Aug 18, 2020 9:20 am I think you're correct that this partly explains that view. However, if you run the optimization under his assumptions and include annuities you get a result that favors annuities over short-term bonds. What is an annuity if not a perfectly duration-matched bond?

Additionally, it is very easy to underestimate the impact that the CRRA assumption has on the implied "optimal" solution. Maximizing expected utility using CRRA will, by definition, dictate a market-based approach. So when Uncorrelated says that under his assumptions investors "will see a larger impact in expected utility if they optimize their equity allocation instead of their bond allocation", my first thought is "yes, and???". 1) that flows from the assumption and 2) it doesn't address the question of which duration of bonds to hold.

There are undoubtedly some investors whose utility function is well-described as expected utility maximizing with CRRA or DRRA. It's definitely not ALL investors, and I think there is good evidence that it's not even most investors.
Annuities are good products because they hedge longevity risk, not because they happen to match the investors time horizon.

Campbell also uses a CRRA. If you disagree with the CRRA assumption, find me a better source than Campbell.

The correct duration of bonds to use is greatly dependent on the composition of the overall portfolio. For example if we have two investors, one with a 30% stock allocation and one with a 50% stock allocation, matching bond duration to investment horizon is optimal for at most one of them.
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Re: Matching Bond Duration to Retirement Timeline Question

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vineviz wrote:Why would you do that? The point of duration matching is to match the duration of the liability, not maintain a constant duration.
That's fine. An 18% shortfall in real terms over 10 years is a significant mismatch, and it would have been worse if a longer duration bond were held.
vineviz wrote: So, yes, if you pick a period of time like 1972 to 1981 where unexpected inflation was the highest in recent history then you've found an example of inflation risk. Congratulations.
But that's the point. You are taking substantial inflation risk by matching a long-term nominal asset with real liabilities. Hopefully that risk won't materialize, and it certainly doesn't appear imminent, but when a risk has actually materialized in the past, it is not a theoretical risk.

If we compare holding long-term treasuries with shorter duration treasuries in a stock/bond portfolio the claim that the longer duration portfolio takes less term risk due to duration matching with liabilities is an incomplete picture because it takes significantly more inflation risk.
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Re: Matching Bond Duration to Retirement Timeline Question

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Uncorrelated wrote: Tue Aug 18, 2020 12:04 pm 1) That is a reverse lifecycle investing model. If we assume i.i.d. (lifecycle without i.i.d. is not yet solved?), then the optimal allocation must always be mean-variance optimal. It appears obvious that holding bonds to maturity is never optimal.
I couldn't agree more. Given i.i.d, the optimal allocation has to be MVO, of course and independent of time horizon. My point is that holding bonds to maturity creates a condition where returns are not i.i.d. Again, if you have a 2Y bond, given the returns on year 1, I know for sure the returns of year 2 (it is NOT i.i.d).

At this point, I'm not even sure what you're arguing against. We know holding bonds to maturity will produce returns that aren't i.i.d (ex: again, if you have a 2Y bond, given the returns on year 1, I know for sure the returns of year 2 (it is NOT i.i.d)). Why do you insist on using methods that do assume i.i.d in order to claim holding bonds to maturity isn't optimal 0_o
Uncorrelated wrote: Tue Aug 18, 2020 12:04 pm 2) that is not wat Campbell says. Campbell says that if you have a 2Y bond and the short term interest rate decreases, then a 2Y bond will have higher expected return in the future. Whether the bonds are held to maturity isn't relevant for Campbell's argument, and indeed the mathematics in chapter 3 only consider constant maturity bonds.
Yeah, I agree and you know I agree 0_o. Ch 3 uses constant maturity. Constant maturity does have some inter-temporal hedging properties towards the beginning. However, towards the end of the lifecycle, this hedge largely goes away. If 10Y bonds suffer a loss but you only have 1 year of life left, the added return the year after isn't as effective as it used to be when you'd enjoy that return for decades.

So I'm the one making the logical step of "well, change the duration every year to maintain that hedge".
Uncorrelated wrote: Tue Aug 18, 2020 12:04 pm It can be observed on page 94 on figure 4.2 (top pane, parameters estimated from 1892-1998) that rolled-long term bonds are more risky than bonds held to maturity. But in the bottom pane (1953-1999), he draws exactly the opposite conclusion and rolled T-bills are least risky. How's that for parameter estimation errors...
OK, NOW we're talking. I'm not sure what it means to "hold a bond to maturity" when the horizon is 100 years but presumably Campbell is synthesizing bond data (creating a 100Y bond) based on interest rates.

In any case, this is the ONLY graph or argument thus far you've presented that really resonates. If vineviz and I are claiming holding a k maturity bond when you have a k year horizon is less risky than rolling T Bills, we should see it here right? So what's going on?

Why is it that Figure 4.2 doesn't show that? That's easy, he says it himself:
"Of the two bond strategies, rolling bonds is riskier at short horizons, but buying and holding is riskier at long horizons since it exposes investors to the persistent variation in inflation that has been characteristic of the postwar period."

Which makes perfect sense to me. Vineviz has been adamant that holding LT nominal bonds to maturity, while duration-matching, is less risky than rolling T-Bills. Northtern Flicker has been claiming the opposite. Personally, I never felt strongly either way. Yes, duration-matching is good, but ST bills should track inflation better. So we see that we have two graphs, one showing the former, one the latter. Depends on the time period of course.

But my point since the beginning is that, duration-matching, given holding to maturity, with inflation-linked bonds, is always the least risky. I don't think Campbell has a graph of that but since the only reason the B&H of LT bonds wasn't less risky than rolled T-Bills was due to the unexpected inflation of the post-war period, I'm willing to bet that had you used bonds that protected you against that inflation, then you would obtain the result I'm telling you. That, given X horizon, it is less risky to hold a 20Y TIP than rolling 3-month T-Bills. Maybe not 20Y nominal bonds, but yes if TIPs.

Would you agree?
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Re: Matching Bond Duration to Retirement Timeline Question

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vineviz wrote: Mon Aug 17, 2020 4:26 pm
1789 wrote: Mon Aug 17, 2020 4:08 pm If i buy a long term bond fund (say for 100k) that matures in 25 years, and if interest rate goes up by 5% tomorrow isn't the yield locked in already since i purchased it before interest rate rise? So if the interest rate was 2% when i purchase, do i get coupon payments for 2% until the maturity date or i start getting 7% coupon payments after the increased rate until maturity?
The 2% yield you were expecting when you first bought the bond was calculated assuming that yields won't change. Included in this assumption is the premise that your coupon payments will be reinvested in bonds that ALSO pay 2%.

If yields skyrocket to 5% tomorrow, the price of your bond will immediately fall BUT all your coupon payments will be reinvested at 5% instead of 2%. The higher return on the reinvestment will exactly make up for the initial drop in price at a point in time that corresponds to the duration of the bond.

The duration is less than the maturity (in the case let's say the duration of your 25 year bond is actually 20 years), so the easy way to conceptualize this is to state that for every $100 invested today at 2%, you expect to have 1.02^20 * $100= $148.60 on 8/17/2040.

No matter what happens to bond yields between now and then (up to 5%, down to -3%, whatever), if you reinvest your coupon payments in the same bond at whatever the prevailing yield is then your bond will always be worth $148.60 on that date. The path it takes to get there will depend on what happens in the meantime, but that value on that date is certain.
This is the first time I’ve started to really understand how I can use LT nominal bonds to match real liabilities without unexpected inflation completely destroying everything. Thank you
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