Do I understand duration correctly?

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motorcyclesarecool
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Do I understand duration correctly?

Post by motorcyclesarecool » Sat May 19, 2018 8:19 am

Take a bond fund with a duration of 5 in a rising interest rate environment.
Year 1, interest rates increase by 1%. Bond fund should recover in 5 years.
Year 2, interest rates increase by another 1%. Bond fund now requires 9 years to recover.
Year 3, 1% increase, now 13 years to recover.
[edited to add:]
Year 4, 1% increase, now 17 years to recover.
Year 5, 1% increase, now 21 years to recover.

Seems that a duration of 5 could rapidly take more than a decade to recover after a few short years of rising rates. Meaning that I DO NOT want to match my bond duration to my time horizon....

Have I oversimplified or misunderstood?
Understand that choosing an HDHP is very much a "red pill" approach. Most would rather pay higher premiums for a $20 copay per visit. They will think you weird for choosing an HSA.

dbr
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Re: Do I understand duration correctly?

Post by dbr » Sat May 19, 2018 10:11 am

It isn't that simple. As a general mathematical problem the convolution of interest rate increases, changes in NAV and accumulation of interest has to be worked out and the result is not what you quoted. I don't have at hand some of the examples that some posters have put up in the past, but hopefully someone will do that. As an example, I think it is approximately correct that in the case of constantly increasing interest rate the fund with reinvested dividends will be worth what it otherwise would have been worth in about twice the duration. Note that your use of the word "recovered" is ambiguous. The more usual idea is to find the time span to the point of indifference meaning the NAV and the accumulated earnings come out the same whether or not interest rates change.

Personally I think trying to comprehend bonds as components of a long term holding by way of "when do I not lose money" is not useful. Interest rates change all the time and duration is just a way to translate interest rate changes into increments of the return, meaning volatility. Bond return is volatile but much less volatile than stock return so the mixture of the two gets you the portfolio you want. So much for duration.

If you have an investment that is entirely in fixed income and you need to predict that you will can recover exactly a certain amount at a certain time, then you should invest in bonds that mature at that time, or in cash denominated holdings such as CDs. If you really do it right and compute in real, after inflation values, then you can buy TIPS that mature when planned or build an allocation in I bonds. Note a rolling investment in short instruments does not work because you can't predict the available yield at reinvestment.

Random Walker
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Re: Do I understand duration correctly?

Post by Random Walker » Sat May 19, 2018 10:38 am

I know of three useful working definitions for duration:
1. Weighted average time for repayment of all coupons and principal at end
2. Time at which a bond holder is indifferent to a one time change in interest rates because of reinvestment of coupons at new interest rate
3. A measure of price sensitivity to interest rate changes



Dave

dbr
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Re: Do I understand duration correctly?

Post by dbr » Sat May 19, 2018 10:42 am

Random Walker wrote:
Sat May 19, 2018 10:38 am
I know of three useful working definitions for duration:
1. Weighted average time for repayment of all coupons and principal at end
2. Time at which a bond holder is indifferent to a one time change in interest rates because of reinvestment of coupons at new interest rate
3. A measure of price sensitivity to interest rate changes



Dave
Very helpful. Note my post referenced applications of 2. (in a more complex form) and 3.

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arcticpineapplecorp.
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Re: Do I understand duration correctly?

Post by arcticpineapplecorp. » Sat May 19, 2018 10:59 am

read this post about the point of indifference:

viewtopic.php?t=120947

The initial result was:
by Electron » Sun Aug 04, 2013 4:33 pm

The chart shows a bond fund starting out with a yield of 2%. The yield increases by 1% in January 2016, January 2018, and January 2020. Duration of the fund was assumed to be 5.5 years, and the NAV was dropped just slightly under 5.5% following each rate increase.

The lines associated with the three higher interest rates cross the 2% line in July 2021, July 2022, and July 2023. The Point of Indifference does come out very close to 5.5 years after a single rate increase. The combined Point of Indifference for all three rate increases is about 7.5 years.

Image
So it shouldn't take you 13 years to recover as you say from three 1% rate increases, but rather 7.5 years. This is an approximation, not exactly what happens. And you can see after the point of indifference, you get higher returns because of higher interest rate payments. Stay the course.
Last edited by arcticpineapplecorp. on Sat May 19, 2018 11:09 am, edited 1 time in total.
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jeffyscott
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Re: Do I understand duration correctly?

Post by jeffyscott » Sat May 19, 2018 11:03 am

motorcyclesarecool wrote:
Sat May 19, 2018 8:19 am
Take a bond fund with a duration of 5 in a rising interest rate environment. Year 1, interest rates increase by 1%.
Here's my oversimplified way of looking at this:

Let's say it has a yield of 3%, so you lose 5% in NAV, but then are earning 4%. So, $10,000 falls to $9500 and you earn 4% on that, so you end the year at $9880.
Year 2, interest rates increase by another 1%.
I think the duration would fall with the rising interest rate, but let's say it loses another 5% to $9386. You then earn 5% on that and so end the year with $9855.
Year 3, 1% increase
Assume down another 5%, but 6% yield so you end the year with $9924.
Year 4, 1% increase
Continuing these over-simplified calcs, you end this year with $10,088 (you have recovered your principle about 1/2 way through this year so only took ~3.5 years).
Year 5, 1% increase
You end this year with $10,350. Had rates stayed at 3% you would have had $11,593.

After year 6 you would have $11,178 vs. $11,940. Year 7 it's $12,073 vs. $12,298 and for year 8, $13,038 vs. $12,667 and you are now ahead of where you would've been had the interest rate remained unchanged.

I think since I ignored that the duration would become less as yield increases, the break-even point and the point where you come out ahead would happen sooner. So maybe it'd be around 7 years to come out ahead thanks to the rising interest rate?
press on, regardless - John C. Bogle

Random Walker
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Re: Do I understand duration correctly?

Post by Random Walker » Sat May 19, 2018 11:20 am

The maturity of the bond is decreasing over time. After 1 year, the maturity of a 5 year bond is 4 years. Duration is always less than maturity. As maturity shortens and a bigger proportion of the bonds total payout is the final repayment of principal, the duration comes closer to equaling maturity.

Dave

dbr
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Re: Do I understand duration correctly?

Post by dbr » Sat May 19, 2018 11:38 am

Random Walker wrote:
Sat May 19, 2018 11:20 am
The maturity of the bond is decreasing over time. After 1 year, the maturity of a 5 year bond is 4 years. Duration is always less than maturity. As maturity shortens and a bigger proportion of the bonds total payout is the final repayment of principal, the duration comes closer to equaling maturity.

Dave
The OP asked about a bond fund. You are absolutely correct when the question is about a bond.

jalbert
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Re: Do I understand duration correctly?

Post by jalbert » Sat May 19, 2018 1:01 pm

motorcyclesarecool wrote:
Sat May 19, 2018 8:19 am
Take a bond fund with a duration of 5 in a rising interest rate environment.
Year 1, interest rates increase by 1%. Bond fund should recover in 5 years.
Year 2, interest rates increase by another 1%. Bond fund now requires 9 years to recover.
Year 3, 1% increase, now 13 years to recover.
[edited to add:]
Year 4, 1% increase, now 17 years to recover.
Year 5, 1% increase, now 21 years to recover.

Seems that a duration of 5 could rapidly take more than a decade to recover after a few short years of rising rates. Meaning that I DO NOT want to match my bond duration to my time horizon....

Have I oversimplified or misunderstood?
Duration is not a measure of how long it takes for the value to recover. Modified duration is an approximation of how much principal value is lost when rates move.

If you invest in a treasury bond fund with a 5 year duration and yield of 3% on May 31, and rates move up by 1% every June 1 for the next 5 years (or next business day after) then you are earning 4% the first year, 5% the second year etc.

End of year 1 down 1% (5% drop in value offset by 4% yield)

End of year 2, still down 1% from initial investment (5% drop in value offset by 5% yield)

End of year 3 back to matching initial investment (5% drop on top of being down 1% offset by 6% yield)

Subsequent years will see increases in value as yield dominates principal loss.
Last edited by jalbert on Sun May 20, 2018 11:36 pm, edited 2 times in total.
Risk is not a guarantor of return.

onourway
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Re: Do I understand duration correctly?

Post by onourway » Sat May 19, 2018 1:56 pm

I can give you a real-world example from my own portfolio to show that things are not nearly so dire as you predict.

On January 19, 2017 I purchased $99,000 of Vanguard Total Bond Market Admiral (VBTLX) buying 9,299.81 shares at a NAV of 10.65. On that date the Federal Funds Rate was 0.65%. I have reinvested all dividends, but otherwise contributed no additional money to these holdings.

As of today the Federal Funds Rate sits at 1.69%, the NAV of VBTLX is at $10.35, and I now own 9,615.52 shares for a total value of $99,520.63.

In the meantime the yield has increased from 2.41% at purchase to 3.15% today.

So in practice, despite an increase in the FFR of over 1% in just over a year, while holding a fund with an average duration of over 6 years, I am still above water with this purchase and receiving 30% greater yield than at purchase.

The sky has not fallen.

Random Walker
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Re: Do I understand duration correctly?

Post by Random Walker » Sat May 19, 2018 2:03 pm

Dbr,
I ignored the question and just basically said everything I know about bonds instead :-). Thanks for alerting me to that. People and books always make the point that there is zero difference between individual bonds and a collection of them in a bond fund. Nevertheless it still tricks me up a bit. As you point out, with individual bonds you do get principal back at defined date, and it’s nice to match this date to needs.

Dave

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jeffyscott
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Re: Do I understand duration correctly?

Post by jeffyscott » Sat May 19, 2018 2:42 pm

Random Walker wrote:
Sat May 19, 2018 2:03 pm
People and books always make the point that there is zero difference between individual bonds and a collection of them in a bond fund.
I think it's more that there is no difference between a collection of bonds that you hold directly and a collection of the same in a fund. If you own and maintain a rolling bond ladder it's the same as owning a fund.
press on, regardless - John C. Bogle

VaR
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Re: Do I understand duration correctly?

Post by VaR » Sat May 19, 2018 2:42 pm

motorcyclesarecool wrote:
Sat May 19, 2018 8:19 am
Take a bond fund with a duration of 5 in a rising interest rate environment.
Year 1, interest rates increase by 1%. Bond fund should recover in 5 years.
Year 2, interest rates increase by another 1%. Bond fund now requires 9 years to recover.
Year 3, 1% increase, now 13 years to recover.
[edited to add:]
Year 4, 1% increase, now 17 years to recover.
Year 5, 1% increase, now 21 years to recover.

Seems that a duration of 5 could rapidly take more than a decade to recover after a few short years of rising rates. Meaning that I DO NOT want to match my bond duration to my time horizon....

Have I oversimplified or misunderstood?
I think you've misunderstood.

OP, what do you mean by "recover"? There seem to be two possible meanings:
1. Recover = total return of the bond fund is 0%
2. Recover = total return of the bond fund returns to the expected total return as if interest rates had not changed. For simplicity, let's say 3%.

You don't have to answer. Instead, I'll convert your analysis into dollar terms and I think it will have explanatory power:
Today, I invest $100 in a bond fund with a duration of 5 (years) and an SEC yield of 3%.
Tomorrow, interest rates increase in parallel across the yield curve by 1%. My holdings are worth $95. SEC yield of the fund is 4%.
End of year 1: My holdings are worth $99 ($95 + 4% = $98.80)
Year 1 + 1 day, interest rates increase in parallel across the yield curve by 1% again. My holdings are worth $94. SEC yield of the fund is 5%.
End of year 2: My holdings are worth $99 ($93.86 + 5% = $98.55)
Year 2 + 1 day, interest rates increase in parallel across the yield curve by 1% again. My holdings are worth $94. SEC yield of the fund is 6%.
End of year 3: My holdings are worth $100 ($93.62 + 6% = $99.24)
Year 3 + 1 day, etc.

Under the second definition of recovery, you basically have to wait a little more than 5 years from the last 1 percent interest rate move to get to where you thought you would be. @arcticpineapplecorp.'s graph of point of indifference illustrates this.

motorcyclesarecool
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Re: Do I understand duration correctly?

Post by motorcyclesarecool » Sat May 19, 2018 9:04 pm

How would I go about reducing my average duration as my time horizon grows shorter?
Understand that choosing an HDHP is very much a "red pill" approach. Most would rather pay higher premiums for a $20 copay per visit. They will think you weird for choosing an HSA.

venkman
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Re: Do I understand duration correctly?

Post by venkman » Sat May 19, 2018 9:17 pm

motorcyclesarecool wrote:
Sat May 19, 2018 9:04 pm
How would I go about reducing my average duration as my time horizon grows shorter?
Invest in individual bonds or CD's instead of bond funds.

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arcticpineapplecorp.
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Re: Do I understand duration correctly?

Post by arcticpineapplecorp. » Sat May 19, 2018 9:28 pm

motorcyclesarecool wrote:
Sat May 19, 2018 9:04 pm
How would I go about reducing my average duration as my time horizon grows shorter?
Switch to a shorter term bond fund if you so desire. But doing so provides less reward (interest) because you're taking less risk.

The short term bond index fund has an average duration of 2.7 years and SEC yield of 2.70% (source: https://personal.vanguard.com/us/funds/ ... true#tab=0)

The total bond market index fund has an average duration of of 6.1 years and SEC yield of 3.07% (source: https://personal.vanguard.com/us/funds/ ... true#tab=0)

Risk and return. Some say, well if it's return I want I'll go for long term bonds. Don't do that. That's taking on too much risk. You take your risk on the stock side of the portfolio. Bonds are for stability, safety, not growth. The sweet spot for bonds is intermediate term.

There is a risk with short term bonds too. That is, they carry an opportunity cost (of making more). If you move to short term due to fear of rising interest rates, you may lose interest over time if rates don't rise as expected (as this nice article by Rick Ferri explains):

https://www.forbes.com/sites/rickferri/ ... 2e589ff67b
"Invest we must." -- Jack Bogle | “The purpose of investing is not to simply optimise returns and make yourself rich. The purpose is not to die poor.” -- William Bernstein

CedarWaxWing
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Re: Do I understand duration correctly?

Post by CedarWaxWing » Sat May 19, 2018 9:34 pm

If I may ad a convolution to the question:

The illustrations apply as if the bond funds returns are reinvested.

How much longer does it take if the returns are used as income and NOT reinvested into the same bond fund?

Does it ever recover, as bonds all eventually mature, or does the manager's selling old bonds and buying new bonds prevent the "recovery" of the bonds values?

jalbert
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Re: Do I understand duration correctly?

Post by jalbert » Sat May 19, 2018 11:05 pm

CedarWaxWing wrote:
Sat May 19, 2018 9:34 pm
If I may ad a convolution to the question:

The illustrations apply as if the bond funds returns are reinvested.

How much longer does it take if the returns are used as income and NOT reinvested into the same bond fund?

Does it ever recover, as bonds all eventually mature, or does the manager's selling old bonds and buying new bonds prevent the "recovery" of the bonds values.
Rising rates don’t really change income produced as you end up with a lower principal value earning a higher yield. This is true whether you hold the bonds yourself or hold a bond fund.
Risk is not a guarantor of return.

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#Cruncher
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Re: Do I understand duration correctly?

Post by #Cruncher » Sun May 20, 2018 1:34 pm

motorcyclesarecool wrote:
Sat May 19, 2018 8:19 am
Take a bond fund with a duration of 5 in a rising interest rate environment.
Year 1, interest rates increase by 1%. Bond fund should recover in 5 years.
Year 2, interest rates increase by another 1%. Bond fund now requires 9 years to recover.
It takes much less than nine years to "recover" after two 1% point yield increases. I can illustrate this with a hypothetical bond fund consisting of a single zero coupon bond. Initially $10,000 is invested in a zero yielding 3% that matures in six years. At the end of each year it is sold and the proceeds reinvested in a new six year zero. (The fund's duration varies between 5 and 6. [*]) The following chart shows the growth of the fund if yields remain at 3% and five scenarios of rising yields with the number of years until their value will equal or exceed the case where yields were unchanged.

Code: Select all

Year when
 Recover
    6      Yields rise 1% point at end of         first   year  then remain at 4%
    7      Yields rise 1% point at end of each of first 2 years then remain at 5%
    7      Yields rise 1% point at end of each of first 3 years then remain at 6%
    8      Yields rise 1% point at end of each of first 4 years then remain at 7% 
    8      Yields rise 1% point at end of each of first 5 years then remain at 8%
Image

(I assume the yield curve is flat. E.g., yields are the same for a 5-year and 6-year zero coupon bond. Note that the value of each case recovers to the value of the previous case exactly five years after the last rise.) To illustrate the calculations, here are the first seven years for the case of yields rising 1% point the first three years and then remaining at 6%. At that time the value has grown to $12,301, almost identical to the case where the yield remains at 3%: $12,299 = 10000 * 1.03 ^ 7.

Code: Select all

        Market                       Pct    Maturity
Year    Value                        Chg     Value
----   -------                       ---     ------
   0   $10,000                               11,941 = 10000 * 1.03 ^ 6
   1     9,814 = 11941 / 1.04 ^ 5   -1.9%    12,418 =  9814 * 1.04 ^ 6
   2     9,730 = 12418 / 1.05 ^ 5   -0.9%    13,039 =  9730 * 1.05 ^ 6
   3     9,744 = 13039 / 1.06 ^ 5   +0.1%    13,821 =  9744 * 1.06 ^ 6
   4    10,328 = 13821 / 1.06 ^ 5   +6.0%    14,651 = 10328 * 1.06 ^ 6
   5    10,948 = 14651 / 1.06 ^ 5   +6.0%    15,530 = 10948 * 1.06 ^ 6
   6    11,605 = 15530 / 1.06 ^ 5   +6.0%    16,462 = 11605 * 1.06 ^ 6
   7    12,301 = 16462 / 1.06 ^ 5   +6.0%    17,449 = 12301 * 1.06 ^ 6

CedarWaxWing wrote:
Sat May 19, 2018 9:34 pm
How much longer does it take if the returns are used as income and NOT reinvested into the same bond fund?
This has little effect as shown in the following table. Each of the six cases is the same as above except that $300 is withdrawn at the end of each year. As you'd expect the value remains at $10,000 for the case where yields stay at 3%. I've used "[]" to indicate the year where the value for each other case reaches $10,000. This is generally about one year longer than the case above where nothing is withdrawn.

Code: Select all

 Year   No Incr  1 Incr   2 Incr   3 Incr   4 Incr   5 Incr
----    ------   ------   ------   ------   ------   ------
    0   10,000   10,000   10,000   10,000   10,000   10,000 
    1   10,000    9,514    9,514    9,514    9,514    9,514 
    2   10,000    9,595    9,133    9,133    9,133    9,133 
    3   10,000    9,679    9,289    8,845    8,845    8,845 
    4   10,000    9,766    9,454    9,076    8,646    8,646 
    5   10,000    9,856    9,626    9,321    8,951    8,531 
    6   10,000    9,951    9,808    9,580    9,278    8,913 
    7   10,000  [10,049]   9,998    9,855    9,627    9,326 
    8   10,000   10,151  [10,198] [10,146] [10,001]   9,772 
    9   10,000   10,257   10,408   10,455   10,401  [10,254]
   10   10,000   10,367   10,628   10,782   10,829   10,775
* Macaulay duration of a zero-coupon bond equals its maturity. Its Modified duration can be slightly different.

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Re: Do I understand duration correctly?

Post by jalbert » Mon May 21, 2018 2:27 pm

motorcyclesarecool wrote:
Sat May 19, 2018 9:04 pm
How would I go about reducing my average duration as my time horizon grows shorter?
If you are holding bonds to diversify the risk of holding stocks, then your time horizon should factor into deciding the ratio of stocks to bonds. You would not normally try to match the duration of the bond portfolio to your investment horizon.

If you are holding bonds to cover future liabilities, then you would want to match the duration of the bond portfolio to the duration of the liabilities, as well as having enough value in bonds to cover the liabilities.

Assuming you are holding bonds to diversify the risk of holding stock, then you likely want an intermediate-term or shorter-term duration in the range of 2-6 years. I consider about a 5-year duration optimal for this purpose but there is no one right answer.
Risk is not a guarantor of return.

motorcyclesarecool
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Re: Do I understand duration correctly?

Post by motorcyclesarecool » Mon May 21, 2018 7:32 pm

jalbert wrote:
Mon May 21, 2018 2:27 pm
If you are holding bonds to diversify the risk of holding stocks, then your time horizon should factor into deciding the ratio of stocks to bonds. You would not normally try to match the duration of the bond portfolio to your investment horizon.

If you are holding bonds to cover future liabilities, then you would want to match the duration of the bond portfolio to the duration of the liabilities, as well as having enough value in bonds to cover the liabilities.

Assuming you are holding bonds to diversify the risk of holding stock, then you likely want an intermediate-term or shorter-term duration in the range of 2-6 years. I consider about a 5-year duration optimal for this purpose but there is no one right answer.
I didn’t begin this thread with the intention of it devolving into, “Why bonds?” I promise I’m not going there now. My motive for holding bonds is mostly for matching of future liabilities. Perhaps I need to have a sort of “lmp” made up of individual securities with set maturity dates. I wish my kids’ §529s and my TSP allowed me to do that.
Understand that choosing an HDHP is very much a "red pill" approach. Most would rather pay higher premiums for a $20 copay per visit. They will think you weird for choosing an HSA.

motorcyclesarecool
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Re: Do I understand duration correctly?

Post by motorcyclesarecool » Mon May 21, 2018 7:33 pm

jalbert wrote:
Mon May 21, 2018 2:27 pm
If you are holding bonds to diversify the risk of holding stocks, then your time horizon should factor into deciding the ratio of stocks to bonds. You would not normally try to match the duration of the bond portfolio to your investment horizon.

If you are holding bonds to cover future liabilities, then you would want to match the duration of the bond portfolio to the duration of the liabilities, as well as having enough value in bonds to cover the liabilities.

Assuming you are holding bonds to diversify the risk of holding stock, then you likely want an intermediate-term or shorter-term duration in the range of 2-6 years. I consider about a 5-year duration optimal for this purpose but there is no one right answer.
I didn’t begin this thread with the intention of it devolving into, “Why bonds?” I promise I’m not going there now. My motive for holding bonds is mostly for matching of future liabilities. Perhaps I need to have a sort of “lmp” made up of individual securities with set maturity dates. I wish my kids’ §529s and my TSP allowed me to do that.
Understand that choosing an HDHP is very much a "red pill" approach. Most would rather pay higher premiums for a $20 copay per visit. They will think you weird for choosing an HSA.

VaR
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Re: Do I understand duration correctly?

Post by VaR » Mon May 21, 2018 8:14 pm

motorcyclesarecool wrote:
Mon May 21, 2018 7:33 pm
Perhaps I need to have a sort of “lmp” made up of individual securities with set maturity dates. I wish my kids’ §529s and my TSP allowed me to do that.
What do you mean by "lmp"? (Unsolicited advice to the board: What we write here is read by hundreds or even thousands. I try to avoid shorthand)

What TSP fund are you using for fixed income? I want to make sure you know that the G fund has special properties.

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Re: Do I understand duration correctly?

Post by jalbert » Mon May 21, 2018 8:20 pm

When you get into what the duration should be with respect to time horizon, you are implicitly in the “why bonds? territory”.

If you hold an individual bond to maturity, it’s duration shortens continuously over the time you hold it. So if you set up a bond portfolio holding individual bonds matched to liabilities, you do not have to adjust duration. Just be sure they are not callable bonds or callable CDs. And taking credit risk would not be advisable as it would not be sufficiently diversified. CDs, treasuries, and TIPS would be the instruments to consider for that.

If you hold a bond fund, you will have to use combinations of funds of different durations and cash to control duration.
Risk is not a guarantor of return.

motorcyclesarecool
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Re: Do I understand duration correctly?

Post by motorcyclesarecool » Mon May 21, 2018 8:53 pm

VaR wrote:
Mon May 21, 2018 8:14 pm
motorcyclesarecool wrote:
Mon May 21, 2018 7:33 pm
Perhaps I need to have a sort of “lmp” made up of individual securities with set maturity dates. I wish my kids’ §529s and my TSP allowed me to do that.
What do you mean by "lmp"? (Unsolicited advice to the board: What we write here is read by hundreds or even thousands. I try to avoid shorthand)

What TSP fund are you using for fixed income? I want to make sure you know that the G fund has special properties.
1. Sorry for the jargon. Lmp = Liability Matching Portfolio.
2. I wish more bond funds were like the G-fund. I aim to use it as my sole bond fund. Due to its lower risk and return, I can carry a higher stock allocation.
3. Sadly, the G-Fund is not available in any §529 or ESA. I feel the bond fund options with the target date glide paths are too long of a duration, and my §539 plan won’t allow me to rebalance on my schedule.
Understand that choosing an HDHP is very much a "red pill" approach. Most would rather pay higher premiums for a $20 copay per visit. They will think you weird for choosing an HSA.

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Re: Do I understand duration correctly?

Post by Kevin M » Mon May 21, 2018 9:32 pm

dbr wrote:
Sat May 19, 2018 10:11 am
Note a rolling investment in short instruments does not work because you can't predict the available yield at reinvestment.
Although technically this is correct if you really want to match the duration of the bond to the duration of the liability (nominal or real), historically rolling short-term bonds has done a pretty good job of keeping up with inflation. This is because normally short-term nominal yields increase along with inflation, so rolling them over frequently as nominal yields and inflation increased has tended to do OK.

The exceptions have been when the government has capped short-term rates during periods of high inflation, as in the 1940s as I recall. Of course this also was true to a lesser extent while the Fed held short-term rates at about 0% from late 2008 until early 2016; even though inflation has not been high, it has been higher than 0%. Direct CDs with low early withdrawal penalties worked out pretty well over most of that period.

Kevin
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jalbert
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Re: Do I understand duration correctly?

Post by jalbert » Tue May 22, 2018 12:12 am

Kevin M wrote:
Mon May 21, 2018 9:32 pm
dbr wrote:
Sat May 19, 2018 10:11 am
Note a rolling investment in short instruments does not work because you can't predict the available yield at reinvestment.
Although technically this is correct if you really want to match the duration of the bond to the duration of the liability (nominal or real), historically rolling short-term bonds has done a pretty good job of keeping up with inflation. This is because normally short-term nominal yields increase along with inflation, so rolling them over frequently as nominal yields and inflation increased has tended to do OK.
The risk of using a shorter duration is not inflation but disinflation or deflation. If interest rates fall, the present value of the longer duration liabilities will increase more than the value of the shorter duration portfolio will increase.

This is just another way of stating what dbr was stating. If interest rates are lower when the portfolio turns over it will take a larger principal to cover the liability due to less interest earned after reinvestment at the lower rate.
Risk is not a guarantor of return.

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Re: Do I understand duration correctly?

Post by magician » Tue May 22, 2018 2:04 am

Random Walker wrote:
Sat May 19, 2018 10:38 am
I know of three useful working definitions for duration:
1. Weighted average time for repayment of all coupons and principal at end
2. Time at which a bond holder is indifferent to a one time change in interest rates because of reinvestment of coupons at new interest rate
3. A measure of price sensitivity to interest rate changes

Dave
For whatever it's worth, 1 and 2 are Macaulay duration, 3 is modified (or effective) duration.

For fixed-rate bonds without options, Macaulay duration is close to modified duration (and modified duration equals effective duration). For bonds with options (e.g., callable bonds, putable bonds, prepayable bonds (such as mortgage-backeds)) or floating-rate bonds, Macaulay duration is close to modified duration, but modified duration could be very different from effective duration.

For fixed-rate bonds without options, modified duration is a good measure of price sensitivity to changes in yield. For bonds with options, or floating-rate bonds, modified duration is a poor measure of price sensitivity, but effective duration is a good measure.

And then there's convexity . . . .
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Re: Do I understand duration correctly?

Post by Random Walker » Tue May 22, 2018 8:15 am

Magician,
You’re way beyond my league :-) thanks,

Dave

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Re: Do I understand duration correctly?

Post by Kevin M » Tue May 22, 2018 11:31 am

jalbert wrote:
Tue May 22, 2018 12:12 am
Kevin M wrote:
Mon May 21, 2018 9:32 pm
dbr wrote:
Sat May 19, 2018 10:11 am
Note a rolling investment in short instruments does not work because you can't predict the available yield at reinvestment.
Although technically this is correct if you really want to match the duration of the bond to the duration of the liability (nominal or real), historically rolling short-term bonds has done a pretty good job of keeping up with inflation. This is because normally short-term nominal yields increase along with inflation, so rolling them over frequently as nominal yields and inflation increased has tended to do OK.
The risk of using a shorter duration is not inflation but disinflation or deflation. If interest rates fall, the present value of the longer duration liabilities will increase more than the value of the shorter duration portfolio will increase.

This is just another way of stating what dbr was stating. If interest rates are lower when the portfolio turns over it will take a larger principal to cover the liability due to less interest earned after reinvestment at the lower rate.
Again, technically this is correct, and there is no argument that a portfolio of TIPS matched to the duration of your real liabilities is the closest thing to a risk-free investment you can find. However, historically shorter-term nominal Treasuries also provided decent real returns during the last period of major disinflation, staring in 1980, as we can see below. The chart shows year over year percent change in CPI, along with 1-year and 3-year Treasury yields.

Image

Again, the bigger problem was the period toward the right end of the chart, when shorter-term yields were held down by the Fed, while inflation was higher than these shorter-term nominal yields much of the time. Again, this was the period when direct 5-year CDs with yield premiums of 100-150 basis points above Treasuries and low EWPs came to the rescue.

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Re: Do I understand duration correctly?

Post by jalbert » Tue May 22, 2018 2:09 pm

The graph is misleading. 1 and 3 year treasuries may have seen their yields fall at a similar rate, but a rolling portfolio of 1-year treasuries will incorporate the lower yields more aggressively through reinvestment. I think portfolio return is the more important measure, and the correlation with equity returns may matter more to people using the bonds to diversify equity risk.
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Re: Do I understand duration correctly?

Post by Kevin M » Tue May 22, 2018 6:33 pm

The graph may be misleading, but in the opposite way you state. The bond yields represent returns for the subsequent 1 or 3 year periods, while the inflation line is for the previous year. So the real yield of the bond is relative to the CPI change a year later--even better than just eyeballing the gap at a point in time.
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Re: Do I understand duration correctly?

Post by bayview » Tue May 22, 2018 8:14 pm

motorcyclesarecool wrote:
Mon May 21, 2018 8:53 pm
VaR wrote:
Mon May 21, 2018 8:14 pm
motorcyclesarecool wrote:
Mon May 21, 2018 7:33 pm
Perhaps I need to have a sort of “lmp” made up of individual securities with set maturity dates. I wish my kids’ §529s and my TSP allowed me to do that.
What do you mean by "lmp"? (Unsolicited advice to the board: What we write here is read by hundreds or even thousands. I try to avoid shorthand)

What TSP fund are you using for fixed income? I want to make sure you know that the G fund has special properties.
1. Sorry for the jargon. Lmp = Liability Matching Portfolio.
2. I wish more bond funds were like the G-fund. I aim to use it as my sole bond fund. Due to its lower risk and return, I can carry a higher stock allocation.
3. Sadly, the G-Fund is not available in any §529 or ESA. I feel the bond fund options with the target date glide paths are too long of a duration, and my §539 plan won’t allow me to rebalance on my schedule.
Isn’t the G fund considered to have a duration of 0?

Can you move any funds from your other investment vehicles into TSP?
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Re: Do I understand duration correctly?

Post by motorcyclesarecool » Tue May 22, 2018 8:28 pm

bayview wrote:
Tue May 22, 2018 8:14 pm
Isn’t the G fund considered to have a duration of 0?

Can you move any funds from your other investment vehicles into TSP?
By some definitions, I suspect its duration could be an undefined, negative number.

It is possible to transfer some sorts of tax advantaged accounts to the TSP, but ESA, HSA, Roth IRA, and §529 cannot. TSP is a great place to sweep Traditional IRA funds to clear the decks for backdoor Roth.
Understand that choosing an HDHP is very much a "red pill" approach. Most would rather pay higher premiums for a $20 copay per visit. They will think you weird for choosing an HSA.

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