## Bond fund duration question

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Topic Author
Richard1580
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### Bond fund duration question

Suppose I have \$100K invested in an intermediate bond fund/ETF with a duration of 5 years and the current SEC yield is 2%. All dividends/interest are reinvested in the fund/ETF.

If intermediate interest rates jump 1%, I can expect the value of the fund to drop 5% (change in yield * duration).

Given the 5-year duration and that I am reinvesting all earnings back into the fund, am I correct in assuming that at the end of 5 years, regardless of how much interest rates increase, my investment in the fund should still be worth at least \$100K?

From what I have read, this would seem to be the case since it is accounting for both the increase in the yield and reinvesting the earnings back into the fund at a lower price. I am just trying to determine whether I am interpreting this correctly or whether I am missing something.

Any insight would be greatly appreciated.

averagedude
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### Re: Bond fund duration question

If interest rates shot up 1% gradually over a 5 year period and the SEC yield was 2% at the beginning of the period, I estimated that you would have \$105,700 after 5 years which would give you a 1.10% compound rate of return in nominal dollars. More than likely in this scenario, you would have a negative rate of return, but it would depend upon what the inflation rate was during this 5 year period. I would be interested also what someone else came up with and how they did the math. I did the math by estimating that interest rates increased 0.2% per year, but every year you got a higher yield due to the fund adding new bonds that paid higher yields. Of course you always have to figure that the bond market is always pricing in what they think future rates will be, so there is no way to estimate this with exact accuracy. Please keep in mind, I am probably wrong because i am really only guessing.

305pelusa
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### Re: Bond fund duration question

Richard1580 wrote:
Fri Nov 15, 2019 10:30 pm
Suppose I have \$100K invested in an intermediate bond fund/ETF with a duration of 5 years and the current SEC yield is 2%. All dividends/interest are reinvested in the fund/ETF.

If intermediate interest rates jump 1%, I can expect the value of the fund to drop 5% (change in yield * duration).

Given the 5-year duration and that I am reinvesting all earnings back into the fund, am I correct in assuming that at the end of 5 years, regardless of how much interest rates increase, my investment in the fund should still be worth at least \$100K?
Not necessarily, because the fund continues to maintain a 5 year duration. So say after 4 years, rates then jumped up another 1%, it would drop once again by 5% and that will take another 5 years to make up. In other words, it will have made up that first 5% drop after the 5 years, but will need another 5 years from whichever other drop happens in the meantime.

What you describe only occurs if you bought a 5 year duration bond. The difference is that the bond's duration does decrease as time goes by.

Dude2
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### Re: Bond fund duration question

When the interest rate rises (and the NAV falls), that's when you start the clock on the duration. If there are a series of rises, the calculation gets more complicated, but the concept still works in a general, linear sense. Bond traders account for convexity (non-linearity) too, but a general rule of thumb would be: to break even in a rising interest rate environment, plan to hang on to your bond fund for at least the duration from the last rise.

dbr
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### Re: Bond fund duration question

If you want to be sure that your investment principal be returned to you at any particular future date you don't invest in a bond fund. For those who are invested in a bond fund duration is perhaps better interpreted as a risk factor predicting the variability of annual returns associated with variability in interest rates over time. Since interest rates are always changing there is no "time after the last interest rate change."

In reality interest rates are almost always stable enough and high enough that it would be a rare case that a person would end up after some time actually getting back less money than originally invested if combining principal left and interest reinvested. The concept of duration measuring the time to recovery of initial expectations assumes interest is reinvested.

patrick013
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### Re: Bond fund duration question

dbr wrote:
Sat Nov 16, 2019 10:20 am
If you want to be sure that your investment principal be returned to you at any particular future date you don't invest in a bond fund.

...

In reality interest rates are almost always stable enough and high enough that it would be a rare case that a person would end up after some time actually getting back less money than originally invested if combining principal left and interest reinvested. The concept of duration measurinFor those who are invested in a bond fund duration is perhaps better interpreted as a risk factor predicting the variability of annual returns associated with variability in interest rates over time. Since interest rates are always changing there is no "time after the last interest rate change."g the time to recovery of initial expectations assumes interest is reinvested.

I would use a YTM or a bond price calculator to measure interest rate sensitivity.

I would use target date maturity for liability matching.

So in a nutshell I would rely very little on duration for any useful purpose.

If you have a bond fund that maintains a constant avg maturity you will receive a higher
YTM than today if interest rates rise, and vice-versa if interest rates fall, when
the bond fund investment is held for the fund avg maturity and then sold. Barring excessive
spikes or crashes in the overall market.

Duration - has it's limitations

But don't worry I'm still of the few that think APT might still be viable, at least in some
cases.
age in bonds, buy-and-hold, 10 year business cycle

GrowthSeeker
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### Re: Bond fund duration question

My take, having not read the other responses yet is this:
You start at SEC of 2% and a duration of 5 years. The 1% increase means you're now being paid 3%, but your account value dropped 5% from, say, \$10,000 to \$9,500.
If interest rates stayed at 2%, you'd have about \$11,000 after 5 years
If interest rates jumped on day 1 to 3%, you'd still have about \$11,000 after 5 years.

For each time there is a change in interest rate, the point of indifference for THAT rate change is 5 years later.
(not mathematically precise, just my idea of how it is supposed to work wrt duration)
Just because you're paranoid doesn't mean they're NOT out to get you.

Topic Author
Richard1580
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Joined: Fri Aug 25, 2017 7:53 pm

### Re: Bond fund duration question

Thanks to everyone who responded. This cleared up some of my misconceptions and I think I have a better understanding of how to apply duration.

My biggest concern was how an intermediate bond fund (FXNAX in my case) would respond to interest rate increases. Looking back at the 2003-2006 period when 5 year treasuries rose from 2% to 5% and then looking at how FXNAX fared has eased some of my concerns (FXNAX rose about 4.5% during that period - assuming reinvesting). I am still trying to feel comfortable with bonds and how best to allocate them. More reading to pursue.

Kevin M
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### Re: Bond fund duration question

Richard1580 wrote:
Fri Nov 15, 2019 10:30 pm
Suppose I have \$100K invested in an intermediate bond fund/ETF with a duration of 5 years and the current SEC yield is 2%. All dividends/interest are reinvested in the fund/ETF.

If intermediate interest rates jump 1%, I can expect the value of the fund to drop 5% (change in yield * duration).

Given the 5-year duration and that I am reinvesting all earnings back into the fund, am I correct in assuming that at the end of 5 years, regardless of how much interest rates increase, my investment in the fund should still be worth at least \$100K?

From what I have read, this would seem to be the case since it is accounting for both the increase in the yield and reinvesting the earnings back into the fund at a lower price. I am just trying to determine whether I am interpreting this correctly or whether I am missing something.

Any insight would be greatly appreciated.
Others have provided inputs on various scenarios, but as I read your post literally, you are asking about a one-time increase in "rates" ("interest rates jump 1%"). If we assume a one-time jump of all rates by one percentage point, or any other amount, and no further changes in rates for five years, then the fund will lose about 5% when the rates "shoot up", but will end up earning 2% by the end of the 5-year holding period--so not just your principal, but your principal plus 2% per year growth. This is the "point of indifference" interpretation of duration.

As others have noted, the reality is that interest rates change continually, so this is a purely hypothetical, and completely unrealistic scenario.
Richard1580 wrote:
Sun Nov 17, 2019 4:33 pm
My biggest concern was how an intermediate bond fund (FXNAX in my case) would respond to interest rate increases. Looking back at the 2003-2006 period when 5 year treasuries rose from 2% to 5% and then looking at how FXNAX fared has eased some of my concerns (FXNAX rose about 4.5% during that period - assuming reinvesting). I am still trying to feel comfortable with bonds and how best to allocate them. More reading to pursue.
Some years ago I did some investigation of 5-year and 10-year returns of various bond funds for the history of the funds, including total bond market index and other intermediate-term funds, and found that the annualized return usually was +/-0.5 percentage points of the initial SEC yield, but sometimes +/-1pp or even more. The results are posted in this forum.

So it's reasonable to use the SEC yield as the expected return, perhaps adding a bit for possible roll-down return, but understanding that the expected return is just the average of a range of possible returns. For the periods I examined, the average was actually a bit higher than SEC yield, as one would expect with some rolldown return on average, but note that this also was in a period of generally declining yields.

Kevin
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Topic Author
Richard1580
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### Re: Bond fund duration question

Kevin M wrote:
Sun Nov 17, 2019 4:49 pm
As others have noted, the reality is that interest rates change continually, so this is a purely hypothetical, and completely unrealistic scenario.

Kevin
Exactly, and this was where my confusion arose. A one time change in interest rates is not even remotely realistic. I was trying to determine what would happen over a period of years of rising interest rates - how much impact would that have on an intermediate bond fund. Obviously that depends on much and how quickly interest rates rose, but that was the crux of my dilemma. From what limited research I have done, I am no longer as concerned about gradual (1-2% per annum) increases.

Thanks for your input.

dbr
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### Re: Bond fund duration question

There were some postings by nisiprius in this thread that had charts: viewtopic.php?t=101649

Unfortunately the links to the charts are broken. I know I have seen charts posted by someone who worked out NAV as a function of time for various scenarios of interest rate vs time such as step function increase, constant linear increase etc.

But the bottom line is that damage to investors from increasing interest rates is temporary and actually to the advantage of the investor in the long run for reasonable value of things.

Topic Author
Richard1580
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### Re: Bond fund duration question

dbr wrote:
Sun Nov 17, 2019 5:23 pm
There were some postings by nisiprius in this thread that had charts: viewtopic.php?t=101649

Unfortunately the links to the charts are broken. I know I have seen charts posted by someone who worked out NAV as a function of time for various scenarios of interest rate vs time such as step function increase, constant linear increase etc.

But the bottom line is that damage to investors from increasing interest rates is temporary and actually to the advantage of the investor in the long run for reasonable value of things.
Thanks for the link. Even without the charts, the discussion was interesting. For my purposes, bonds are an emergency reserve chute (or perhaps a second emergency reserve chute). Still trying to get a good grasp on what happens to fixed income in a prolonged period of rising interest rates and when "my but that is disappointing" turns into "WTF!!!!" . Although, the way things are going I should probably be looking into how to handle negative rates.

Kevin M
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### Re: Bond fund duration question

Richard1580 wrote:
Sun Nov 17, 2019 5:46 pm
<snip>
Still trying to get a good grasp on what happens to fixed income in a prolonged period of rising interest rates and when "my but that is disappointing" turns into "WTF!!!!" .<snip>
One problem is that most bond funds have only been in existence during a period of generally declining rates--since the early 1980s. We need to look at something like the early 1950s to the early 1980s to evaluate performance in a generally-increasing interest-rate environment:

If you want to see simulated historical results for prolonged, generally rising rates, you can use the Simba/siamond backtest spreadsheet, and look at simulations for various bond funds from the early 1950s to the early 1980s. It's important to look at the real returns, not just the nominal returns, since inflation during this period had a significant, negative impact on real returns.

Selecting 1954 - 1981 (inclusive), I see these simulated, annualized returns:

Fund, nominal, real

TBM, 3.86%, -0.68%
ITT, 3.55%, -0.98%
LTT, 1.76%, -2.69%
STT, 4.71%, 0.13%

So all but short-term Treasuries had negative (simulated) real returns for this 28-year period.

It might be more instructive to look at the cumulative returns. Looking at the worst, long-term Treasuries, the annualized real return of -2.69% results in a cumulative real return of -53%, so \$10K "grew" to \$4.7K. Ouch! For TBM the cumulative real return was -17%, so \$10K "grew" to \$8.3K.

This is a counterpoint to those who confidently state that you'll lose money by sticking with short-term bonds for a long period of time.

Kevin
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dbr
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### Re: Bond fund duration question

Kevin M wrote:
Sun Nov 17, 2019 8:47 pm

This is a counterpoint to those who confidently state that you'll lose money by sticking with short-term bonds for a long period of time.

Kevin
I was one person that made that comment but it was not that you would lose money. It was that you would not make as much one way as another. The context was that if a prediction of a 1960-1980 scenario does NOT come to pass and instead what comes to pass in the near future is a so-called "normal" yield curve of perhaps 2% for short term and 4%-5% for intermediate term one would not make as much money in short bonds as in intermediate bonds, assuming a two decade time frame. You would give up that 5% yield holding 2% investments waiting for an interest rate increase that never comes. I don't remember my exact words but that was the idea. It is also true that if the future looks like today, then you can invest in anything and you will get 2%. This also assumes inflation is not involved. 1960-1980 was an extreme peak in inflation, in real rates, and in nominal rates.

Of course the real point is that one should not make assumptions about future interest rates, not that we will repeat 1960-1980, not that we will get a 2%-5% yield curve, not that everything will be stuck at 2%. On the other hand 1960-1980 seems to have been extraordinary and a flat yield curve is not typical, so if you are going to throw you hand in with something it would be IT bonds. Or it would be continually shopping for yield in CDs and the like. Or . . . it would be . . .

The comment also has a another context. The context is that of being very worried about one risk one can identify and not considering the cost of defending against that risk if one is wrong. Figuring out a most effective middle of the road in the absence of being able to predict the future is not simple. I certainly don't mind people loading money into 2%-3% CDs and waiting to see what happens. I also don't mind people just buying intermediate bonds and riding them through thick or thin. I don't even mind people buying long bonds to hold with high stock allocations for the long term. And I don't mind people buying very short fixed income and targeting their portfolio for better return by holding a little more in stocks. And I don't mind someone holding only small cap value stocks and more bonds to target the portfolio to the right risk. I would say this latter idea probably has the best theoretical support but is the hardest to commit to in real life. The other idea that has good theoretical support is the high stock/long bonds idea, another idea that is hard to commit to in real life.

Dude2
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### Re: Bond fund duration question

dbr wrote:
Sun Nov 17, 2019 9:04 pm
The context is that of being very worried about one risk one can identify and not considering the cost of defending against that risk if one is wrong. Figuring out a most effective middle of the road in the absence of being able to predict the future is not simple. I certainly don't mind people loading money into 2%-3% CDs and waiting to see what happens. I also don't mind people just buying intermediate bonds and riding them through thick or thin. I don't even mind people buying long bonds to hold with high stock allocations for the long term. And I don't mind people buying very short fixed income and targeting their portfolio for better return by holding a little more in stocks. And I don't mind someone holding only small cap value stocks and more bonds to target the portfolio to the right risk. I would say this latter idea probably has the best theoretical support but is the hardest to commit to in real life. The other idea that has good theoretical support is the high stock/long bonds idea, another idea that is hard to commit to in real life.
Agreed. The market will price the risks accordingly as changes happen going forward, i.e. people will flock from this to that, trying to make a buck. However, it's the timing of the actions that will probably be a losing game for the average investor. That's why we all try to stay diversified, pick a plan, and stick to it. Nothing wrong with taking less risk if you don't need to take it. Particular investments are known to come with less risk and less reward, but, of course, let's be smart about not investing our money in something less risky that is going to be eaten away over time.

Scooter57
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### Re: Bond fund duration question

Where did you get the idea that 2% was normal for short term bonds and 4-5% for intermediate bonds? Those are much lower than the rates through most of the past 50 years.

dbr
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### Re: Bond fund duration question

Scooter57 wrote:
Sun Nov 17, 2019 10:56 pm
Where did you get the idea that 2% was normal for short term bonds and 4-5% for intermediate bonds? Those are much lower than the rates through most of the past 50 years.
The "normal" is in " " to suggest that it is not more normal than anything else. It is just an example of one thing that could be. We could put in numbers for some historical averages or just some higher numbers and it all makes the same points.

JoMoney
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### Re: Bond fund duration question

It is possible that over a 5 year period a bond fund with a duration of 5 years could see a loss if interest rates rise steeply enough at the wrong time (think very low rates with gradual hikes, then a sudden large rate hikes towards the end).
But over the history of the Barclays Aggregate Index (Total Bond), it hasn't had a 5 year rolling period with negative returns.
Mstar Chart

FWIW, I prefer to think of 'duration' as it would compare to a portfolio of laddered bonds. A bond ladder that had a duration of 5 years would be something close to a ladder of bonds ranging from 1 to 10 years out. If you a had a mixture of funds with different durations you could roughly simulate a laddered portfolio by adjusting your portfolio of funds duration to match that of a laddered portfolios duration as it moved closer to each ladders rung maturing.

Here's another chart showing the rolling 5 year returns of a portfolio of Intermediate Term Government Bonds (Ibbotson data). No 5 year period with negative returns since 1925.
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham

Topic Author
Richard1580
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### Re: Bond fund duration question

JoMoney wrote:
Mon Nov 18, 2019 9:24 am
It is possible that over a 5 year period a bond fund with a duration of 5 years could see a loss if interest rates rise steeply enough at the wrong time (think very low rates with gradual hikes, then a sudden large rate hikes towards the end).
But over the history of the Barclays Aggregate Index (Total Bond), it hasn't had a 5 year rolling period with negative returns.
Mstar Chart

Here's another chart showing the rolling 5 year returns of a portfolio of Intermediate Term Government Bonds (Ibbotson data). No 5 year period with negative returns since 1925.
Thanks for the links. That quells most of my worries regarding intermediate bonds.

rich126
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### Re: Bond fund duration question

Kevin M wrote:
Sun Nov 17, 2019 8:47 pm
Richard1580 wrote:
Sun Nov 17, 2019 5:46 pm
<snip>
Still trying to get a good grasp on what happens to fixed income in a prolonged period of rising interest rates and when "my but that is disappointing" turns into "WTF!!!!" .<snip>
One problem is that most bond funds have only been in existence during a period of generally declining rates--since the early 1980s. We need to look at something like the early 1950s to the early 1980s to evaluate performance in a generally-increasing interest-rate environment:

If you want to see simulated historical results for prolonged, generally rising rates, you can use the Simba/siamond backtest spreadsheet, and look at simulations for various bond funds from the early 1950s to the early 1980s. It's important to look at the real returns, not just the nominal returns, since inflation during this period had a significant, negative impact on real returns.

Selecting 1954 - 1981 (inclusive), I see these simulated, annualized returns:

Fund, nominal, real

TBM, 3.86%, -0.68%
ITT, 3.55%, -0.98%
LTT, 1.76%, -2.69%
STT, 4.71%, 0.13%

So all but short-term Treasuries had negative (simulated) real returns for this 28-year period.

It might be more instructive to look at the cumulative returns. Looking at the worst, long-term Treasuries, the annualized real return of -2.69% results in a cumulative real return of -53%, so \$10K "grew" to \$4.7K. Ouch! For TBM the cumulative real return was -17%, so \$10K "grew" to \$8.3K.

This is a counterpoint to those who confidently state that you'll lose money by sticking with short-term bonds for a long period of time.

Kevin
Thank you for your replies, I always find them interesting and useful.

As someone who has generally avoided bonds in investing but nearing retirement I've tried to diversify into bonds but have had some issues with doing so. If I had to bet, I think low rates are here to stay for a while although certain events could change that quickly. And while I believe rates may stay low, I will readily admit there seems to be real risk to the up side since going from 2% to 6% wouldn't be unheard of, and losing money (real returns) would be painful.

People have been "lucky" over the last decade since bond funds have risen in value due to the declining rates but going forward maybe it is safer just to (mostly) tread water with inflation using CDs. Hard to say, but I think many are too optimistic with 50% holdings in bonds. A decade or two of negative real returns won't help many portfolios (50% declines are never good).

Kevin M
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### Re: Bond fund duration question

Richard1580 wrote:
Mon Nov 18, 2019 9:52 am
JoMoney wrote:
Mon Nov 18, 2019 9:24 am
It is possible that over a 5 year period a bond fund with a duration of 5 years could see a loss if interest rates rise steeply enough at the wrong time (think very low rates with gradual hikes, then a sudden large rate hikes towards the end).
But over the history of the Barclays Aggregate Index (Total Bond), it hasn't had a 5 year rolling period with negative returns.
Mstar Chart

Here's another chart showing the rolling 5 year returns of a portfolio of Intermediate Term Government Bonds (Ibbotson data). No 5 year period with negative returns since 1925.
Thanks for the links. That quells most of my worries regarding intermediate bonds.
Why? Do you eat nominal returns or real returns? In other words, do you care more about returns not factoring in or factoring in the impact of inflation on purchasing power? If it's purchasing power that matters to you, then go back and review my post showing negative real returns for intermediate-term bonds for the 28-year period starting in 1954. Both linked charts show nominal returns, not real returns.

Also, I thought you were concerned about a prolonged, rising-rate environment. The period covered by the first chart is one of mostly generally falling rates, so not applicable to this particular concern.

Kevin
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Topic Author
Richard1580
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### Re: Bond fund duration question

Kevin M wrote:
Mon Nov 18, 2019 4:14 pm

Why? Do you eat nominal returns or real returns? In other words, do you care more about returns not factoring in or factoring in the impact of inflation on purchasing power? If it's purchasing power that matters to you, then go back and review my post showing negative real returns for intermediate-term bonds for the 28-year period starting in 1954. Both linked charts show nominal returns, not real returns.

Also, I thought you were concerned about a prolonged, rising-rate environment. The period covered by the first chart is one of mostly generally falling rates, so not applicable to this particular concern.

Kevin
Your points are very valid and punching the numbers into the Simba spreadsheet shows that. Nothing overly surprising - in a period of rising interest rates shorter duration bonds will outperform longer duration ones. The inverse is also true. Real returns are the better measure than nominal as a measure of rate of return. No argument.

There are three things I know with absolute certainty:
- Interest rates will rise and do so for a prolonged period.
- Interest rates will fall and do so for a prolonged period.
- I have absolutely no idea about the timeframes when these events will occur.

Given that my rationale for having money in bonds is to preserve capital (in my case as a hedge against a cataclysmic meltdown in the stock market), I am trying to determine where the "sweet spot" is for parking bond money. I have been tempted to go with TIPS, but the coupons are so abysmally low that I cannot bring myself to go that route. I may be wrong about that, but it is an issue I find difficult to get past.

I used to think that 0% interest rates were a hard floor. Apparently not. In regard to interest rates, we seem to have entered into a new dimension where 2+2 equals ...... fish. At this point, my primary concern regarding my bond investments is, "Don't f*ck up."