Which Bond Fund Will Perform Best With Rising Rates?

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Munir
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Which Bond Fund Will Perform Best With Rising Rates?

Post by Munir » Wed Sep 13, 2017 11:46 am

Can an intelligent guess be made which of these four Vanguard intermediate bond funds will perform best in a rising interest rate environment : Total Bond Market Index (VBTLX), Intermediate Investment Grade (VFIDX), Intermediate Bond Index (VBILX), and the Core Bond Fund (VCOBX)? I know that nothing is certain, the past is no predictor of the future, and that credit risk, interest rate risk, and duration are the usual parameters one looks at, but which of these funds will do best (just a guess and not a prediction) if one assumes a gradual rise in rates from where we are now?

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by Jack FFR1846 » Wed Sep 13, 2017 11:52 am

I like to fall back on a quote from Jack Bogle to answer a question like this. "Nobody knows nothin'"
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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by livesoft » Wed Sep 13, 2017 11:56 am

I will predict that they will all perform about the same. The biggest difference will be the price you pay on the day you buy one of them, so pick the one that has dropped the most on the day you decide to buy shares.
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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by saltycaper » Wed Sep 13, 2017 12:15 pm

I guess the fund with the lowest duration and the highest percentage of corporate bonds will outperform the others, at first. Then it will underperform. In conclusion, it does not matter.
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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by midareff » Wed Sep 13, 2017 12:20 pm

No one can tell you what will do best in the future but I suspect the bond fund with the highest SEC % per year of duration will be a better performer in a rising interest rate environment ASSUMING equal measures of risk and credit quality in the fund.

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by billyt » Wed Sep 13, 2017 1:00 pm

All bond investors should pray for rising rates. In the big picture, all bond funds will perform better if rates increase.

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by saltycaper » Wed Sep 13, 2017 1:25 pm

It is important to define the parameters of the word "environment" if planning on responsive changes to an asset allocation. Is the environment in question the same as the current environment in all other ways? If not, how will it differ? In addition to the way(s) you anticipate it will differ, how else will it differ? When will the current environment change to this new environment? At what rate will it change? How long will this new environment persist? (Please describe each of the characteristics of the new environment and how long they will persist individually.) Since the rates and duration of changes will differ, how will you determine when the new environment is sufficiently different from the current environment to be considered the new environment, and how will you determine when the new environment is sufficiently different from itself that you will define a second new environment? Please define the second new environment to ensure the decisions you make to suit the first new environment are not ill-considered. Please define all time parameters and characteristics of the second new environment as you have done for the first new environment to ensure proper planning.
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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by mptfan » Wed Sep 13, 2017 1:36 pm

That depends on what you mean by "perform best." Of those four funds, I think the NAV of the intermediate term investment grade fund would fall the least as interest rates rise because the duration is the shortest. However, that does not mean it will "perform the best" over the long term...coincidentally I would pick the same fund of the four you provided because the average coupon is the highest (primarily because it has the lowest allocation to treasury bonds), and over the long term, rising interest rates are good for bond funds despite the fear mongering that you might otherwise hear.
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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by JBTX » Wed Sep 13, 2017 2:32 pm

Perhaps TIPS?

Also, don't assume interest rates will go back up a lot anytime soon. Look at 1930-1960ish

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by aristotelian » Wed Sep 13, 2017 2:37 pm

billyt wrote:
Wed Sep 13, 2017 1:00 pm
All bond investors should pray for rising rates. In the big picture, all bond funds will perform better if rates increase.
Yes, in the long term and if the interest rate increase is gradual.

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by miles monroe » Wed Sep 13, 2017 2:41 pm

i think the answer is no one knows -- but if i was a betting man -- i'd put my chips on tips.

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by mptfan » Wed Sep 13, 2017 3:40 pm

aristotelian wrote:
Wed Sep 13, 2017 2:37 pm
billyt wrote:
Wed Sep 13, 2017 1:00 pm
All bond investors should pray for rising rates. In the big picture, all bond funds will perform better if rates increase.
Yes, in the long term and if the interest rate increase is gradual.
It's true even if the interest rate increase is not gradual.
I eat risk for breakfast. :)

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by #Cruncher » Wed Sep 13, 2017 3:58 pm

mptfan wrote:
Wed Sep 13, 2017 3:40 pm
aristotelian wrote:
Wed Sep 13, 2017 2:37 pm
billyt wrote:
Wed Sep 13, 2017 1:00 pm
... In the big picture, all bond funds will perform better if rates increase.
Yes, in the long term and if the interest rate increase is gradual.
It's true even if the interest rate increase is not gradual.
The best case is if the increase is quick; the worst case is if it is delayed; and the gradual case is in between. Consider a 10-year zero-coupon bond that is rolled over every year. Assume yields of 10-year (and 9-year) zeroes increase from 2% to 6%.
  • Quick case: increase 4% points first year
  • Gradual case: increase 0.4% point each year for ten years
  • Delayed case: increase 4% points in 10th year.

Code: Select all

       ---- Quick ----   --- Gradual ---   --- Delayed ---
Year   Yield    Value    Yield    Value    Yield    Value
  0     2.0%  1,000.00    2.0%  1,000.00    2.0%  1,000.00
  1     6.0%    721.52    2.4%    984.70    2.0%  1,020.00 [1]
  2     6.0%    764.81    2.8%    973.56    2.0%  1,040.40
  3     6.0%    810.70    3.2%    966.45    2.0%  1,061.21
  4     6.0%    859.34    3.6%    963.24    2.0%  1,082.43
  5     6.0%    910.90    4.0%    963.90    2.0%  1,104.08
  6     6.0%    965.56    4.4%    968.42    2.0%  1,126.16
  7     6.0%  1,023.49    4.8%    976.82    2.0%  1,148.69
  8     6.0%  1,084.90    5.2%    989.21    2.0%  1,171.66
  9     6.0%  1,149.99    5.6%  1,005.70    2.0%  1,195.09
 10     6.0%  1,218.99    6.0%  1,026.49    6.0%    862.28
In the "Quick" case $1,000 grows to $1,219 [2] after ten years. In the "Gradual" case it increases to only $1,026. In the "Delayed" case it shrinks to $862.
  1. Calculated as follows:

    Code: Select all

      721.52 = 1000 * 1.02 ^ 10 / 1.06  ^ 9
      984.70 = 1000 * 1.02 ^ 10 / 1.024 ^ 9
    1,020.00 = 1000 * 1.02 ^ 10 / 1.02  ^ 9
  2. $1,219 is also what $1,000 would grow to if the yield remained at 2%. (1,218.99 = 1000 * 1.02 ^ 10)
Edited 9/16/2017 to use a different example of a "gradual" increase.
Last edited by #Cruncher on Sat Sep 16, 2017 2:37 pm, edited 2 times in total.

lack_ey
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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by lack_ey » Wed Sep 13, 2017 4:44 pm

Of those, Intermediate-Term Investment Grade has a likely edge under those circumstances for reasons given by saltycaper. But it really depends.

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by venkman » Wed Sep 13, 2017 9:17 pm

Well, the last year has been a gradually-rising rate environment, so it might be a good indicator.

1-yr returns as of 8/31/17
VBTLX: 0.33%
VFIDX: 1.61%
VBILX: 0.51%
VCORX: 0.52%

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by #Cruncher » Thu Sep 14, 2017 6:35 am

saltycaper wrote:
Wed Sep 13, 2017 12:15 pm
I guess the fund with the lowest duration and the highest percentage of corporate bonds will outperform the others, at first. Then it will underperform. (underline added)
Yes, after a one time uniform rise in the yield curve, the shortest duration bond (and bond fund) will likely do best at first. But as time passes, longer term ones will do best. The following table illustrates this. It uses the 9/14/2017 yields from the Treasury constant maturity yield curve and assumes a uniform 1% point yield increase after one year.

Code: Select all

         2 YR      3 YR      5 YR      7 YR     10 YR     20 YR     30 YR
Year    1.35%     1.48%     1.78%     2.01%     2.20%     2.53%     2.79%    Best

Code: Select all

  0     1,000     1,000     1,000     1,000     1,000     1,000     1,000  
  1    =1,004=      995       979       962       936       853       776  <- 2 YR
  2    =1,027=    1,020     1,006       991       966       883       806  
  3    =1,051=    1,045     1,034     1,021       997       914       836  
  4    =1,076=    1,071     1,063     1,052     1,029       946       868  
  5    =1,101=    1,098     1,092     1,083     1,062       980       901  
  6    =1,127=    1,125     1,123     1,116     1,096     1,014       935  
  7     1,154     1,153    =1,154=    1,149     1,131     1,050       970  <- 5 YR
  8     1,181     1,181    =1,186=    1,184     1,167     1,087     1,007  
  9     1,209     1,211     1,219    =1,220=    1,205     1,125     1,045  <- 7 YR
 10     1,237     1,241     1,253    =1,256=    1,243     1,165     1,085  
 11     1,266     1,271     1,288    =1,294=    1,283     1,206     1,126  
 12     1,296     1,303     1,323    =1,333=    1,324     1,249     1,169  
 13     1,326     1,335     1,360    =1,373=    1,366     1,293     1,213  
 14     1,357     1,368     1,398    =1,415=    1,410     1,339     1,259  
 15     1,389     1,402     1,437    =1,457=    1,455     1,386     1,307  
 16     1,422     1,437     1,477     1,501    =1,502=    1,435     1,356  <- 10 YR
 17     1,455     1,473     1,518     1,546    =1,550=    1,485     1,408  
 18     1,490     1,509     1,560     1,593    =1,599=    1,538     1,461  
 19     1,525     1,547     1,603     1,641    =1,651=    1,592     1,516  
 20     1,560     1,585     1,648     1,690    =1,703=    1,648     1,574  
 21     1,597     1,624     1,694     1,741    =1,758=    1,706     1,634  
 22     1,635     1,665     1,741     1,793    =1,814=    1,767     1,695  
 23     1,673     1,706     1,789     1,847    =1,872=    1,829     1,760  
 24     1,712     1,748     1,839     1,903    =1,932=    1,894     1,826  
 25     1,753     1,791     1,890     1,960    =1,994=    1,960     1,896  
 26     1,794     1,836     1,943     2,019    =2,058=    2,030     1,967  
 27     1,836     1,881     1,997     2,080    =2,124=    2,101     2,042  
 28     1,879     1,928     2,052     2,143    =2,192=    2,175     2,119  
 29     1,923     1,976     2,109     2,207    =2,262=    2,252     2,200  
 30     1,968     2,025     2,168     2,274    =2,334=    2,332     2,283  
 31     2,015     2,075     2,228     2,342     2,409    =2,414=    2,370  <- 20 YR
 32     2,062     2,127     2,290     2,413     2,486    =2,499=    2,459  
 33     2,110     2,179     2,354     2,485     2,565    =2,587=    2,553  
 34     2,160     2,233     2,419     2,560     2,647    =2,679=    2,649  
 35     2,211     2,289     2,486     2,637     2,732    =2,773=    2,750  
 36     2,263     2,345     2,556     2,716     2,820    =2,871=    2,854  
 37     2,316     2,404     2,627     2,798     2,910    =2,973=    2,962  
 38     2,370     2,463     2,700     2,882     3,003    =3,078=    3,074  
 39     2,426     2,524     2,775     2,969     3,099     3,186    =3,191= <- 30 YR
 40     2,483     2,587     2,852     3,059     3,198     3,299    =3,312=
To simplify calculation I treat each maturity as a zero-coupon bond rolled over every year. Values are calculated the same was as in my previous post. Here are examples for year 1:

Code: Select all

 2YR: 1004 = 1000 * 1.0135 ^  2 / 1.0235 ^  1
30YR:  776 = 1000 * 1.0279 ^ 30 / 1.0379 ^ 29

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by nisiprius » Thu Sep 14, 2017 7:42 am

It depends on exactly how you define "performance," because the general characteristic of what bonds and bond funds do when interest rates rise is a short-term loss (which is what people tend to fixate on), followed by recovery, followed by long-term gains.

Since the yield curve is usually rising, usually longer-term bonds have higher interest rates than short-term bonds, and when rates settle down the return is basically the interest rate (of the bonds in the fund. In a fund, of course, you have to wait for the older, lower-interest-rate bonds to be replaced by newer, higher-interest-rate bonds).

So, the longer the bond fund's duration, when rates rise, the worse the short-term effects will be, but the better the long-term performance will be.

Everything's a compromise and the reason why intermediate-term bond funds like Total Bond are recommended is that short-term bond funds are not "different enough" from bank accounts, while with long-term bond funds you may have to wait much too long for the long-term gains to overcome the short-term losses.

I don't believe there's any magic and I put practically zero credence in claims that any specific flavor of bond fund can be guaranteed to perform much better than another in a "rising rate environment." A rising rate sinks all boats, bond math is bond math.

I think the basic guideline is to decide what the time horizon of your investment is--how long you can plan on holding it without touching it--and choose a bond fund whose duration is roughly comparable to is not any longer than your time horizon. For example, the duration of Total Bond is about 6 years, Vanguard classifies it on a 1-5 rough risk categorization as having "risk level 2," and says
Conservative to moderate funds—Risk level 2
Vanguard funds classified as conservative to moderate are subject to low-to-moderate fluctuations in share prices. In general, such funds may be appropriate for investors with medium-term investment horizons (four to ten years).
So, roughly match the duration to your investment horizon, no matter what you think interest rates will do.

And never forget that in April 2014, Bloomberg asked 67 economists what they thought interest rates would do in the next six months, and 67 out of 67 said they would rise.

And they fell.
Last edited by nisiprius on Fri Sep 15, 2017 5:09 pm, edited 1 time in total.
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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by #Cruncher » Thu Sep 14, 2017 8:41 am

nisiprius wrote:
Thu Sep 14, 2017 7:42 am
(... In a fund, of course, you have to wait for the older, lower-interest-rate bonds to be replaced by newer, higher-interest-rate bonds.)
This is a common misconception. Once yields rise, existing bonds will immediately be yielding the higher rate. It's not necessary to wait for them to be replaced.
nisiprius in same post wrote:So, roughly match the duration to your investment horizon, no matter what you think interest rates will do.
Are you really saying that a 35-year old planning for retirement in 30 years, should buy 30-year bonds (or a fund with an average maturity of 30 years) for the bond portion of his portfolio?

By the way, Nisi, I've sent you two private messages since July and both are still sitting in my Outbox, indicating that you haven't opened them. Is there something wrong with your mailbox?

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by grabiner » Thu Sep 14, 2017 9:22 pm

The issue is that there is not just one interest rate. Your four example funds have about the same duration, so they will all lose 6% if all bond rates rise by 1%. But if corporate bond rates rise more (because of increased default risk), then Total Bond Market Index, which is mostly government bonds, will perform the best, and Intermediate-Term Investment-Grade, which is almost all corporate, will perform the worst. You can see this in a comparison of the 2008 returns of the three funds which existed at the time.
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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by Munir » Fri Sep 15, 2017 12:29 am

grabiner wrote:
Thu Sep 14, 2017 9:22 pm
The issue is that there is not just one interest rate. Your four example funds have about the same duration, so they will all lose 6% if all bond rates rise by 1%. But if corporate bond rates rise more (because of increased default risk), then Total Bond Market Index, which is mostly government bonds, will perform the best, and Intermediate-Term Investment-Grade, which is almost all corporate, will perform the worst. You can see this in a comparison of the 2008 returns of the three funds which existed at the time.
Thank you for all the responses.

The durations of these funds in years are VFIDX (Int. Inv. Grade) 5.5; VCOBX (Core Bond) 6.1; VBTLX (Total Bond Market) 6.1; and VBILX (Int. Bond Index) 6.5.

In 2008, VFIDX had a transient significant drop from which it recovered within a year then surpassed the others. Unless there was panic selling of that fund, or a sale to get cash for portfolio rebalancing purposes, it performed very well during 2008-2009. It has generally outperformed the others over the past 1 year, 3 years, and five years (VCOBX only existed for 1 1/2 years).

Does anyone know what percent of VFIDX's corporate bond holdings ever defaulted- if any?

Nisi: Vanguard considers all four funds to have the same risk potential of 2. M* considers VBILX slightly more risky possibly because of its longer duration and/or increased volatility.

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by TBillT » Fri Sep 15, 2017 10:56 am

Perhaps somebody already mentioned Bank Loan Funds such as Fidelity FFRHX, which I use to balance against rising rates.

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by tom0153 » Fri Sep 15, 2017 1:50 pm

grabiner wrote:
Thu Sep 14, 2017 9:22 pm
The issue is that there is not just one interest rate. Your four example funds have about the same duration, so they will all lose 6% if all bond rates rise by 1%. But if corporate bond rates rise more (because of increased default risk), then Total Bond Market Index, which is mostly government bonds, will perform the best, and Intermediate-Term Investment-Grade, which is almost all corporate, will perform the worst. You can see this in a comparison of the 2008 returns of the three funds which existed at the time.
I follow this thread with interest.

I am wondering, and I'll try to put this in the structure of a question, but if we know that bond yields have been artificially suppressed by actions of the Federal Reserve, either in buying up securities in the past and now set to unwind them, or, in setting bank rates at a low rate and now letting them rise (and particularly, with the speed at which these rates will rise now expected to pick up some velocity), is there any way to mitigate the rise in interest rates to what might be more normal rates over the relatively shorter term?

How far ahead does the market price such expected moves into bond pricing? I know that is something of a silly question based on guessing when and if the Fed is going to do something.

I have been dribbling amounts from a short term fund into an intermediate fund, and I can slow or stop this, or I might even look elsewhere if there was something like a good hedge against these rising rates.

Thanks.
Best, Tom

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by nisiprius » Fri Sep 15, 2017 5:09 pm

#Cruncher wrote:
Thu Sep 14, 2017 8:41 am
nisiprius wrote:
Thu Sep 14, 2017 7:42 am
(... In a fund, of course, you have to wait for the older, lower-interest-rate bonds to be replaced by newer, higher-interest-rate bonds.)
This is a common misconception. Once yields rise, existing bonds will immediately be yielding the higher rate. It's not necessary to wait for them to be replaced.
I might have used the wrong language but I don't think I'm conceptually wrong. If interest rates rise, the actual dollar value of the interest payments being made by the bonds in the fund stays the same. Since the price of the mutual fund has dropped, the yield has increased. But for a person who has already bought shares of the mutual fund, there is no benefit. Now suppose interest rates remain stable. Over time, the bonds in the fund get close to maturity. I still don't have any precise description of what real bond funds really do, but conceptually the bonds mature, pay out their face value, and that payment is then used to buy new bonds which pay out larger interest payments. Therefore, from the point of view of someone who has already bought the bond fund: they paid a certain number of dollars to pay the fund, they are receiving a dollar stream of income, as interest rates rise their income neither increases nor decreases, but over time as the bonds in the fund are replaced by higher-interest bonds their income gradually increases.

Here's an illustration. This is a rolling bond portfolio in which bonds are replaced as they mature. The duration of the portfolio is 2.8 years. The interest rate rises from 1.5% to 2.5% in the fourth year. The low chart shows the interest rate. In the upper chart, the solid line shows the total value of the fund with bond interest being reinvested. The dotted line shows the value of those interest payments. When interest rates rise, the dollar value of the interest payments from the portfolio begin to rise, but continue to rise slowly for six years.
Image
nisiprius in same post wrote:So, roughly match the duration to your investment horizon, no matter what you think interest rates will do.
Are you really saying that a 35-year old planning for retirement in 30 years, should buy 30-year bonds (or a fund with an average maturity of 30 years) for the bond portion of his portfolio?[/quote]Hmmm. I have to think about that. It's not crazy, but it's not sound advice, either. I'm to to strike that out.
By the way, Nisi, I've sent you two private messages since July and both are still sitting in my Outbox, indicating that you haven't opened them. Is there something wrong with your mailbox?
No, just lack of attention. Sorry. You wanted to know some details you thought I might have in brokerage statements from 2009. I'm not sure I have them but I will take a look and get back to you--probably to say I couldn't find them.
Last edited by nisiprius on Fri Sep 15, 2017 7:56 pm, edited 2 times in total.
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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by grabiner » Fri Sep 15, 2017 6:23 pm

#Cruncher wrote:
Thu Sep 14, 2017 8:41 am
nisiprius wrote:
Thu Sep 14, 2017 7:42 am
So, roughly match the duration to your investment horizon, no matter what you think interest rates will do.
Are you really saying that a 35-year old planning for retirement in 30 years, should buy 30-year bonds (or a fund with an average maturity of 30 years) for the bond portion of his portfolio?
No. Your bond duration should not exceed your time horizon, but there are good reasons it might be shorter.

One of the most important reasons is that individual investors are not adequately rewarded for taking the risk of long-term bonds. The main risk of a long-term bond is inflation; a guaranteed $10,000 value in 30 years has unknown purchasing power. Pension funds and insurance companies have known fixed-dollar liabilities, so they do not care about this risk, and thus they buy long-term bonds to match their long-term liabilities.

Long-term TIPS reduce this risk, and there is nothing wrong with an investor who will not need the money in 30 years buying 30-year TIPS. (Many such investors do buy I-Bonds, with the intention of holding them for 30 years, and the extra tax benefit.) The returns are not great, but they are guaranteed.

However, mathematically, if you won't need money for 30 years, you may not need bonds at all; 100% stock should have the best 30-year returns for the risk level. If you aren't 100% stock 30 years from retirement, this is because of your psychological risk tolerance, and you may prefer shorter-term bonds.
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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by lack_ey » Fri Sep 15, 2017 6:28 pm

grabiner wrote:
Fri Sep 15, 2017 6:23 pm
However, mathematically, if you won't need money for 30 years, you may not need bonds at all; 100% stock should have the best 30-year returns for the risk level. If you aren't 100% stock 30 years from retirement, this is because of your psychological risk tolerance, and you may prefer shorter-term bonds.
That's not necessarily true, given that actual retirement dates are in practice unknown and the "optimal" allocation may not be attempting to maximize risk/return. Over 30 years stocks should have better overall characteristics for sure, but that doesn't mean the 5 percentile (as an example) portfolio outcome with 100% stocks is better than any other portfolio allocation. Additionally, given the risk budget of 100% stocks, some kind of tilted (riskier, or at least higher returning on average) equity allocation paired with some amount of bonds may have better returns overall.

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nisiprius
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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by nisiprius » Fri Sep 15, 2017 7:02 pm

Whoops, I said "here's an illustration" and forgot to put it in. Apparently nobody has noticed so I guess it wasn't important. Anyway, it's now in there, in this post.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

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Re: Which Bond Fund Will Perform Best With Rising Rates?

Post by motorcyclesarecool » Fri Sep 15, 2017 7:24 pm

TSP "G" Fund. Available to the public through Treasury MyRA
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: Which Bond Fund Will Perform Best With Rising Rates?

Post by #Cruncher » Fri Sep 15, 2017 8:27 pm

nisiprius wrote:
Fri Sep 15, 2017 5:09 pm
... from the point of view of someone who has already bought the bond fund ... as interest rates rise their income neither increases nor decreases, but over time as the bonds in the fund are replaced by higher-interest bonds their income gradually increases.
If we grant that "income" is more than just the coupon interest [1], I maintain that it does increase whether or not the fund replaces the old low coupon bonds with new higher coupon bonds. To illustrate assume a fund
  • Buys a $1,000 bond at par that matures in five years and pays 2% interest at the end of each year.
  • Immediately yields rise 1% point to 3% causing the value of the bond to fall.
  • Case A: The fund holds on to the 2% coupon bond.
  • Case B: Immediately after the rate increase, the fund sells the 2% coupon bond and uses the proceeds to buy a new 3% coupon bond at par.
Assuming yields remain at 3% the following table shows what happens after one year:

Code: Select all

                            Case A   Case B
                            ------   ------
Value after rate increase   954.20   954.20 [2]

1 year coupon interest       20.00    28.63
Bond value in 1 year        962.83   954.20 [2]
                            ------   ------
Total                       982.83   982.83
The value of the bond in Case A increases $8.63 from $954.20 to $962.83. Thus the total one-year "income" is $28.63 for both cases. It makes no difference whether the bond is replaced or not.

If yields remain at 3%, over the remaining four years the annual dollar amount of "income" increases for Case A:

Code: Select all

Years    Value  "Income"  Return
-----   ------   ------   ------
  5     954.20 		
  4     962.83    28.63    3.00%
  3     971.71    28.88    3.00% [2]
  2     980.87    29.15    3.00%
  1     990.29    29.43    3.00%
  0   1,000.00    29.71    3.00%
The "income" increases such that the annual return remains at 3%, the same as for Case B where 3% = 28.63 / 954.20. This should come as no surprise since Case A (holding the bond) is the same as selling it and buying a new 2% bond at a discount (ignoring possible tax consequences). And if one replaces the bond, one should expect (assuming a flat yield curve) to get the same return or yield-to-maturity whether one buys a 3% bond at par or a 2% bond at a discount.
  1. If coupon interest were the only "income" from a bond, then for a discount bond it would exclude the annual accretion of principal as the bond approaches maturity. (The extreme example of this is a zero-coupon bond where the principal accretion is the only return.) On the flip-side, I believe one is overstating "income" on a bond purchased above par if one fails to reduce the coupon interest by the amortization of premium as the bond approaches maturity.
  2. Values calculated as follows using the Excel PV function:

    Code: Select all

    954.20 = -PV(3%, 5, 20,    1000,    0)
    962.83 = -PV(3%, 4, 20,    1000,    0)
    954.20 = -PV(3%, 4, 28.63,  954.20, 0)
    971.71 = -PV(3%, 3, 20,    1000,    0)

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