Risk of Long Term Government Bond Index Fund (VLGSX)

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JuniorRob
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Risk of Long Term Government Bond Index Fund (VLGSX)

Post by JuniorRob » Sun Oct 08, 2017 2:29 pm

If interest rates skyrocket, could the value of some individual long term bonds fall to zero?
Or is not possible for a bond's value to fall all the way to zero?
If the value of a bond due to be sold out of the fund becomes zero, how would this be handled?
Could someone give an approximation of how much the price of VLGSX would decline in an extreme scenario?
Lets say the interest rate on new long term govt bonds rises to 13% within the next 10 years, with it currently at approximately 3%.

Appreciate any help.

At some point I would like to pair this fund with the G Fund, for the bond portion of my portfolio, but I do have some reservations.

Bacon+Beans
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Re: Risk of Long Term Government Bond Index Fund (VLGSX)

Post by Bacon+Beans » Sun Oct 08, 2017 3:44 pm

If you go to the VLGSX page and then the "portfolio and management" bar, you will see that the fund has "duration" of 17.6. This is a purely mathematical quantity that is very informative; it says that if the interest rate on this fund goes UP by 1% (say from 3% to 4%), then the value of your position (your balance) goes DOWN by 17.6%. This is a brutal loss on what you might hope to be a conservative part of your portfolio; in fact it is very risky.

You should surely consider moving to either the intermediate term government fund or the short term government fund, the later has a duration of about 2.8, last time I looked. Your interest rate is a little less but your risk is a lot lower. Long term bonds --- even government bonds --- are very risky. They have a role in the world (or they would not exists), but it's hard to think that they have much of a role in an individual portfolio at this point in our financial history.

JuniorRob
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Re: Risk of Long Term Government Bond Index Fund (VLGSX)

Post by JuniorRob » Sun Oct 08, 2017 4:09 pm

Bacon+Beans wrote:
Sun Oct 08, 2017 3:44 pm
If you go to the VLGSX page and then the "portfolio and management" bar, you will see that the fund has "duration" of 17.6. This is a purely mathematical quantity that is very informative; it says that if the interest rate on this fund goes UP by 1% (say from 3% to 4%), then the value of your position (your balance) goes DOWN by 17.6%. This is a brutal loss on what you might hope to be a conservative part of your portfolio; in fact it is very risky.
but what if rates rise by say 6% over a short period of time. 17.6 X 6 = 105%.
Can an individual bond have a value of zero or does the duration equation not work at some point?

mhalley
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Re: Risk of Long Term Government Bond Index Fund (VLGSX)

Post by mhalley » Sun Oct 08, 2017 4:16 pm

I don’t think the individual bond will go to zero, because you still get the principal back if held to maturity. With a bond fund, the fund will be buying higher yielding bonds each year, so you will get a little more yield each year.

dbr
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Re: Risk of Long Term Government Bond Index Fund (VLGSX)

Post by dbr » Sun Oct 08, 2017 4:25 pm

JuniorRob wrote:
Sun Oct 08, 2017 4:09 pm
Bacon+Beans wrote:
Sun Oct 08, 2017 3:44 pm
If you go to the VLGSX page and then the "portfolio and management" bar, you will see that the fund has "duration" of 17.6. This is a purely mathematical quantity that is very informative; it says that if the interest rate on this fund goes UP by 1% (say from 3% to 4%), then the value of your position (your balance) goes DOWN by 17.6%. This is a brutal loss on what you might hope to be a conservative part of your portfolio; in fact it is very risky.
but what if rates rise by say 6% over a short period of time. 17.6 X 6 = 105%.
Can an individual bond have a value of zero or does the duration equation not work at some point?
Technically this is more like slope of a curve that can be estimated in the vicinity of a point but may not be the same at distant point. So, the duration does not apply after large changes in interest rate. Scroll down in this article for more (convexity): http://www.investopedia.com/articles/bo ... vexity.asp

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Re: Risk of Long Term Government Bond Index Fund (VLGSX)

Post by Call_Me_Op » Sun Oct 08, 2017 5:08 pm

JuniorRob wrote:
Sun Oct 08, 2017 4:09 pm
but what if rates rise by say 6% over a short period of time. 17.6 X 6 = 105%.
Can an individual bond have a value of zero or does the duration equation not work at some point?
Duration is the first derivative of the price-yield curve. That is, strictly speaking, it (the linear relationship) is valid only for very small changes in interest rate. For larger rate changes, and for an ordinary bond, the impact is less than would be predicted by the first derivative.
Best regards, -Op | | "In the middle of difficulty lies opportunity." Einstein

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Re: Risk of Long Term Government Bond Index Fund (VLGSX)

Post by Kevin M » Sun Oct 08, 2017 5:38 pm

JuniorRob wrote:
Sun Oct 08, 2017 4:09 pm
Bacon+Beans wrote:
Sun Oct 08, 2017 3:44 pm
If you go to the VLGSX page and then the "portfolio and management" bar, you will see that the fund has "duration" of 17.6. This is a purely mathematical quantity that is very informative; it says that if the interest rate on this fund goes UP by 1% (say from 3% to 4%), then the value of your position (your balance) goes DOWN by 17.6%. This is a brutal loss on what you might hope to be a conservative part of your portfolio; in fact it is very risky.
but what if rates rise by say 6% over a short period of time. 17.6 X 6 = 105%.
Can an individual bond have a value of zero or does the duration equation not work at some point?
As explained above, duration is not linear, so does not apply well over larger yield changes. You can use bond math formulas to determine the actual change in price of a bond for a given change in yield.

The yield on the 20-year Treasury is about 2.7%, and duration for a par bond at that yield is about 15.6. If the yield increased by 6 percentage points to 8.7% very quickly, the bond would lose 56% of its value: =-PV(8.7%,20,2.7%,1)-1. The bond would recover the entire loss by maturity, and the 20-year annualized return would be about 2.7%, with some uncertainty due to the unknown coupon reinvestment rates. Of course that wouldn't be much consolation if someone who bought a 20-year bond shortly after you earned 8.7% annualized.

Kevin
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Re: Risk of Long Term Government Bond Index Fund (VLGSX)

Post by bligh » Sun Oct 08, 2017 5:39 pm

JuniorRob wrote:
Sun Oct 08, 2017 4:09 pm
Bacon+Beans wrote:
Sun Oct 08, 2017 3:44 pm
If you go to the VLGSX page and then the "portfolio and management" bar, you will see that the fund has "duration" of 17.6. This is a purely mathematical quantity that is very informative; it says that if the interest rate on this fund goes UP by 1% (say from 3% to 4%), then the value of your position (your balance) goes DOWN by 17.6%. This is a brutal loss on what you might hope to be a conservative part of your portfolio; in fact it is very risky.
but what if rates rise by say 6% over a short period of time. 17.6 X 6 = 105%.
Can an individual bond have a value of zero or does the duration equation not work at some point?
I dont think that is how it works.

It would be 17.5% of the reduced amount and so on.

So for example. For a 10 year duration -

(1% rise) 100 - 10% = 90
(2% rise) 90 - 10% = 81
(3% rise) 81 - 10% = 73
(4% rise) 73 - 10% = 65.5
(5% rise) 65.5 - 10% = 59

you get the idea. So a 5% increase in yield isn't a straight 5 * 10 = 50% drop in value.. but more like a 41% drop.

JuniorRob
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Re: Risk of Long Term Government Bond Index Fund (VLGSX)

Post by JuniorRob » Mon Oct 09, 2017 7:53 am

Thank yall very much. I knew there had to be more to duration that I wasn't understanding.

I know this isn't a simple equation, but could someone provide a ballpark estimate of the percent loss of VLGSX if interest rates increased by 10% over a lets say 5 year period?

75%?

I just want to get an idea of how much could be lost in an extreme scenario.

dbr
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Re: Risk of Long Term Government Bond Index Fund (VLGSX)

Post by dbr » Mon Oct 09, 2017 8:21 am

JuniorRob wrote:
Mon Oct 09, 2017 7:53 am
Thank yall very much. I knew there had to be more to duration that I wasn't understanding.

I know this isn't a simple equation, but could someone provide a ballpark estimate of the percent loss of VLGSX if interest rates increased by 10% over a lets say 5 year period?

75%?

I just want to get an idea of how much could be lost in an extreme scenario.
There have been some examples of such calculations posted before. Maybe someone will find them. I am not sure the LT fund was in the examples I remember. The loss won't be as much as 75% because the fund already starts to gain value from the increased yield reinvested. In other words a problem with winging out that loss = duration * interest rate change is that such a thing is a point change due to point change in interest rates but here we have a gradual change over time and tracking of the gradual recovery of the fund. Note that another interpretation of duration is the number of years to reach a point of indifference whether or not interest rates increased. After that one benefits from the increase. In the meantime interest rates themselves move up and down (see below).

A different issue regarding risk is that not only does one have to compute the complexities of duration, but one also has to have a reasonable estimate of future interest rates, which is extraordinarily hard to do. A look at the history of interest rates over the centuries show that the eighty year rise and fall of interest rates in the US, peaking in 1980, looks like a one of a kind excursion. The idea that having come down from that one should expect to go back up such a curve takes a lot of speculating.

All that said, there certainly is enough risk in long term bonds that lots of investors are content to stay at intermediate terms as a more optimum trade-off of risk and return. You could apply a rule of thumb suggested by Larry Swedroe that extending duration in bonds is worthwhile if one can gain 20bps in return for every year of longer duration. Another point of view is that regarding performance of the portfolio as a whole the portfolio optimum for risk and return of a high stock portfolio is greater when paired with long bonds, but that is not so true for more balanced allocations.

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Re: Risk of Long Term Government Bond Index Fund (VLGSX)

Post by grabiner » Mon Oct 09, 2017 8:22 pm

JuniorRob wrote:
Mon Oct 09, 2017 7:53 am
Thank yall very much. I knew there had to be more to duration that I wasn't understanding.

I know this isn't a simple equation, but could someone provide a ballpark estimate of the percent loss of VLGSX if interest rates increased by 10% over a lets say 5 year period?
Use a spreadsheet, which can compute the present value of a bond given the yield and payment schedule.

It's easiest to understand the math with a zero-coupon bond, which has a single payment. Suppose that you have a $1000 bond with a 20-year maturity, and a current 3% yield. The value is 1000/(1.03)^20=$554. If rates rise to 8%, the value will be 1000/(1.08)^20=$214, a 61% loss.

Part of the issue here is compounding. If the bond price declines by 20% when rates rise from 3% to 4% (and it doesn't decline by quite that much), and then by another 20% from 4% to 5%, the two losses compound to 36%, not 40%.
David Grabiner

Bacon+Beans
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Re: Risk of Long Term Government Bond Index Fund (VLGSX)

Post by Bacon+Beans » Fri Oct 13, 2017 1:16 pm

Mathematically, duration is the (minus of the) derivative of the bond price with respect to the yield. If the duration is D and the yield goes up by a small amount x, the bond price goes down by the amount xD. With respect to your example, the first 1% the interest rate goes up will send the price down 17.6%. At that point you will have a bond with a new duration D' which is smaller than D. The next x percent up in yields will send the bond down xD'. In this kind of approximation, you have to think in terms of "small x", and 1% would qualify --- while 8% would not.

In any case, if you think there is a good chance that long term government rates will go up 1%, then you have to think that there is also there is a good chance the price will go down 17.6%. This is a risk reward trade-off, and you have to decide if the risk is worth taking.

BTW, you can get a "fund" of any duration you like by putting some money in a money market and some in a long term fund. The duration of the average is the average of the two durations. For example, a MM has duration zero, so 90% MM and 10% VLSGX gives you a bond portfolio with duration 1.76% which is just a bit more than the Vanguard Ultra Short Term bond fund. This "barbell portfolio" may have some advantages over the Ultra short fund. It depends on what happens to the slope of the yield curve.

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Re: Risk of Long Term Government Bond Index Fund (VLGSX)

Post by #Cruncher » Fri Oct 13, 2017 4:49 pm

JuniorRob wrote:
Sun Oct 08, 2017 2:29 pm
Could someone give an approximation of how much the price of VLGSX would decline in an extreme scenario? Lets say the interest rate on new long term govt bonds rises to 13% within the next 10 years, with it currently at approximately 3%.
JuniorRob wrote:
Mon Oct 09, 2017 7:53 am
... could someone provide a ballpark estimate of the percent loss of VLGSX if interest rates increased by 10% over a lets say 5 year period?
grabiner wrote:
Mon Oct 09, 2017 8:22 pm
Use a spreadsheet, which can compute the present value of a bond given the yield and payment schedule. It's easiest to understand the math with a zero-coupon bond, which has a single payment.
Following grabiner's suggestion, I'll model this with a hypothetical portfolio consisting of a single 18-year zero coupon bond that is rolled over every year. Since this is a zero-coupon bond, its duration is close to its maturity -- which makes it a good stand-in for the Vanguard Long-Term Government Bond Index Fund Admiral Shares (VLGSX) with its duration of 17.6. The initial value and yield-to-maturity (YTM) are assumed to be $1,000.00 and 2.7%. The yield is assumed to rise evenly each year until it reaches 12.7% and then remain there. I'll compute the results for 18 years for the following three cases:
  1. Yield increases 1% points each year for 10 years.
  2. Yield increases 2% points each year for 5 years.
  3. Yield increases 10% points the first year.

Code: Select all

       --- Case A ---   --- Case B ---   --- Case C ---
Year   Yield    Value   Yield    Value   Yield    Value

Code: Select all

   0    2.7% 1,000.00    2.7% 1,000.00    2.7% 1,000.00
   1    3.7%   871.02    4.7%   739.90   12.7%  [211.62] [*]
   2    4.7%   767.28    6.7%   561.59   12.7%   238.50  [*]
   3    5.7%   683.47    8.7%   437.00   12.7%   268.79
   4    6.7%   615.56   10.7%   348.42   12.7%   302.92
   5    7.7%   560.49   12.7%  [284.48]  12.7%   341.39
   6    8.7%   515.88   12.7%   320.61   12.7%   384.75
   7    9.7%   479.92   12.7%   361.32   12.7%   433.62
   8   10.7%   451.21   12.7%   407.21   12.7%   488.68
   9   11.7%   428.68   12.7%   458.93   12.7%   550.75
  10   12.7%  [411.51]  12.7%   517.21   12.7%   620.69
  11   12.7%   463.77   12.7%   582.90   12.7%   699.52  [*]
  12   12.7%   522.67   12.7%   656.93   12.7%   788.36
  13   12.7%   589.05   12.7%   740.36   12.7%   888.48
  14   12.7%   663.86   12.7%   834.38   12.7% 1,001.32
  15   12.7%   748.17   12.7%   940.35   12.7% 1,128.49
  16   12.7%   843.18   12.7% 1,059.77   12.7% 1,271.80
  17   12.7%   950.27   12.7% 1,194.36   12.7% 1,433.32
  18   12.7% 1,070.95   12.7% 1,346.05   12.7% 1,615.36
Case A, with rates rising the slowest, has the least drop in value (59%); but also the smallest value after 18 years. Case C, with rates rising the fastest, has the greatest drop in value (79%); but also the largest value after 18 years. Case B is in between with a drop of 72% and a middling value after 18 years. Note (as pointed out by Kevin M in this post) that the value of Case C after 18 years is the same as if yields had remained at 2.7% (1,615.36 = 1000 * 1.027 ^ 18).

* Example of calculation for Case A years 1, 2, and 11:

Code: Select all

 1: 871.02 = 1000.00 * 1.027 ^ 18 / 1.037 ^ 17
 2: 767.28 =  871.02 * 1.037 ^ 18 / 1.047 ^ 17
11: 463.77 =  411.51 * 1.127 ^ 18 / 1.127 ^ 17 = 411.51 * 1.127

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