How do I calculate the current risk involved with US Bond Index Funds?

For months I have been trying to wrap my head around the concept of risk involved with the US Bond Index Funds in my portfolio. My initial conclusion is that the risk of long-term damage to my portfolio at this point may warrant changing my asset allocation drastically. Here is the scenario I'm trying to understand.

Say we have a hypothetical portfolio made up of 50% Total US Bond Index Fund and 50% S&P 500 Index Fund. An example of the bond fund is Vanguard's BND fund which has an average maturity of 7 years. If we use the 10 year US treasury as a guide it is currently at around 1.6%. The S&P 500 is around 1375. Looking at the 5 year chart for both indexes we see that the 10 year treasury peaks at 5.19% and the S&P at 1464.

If the 10 year treasury went anywhere near 5% what is the potential loss in value on the BND fund? Do the managers hold till maturity or do they have to liquidate holdings for cash on a regular basis? Also, since treasury prices are typically stable in a normal environment if they treasury price stayed above 5% is that a permanent loss in the portfolio?

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If you owned a 7 year note, face value (i.e. value at maturity) \$1000, and it had a 1.6% rate, therefore a \$16/yr coupon, and rates went to 5%, the present value would drop to \$803.

This is simply how bonds work. As a new buyer, I plug in the face value, the \$16/year, and 5% as the current rate I expect to earn. \$803 is the result. Newly issued 7 year notes would have a \$50 coupon and sell for \$1000.

As Kirill showed, the BND you cite is atypical, not reflecting the 7-10 yr bonds. A movement in rates would cause a normal mix of bonds to react as I described.

Edit- this discussion is for a single note or bond, the fact that a fund has an average maturity, but no actual maturity date means my analysis works at the margin, but fails for the fact that there's no option to "hold to maturity."

To be clear - the concept of "duration" answers the question of the effect of a rate change on price, it's a bit shorter than average maturity. But, unlike a single bond where the buyer can hold to maturity, i.e. the duration drops about one tear for each year of real time passing, a fund of treasuries will never mature, the duration will remain somewhat constant as new treasuries are purchased when others mature or new money comes in. The example I offer assumes a 7 year duration. A sudden rise in rates will impact the basket of treasuries as I show. But long term, the value will not match the individual bond. To add to the confusion, the fund the OP asked about has other components that seem to have negated the price drop that should have occurred during a period of rising rates.

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Are you assuming 7 years remaining on the 7 year note when it goes from 1.6% to 5%? Doesn't the PV of the bond depend on the remaining years to maturity? – tp9 Jul 5 '12 at 21:13
tp9 yes. My math is for a single bond to illustrate the cause/effect of rate change to price. For a fund, the instant change in value, i.e. change in value for a given change in rate, will be close, but my remarks about maturing to full value only applies to individual bonds, not funds. – JoeTaxpayer Jul 5 '12 at 21:19
I want to make sure I understand you correctly. Are you saying that there is no easy way to determine the risk involved in a basket of treasuries? – tp9 Jul 6 '12 at 20:22
tp9 - I added more above. – JoeTaxpayer Jul 6 '12 at 20:52
JoeTaxpayer I crunched the numbers and I came out with the following, can you correct my math please? \$803 * .05 * 7 years = \$281.05 -> \$803 + \$281.05 = \$1084.05 versus \$1000 + (16 * 7) = \$1112. Doing the math this way makes the \$803 at 5% about \$30 cheaper than holding to maturity. Is this a premium paid by the seller? How is that difference figured out? – tp9 Jul 8 '12 at 18:54

It is tough to say what the loss will be to the BND if the 10 year US treasury yield goes up to 5%. The main reason is because the BND is not comprised of just US treasuries. In addition the holdings of the BND fund can change.

``````------------ What is the BND ------------
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The fund employs an indexing investment approach designed to track the performance of the Barclays U.S. Aggregate Float Adjusted Bond Index. This index measures a wide spectrum of public, investment-grade, taxable, fixed income securities in the United States—including government, corporate, and international dollar-denominated bonds, as well as mortgage-backed and asset-backed securities, all with maturities of more than 1 year. The fund invests by sampling the index, meaning that it holds a range of securities that, in the aggregate, approximate the full index in terms of key risk factors and other characteristics...

More information can be found here - Vanguard Total Bond Market ETF

As of 05/31/2012 69.7% of the BND is in U.S. Treasury, U.S. Agency, and U.S. Agency mortgage-backed securities. They do not specify an exact amount in the 10 Year Treasury. - Portfolio composition

``````------------ Attempting to gauge potential losses ------------
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We can try to gauge potential losses by just using some basic analysis.

For this example and to make it simple we will pretend 70% of the fund is in 10 Year Treasuries(IT IS NOT!)

By getting rid of all other variables and just focusing in on the 10 Year it would be logical to assume that for each X amount the 10 Year price decreased 70% of BND would be effected by that same amount.

However 70% of BND is not in 10 Year Treasuries. Also if the yield were to go up we would have to ask -- "Why is it going up?", "How will other debt be affected?", "Will the funds management react? And if so how?"

Another way to assess how BND would be affected by an increase in the 10 Year yield would be to just look at previous situations. We can use charts for that.

^TNX vs BND - Yahoo (it's important to note that TNX is the value of the yield so if the price is 2.00 then the yield is 2%)

This is a 5 year chart of BND and the yield of the 10 year treasury. From looking at certain time periods we can see how the BND reacts to increases/decreases in the yield.

For example if you look at 12/30/2008 - 6/11/2009 the yield went from 2.08% to just under 4% at which time BND barely nudged.

I suggest looking at the prospectus and additional information provided to understand the risks involved.

Here are the Distributions for BND.

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Thank you for sharing the methodology you use. – tp9 Jul 8 '12 at 4:36

Finally completed this question. Learned a couple of things.

1. I was calculating the loss of capital incorrectly. JoeTaxpayer gave me an equation to run through my HP 10B calculator to figure out the current value of a bond with a yield change.

2. Kirill Fuchs pointed out that because a bond index tracks a basket of fixed-income instruments I can't reasonably compare it to a particular treasury like the 10-year US treasury.

3. I actually found the answer posted on the Bogleheads forum. They referenced a Morningstar article: ARTICLE

"To estimate how much an investor could lose during a 12-month period if Treasury yields increased by 1 percentage point during that same 12 months, subtract a fund's SEC yield from its current duration."

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