Calculating TIPS duration?

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richard
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Calculating TIPS duration?

Post by richard »

I'm trying to calculate the duration of some individual TIPS I own. The purpose of the exercise is to make sure the average duration of my total bond portfolio is within a range I find acceptable. I'm looking for a method that's approximately correct.

As an example, I own some of the 2% Jan 2026, currently trading at about 115.2 and 0.5%

1) Use Excel's mduration function (Macauley modified duration), with a settlement date of today. result = 9.9%

2) Use Excel's mduration function on a nominal treasury with a low coupon and similar maturity, for example, the 2% Feb 2025. result = 9%

3) Look at how this TIPS reacted to a change in rates. About a year ago, it was trading at 113.2 and 0.766% - price changed +1.96 and yield changed -0.266%, the equivalent of a 1% decrease in yield increasing price by 6.4%

Which method would you use? If none of these, what would you recommend?

Here's a prior thread on the general topic:
http://www.bogleheads.org/forum/viewtopic.php?p=946003
dkturner
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Re: Calculating TIPS duration?

Post by dkturner »

richard wrote:I'm trying to calculate the duration of some individual TIPS I own. The purpose of the exercise is to make sure the average duration of my total bond portfolio is within a range I find acceptable. I'm looking for a method that's approximately correct.
Here's a prior thread on the general topic:
http://www.bogleheads.org/forum/viewtopic.php?p=946003
The prior thread you referenced contains a lot of good information concerning the relationship between TIPS coupon rates and duration. I particularly like Doc's observation that changes in future inflation rates have a disproportionate impact on TIPS duration because of their unusually low coupon rates. Think of how zero coupon bonds behave when trying to determine which estimate you choose to follow. Also, take a look at how long term low coupon TIPS behaved in 2013, when interest rates rose substantially while inflation actually declined.
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richard
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Re: Calculating TIPS duration?

Post by richard »

dkturner wrote:The prior thread you referenced contains a lot of good information concerning the relationship between TIPS coupon rates and duration.
That's why I referenced it :D
dkturner wrote:I particularly like Doc's observation that changes in future inflation rates have a disproportionate impact on TIPS duration because of their unusually low coupon rates.
My take is that lower rate bonds have longer durations, all things equal. With positive inflation, TIPS have lower quoted rates than nominals.
dkturner wrote:Think of how zero coupon bonds behave when trying to determine which estimate you choose to follow. Also, take a look at how long term low coupon TIPS behaved in 2013, when interest rates rose substantially while inflation actually declined.
Jan 2028 tip, 1.75 coupon:
Jan 2, 2013: 128.17, -0.143% (1.114 index)
Dec 30, 2013: 107.23, 1.139% (1.104 index)
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Doc
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Re: Calculating TIPS duration?

Post by Doc »

richard wrote:I'm trying to calculate the duration of some individual TIPS I own. The purpose of the exercise is to make sure the average duration of my total bond portfolio is within a range I find acceptable. I'm looking for a method that's approximately correct
Unfortunately "you can't get there from here".

1) Most people on this board think of duration as a measure of the price change with a change in market rates. But what market rate? The real rate or the nominal rate? If the nominal rate changes because interest rates go up the price of nominal bonds goes down but the nominal price (ie adjusted) of TIPS goes up. Opps.

2) Another "definition" of duration is the time it takes to get your money back. In that case in inflation rates go up you get you money back faster with TIPS than nominals. Opps.

3) How do we "estimate" interest rates on a daily basis? Oh, we subtract the TIPS rate from the nominal rate. Opps.

#cruncher is interested in comparing TIPS funds on a consistent basis since there are no standards. Real duration makes a lot of sense for this purpose. But if we want to find out what our overall portfolio that contains both real and nominal bonds does then this idea doesn't work.

For a while I tried to use the Macauley duration function with an assumed inflation rate. This was cumbersome and involved a lot of do over each time that the inflation rate changed which I don't even know until after the fact.

What I do now is to take advantage of the bond ladder "tool" at Vanguard. I create a ladder with the TIPS being replaced with the closest "nominal". I try to use a low coupon nominal and shorter rather than longer maturity if I can't get an exact match. Vanguard calculates all the data for me with no effort as long as the market is open. I only need to expend any effort if I buy or sell one of the bonds. (I do keep the actual TIPS in the ladder but with a zero quantity for reference purposes.)
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.
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richard
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Re: Calculating TIPS duration?

Post by richard »

Doc wrote:What I do now is to take advantage of the bond ladder "tool" at Vanguard. I create a ladder with the TIPS being replaced with the closest "nominal". I try to use a low coupon nominal and shorter rather than longer maturity if I can't get an exact match. Vanguard calculates all the data for me with no effort as long as the market is open. I only need to expend any effort if I buy or sell one of the bonds. (I do keep the actual TIPS in the ladder but with a zero quantity for reference purposes.)
That's a nice tool. It even seems to work after hours.
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Re: Calculating TIPS duration?

Post by #Cruncher »

richard in original post wrote:As an example, I own some of the 2% Jan 2026 [TIPS], currently trading at about 115.2 and 0.5% ... About a year ago, it was trading at 113.2 and 0.766% - price changed +1.96 and yield changed -0.266%, the equivalent of a 1% decrease in yield increasing price by 6.4% (underline added)
The price increase is the net result of two offsetting effects::
  1. The bond being one year nearer to maturity which causes its price to fall.
  2. The decrease in yield from 0.766% to 0.5% which causes its price to rise.
For example, if the yield had remained at 0.766% the price would have fallen about 1%:

Code: Select all

114.016 = price 1 year ago =PRICE(DATE(2014, 2, 18), DATE(2026, 1, 15), 2%, 0.766%, 100, 2, 1)
112.887 = price today      =PRICE(DATE(2015, 2, 18), DATE(2026, 1, 15), 2%, 0.766%, 100, 2, 1)
Therefore, when a bond is priced at other than par, a price change that occurs over time isn't attributable solely to the change in yield.

By the way, Richard, I don't come up with the 113.2 price you report for "a year ago". As shown above a 0.766% yield equates to a price of about 114.0 on 2/18/2014 -- not 113.2.
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Re: Calculating TIPS duration?

Post by Doc »

richard wrote:That's a nice tool. It even seems to work after hours.
The price data may not be erroneous outside of market hours and some individual issues may not show up in the "search" list".
A scientist looks for THE answer to a problem, an engineer looks for AN answer and lawyers ONLY have opinions. Investing is not a science.
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