what is an ibonds duration?

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what is an ibonds duration?

Postby LH » Fri Mar 22, 2013 1:04 am

Say I hold a current ibond now, and hold it 30 years, what would the that ibonds duration?

Now, say I buy a current ibond now, and sell it in 6 years, what would its duration be then?

Are the two answers the same?

Thanks,

LH
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Re: what is an ibonds duration?

Postby friar1610 » Fri Mar 22, 2013 10:19 am

I'm no expert on this and I'll leave it to someone else to give a technical answer. But just thinking it through, I'm not sure that a savings bond has a duration. I understand the definition of duration as a measure of the sensitivity of a bond's underlying value to changes in interest rates. (With a longer duration, an increase in prevailing interest rates causes the value of the bond to decrease more than a bond with a shorter duration.) Since there is no secondary market for savings bonds and any I-Bond can be redeemed after a year at face value (less a small interest penalty if redeemed in less than 5 years), the price/value of the bond is no different in a high interest rate environment than in a low environment. Therefore, I conclude that I-Bonds (or any savings bonds, for that matter) have no duration.

If I've got it wrong I'm sure open to another explanation.
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Re: what is an ibonds duration?

Postby larryswedroe » Fri Mar 22, 2013 10:21 am

IMO duration of real return bond not relevant like it is for nominal return bond
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Re: what is an ibonds duration?

Postby Iorek » Fri Mar 22, 2013 10:57 am

I think duration, as you normally think of it, isn't a useful concept for savings bonds because of the embedded put option.

There is an interesting wikipedia article on bond duration, and if you look at the section on embedded options you will see that they discuss that you need to use a different form/calculation of duration if you want to usefully value a puttable bond.
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Re: what is an ibonds duration?

Postby SSSS » Fri Mar 22, 2013 11:29 am

Savings bonds are not actually bonds.
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Re: what is an ibonds duration?

Postby jeffyscott » Sat Mar 23, 2013 9:53 am

After 1 year, I-bonds and EE bonds are more like a savings account...maybe that's why they call them "savings bonds". So wouldn't the duration be 0 or close to that, at least after the first year?

At most they are maybe like a floating rate bond, these have very short duration, T. Rowe's floating rate fund has duration of 0.46 years.
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Re: what is an ibonds duration?

Postby Epsilon Delta » Sat Mar 23, 2013 2:43 pm

CDs are not bonds, but they also have duration.

One definition of duration is just the weighted average of the times of the cash flows. This is calculable for any fixed income asset. It may not always be meaningful, but it can be calculated. It is true that I-bonds are real rather than nominal and that savings bonds have a put, but people do compute durations for tips and callable bonds. For a bond with a put you can at least compute the duration to best and worst cases.
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Re: what is an ibonds duration?

Postby #Cruncher » Sat Mar 23, 2013 2:45 pm

larryswedroe wrote:IMO duration of real return bond not relevant like it is for nominal return bond
Larry, what do you mean by "real return bond"? If you mean just I Bonds, I agree with you. But if you mean to include TIPS, please elaborate. I consider duration to be as relevant for them as for nominal bonds.
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Re: what is an ibonds duration?

Postby nisiprius » Sat Mar 23, 2013 2:50 pm

In my arrogant opinion...

The duration of a series I savings bond is zero.
:!: :!: :!: :!: :!: :!: :!: :!: :!:

I am taking one of several definitions of duration, specifically, that duration is the percentage change in the value of the bond divided by the prevailing annual percentage interest rate. For example, if a 1% rise in interest rate causes a 4% drop in bond value, the duration is (4% / (1%/year)) = 4 years.

The value of a series I savings bond is unaffected by interest rate changes. They are non-marketable securities and they are redeemed directly with the Treasury, per agreement, not sold at auction to other investors. The value of a current series I savings bond is the purchase price times the cumulative CPI change between purchase and redemption. The value of any savings bond depends on the cumulative CPI change and the "fixed rate." The current interest rate does not come into the equation.

A 1% rise in the interest rate does not have any effect on the redemption value of a series I savings bond. It drops in value by zero. The duration is zero.

This is precisely one of the reasons why series I savings bonds are interesting despite paying less than TIPS.
Epsilon Delta wrote:CDs are not bonds, but they also have duration.

One definition of duration is just the weighted average of the times of the cash flows. This is calculable for any fixed income asset. It may not always be meaningful, but it can be calculated. It is true that I-bonds are real rather than nominal and that savings bonds have a put, but people do compute durations for tips and callable bonds. For a bond with a put you can at least compute the duration to best and worst cases.
I would argue that this is not true because series I savings bonds are not marketable. You can perform the calculation you suggest but it's meaningless, because there is no way you can sell that bond for that amount of money. The calculation may show that the bond is "worth" $1100 or that it is "worth" $900 but it is irrelevant, because you cannot sell it to another investor. The only thing you can do is redeem it with the Treasury--per schedule, for accumulated-CPI-plus-fixed-rate--regardless of whether the number you calculated was higher or lower.
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Re: what is an ibonds duration?

Postby rmelvey » Sat Mar 23, 2013 4:14 pm

I bonds are like a long term TIP that you can't trade with other investors, but with an embedded put option to sell it back to the Treasury at par :D They are such a free lunch its pretty incredible!
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Re: what is an ibonds duration?

Postby Call_Me_Op » Sat Mar 23, 2013 4:48 pm

Duration is not applicable to an I-Bond. Its value has no interest rate sensitivity.
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Re: what is an ibonds duration?

Postby Mel Lindauer » Sat Mar 23, 2013 4:57 pm

I agree with those who say that I Bonds don't have a duration. The value never can go below par, they aren't bought or sold in any secondary market, and they can be redeemed anytime after one year. You simply can't lose money when you invest in I Bonds as you can with traditional bonds.
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Re: what is an ibonds duration?

Postby Epsilon Delta » Sat Mar 23, 2013 5:44 pm

Non marketability is a red herring.

You can compute a "model value" for an I-bond by considering the various payments and the current yield curve. If the I-bond were marketable this would be the market value (assuming an efficient market). This "model value" is still meaningful even though you can't sell the I-bond. If the current redemption value is higher than the model value you can redeem the bond and buy better payments on the open market. So the "model value" matters and is actionable, it affects the hold or redeem decision. The duration affects how the model value responds to market changes so it is also meaningful.

More complicatedly the duration of I bonds will affect the behavior of a portfolio containing them and you can adjust your other holdings to get the desired overall behavior.
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Re: what is an ibonds duration?

Postby Mel Lindauer » Sat Mar 23, 2013 6:01 pm

Epsilon Delta wrote:Non marketability is a red herring.

You can compute a "model value" for an I-bond by considering the various payments and the current yield curve. If the I-bond were marketable this would be the market value (assuming an efficient market). This "model value" is still meaningful even though you can't sell the I-bond. If the current redemption value is higher than the model value you can redeem the bond and buy better payments on the open market. So the "model value" matters and is actionable, it affects the hold or redeem decision. The duration affects how the model value responds to market changes so it is also meaningful.

More complicatedly the duration of I bonds will affect the behavior of a portfolio containing them and you can adjust your other holdings to get the desired overall behavior.


You can buy new I Bonds without redeeming the current ones. And since you can only buy $10k per year, many folks don't want to redeem old bonds, pay taxes and then buy new ones with what's left; they'd rather just add to their current holdings by buying additional I Bonds.

Remember, many folks use I Bonds for tax shifting (buying while in a high tax bracket and redeeming when they're retired and in a lower tax bracket), so the last thing those folks want to do is redeem I Bonds and pay a high tax rate.
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Re: what is an ibonds duration?

Postby blevine » Sat Mar 23, 2013 6:22 pm

Not only can't you lose, you can't gain either, solidifying the argument for zero duration.
Duration is what allowed all those gains on long term bonds last few years.
Ibonds did not have principal gains, no duration.

Works both ways. No downside nor upside.
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Re: what is an ibonds duration?

Postby John151 » Sat Mar 23, 2013 6:39 pm

I've been classifying my I Bonds as having a duration of 1 during the first year, and then 0 thereafter. That's how I've been classifying my EE Bonds as well.
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Re: what is an ibonds duration?

Postby Epsilon Delta » Sat Mar 23, 2013 7:46 pm

Mel Lindauer wrote:
Epsilon Delta wrote:Non marketability is a red herring.

You can compute a "model value" for an I-bond by considering the various payments and the current yield curve. If the I-bond were marketable this would be the market value (assuming an efficient market). This "model value" is still meaningful even though you can't sell the I-bond. If the current redemption value is higher than the model value you can redeem the bond and buy better payments on the open market. So the "model value" matters and is actionable, it affects the hold or redeem decision. The duration affects how the model value responds to market changes so it is also meaningful.

More complicatedly the duration of I bonds will affect the behavior of a portfolio containing them and you can adjust your other holdings to get the desired overall behavior.


You can buy new I Bonds without redeeming the current ones. And since you can only buy $10k per year, many folks don't want to redeem old bonds, pay taxes and then buy new ones with what's left; they'd rather just add to their current holdings by buying additional I Bonds.

Remember, many folks use I Bonds for tax shifting (buying while in a high tax bracket and redeeming when they're retired and in a lower tax bracket), so the last thing those folks want to do is redeem I Bonds and pay a high tax rate.

Peoples individual tax circumstances do not affect the duration of a bond. Neither do purchase limits etc. Duration is a property of the bond, not the bond holder.

A duration of zero means that your choice to hold I-bonds is independent of interest rates. It means you will continue to hold your current I-bonds even if tips offer 5% real. I doubt most investors would do that.
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Re: what is an ibonds duration?

Postby Mel Lindauer » Sat Mar 23, 2013 7:53 pm

Epsilon Delta wrote:
Mel Lindauer wrote:
Epsilon Delta wrote:Non marketability is a red herring.

You can compute a "model value" for an I-bond by considering the various payments and the current yield curve. If the I-bond were marketable this would be the market value (assuming an efficient market). This "model value" is still meaningful even though you can't sell the I-bond. If the current redemption value is higher than the model value you can redeem the bond and buy better payments on the open market. So the "model value" matters and is actionable, it affects the hold or redeem decision. The duration affects how the model value responds to market changes so it is also meaningful.

More complicatedly the duration of I bonds will affect the behavior of a portfolio containing them and you can adjust your other holdings to get the desired overall behavior.


You can buy new I Bonds without redeeming the current ones. And since you can only buy $10k per year, many folks don't want to redeem old bonds, pay taxes and then buy new ones with what's left; they'd rather just add to their current holdings by buying additional I Bonds.

Remember, many folks use I Bonds for tax shifting (buying while in a high tax bracket and redeeming when they're retired and in a lower tax bracket), so the last thing those folks want to do is redeem I Bonds and pay a high tax rate.

Peoples individual tax circumstances do not affect the duration of a bond. Neither do purchase limits etc. Duration is a property of the bond, not the bond holder.

A duration of zero means that your choice to hold I-bonds is independent of interest rates. It means you will continue to hold your current I-bonds even if tips offer 5% real. I doubt most investors would do that.


Making a decision whether to buy something else that might be more attractive doesn't require what you own to have a duration. Think cash, CDs, equities. We always consider whether one option is more desirable than another throughout our investing lives without considering duration in every case.

Whatever works for you.
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Re: what is an ibonds duration?

Postby magician » Sat Mar 23, 2013 10:38 pm

Call_Me_Op wrote:Duration is not applicable to an I-Bond. Its value has no interest rate sensitivity.

Thus, its (effective) duration is zero. It's applicable, it's just zero.

See nisiprius' post, above.
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Re: what is an ibonds duration?

Postby market timer » Sat Mar 23, 2013 11:53 pm

Epsilon Delta wrote:Non marketability is a red herring.

You can compute a "model value" for an I-bond by considering the various payments and the current yield curve. If the I-bond were marketable this would be the market value (assuming an efficient market). This "model value" is still meaningful even though you can't sell the I-bond. If the current redemption value is higher than the model value you can redeem the bond and buy better payments on the open market. So the "model value" matters and is actionable, it affects the hold or redeem decision. The duration affects how the model value responds to market changes so it is also meaningful.

More complicatedly the duration of I bonds will affect the behavior of a portfolio containing them and you can adjust your other holdings to get the desired overall behavior.

+1
Was scrolling down the list hoping someone had written this so I wouldn't have to. Only thing I'd add is that an individual's potential demand for liquidity could affect model value.
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Re: what is an ibonds duration?

Postby Epsilon Delta » Sun Mar 24, 2013 12:03 am

magician wrote:
Call_Me_Op wrote:Duration is not applicable to an I-Bond. Its value has no interest rate sensitivity.

Thus, its (effective) duration is zero. It's applicable, it's just zero.

See nisiprius' post, above.


Try it another way.

Look at the formula for Macaulay duration.
Image
In the case of a I Bond with a zero real coupon there is exactly one payment, when the bond is redeemed.
So the duration is the age of the bond when it's redeemed, somewhere between 0 and 30 years at the bond holders discretion. It's zero if real interest rates go above zero and 30 years if real interest rates stay below zero. Saying the duration is zero is missing a big part of the picture.

The value of a I bond is not the redemption value. If it were people would be willing to redeem those juicy 3% real rate I bonds.
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Re: what is an ibonds duration?

Postby magician » Sun Mar 24, 2013 1:53 am

Epsilon Delta wrote:
magician wrote:
Call_Me_Op wrote:Duration is not applicable to an I-Bond. Its value has no interest rate sensitivity.

Thus, its (effective) duration is zero. It's applicable, it's just zero.

See nisiprius' post, above.

Try it another way.

Look at the formula for Macaulay duration.
Image
In the case of a I Bond with a zero real coupon there is exactly one payment, when the bond is redeemed.
So the [Macaulay] duration is the age of the bond when it's redeemed, somewhere between 0 and 30 years at the bond holders discretion. It's zero if real interest rates go above zero and 30 years if real interest rates stay below zero. Saying the [what kind of?] duration is zero is missing a big part of the picture.

The value of a I bond is not the redemption value. If it were people would be willing to redeem those juicy 3% real rate I bonds.

The Macaulay duration - the weighted-average time to receive one's money - is the age of the bond when it's redeemed.

The effective duration - the (negative of the) percentage price change for a 1% change in YTM, allowing for changes in cash flows - is zero. You'll note that I specified effective duration. Nobody said that the Macaulay duration is zero.

This discussion points to one immutable fact: using simply the word "duration" is ambiguous; to be clear one needs to specify whether it's Macaulay duration, modified duration, effective duration, spread duration, key-rate duration, and so on.

I did make one error, however. I should have specified that the effective duration is zero years, not merely zero.
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Re: what is an ibonds duration?

Postby jeffyscott » Sun Mar 24, 2013 11:08 am

John151 wrote:I've been classifying my I Bonds as having a duration of 1 during the first year, and then 0 thereafter. That's how I've been classifying my EE Bonds as well.


They are zero coupon bonds and the duration of a zero is equal to the maturity. Maturity is the date you get your money, which may be the end of the first year or any time after that. So, in that way, this makes sense, though actually the initial duration would be 1 year and would continuously decline reaching zero after 12 months.

(Since you can buy anytime during the month and the purchase date is recorded as the 1st, the initial duration, looked at this way, would actually be 11-12 months.)
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Re: what is an ibonds duration?

Postby market timer » Sun Mar 24, 2013 12:16 pm

I'll attempt to answer the original question.

Let's assume the I bond holder in question is very liquid, such that he discounts cash flows by something close to the Treasury rate. This is important--if the individual had lots of high interest debt, he should redeem the I bond immediately to pay down the debt.

Second, let's look at 0% fixed rate I bonds. The fixed rate is also important for this question. Consider two I bonds with the same redemption value: one at 1% fixed, the other at 0% fixed. Although they have the same redemption value, the former is clearly more valuable. How much more valuable? Well, that depends on how long we plan to hold these bonds (i.e., their duration). The 0% bond would be redeemed earlier than the 1% bond, all else equal, because it is less valuable to the holder. Therefore, it has a lower duration.

Finally, let's look at the real yield curve: http://www.treasury.gov/resource-center ... =realyield

As of March 22, 5-year TIPS pay -1.4% real and 10-year TIPS pay -0.6%. Over 5 years, you'll lose roughly 7% in buying power holding 5-year TIPS. Over 10 years, you'll lose roughly 6% in buying power holding 10-year TIPS. Since a 10-year TIPS can be thought of as a combination of a 5-year TIPS that matures in 2018 and another 5-year TIPS that is issued in 2018 and matures in 2023, we can back out what the market expects the 5-year TIPS maturing in 2023 will yield. Roughly, the expected real return over those five years is -6% - (-7%) = 1%, or 0.2% annualized. In other words, 5-year TIPS are expected to start yielding a positive real return just before 2018.

If a holder of 0% I bonds intended to redeem the I bonds as soon as 5-year TIPS started offering a positive real return, he'd likely calculate the duration around 5 years. This would be a mistake, though. He'd be giving up the redemption option, which is basically a free put option on real rates. For example, if real rates rose well above 0%, having bought 5-year TIPS and losing money would clearly be inferior simply to holding onto an I bond, because the I bond redemption value would not fall in a rising rate environment. Therefore, the I bond holder should wait until short term real rates are higher, perhaps 0.5% or more, until redeeming the I bond.

Back of the envelope, I'd estimate a duration of 6-8 years for 0% fixed rate I bonds.
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Re: what is an ibonds duration?

Postby Epsilon Delta » Sun Mar 24, 2013 1:38 pm

magician wrote:The effective duration - the (negative of the) percentage price change for a 1% change in YTM, allowing for changes in cash flows - is zero. You'll note that I specified effective duration. Nobody said that the Macaulay duration is zero.

This discussion points to one immutable fact: using simply the word "duration" is ambiguous; to be clear one needs to specify whether it's Macaulay duration, modified duration, effective duration, spread duration, key-rate duration, and so on.


Your using a non-standard definition of "effective duration", or perhaps your using the wrong definition of "price". Boglehead's wiki says:
http://www.bogleheads.org/wiki/Duration#Duration wrote:Bonds and bond funds also compute an effective duration which takes into account the possibility that the bond will be called (paid back early).

Others say the same thing.
http://www.investopedia.com/terms/e/effectiveduration.asp

In short the effective duration for a bond with an option is the Macaulay duration calculated on the payments that will happen if the option holder acts rationally.

If the bond is marketable and the market is rational then the market price will reflect the effective duration. This is not a definition, it a consequence of the definitions of effective duration and efficient markets. The redemption value of an I-bond is not a market price, it cannot be used to calculate duration because it does not reflect the judgment of an efficient market.

To repeat if the duration (of any kind) is zero the value of the bond is indifferent to interest rate changes. This is manifestly not the case for I bonds. You will hold them if real interest rates fall below the "fixed rate" and redeem them if real interest rates are higher. This means they are more valuable at lower interest rates so the duration cannot be zero.
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Re: what is an ibonds duration?

Postby nisiprius » Sun Mar 24, 2013 1:44 pm

Let's try it this way. Forget theory. LH, why are you asking?

Why do you care about duration?

I don't want to put words in your mouth, but the usual reason for asking this question in this forum is that people want to "shorten up" their portfolio's duration to reduce interest rate risk, because they are concerned about a rise in interest rates. Perhaps the bond will regain its value when it matures, and perhaps the bond fund will regain value a few years down the road, but the concern is that you might need money at an arbitrary time, and if interest rates rise it might have a depressed value when you need it.

Shortening duration reduces the effect of an interest rate rise, and reduces the "waiting time" needed for a bond fund to make up the capital loss through accumulated interest.

The I bond is immune to any effect from interest rate changes. After the first year you can redeem it at any time, subject to a small known-in-advance penalty for the first five years. There is no good or bad time to redeem. You redeem them when you need to.

To put it another way, I bonds currently pay inflation-plus-zero-fixed-rate. Let's suppose there were a hypothetical TIPS bond--maybe a 15-year bond? that actually made no coupon payments--the current 0.125% isn't too different from that--and had a real yield of zero, i.e. auctioned for exactly $1,000.

You redeem the I bond any time you like and and you get $1,000 year-2013-dollars.

The TIPS has one specific future moment, its maturity date, when it is worth $1,000 year-2013 dollars. Any time in between, it might be worth considerably more or less than $1,000 year-2013 dollar.

Forget formulas and calculations, for that specific choice can you make a comparison?
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Re: what is an ibonds duration?

Postby nisiprius » Sun Mar 24, 2013 1:50 pm

Epsilon Delta wrote:The redemption value of an I-bond is not a market price, it cannot be used to calculate duration because it does not reflect the judgment of an efficient market.
To me, the dollar value of something is the actual number of dollars I can get in real life, in exchange for relinquishing it. It's an operational definition. I know just what I need to do to get that number of dollars--I redeem the I bonds.

To say that a number of dollars I can actually get--by redeeming it at the Treasury--shouldn't count, and that what counts is some number of dollars from a paper calculation--even though you cannot tell me any real-life procedure for getting that number of dollars in exchange for an I bond--is way too sophisticated for me. If that is how money actually works, I think I will get up a desk on some asteroid and invest in stars.
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Re: what is an ibonds duration?

Postby market timer » Sun Mar 24, 2013 1:54 pm

nisiprius wrote:To say that the number of dollars I can actually get--by redeeming it at the Treasury--shouldn't count, and that what counts is some number of dollars I can't actually get for it... is too sophisticated for me.

As you consume assets in retirement, how do you decide whether to redeem I bonds or liquidate taxable investments? If you choose to redeem I bonds, how do you decide which I bonds to redeem? Each day you choose to hold onto an I bond tells me that you value it more than redemption value.
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Re: what is an ibonds duration?

Postby nisiprius » Sun Mar 24, 2013 1:56 pm

market timer wrote:
nisiprius wrote:To say that the number of dollars I can actually get--by redeeming it at the Treasury--shouldn't count, and that what counts is some number of dollars I can't actually get for it... is too sophisticated for me.

As you consume assets in retirement, how do you decide whether to redeem I bonds or liquidate taxable investments? If you choose to redeem I bonds, how do you decide which I bonds to redeem?
I don't see how the value of some other investment has any effect whatsoever on the value of an I bond. If I redeem an I bond purchased in March 2003 for $1,000 today, I get $1,534.80 for it. It doesn't matter what the yield curve, the Dow, or my marginal tax rate is. The value of the bond is $1,534.80.
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Re: what is an ibonds duration?

Postby magician » Sun Mar 24, 2013 1:58 pm

Epsilon Delta wrote:In short the effective duration for a bond with an option is the Macaulay duration calculated on the payments that will happen if the option holder acts rationally.

This cannot possibly be true: Macaulay duration cannot be negative, but there are bonds (e.g., IO strips) that have negative duration in some yield ranges.

(Furthermore, effective duration is never equal to Macaulay duration unless you have an option-free bond and YTM = 0%. Perhaps you meant modified duration instead of Macaulay duration, but this wouldn't be true either, for the same reason as above: modified duration cannot be negative.)
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Re: what is an ibonds duration?

Postby market timer » Sun Mar 24, 2013 2:00 pm

nisiprius wrote:
market timer wrote:
nisiprius wrote:To say that the number of dollars I can actually get--by redeeming it at the Treasury--shouldn't count, and that what counts is some number of dollars I can't actually get for it... is too sophisticated for me.

As you consume assets in retirement, how do you decide whether to redeem I bonds or liquidate taxable investments? If you choose to redeem I bonds, how do you decide which I bonds to redeem?
I don't see how the value of some other investment has any effect whatsoever on the value of an I bond.

Let me put it a different way. Suppose you own some 2% I bonds worth $10K redemption value. How much would I have to pay you to redeem them today?
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Re: what is an ibonds duration?

Postby patrick » Sun Mar 24, 2013 2:12 pm

nisiprius wrote:
Epsilon Delta wrote:The redemption value of an I-bond is not a market price, it cannot be used to calculate duration because it does not reflect the judgment of an efficient market.
To me, the dollar value of something is the actual number of dollars I can get in real life, in exchange for relinquishing it. It's an operational definition. I know just what I need to do to get that number of dollars--I redeem the I bonds.

To say that a number of dollars I can actually get--by redeeming it at the Treasury--shouldn't count, and that what counts is some number of dollars from a paper calculation--even though you cannot tell me any real-life procedure for getting that number of dollars in exchange for an I bond--is way too sophisticated for me. If that is how money actually works, I think I will get up a desk on some asteroid and invest in stars.


Do you apply this rule to EE bonds also?

Suppose you buy $5000 of EE bonds today. In 20 years the redemption value will be $10000 due to the guaranteed doubling. In 19 years and 11 months the redemption value will be approximately $5203. Does this mean that, in 19 years and 11 months, you'd consider the bond as only worth $5203?
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Re: what is an ibonds duration?

Postby Mel Lindauer » Sun Mar 24, 2013 2:17 pm

nisiprius wrote:
market timer wrote:
nisiprius wrote:To say that the number of dollars I can actually get--by redeeming it at the Treasury--shouldn't count, and that what counts is some number of dollars I can't actually get for it... is too sophisticated for me.

As you consume assets in retirement, how do you decide whether to redeem I bonds or liquidate taxable investments? If you choose to redeem I bonds, how do you decide which I bonds to redeem?
I don't see how the value of some other investment has any effect whatsoever on the value of an I bond. If I redeem an I bond purchased in March 2003 for $1,000 today, I get $1,534.80 for it. It doesn't matter what the yield curve, the Dow, or my marginal tax rate is. The value of the bond is $1,534.80.


Precisely the point I tried to make upstream, nisi. We always make decisions based on what we think is best. If everything needs to have a duration attached to it (as the academics seem to be trying to imply), why doesn't Vanguard publish a duration for their money market accounts, and why don't banks publish a duration for their CDs or money in their checking accounts? And why doesn't the Treasury have to publish a duration for our paper currency? To me, that's just as silly as trying to attach a duration to I Bonds, which are basically "Cash" after one year.

Methinks folks are trying to outhink something that's really rather simple; you redeem your I Bonds when you need the money for something or when they reach final maturity. And you make your decision based on what you think is the best choice for you.
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Re: what is an ibonds duration?

Postby nisiprius » Sun Mar 24, 2013 2:18 pm

market timer wrote:
nisiprius wrote:
market timer wrote:
nisiprius wrote:To say that the number of dollars I can actually get--by redeeming it at the Treasury--shouldn't count, and that what counts is some number of dollars I can't actually get for it... is too sophisticated for me.
As you consume assets in retirement, how do you decide whether to redeem I bonds or liquidate taxable investments? If you choose to redeem I bonds, how do you decide which I bonds to redeem?
I don't see how the value of some other investment has any effect whatsoever on the value of an I bond.
Let me put it a different way. Suppose you own some 2% I bonds worth $10K redemption value. How much would I have to pay you to redeem them today?
Last reply from me, since this is going nowhere; you get the last word if you want it. I would gladly redeem them in exchange for the right to buy, for $10,000, 2.05% series I savings bonds, registered to my name, with a $10,000 redemption value and the same maturity date; [snarky comment removed by admin LadyGeek]
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Re: what is an ibonds duration?

Postby jeffyscott » Sun Mar 24, 2013 4:26 pm

patrick wrote:Suppose you buy $5000 of EE bonds today. In 20 years the redemption value will be $10000 due to the guaranteed doubling. In 19 years and 11 months the redemption value will be approximately $5203. Does this mean that, in 19 years and 11 months, you'd consider the bond as only worth $5203?


Yes, it's worth $5203, but I would also know that in one more month it will be worth $10,000. This is no different than it being worth about $5100 after 10 years, but knowing that in another 10 it will be worth $10,000.

At 10 years the YTM is nearly 7%, this would be useful to know when comparing it to other options and deciding whether to keep it or not. At 19 years 11 months the YTM is astronomical, this is also useful to know.
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Re: what is an ibonds duration?

Postby LH » Mon Mar 25, 2013 6:11 am

nisiprius wrote:In my arrogant opinion...

The duration of a series I savings bond is zero.
:!: :!: :!: :!: :!: :!: :!: :!: :!:

I am taking one of several definitions of duration, specifically, that duration is the percentage change in the value of the bond divided by the prevailing annual percentage interest rate. For example, if a 1% rise in interest rate causes a 4% drop in bond value, the duration is (4% / (1%/year)) = 4 years.

The value of a series I savings bond is unaffected by interest rate changes. They are non-marketable securities and they are redeemed directly with the Treasury, per agreement, not sold at auction to other investors. The value of a current series I savings bond is the purchase price times the cumulative CPI change between purchase and redemption. The value of any savings bond depends on the cumulative CPI change and the "fixed rate." The current interest rate does not come into the equation.

A 1% rise in the interest rate does not have any effect on the redemption value of a series I savings bond. It drops in value by zero. The duration is zero.

This is precisely one of the reasons why series I savings bonds are interesting despite paying less than TIPS.
Epsilon Delta wrote:CDs are not bonds, but they also have duration.

One definition of duration is just the weighted average of the times of the cash flows. This is calculable for any fixed income asset. It may not always be meaningful, but it can be calculated. It is true that I-bonds are real rather than nominal and that savings bonds have a put, but people do compute durations for tips and callable bonds. For a bond with a put you can at least compute the duration to best and worst cases.
I would argue that this is not true because series I savings bonds are not marketable. You can perform the calculation you suggest but it's meaningless, because there is no way you can sell that bond for that amount of money. The calculation may show that the bond is "worth" $1100 or that it is "worth" $900 but it is irrelevant, because you cannot sell it to another investor. The only thing you can do is redeem it with the Treasury--per schedule, for accumulated-CPI-plus-fixed-rate--regardless of whether the number you calculated was higher or lower.



What if you could contract out the income stream, (one would have to bundle them together) like the

I WANT MY MONEY NOW!

commercials, do with annuities lawsuit payouts, generating a lump sum, in return for contractual obligation to the money generated? Then, like anything else, they can be marked to market, and interest rate sensitive.

then, why stop there, rehypothecate em, etc. etc. get some confusion and vaporization going, all good clean fun : P
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Re: what is an ibonds duration?

Postby LH » Mon Mar 25, 2013 6:21 am

Great replies everyone, more interesting range than I thought would be generated.

thanks,

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Re: what is an ibonds duration?

Postby LH » Mon Mar 25, 2013 6:37 am

nisiprius wrote:Let's try it this way. Forget theory. LH, why are you asking?

Why do you care about duration?

I don't want to put words in your mouth, but the usual reason for asking this question in this forum is that people want to "shorten up" their portfolio's duration to reduce interest rate risk, because they are concerned about a rise in interest rates. Perhaps the bond will regain its value when it matures, and perhaps the bond fund will regain value a few years down the road, but the concern is that you might need money at an arbitrary time, and if interest rates rise it might have a depressed value when you need it.

Shortening duration reduces the effect of an interest rate rise, and reduces the "waiting time" needed for a bond fund to make up the capital loss through accumulated interest.

The I bond is immune to any effect from interest rate changes. After the first year you can redeem it at any time, subject to a small known-in-advance penalty for the first five years. There is no good or bad time to redeem. You redeem them when you need to.

To put it another way, I bonds currently pay inflation-plus-zero-fixed-rate. Let's suppose there were a hypothetical TIPS bond--maybe a 15-year bond? that actually made no coupon payments--the current 0.125% isn't too different from that--and had a real yield of zero, i.e. auctioned for exactly $1,000.

You redeem the I bond any time you like and and you get $1,000 year-2013-dollars.

The TIPS has one specific future moment, its maturity date, when it is worth $1,000 year-2013 dollars. Any time in between, it might be worth considerably more or less than $1,000 year-2013 dollar.

Forget formulas and calculations, for that specific choice can you make a comparison?


Well,

Basically that people are talking about
1)shortening duration
2)switching over to ibonds instead of TIPS

1)I do not really buy into, there should be no free lunch I would hazard, even given financial repression, should be hard to time expectantly. But then again, certainly SOME possible financial repression, I would imagine, would generate free lunches that could be exploitable? Who knows, kinda off topic, sorry OP, : P anyway, By shortening duration, you will give up some yield expectantly. then at some point, like all timing, you have to decide when to reverse your timing decision...... Or maybe you never do? Just seems like such a touchy feely human expectant failure kinda thing to do, that makes intuitive "sense" in our guts.

2) is an interesting question, maybe there is a free lunch, because by fiat, ibonds are fixed at 0, and cannot go negative like tips. BUT, that then brings back the comparison that TIPS bond fund will fluctuate, while ibonds will not per se, then TIPS bonds fund fluctuation is partially dependant on duration of said fund. So, if you switch to ibonds, what exactly is that doing to your duration, is it shortening it, or not?

The comparison ibonds to TIPS is an interesting one, of which duration is but a component. Say my TIPS fund, it has gone up in value/price more so than stocks have over what 10 years (hazy on the numbers), now I can and actually have, rebalanced with that difference. Whereas ibonds, I cannot really mark them to market, nor rebalance as easily. They will not spike in value like my TIPS bond fund did. Nor will they drop. My TIPS fund, in terms of portfolio volatility, really dampened it, whereas an ibond equivalent would not of to the same extent, at least not in an easily marked to market, ability to rebalance kind of way.

So its an apples to oranges comparison clearly, and I just wonder if people are conflating the various issues, which I certainly think is reasonable.

My gestalt is to just split the difference, buy some Ibonds, but to suck it up, and keep buying TIPS fund too (even though I could have bought all ibonds to make allocation).

When I try to look past this gestalt more rationally, I get into things like

"what is the duration of an ibond"

I suspect that one should mark to market in some way, for a valid comparision, between tips and ibonds, (of course then there is the wonderful TIPS individaul bond, versus TIPS fund differences as well, great stuff).

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Re: what is an ibonds duration?

Postby richard » Mon Mar 25, 2013 7:21 am

When I compute the weighted average duration of my bonds, I include ibonds at zero. The amount I can sell them for does not vary with changes in interest rates and duration is sensitivity to changes in the relevant interest rate.

I usually use zero for their maturity (due to the embedded put), although using actual maturity may be better (or not).

FWIW, I keep my bond portfolio's weighted average duration and maturity in the general neighborhood of the average duration and maturity of the Total Bond Market fund.
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Re: what is an ibonds duration?

Postby swaption » Mon Mar 25, 2013 1:56 pm

It's an interesting topic, something I have thought about from time to time as a holder of 3.4% I Bonds. If one thinks this matters at all, I don't believe the answer can be 0. Of course there is the arguement of the put option, but is that really all that valid if the put option comes with the requirement that you also have to go out back and literally burn money in order to exercise it? The put option should be given about as much weight as it's value, and in the case of my 3.4% bonds, that is pretty much close to being worthless.

So for a moment, let's suspend reality and pretend the put option does not exist (which in my case that essentially is the case). Does no secondary market invalidate the concept of duration? First off, that's not really the right question. The right question is does a lack of a secondary market invalidate the concept of value? To that my answer is no. One can use any one of a variety of approaches to value an asset or stream of cash flows, and if you can come up with a value, then that value can also change. In the case of I Bonds, they become less valuable as interest rates (real interest rates) rise. In the case of my fundamentally putless bonds, that change is likely relatively close to the behavior of TIPS, so a TIPS duration is probably a pretty good proxy. But as those interest rates continue to rise further (or right away for more recently issued bonds), the value of the put becomes more relevant, mitigating the adverse change in value. In this way, I Bonds likely exhibit some form of negative convexity due to this dampened volatility and at that point the duration would depart from the levels found in comparable TIPS, and in some instances be very short.

Edit: Negative convexity may not be correct. More accurately, it's convexity of some sort, which means duration changes depending on interest rate level. My best guess would be positive convexity given that duration shortens as interst rates increase, the opposite of mbs.
Last edited by swaption on Mon Mar 25, 2013 4:00 pm, edited 1 time in total.
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Re: what is an ibonds duration?

Postby Mel Lindauer » Mon Mar 25, 2013 2:44 pm

swaption wrote:It's an interesting topic, something I have thought about from time to time as a holder of 3.4% I Bonds. If one thinks this matters at all, I don't believe the answer can be 0. Of course there is the arguement of the put option, but is that really all that valid if the put option comes with the requirement that you also have to go out back and literally burn money in order to exercise it? The put option should be given about as much weight as it's value, and in the case of my 3.4% bonds, that is pretty much close to being worthless.

So for a moment, let's suspend reality and pretend the put option does not exist (which in my case that essentially is the case). Does no secondary market invalidate the concept of duration? First off, that's not really the right question. The right question is does a lack of a secondary market invalidate the concept of value? To that my answer is no. One can use any one of a variety of approaches to value an asset or stream of cash flows, and if you can come up with a value, then that value can also change. In the case of I Bonds, they become less valuable as interest rates (real interest rates) rise. In the case of my fundamentally putless bonds, that change is likely relatively close to the behavior of TIPS, so a TIPS duration is probably a pretty good proxy. But as those interest rates continue to rise further (or right away for more recently issued bonds), the value of the put becomes more relevant, mitigating the adverse change in value. In this way, I Bonds likely exhibit some form of negative convexity due to this dampened volatility and at that point the duration would depart from the levels found in comparable TIPS, and in some instances be very short.


Just because something has value doesn't mean it has a duration. A house has value, a car has value, a diamond has value, cash has value, CDs have value, but none has a duration. I Bonds are no different.
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Re: what is an ibonds duration?

Postby swaption » Mon Mar 25, 2013 3:07 pm

Mel Lindauer wrote:
swaption wrote:It's an interesting topic, something I have thought about from time to time as a holder of 3.4% I Bonds. If one thinks this matters at all, I don't believe the answer can be 0. Of course there is the arguement of the put option, but is that really all that valid if the put option comes with the requirement that you also have to go out back and literally burn money in order to exercise it? The put option should be given about as much weight as it's value, and in the case of my 3.4% bonds, that is pretty much close to being worthless.

So for a moment, let's suspend reality and pretend the put option does not exist (which in my case that essentially is the case). Does no secondary market invalidate the concept of duration? First off, that's not really the right question. The right question is does a lack of a secondary market invalidate the concept of value? To that my answer is no. One can use any one of a variety of approaches to value an asset or stream of cash flows, and if you can come up with a value, then that value can also change. In the case of I Bonds, they become less valuable as interest rates (real interest rates) rise. In the case of my fundamentally putless bonds, that change is likely relatively close to the behavior of TIPS, so a TIPS duration is probably a pretty good proxy. But as those interest rates continue to rise further (or right away for more recently issued bonds), the value of the put becomes more relevant, mitigating the adverse change in value. In this way, I Bonds likely exhibit some form of negative convexity due to this dampened volatility and at that point the duration would depart from the levels found in comparable TIPS, and in some instances be very short.


Just because something has value doesn't mean it has a duration. A house has value, a car has value, a diamond has value, cash has value, CDs have value, but none have a duration. I Bonds are no different.


That's right, but the difference is that I Bonds are financial assets that have a value that changes in a relatively direct way with changes in (real) interest rates. I would have hoped that was implied in what I summarized above.
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Re: what is an ibonds duration?

Postby Mel Lindauer » Mon Mar 25, 2013 5:04 pm

swaption wrote:
Mel Lindauer wrote:
swaption wrote:It's an interesting topic, something I have thought about from time to time as a holder of 3.4% I Bonds. If one thinks this matters at all, I don't believe the answer can be 0. Of course there is the arguement of the put option, but is that really all that valid if the put option comes with the requirement that you also have to go out back and literally burn money in order to exercise it? The put option should be given about as much weight as it's value, and in the case of my 3.4% bonds, that is pretty much close to being worthless.

So for a moment, let's suspend reality and pretend the put option does not exist (which in my case that essentially is the case). Does no secondary market invalidate the concept of duration? First off, that's not really the right question. The right question is does a lack of a secondary market invalidate the concept of value? To that my answer is no. One can use any one of a variety of approaches to value an asset or stream of cash flows, and if you can come up with a value, then that value can also change. In the case of I Bonds, they become less valuable as interest rates (real interest rates) rise. In the case of my fundamentally putless bonds, that change is likely relatively close to the behavior of TIPS, so a TIPS duration is probably a pretty good proxy. But as those interest rates continue to rise further (or right away for more recently issued bonds), the value of the put becomes more relevant, mitigating the adverse change in value. In this way, I Bonds likely exhibit some form of negative convexity due to this dampened volatility and at that point the duration would depart from the levels found in comparable TIPS, and in some instances be very short.


Just because something has value doesn't mean it has a duration. A house has value, a car has value, a diamond has value, cash has value, CDs have value, but none have a duration. I Bonds are no different.


That's right, but the difference is that I Bonds are financial assets that have a value that changes in a relatively direct way with changes in (real) interest rates. I would have hoped that was implied in what I summarized above.


Unlike traditional bonds, the I Bond's value isn't affected by changes in real interest rates; the value remains exactly the same as it was prior to the rise in real rates.
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Re: what is an ibonds duration?

Postby market timer » Mon Mar 25, 2013 7:52 pm

swaption wrote:The right question is does a lack of a secondary market invalidate the concept of value? To that my answer is no.

That is a good way of framing the question.
In the case of my fundamentally putless bonds, that change is likely relatively close to the behavior of TIPS, so a TIPS duration is probably a pretty good proxy.

Since you are highly unlikely to redeem your I bond early, and it is a zero coupon bond, its duration is very close to the remaining time to maturity. (There is some small probability real rates rise dramatically and your put becomes in-the-money.)
But as those interest rates continue to rise further (or right away for more recently issued bonds), the value of the put becomes more relevant, mitigating the adverse change in value. In this way, I Bonds likely exhibit some form of negative convexity due to this dampened volatility and at that point the duration would depart from the levels found in comparable TIPS, and in some instances be very short.

I've never modeled this carefully, but I'd be surprised if I bonds exhibited negative convexity in any scenario. Negative convexity typically arises when one owns a bond and is short a call option on that bond; whereas, in the case of I bonds, you are long a bond and long a put option.
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Re: what is an ibonds duration?

Postby STC » Mon Mar 25, 2013 7:55 pm

Conceptually, does the inclusion of IBonds change your "blended duration" within your FI portfolio? And if so, do you adjust your holdings to compensate? Do you think of IBonds as having 0 duration, because there is no interest rate risk? For example:

Target duration: 5 years
IBonds as a % of FI: 50%
Duration of TBM: 5 years
Blended duration: 2.5 years

Should this investor look at longer dated FI instruments to get the blended duration out to the target 5 years?

Edit: By extension, if it is generally accepted that TBM is the baseline that you can tilt from, then should the target duration be that of TBM? So, if you own IBonds or EEBonds you would need to buy some extended maturities along with your core TBM holdings to accurately represent the baseline of TBM?
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Re: what is an ibonds duration?

Postby market timer » Mon Mar 25, 2013 7:59 pm

I own I bonds and EE bonds and consider their duration for portfolio allocation. For reasons mentioned earlier, I ballpark the newly issued I bond duration at 6-8 years. If I were buying I bonds with the intention of using them as an emergency fund, house downpayment, or some other purpose where redemption would not depend on rates in the secondary market, I'd adjust the duration lower. Calculating duration on EE bonds is significantly more complicated, but I'd ballpark it in the 10-12 year range for newly issued EE bonds, assuming optimal redemption.
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Re: what is an ibonds duration?

Postby JamesSFO » Mon Mar 25, 2013 8:52 pm

I don't think having a duration is a requirement for comparability. For example, if you are looking at selling two financial assets, e.g. Total Stock vs. Bond CUSIP 123456, total stock does not have a duration and you can still make a decision.

I find myself landing in the camp that I and EE bonds have enough quirky features (esp lack of secondary market, put options, lack of ability to replace due to purchase limits) that duration even if calculable is not all that helpful.
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Re: what is an ibonds duration?

Postby swaption » Mon Mar 25, 2013 10:28 pm

market timer wrote:I've never modeled this carefully, but I'd be surprised if I bonds exhibited negative convexity in any scenario. Negative convexity typically arises when one owns a bond and is short a call option on that bond; whereas, in the case of I bonds, you are long a bond and long a put option.


I guess you missed my last edit, which I'll copy here:

Edit: Negative convexity may not be correct. More accurately, it's convexity of some sort, which means duration changes depending on interest rate level. My best guess would be positive convexity given that duration shortens as interst rates increase, the opposite of mbs.
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Re: what is an ibonds duration?

Postby swaption » Mon Mar 25, 2013 10:40 pm

Mel Lindauer wrote:
swaption wrote:
Mel Lindauer wrote:
swaption wrote:It's an interesting topic, something I have thought about from time to time as a holder of 3.4% I Bonds. If one thinks this matters at all, I don't believe the answer can be 0. Of course there is the arguement of the put option, but is that really all that valid if the put option comes with the requirement that you also have to go out back and literally burn money in order to exercise it? The put option should be given about as much weight as it's value, and in the case of my 3.4% bonds, that is pretty much close to being worthless.

So for a moment, let's suspend reality and pretend the put option does not exist (which in my case that essentially is the case). Does no secondary market invalidate the concept of duration? First off, that's not really the right question. The right question is does a lack of a secondary market invalidate the concept of value? To that my answer is no. One can use any one of a variety of approaches to value an asset or stream of cash flows, and if you can come up with a value, then that value can also change. In the case of I Bonds, they become less valuable as interest rates (real interest rates) rise. In the case of my fundamentally putless bonds, that change is likely relatively close to the behavior of TIPS, so a TIPS duration is probably a pretty good proxy. But as those interest rates continue to rise further (or right away for more recently issued bonds), the value of the put becomes more relevant, mitigating the adverse change in value. In this way, I Bonds likely exhibit some form of negative convexity due to this dampened volatility and at that point the duration would depart from the levels found in comparable TIPS, and in some instances be very short.


Just because something has value doesn't mean it has a duration. A house has value, a car has value, a diamond has value, cash has value, CDs have value, but none have a duration. I Bonds are no different.


That's right, but the difference is that I Bonds are financial assets that have a value that changes in a relatively direct way with changes in (real) interest rates. I would have hoped that was implied in what I summarized above.


Unlike traditional bonds, the I Bond's value isn't affected by changes in real interest rates; the value remains exactly the same as it was prior to the rise in real rates.


Mel,

Once again what I thought was implied is that by value I mean present value. The put price is not the same as value in that sense. This is not some theoretical game I'm playing. When I do all my calculations, I put a value on my I Bonds well above par. That's how much they are worth to me. If you had a $100,000 30 year bond that paid 100% interest per annum, what value would you ascribe to that? What you are saying is that the lack of a secondary market and the willingness of a committed purchaser to buy the bond at par (how generous!) means that the value is $100,000. That really does not make any sense.
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Re: what is an ibonds duration?

Postby Angst » Tue Mar 26, 2013 12:12 am

To address the OP: I'm in the "No Duration" camp. I think duration is meaningless wrt a non-negotiable security. That's not to say that rate changes won't have an impact on how I value an I or EE savings bond that I own, but there's no neat formula for predicting it.

My question though: If purchase limits for savings bonds did not exist, what would professional financial advisors be telling their clients wrt their complete FI portfolios and the %'s of I or EE bonds they might recommend their clients hold, and how would they explain this wrt to duration? Maybe advisors get to dodge the duration issue (and thread!) b/c they won't be bothered with savings bonds and those little $10k annual purchase limits.
Angst
 
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