Valuation of I Bonds

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Buffetologist
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Valuation of I Bonds

Post by Buffetologist »

A while back posters named The Dan and Market Timer did a fascinating analysis on the valuation of EE bonds in terms of embedded options.

viewtopic.php?f=10&t=151634

Basically Market Timer demonstrated that an EE bond was roughly a 20 year zero coupon bond with a put option. Basically, the doubling caused a increased present value (PV) of the EE bonds relative to the 20 year zero coupon treasury, plus the PV of the EE bond is further increased by the put option which after a year allows redemption for a small amount over the purchase price thereby hedging the huge PV loss that would be incurred in a 20 year zero coupon in response to rapid interest rate increases thereby limiting the downside risk of EE bonds.

Since I've been investing in I bonds (roughly 2010), most often TIPS had negative yields and the investment in I-bonds seemed like a no brainer. This is the first time that TIPS have positive yields at a time when I can buy I bonds.

I'd like to understand how to value I bonds in this context. In particular, I'm trying to figure out if I bonds are currently worth purchasing or does it make sense to wait and hope for a higher fixed rate in May.

The current yield on Vanguard Inflation Protected Securities is 0.25% which is higher than the 0% fixed rate. That would suggest a slight disadvantage to the I bonds currently.

I don't know exactly how they calculate the fixed rate, but if it's based on TIPS, it would seem as though the fixed rate ought to increase in May should fear of deflation continue.

Additionally, the fact that Ibond values can't go down also seems to factor in, but I don't see how to deconstruct that into embedded options to properly value the I bonds relative to TIPS either through Treasury Direct or through the Vanguard fund.

Any insight is welcome. Thanks in advance.
Last edited by Buffetologist on Fri Jan 16, 2015 10:52 am, edited 2 times in total.
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Rob5TCP
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Re: Valuation of I Bonds

Post by Rob5TCP »

I don't know of an easy formula to compare the two -
savings bond advisor has a sheet comparing the differences between the rates of 10 year TIPS and IBonds over the past 11 years

http://savings-bond-advisor.com/series- ... ase-rates/

The differences were as high as 244 basis points (2.44%) during the 2008 crisis
and as little as -.78% when IBonds were zero and TIPS had negative real yields
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Re: Valuation of I Bonds

Post by Grt2bOutdoors »

Buffetologist wrote:A while back posters named The Dan and Market Timer did a fascinating analysis on the valuation of EE bonds in terms of embedded options.

viewtopic.php?f=10&t=151634


Since I've been investing in I bonds (roughly 2010), most often TIPS had negative yields and the investment in I-bonds seemed like a no brainer. This is the first time that TIPS have positive yields at a time when I can buy I bonds. I think I can also choose between I-bonds or EE-bonds for my tax refund and need to decide which is worth more.

Any insight is welcome. Thanks in advance.
You can only receive paper I bonds, the Treasury does not issue EE savings bonds as part of Form 8888. Of course, you can always purchase EE bonds through your Treasury Direct account.
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Re: Valuation of I Bonds

Post by Buffetologist »

Grt2bOutdoors wrote:
Buffetologist wrote:A while back posters named The Dan and Market Timer did a fascinating analysis on the valuation of EE bonds in terms of embedded options.

viewtopic.php?f=10&t=151634


Since I've been investing in I bonds (roughly 2010), most often TIPS had negative yields and the investment in I-bonds seemed like a no brainer. This is the first time that TIPS have positive yields at a time when I can buy I bonds. I think I can also choose between I-bonds or EE-bonds for my tax refund and need to decide which is worth more.

Any insight is welcome. Thanks in advance.
You can only receive paper I bonds, the Treasury does not issue EE savings bonds as part of Form 8888. Of course, you can always purchase EE bonds through your Treasury Direct account.
Good point and thanks. I edited my original post so as to not distract from the discussion I really want to have.
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Re: Valuation of I Bonds

Post by Angst »

Buffetologist wrote:I'd like to understand how to value I bonds in this context. In particular, I'm trying to figure out if I bonds are currently worth purchasing or does it make sense to wait and hope for a higher fixed rate in May.

The current yield on Vanguard Inflation Protected Securities is 0.25% which is higher than the 0.1% fixed rate. That would suggest a slight disadvantage to the I bonds currently.

I don't know exactly how they calculate the fixed rate, but if it's based on TIPS, it would seem as though the fixed rate ought to increase in May should fear of deflation continue.
Your verbiage is unclear to me, but it comes across as if you believe that I Bonds currently have a 0.1% fixed rate. This is wrong - they currently have a 0.0% fixed rate. Moreover, with interest rates very low right now I find it hard to imagine the fixed rate becoming positive in May. Neither would I think a "fear of deflation" would compel Treasury to increase the fixed rate; on the contrary, I might think this would push them to lower it if it were already positive.

I still like I Bonds for a place to park cash for a year or two, or indefinitely, but if I were planning on holding them for 5-10 years, and if I had available tax-deferred space, I'd buy 5 to 10yr TIPS first. I think EE Bonds are great right now if you have room in your fixed income allocation for Long Term Govt bonds. 10 yr Treasury Notes are something like 1.8% and the 20 yr yield curve shows about 2.12%, a lot less than EE Bonds 20 yr rate of 3.53%

If you are unclear about the current fixed rate on I Bonds, I encourage you to read more about them. Treasury Direct has good information. Note the additional sub-links off to the left side of this page. Also, Ibonds.info has some good stuff. #Cruncher's eyebonds.info site also has lots of useful info and links available. And of course the BH Wiki has good stuff, including separate sections on I Bonds and EE Bonds.
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Re: Valuation of I Bonds

Post by Buffetologist »

Angst wrote:
Buffetologist wrote:I'd like to understand how to value I bonds in this context. In particular, I'm trying to figure out if I bonds are currently worth purchasing or does it make sense to wait and hope for a higher fixed rate in May.

The current yield on Vanguard Inflation Protected Securities is 0.25% which is higher than the 0.1% fixed rate. That would suggest a slight disadvantage to the I bonds currently.

I don't know exactly how they calculate the fixed rate, but if it's based on TIPS, it would seem as though the fixed rate ought to increase in May should fear of deflation continue.
Your verbiage is unclear to me, but it comes across as if you believe that I Bonds currently have a 0.1% fixed rate. This is wrong - they currently have a 0.0% fixed rate. Moreover, with interest rates very low right now I find it hard to imagine the fixed rate becoming positive in May. Neither would I think a "fear of deflation" would compel Treasury to increase the fixed rate; on the contrary, I might think this would push them to lower it if it were already positive.

I still like I Bonds for a place to park cash for a year or two, or indefinitely, but if I were planning on holding them for 5-10 years, and if I had available tax-deferred space, I'd buy 5 to 10yr TIPS first. I think EE Bonds are great right now if you have room in your fixed income allocation for Long Term Govt bonds. 10 yr Treasury Notes are something like 1.8% and the 20 yr yield curve shows about 2.12%, a lot less than EE Bonds 20 yr rate of 3.53%

If you are unclear about the current fixed rate on I Bonds, I encourage you to read more about them. Treasury Direct has good information. Note the additional sub-links off to the left side of this page. Also, Ibonds.info has some good stuff. #Cruncher's eyebonds.info site also has lots of useful info and links available. And of course the BH Wiki has good stuff, including separate sections on I Bonds and EE Bonds.
Thanks. I edited my post. I am interested in long term and allocate a portion of my portfolio to raw inflation protection distinct from bonds. When I initially bought I bonds, I was using them as short-term cash substitutes, but as I learned more, I saw their value relative to TIPS which were in negative yield range.

What I am looking for is how to deconstruct I bonds into an equivalent TIPS plus the associated embedded options in a similar manner as the EE bonds in the link I cited. As an amateur student of finance, I am struggling with setting up this decomposition.
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Re: Valuation of I Bonds

Post by tipswatcher »

On I Bonds, I would suggest holding off on buying a 2015 allocation at least until May 1, and mostly likely after Nov. 1.

On May 1, the fixed rate is likely to remain at 0.0%, but the inflation-adjusted rate (for all I Bonds, not matter when they were issued) is very likely to drop below zero. Right now, three months into the rate period (September to December) non-seasonally adjusted inflation is running -1.36%. That deflationary number is not likely to rise above zero in the next three months, so the inflation-adjusted rate will be negative.

I Bonds can't pay less than 0.0%, though, so that is likely to be the return of I Bonds purchased in before Nov. 2015: 0.0%. Zero.

You can follow the monthly trend here: http://tipswatch.com/tracking-inflation-and-i-bonds/

Now, it is possible that the Treasury will see this and decide to add a fixed-rate boost on May 1, let's say to 0.2%, or even 0.1%. If that happened, I Bonds would probably be attractive enough to buy, because that fixed rate sticks with the I Bond for 30 years. But would the Treasury do this? Probably not.

So, no harm in waiting. An I Bond you buy today will pay a fixed rate of 0.0% and an inflation-adjusted rate of 0.0% for six months. Highly likely.

Just wait until Nov. 1, and if everything remains 0.0% - I'd still buy them and suffer the six months of nothingness.
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Re: Valuation of I Bonds

Post by Buffetologist »

The analogy I'm looking for is

value of ($10,000 EE bond) = value of 20 year zero-coupon treasury producing $20K in 20 years + value of put option to sell the bond back after at least one year for $10,000 plus accumulation of 0.1% interest.

In the original post I cited, the value was computed to be about $12,000 - about $11,500 for the future cash flow, plus about $500 for the option. Therefore, buying a $10,000 EE bond was a great deal.

For I bonds we have
value of ($10,000 I bond) = value of 30 year TIPS +/ some combination of options and other bonds.

I'm trying to understand what that combination is so that the present value of Ibonds can be calculated.

Thanks
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Re: Valuation of I Bonds

Post by convert949 »

Basically Market Timer demonstrated that an EE bond was roughly a 20 year zero coupon bond with a put option. Basically, the doubling caused a increased present value (PV) of the EE bonds relative to the 20 year zero coupon treasury, plus the PV of the EE bond is further increased by the put option which after a year allows redemption for a small amount over the purchase price thereby hedging the huge PV loss that would be incurred in a 20 year zero coupon in response to rapid interest rate increases thereby limiting the downside risk of EE bonds.
Another difference in this scenario would be that you could replace the zero coupon treasury regardless of the face value. I am not sure if the same is true of EE or I Bonds. If redeemed as suggested to take advantage of increasing rates, it is possible that you would still be subject to the $10K per year per account purchase limit... Anyone have better information?
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Re: Valuation of I Bonds

Post by Buffetologist »

convert949 wrote:
Basically Market Timer demonstrated that an EE bond was roughly a 20 year zero coupon bond with a put option. Basically, the doubling caused a increased present value (PV) of the EE bonds relative to the 20 year zero coupon treasury, plus the PV of the EE bond is further increased by the put option which after a year allows redemption for a small amount over the purchase price thereby hedging the huge PV loss that would be incurred in a 20 year zero coupon in response to rapid interest rate increases thereby limiting the downside risk of EE bonds.
Another difference in this scenario would be that you could replace the zero coupon treasury regardless of the face value. I am not sure if the same is true of EE or I Bonds. If redeemed as suggested to take advantage of increasing rates, it is possible that you would still be subject to the $10K per year per account purchase limit... Anyone have better information?
If the PV of the EE bond was less than $10K + accumulated interest, then you could cash the bond for the $10K plus accumulated interest. The equivalent zero coupon would be worth a lot less. That's why the put option that comes with the EE bond hedges your downside exposure. You could reinvest in anything you wanted to. It doesn't have to be an EE bond.
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Re: Valuation of I Bonds

Post by Kevin M »

I Bonds are much simpler than EE bonds, so I don't think you need to get into the complexity as in the thread you linked.

The main reason you need to think about EE bonds like a zero-coupon bond with a put option is because they pay essentially no interest unless you hold to maturity. By contrast, I Bonds pay reasonable interest that is reinvested, and that is part of your redemption value. You still have the cheap put option (three months of interest if redeemed within five years, free thereafter) with I Bonds, which essentially reduces your term risk to almost nothing.

So I just compare the rate and term risk of an I Bond compared to that of TIPS. Currently TIPS have negative real yields out to about five year maturities, and a 5-year TIPS has much more term risk than an I Bond. Therefore, an I Bond at 0% real currently is a much better deal than a TIPS. Maybe you want to take more term risk by extending TIPS maturity beyond five years, but that's a different discussion.

Note that Treasury Inflation-Protected Securities (TIPS) - Markets Data Center - WSJ.com shows positive yields for TIPS out to about one year maturity, but it has been explained that for very short-term TIPS, the market has discounted the possibility of much unexpected inflation, and priced them to be comparable to nominal short-term Treasuries. I don't really understand the math of this, since a 1-year Treasury has a negative real yield unless one assumes inflation will run at less than 0.16% over the next year. Maybe someone can walk us through an example to explain these TIPS quotes:

Code: Select all

Maturity     Coupon   Bid   Asked   Chg  Yield* Accrued
                                                principal
-----------  ------ ------  ------  ---- -----  ---------
2015 Apr 15  0.500   98.22   98.24  unch.5.651  1092
2015 Jul 15  1.875  100.06  100.08  + 1  1.353  1217
2016 Jan 15  2.000  101.14  101.16  + 2  0.483  1193


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Re: Valuation of I Bonds

Post by lazyday »

Kevin, it's being discussed in this thread: viewtopic.php?f=10&t=155675

Seems to me that yesterday, Thur 1/15, the real yield reported was not accounting for 2 months of deflation history (Nov 15-Jan 15).

But I don't really follow this either.
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Re: Valuation of I Bonds

Post by letsgobobby »

Couple of questions on this note:

1. Is this a year to skip the $5k I bond purchase on a tax return? it will be before May 1, and it seems the return will be doggishly low.

2. Is this a year to skip I bonds altogether, and buy EE bonds instead (assume can hold for 20 years)? In 20 years I'll be 61... definitely planning to be partly retired with relatively lower income at that time. And the 3.6% annualized return on an EE bond looks pretty darn attractive right now.
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Re: Valuation of I Bonds

Post by Dutch »

letsgobobby wrote:Couple of questions on this note:

1. Is this a year to skip the $5k I bond purchase on a tax return? it will be before May 1, and it seems the return will be doggishly low.

2. Is this a year to skip I bonds altogether, and buy EE bonds instead (assume can hold for 20 years)? In 20 years I'll be 61... definitely planning to be partly retired with relatively lower income at that time. And the 3.6% annualized return on an EE bond looks pretty darn attractive right now.
Yes, that's my takeaway. I've done the max on I bonds (including the 5,000 tax return) and EE bonds for a number of years now.

I will continue the EE bonds this year in January and wait for May and October to see if the 10,000 I bonds through Treasury Direct makes sense for 2015. But hold off on the 5,000 tax refund I bonds for this year.
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Re: Valuation of I Bonds

Post by Kevin M »

lazyday wrote:Kevin, it's being discussed in this thread: viewtopic.php?f=10&t=155675
Perfect! Exactly what I was looking for.

Thanks,

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Re: Valuation of I Bonds

Post by market timer »

I bonds are currently far more complicated to value, using an embedded options framework, than EE bonds. The real yield curve is currently positive at 5 years and longer--the 5-year constant maturity real yield at 0.1%. What this means is that the redemption option (put option) on a 0% fixed rate I bond is in-the-money relative to these TIPS. The question of whether to redeem or not means balancing the value of the option against the cost of the yield differential. Further, the real yield curve is much flatter now than it has been--the 30-year real yield is only 0.66%. This means there is a reasonable chance one might want to carry this I bond all the way to maturity. We can't just make an assumption like, well, the 5-year forward 5-year real yield is 3% so we can ignore the chance that we keep this I bond longer than 5 years. In fact, by my back-of-the-envelope calculation, the 5-year forward 5-year real yield is only about 0.36%.

To get some idea for how to value the I bond, I'd break it down into slightly easier pieces and build up complexity from there. As before, let's ignore tax deferral to keep the comparison simple. First, imagine that by buying the I bond, you are locking yourself into a minimum 5-year holding period. Relative to a 5-year TIPS, you lose 0.1% carry/year, a total of roughly 0.5% over 5 years. After 5 years, suppose you have the option to renew only once for another 5 years (renew meaning lock yourself into another 5-year contract), then the I bond matures after 10 years (not 30). So, the question is how much is the option to renew worth today? As noted earlier, the 5-year forward 5-year real yield is 0.36%. If the 5-year real yield declines substantially after 5 years (note below that it fell to -1.5% a couple years ago), you benefit from having kept the I bond. Your "breakeven" yield in 5 years, relative simply to having bought and rolled over a 5-year TIPS, is -0.1%.

Image

To model the value of the I bond, you will want to get a sense of the implied volatility of the 5-year forward 5-year real yield. I don't know where this information is available publicly, perhaps someone with Bloomberg can help here?

After you have an estimate of the value implied by this simpler model, which doesn't attribute any value to the I bond beyond 10 years, you can iterate. Find the value of the I bond recursively, where you not only have the option to renew at 5 years, but renewing gives you a similar renewal option after another 5 years, all the way out to year 30. I don't think you lose that much precision by limiting the renewal events to every 5 years, and it greatly simplifies the math. Lastly, you can add other details, such as the deflation floor (can never lose principal during any semi-annual period), and tax deferral.

I'm just about out the door to leave for vacation, so that's about all I can offer now. Between EE bonds and I bonds, I think EE bonds are the better value today if you can hold for 20 years.
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Re: Valuation of I Bonds

Post by Noobvestor »

I think the biggest value difference has to do with taxation - how valuable is it to you to be able to defer taxes for anywhere between 1 year and 30 years (I Bonds), versus having to deal with taxes either continuously (TIPS taxable) or whenever retirement rolls around (TIPS tax-advantaged). Also, how much use is extra effectively tax-deferred space worth to you? Due to these factors, I don't see a 'clean' way to compare I Bonds and TIPS - it will depend on personal circumstances. For me, I Bonds remain a good way to extend tax-advantaged space and have flexible tax deferral as well.
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Re: Valuation of I Bonds

Post by Kevin M »

I disagree with all of this excessively complex analysis. Again, the term risk of I Bonds is minuscule compared to a 5-year TIPS, yet the yield is only slightly less (even more slightly less yesterday, with the 5-year CMT real at 0.04%), and if you look at real market quotes (not the CMT yield), the 5-year TIPS yield is negative.

A real yield of 0% with a max downside risk of 3 months of interest (which could be $0 if we get zero inflation for a six month period) is gold when you have to go out 5-years to barely break 0% real (or maybe even not). If you want to take much more term risk for a tiny (or maybe no) additional yield, go ahead, but I think it's silly to compare an I Bond to a 5-year TIPS.

Maybe it makes sense to wait to see if there will be six months of 0% nominal on the I Bond, and maybe try to avoid that. But buy a 5-year TIPS instead? No thanks.

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Re: Valuation of I Bonds

Post by market timer »

I agree that I bonds are more attractive than today's 5-year TIPS. The question we're trying to answer is, by how much? The answer depends on the value of the redemption option.
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Re: Valuation of I Bonds

Post by Angst »

Kevin M wrote:I disagree with all of this excessively complex analysis. Again, the term risk of I Bonds is minuscule compared to a 5-year TIPS, yet the yield is only slightly less (even more slightly less yesterday, with the 5-year CMT real at 0.04%), and if you look at real market quotes (not the CMT yield), the 5-year TIPS yield is negative.

A real yield of 0% with a max downside risk of 3 months of interest (which could be $0 if we get zero inflation for a six month period) is gold when you have to go out 5-years to barely break 0% real (or maybe even not). If you want to take much more term risk for a tiny (or maybe no) additional yield, go ahead, but I think it's silly to compare an I Bond to a 5-year TIPS.

Maybe it makes sense to wait to see if there will be six months of 0% nominal on the I Bond, and maybe try to avoid that. But buy a 5-year TIPS instead? No thanks.

Kevin
Kevin, if it makes sense to wait on rates for next May's I Bond, shouldn't it also make sense to wait and look for a certain specific, positive indicative yield on the next 5 yr TIPS auction in April? At some point, the I Bond put option is going to be worth less than some real return on a 5 yr TIPS at auction held to maturity. When does the real rate on a 5 yr TIPS at auction become not silly? At the end of December, the R-CMT table twice pegged the 5 yr rate at 0.5%! I'd gladly take that as an indicative yield at auction in April over the current 0% fixed rate I Bond. Wishful thinking? Perhaps, or maybe I just don't value the put option of I Bonds as much you do? I like I Bonds as cash, to a point. It sure feels better though when they have something of a fixed rate.
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Re: Valuation of I Bonds

Post by Kevin M »

Selecting a 5-year TIPS to compare to seems completely arbitrary. Why not a 1-year or 10-year TIPS? I'd say the term risk on the I Bond is closer to that of a 1-year TIPS (for the first five years, and after that no term risk at all), if not even less. So as long as you can get the yield of a TIPS with a maturity of longer than one year, the I Bond probably is a better deal.

Selecting a 20-year zero-coupon bond to compare to an EE bond makes more sense to me, since the EE bond is worth almost nothing until the 20-year mark, and 0.1% is close enough to 0%.

If you want to pursue the complex modeling for fun, enjoy. I'll do my best to follow along, but when the discussion gets too deep into options and futures, I lose interest, especially when the decision seems so easy without doing so.

For me the more relevant question is when to buy I Bonds. I was thinking of splitting purchases into three buckets to hedge my bets: now, after the May rate change (and defer if the nominal rate drops to 0%), and after the November rate change. But after seeing a post pointing out that if we buy now, chances are high that we'll have at least one six-month period of a 0% nominal rate, I'm thinking it might make more sense to wait until November. Six months of about 1.5% and six months of 0% is about 0.75% for the year, so unless you figure the tax deferral and state tax savings are somehow worth 0.25%, might as well leave it in a 1% savings account. Of course, if the May and November combined rates both end up being 0%, that will be the losing bet.

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Re: Valuation of I Bonds

Post by market timer »

Agree that one should not redeem I bonds when 1-year TIPS yield less (barring idiosyncratic reasons). The reason I suggested 5-year TIPS as the basis for comparison is analytic tractability. The framework I suggested cuts down the redemption option events to 5, every 5 years. This sacrifices some precision.
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Re: Valuation of I Bonds

Post by Angst »

Kevin M wrote:Selecting a 5-year TIPS to compare to seems completely arbitrary. Why not a 1-year or 10-year TIPS? I'd say the term risk on the I Bond is closer to that of a 1-year TIPS (for the first five years, and after that no term risk at all), if not even less. So as long as you can get the yield of a TIPS with a maturity of longer than one year, the I Bond probably is a better deal.
I Bonds do have a penalty that goes away at 5 years, and 5 yr TIPS are the shortest issue sold at auction, so 5 year TIPS does not seem completely arbitrary to me. Personally, I prefer to buy TIPS at auction.

Kevin - Is there a minimum yield on 5 year TIPS at April auction that would cause you to say you're not going to buy 0.0% fixed rate I Bonds but will buy 5 year TIPS? My suspicion is that it's just too much of an apples vs oranges kind of thing to you that just asking question is still almost illogical, and you're not going to lock in a 5 yr TIPS in lieu of buying I Bonds. For me though, these apples are not necessarily so different from those oranges. But it's surely not because one of us is right and the other is wrong, it's because we just value the different characteristics of these two very different instruments differently. And that in itself doesn't seem unreasonable to me.
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Re: Valuation of I Bonds

Post by Kevin M »

I wouldn't compare the 5-year TIPS to I Bonds in isolation. It also would depend on the steepness of the real yield curve, and on TIPS rates relative to historical values. So I would first compare an I Bond to a fairly short-term maturity bond. The next question would be whether or not the yield curve is steep enough to justify taking more term risk.

So maybe at some point TIPS with maturities somewhere in the 2-3 year range will offer real returns enough higher than I Bonds that I would prefer those. Maybe the yield curve will be steep enough at some point to coax me into buying 5-year or 10-year TIPS.

From my perspective, nominal and real yields are too low, relative to historical values, to take much term risk. So currently I prefer fixed income that has higher yields than marketable bonds of similar maturity, but with much less term risk.

As I've mentioned in many posts, I still have about 25% in intermediate-to-long-term investment-grade and tax-exempt bond funds, so that's where I've been taking some term risk. That risk has been generously rewarded in recent years, but the lower rates go, the more I want to reduce that term risk, and shift more from bond funds into safer fixed income that provides me with maybe a 1% premium over comparable marketable securities.

The comparison is more straightforward and the trade-offs more obvious for CDs and nominal Treasuries. With I Bonds it's more like, heck, 0% real with almost no risk, and I can only buy $20K/year--might as well build up a little inflation hedge with this nice deal the government is giving us; it's not going to make a huge difference either way, but I hate to pass up a good deal. And if TIPS rates increase enough to justify more term risk, I'll sell the I Bonds and buy TIPS--it won't cost me much if anything. I don't feel the need to quantify the value of the put option--I just know it's really cheap, so the decision to sell I Bonds will be easy if and when the time comes. For me, it's not something to think much about now.

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Re: Valuation of I Bonds

Post by market timer »

TL;DR version: Recent vintage 0% fixed rate I bonds are conservatively worth 3% more than redemption value. My best guess for "true" value is 4.5% above redemption value.

Since it looks like the only source of information at my disposal on relevant TIPS options prices is from the iShares TIPS bond ETF (TIP), I'll use that. I'm going to use TIP as a proxy for an 8-year TIPS, and assume TIP trades at $115/share when the real yield on the 8-year TIPS is exactly 0%. The effective duration of TIP is 7.7 years, real yield is about 0.15%, and current price is $113.88. My goals are to establish a conservative lower bound on the value of an I bond and provide some guidance toward an optimal redemption strategy. I'll make a few modest assumptions and try to make them explicit. My emphasis is on valuation framework, so I'm intentionally ignoring things like tax deferral, where the value depends on your individual tax bracket. Think of this analysis as specific to someone in the 0% tax bracket.

One way to interpret a recent vintage I bond with 0% fixed rate is as a cash-like security paying 0% real plus the option to buy a TIPS (with any maturity up to 30 years) yielding 0% real, which you can hold until maturity (obviously, you cannot resell the hypothetical TIPS since the I bond isn't marketable). In particular, you have the option to buy an 8-year TIPS yielding 0%. Here is the key question I'd like to answer: At what yield on 8-year TIPS would you rather redeem your I bond, using the proceeds to buy 8-year TIPS? Let's call this yield y. The yield curve can move in all sorts of directions (i.e., flatten or steepen), but I'm going to assume that once the 8-year TIPS yield reaches y, the real yield curve is flat. The real yield curve is already pretty flat, as noted in a post above, and we should expect it to flatten further once the Fed starts hiking rates, as implied by the forward curve.

So, what are the benefits and costs of holding this option? Currently, you earn more on the I bond than you do on other short term Treasuries, so there is no cost to preserving your right to buy an 8-year TIPS yielding 0% real. In fact, there is only a cost to holding the I bond when you can earn a higher rate on short term Treasuries. Once the real yield curve rises (and flattens) to yield y>0, the ongoing cost to preserve optionality is y. In other words, you forego the opportunity to earn a higher yield by holding onto the lower yielding I bond. The benefit to maintaining optionality is the ability to buy a (hypothetical) 8-year TIPS at a discount on the off-chance that real yields decline.

Let's put some numbers to this. Currently, options on TIP go out to June 19, 2015, only five months away. Unfortunately, there are no LEAPS on TIP, so we are working with short term options. Recall that TIP is our proxy for an 8-year TIPS, so we can think of our right to buy an 8-year TIPS yielding 0% as like a call option on TIP with a strike price of $115. Currently, the market on this option is $1.05 x $1.25 (implied volatility ~6%). Suppose we could sell this option back to the market at the mid price of $1.15 (selling 1 contract for every $11,500 worth of I bonds we own). This would effectively monetize the embedded option, and increase our yield by 1% (2.4% annualized between now and July 19). This actually underestimates the value of our I bond's optionality, since we can hypothetically purchase any TIPS with a real yield of 0%, not just 8-year TIPS. Like I said, I'm looking for a conservative lower bound.

Now we can turn attention to solving for the yield y, where the benefit of preserving optionality is exactly offset by the cost of foregoing a higher yield in the secondary market. Suppose you continue to hold I bonds and rolling over a short position in the longest-dated TIP 115 calls. One I bond redemption strategy is to continue holding the bond when the following inequality holds:

I bond fixed rate + annualized premium on 115 strike TIP calls >= real yield on short term Treasuries

The left hand side is to account for the I bond coupon plus the flow value of the embedded option. The right hand side is simply the return from buying Treasuries of the same duration as the remaining time to expiration of the TIP calls. When the real yield on short term Treasuries rises above y, this inequality is reversed, and the strategy involves redeeming I bonds and investing the proceeds in 8-year TIPS. Note that secondary market interest rate affects both sides of the inequality. Not only does a rising interest rate clearly increase the right hand side, but it also lowers the value of the 115 strike TIP calls (the price of TIP will decline as interest rates increase). Since the right hand side is increasing in the interest rate and the left hand side is decreasing (holding implied volatility constant), there is a unique interest rate, y, where there is equality.

Why does this redemption strategy make sense? Well, firstly, keep in mind I underestimated the value of the embedded option by focusing exclusively on the right to buy 8-year TIPS. Secondly, I'm underestimating the option again by assuming it does not get replaced by another right to buy TIP after the TIP call expires. The I bond owner has the right to buy 8-year TIPS beyond June 19, even after the June 19 call expires. So, while this is not the optimal redemption strategy, it helps gives us a lower bound, and is convenient.

We're now in a place to solve for y, with a few minor assumptions. I'm going to assume we are able to sell TIP 115 calls every six months (or whatever is the future price of TIP corresponding to a 0% real yield on 8-year TIPS), and these options continue to have implied volatility of 6% at the time of sale. I'll evaluate this redemption strategy every six months, just prior to selling the call. Based on these assumptions, my options calculator tells me that the inequality is reversed at y=0.6%. In other words, if real yields were to rise to 0.6% across the curve, and TIP declined to $110.5, it would be optimal to redeem one's 0% fixed rate I bonds. Interestingly, considering hypothetical LEAPS doesn’t change the value of y much at all, so I’ll leave that part out. As this is a 3% decline in the price of TIP, and TIP has a duration of 7.7 years, this implies a 38bp rise in the yield of intermediate duration TIPS (I’ve marked the 8-year TIPS yield at 0.22% based on Friday’s closing price). There are various other combinations of yield curve shifts that would imply redemption--for simplicity, I've just considered the flat real yield curve solution. And of course, taxes would change these numbers.

By these calculations, the I bond owner is indifferent between owning a 0% fixed rate I bond and 8-year TIPS yielding 0.6%. As this is a 38bp increase over current 8-year TIPS yields (equivalent to a 3% drop in price), the I bond owner values the I bond by 3% over today’s 8-year TIPS, and by transitivity (since 8-year TIPS can be swapped into other securities in the secondary market), he is indifferent between an I bond plus 3% and any Treasury security. In other words, he values the I bond at 3% above the redemption value.

With optimal redemption, I believe you could add another 1.5% to the valuation (work not shown here).
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Kevin M
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Re: Valuation of I Bonds

Post by Kevin M »

^Interesting, but a bit too complex for me. I was going to throw out 1% on the 5-year TIPS as something that would induce me to redeem 0% I Bonds, but I figured I'd get laughed at for daring to hope for such a thing. After all, it has been more than 5.25 years seen we've seen 1% on 5-year TIPS. But that's not too much greedier than 0.6% on an 8-year TIPS.

I hadn't noticed that we hit 0.5% on the 5-year TIPS for a few days late last month. Probably should've jumped on some of those ;-)

I was going to throw out 2% on the 10-year TIPS as a strong inducement. It's been about 5.5 years since we've seen that.

Kevin
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Re: Valuation of I Bonds

Post by Noobvestor »

I love the analysis, Timer, and other pieces of this discussion, but I just can't wrap my head around comparing TIPS and I Bonds without regard to differences in tax treatment, though I realize that introduces a lot of person-specific variables that would be impossible to meaningfully simplify.
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Re: Valuation of I Bonds

Post by Buffetologist »

Market TImer, that's exactly the analysis I was looking for. Agree it's beautifully done. Bravo!

I'm struggling a little with your equation and how to fill in the pieces. Does it make sense to use a higher rate than short-term treasuries because FDIC bank accounts are available paying 1.25%? I'm not clear how to calculate the annualized premium on 115 strike TIP calls. Would that be 1% in your example? I sort of follow you reasoning, but I have to study it a little further to digest it. How do you calculate the real rates? Do you just subtract the current inflation rate?

Great job though!
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market timer
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Re: Valuation of I Bonds

Post by market timer »

Noobvestor wrote:I love the analysis, Timer, and other pieces of this discussion, but I just can't wrap my head around comparing TIPS and I Bonds without regard to differences in tax treatment, though I realize that introduces a lot of person-specific variables that would be impossible to meaningfully simplify.
Accounting for tax deferral is complicated, since you would likely not even purchase TIPS in a taxable account. If you redeem an I bond, you might use the proceeds to buy stocks in taxable, while simultaneously swapping from stocks into TIPS in an IRA. Alternatively, if one is in a high tax bracket with limited tax deferred space, one would likely sell the I bond and use the proceeds to buy muni bonds. Such actions offset the value of tax deferral value of I bonds relative to TIPS. Also, given the low fixed rate on recent vintage I bonds, redemption is likely in the next couple years, meaning tax deferral is not terribly valuable (short time horizon, probably still going to be in a high tax bracket at time of redemption). This is in contrast to EE bonds, which are unlikely to be redeemed for 20 years.
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Re: Valuation of I Bonds

Post by market timer »

Buffetologist wrote:I'm struggling a little with your equation and how to fill in the pieces. Does it make sense to use a higher rate than short-term treasuries because FDIC bank accounts are available paying 1.25%?
There is this recent thread from Kevin M showing that CDs have on average yielded 100bps over comparable duration Treasuries over the past 5 years. I agree that it makes sense to use a higher discount rate than Treasuries to calculate asset values for retail investors if CDs reliably offer a higher yield. This issue also came up in the earlier discussion on EE bonds. In particular, if CDs reliably offer 100bps above Treasuries, that implies that our I bond investor in the 0% tax bracket would likely favor CDs instead of recent vintage I bonds.
I'm not clear how to calculate the annualized premium on 115 strike TIP calls. Would that be 1% in your example?
The premium is 1% ($1.15/$115) and the time to expiration is 5 months, so the annualized premium is 2.4%.
How do you calculate the real rates? Do you just subtract the current inflation rate?
I'm looking at the constant maturity real yield curve for longer maturity TIPS yields. For short term rates (the right hand side of the inequality), I'd recommend using short term nominal Treasury rates, which have inflation expectations built into the price. Then you can use the I bond composite rate on the left hand side (annualized fixed coupon + inflation adjustment). You don't actually need to subtract inflation expectations from both sides.
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