Treasury bonds with same YTM but differing coupon rates

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Lecture
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Treasury bonds with same YTM but differing coupon rates

Post by Lecture »

Hello, I am thinking of a 5 yr Treasury bond for my tax-free retirement fund (SEP). On my self-directed brokerage site, there's a 5 yr Treasury priced at ~ 87.8, Yield to worst is 3.18%, coupon rate is 0.5%. Then there's another 5 yr Treasury priced higher at 97.6, yield to worst is 3.15%, coupon rate is much higher at 2.63%.
If I plan on holding the bond to full maturity, isn't the best option the lower priced bond, despite the lower coupon rate? Thanks in advance for any education on this!
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grabiner
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Re: Treasury bonds with same YTM but differing coupon rates

Post by grabiner »

Welcome to the forum!

The yield to maturity is computed from the current price, so your total return on the same dollar amount will be the same on two bonds with the same yield if you reinvest the coupons at that yield. It will be close to the same if rates change so that coupons are reinvested at a different rate from the current yield.

If you buy 9 bonds priced at 100, you have to spend $9000, and you will get $9000 at maturity, plus the full coupon payment. If you instead buy 10 bonds priced at 90, you also spend $9000, and you will get $10,000 at maturity, but you will receive about $1000 less in coupons. (The reason the coupon difference is not exactly $1000 is that coupons grow to more than their value if reinvested.)

There won't even be a significant tax difference. If you buy a bond at a discount, you amortize the discount for tax purposes. You increase the principal annually, and pay tax on that increased amount, rather than getting it as a capital gain at maturity.
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jjj_22
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Re: Treasury bonds with same YTM but differing coupon rates

Post by jjj_22 »

grabiner wrote: Sat Jun 25, 2022 6:35 pm If you buy a bond at a discount, you amortize the discount for tax purposes. You increase the principal annually, and pay tax on that increased amount, rather than getting it as a capital gain at maturity.
If you buy through a brokerage does the end of year 1099 include the amortization for you in a way that’s easy to do your taxes? I have only ever used bond funds but I have started looking at individual treasuries to start saving up for a known expense coming in a couple years.
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Blues
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Re: Treasury bonds with same YTM but differing coupon rates

Post by Blues »

jjj_22 wrote: Sat Jun 25, 2022 7:24 pm
grabiner wrote: Sat Jun 25, 2022 6:35 pm If you buy a bond at a discount, you amortize the discount for tax purposes. You increase the principal annually, and pay tax on that increased amount, rather than getting it as a capital gain at maturity.
If you buy through a brokerage does the end of year 1099 include the amortization for you in a way that’s easy to do your taxes? I have only ever used bond funds but I have started looking at individual treasuries to start saving up for a known expense coming in a couple years.
I'll be interested in learning this as well...as I have only recently begun purchasing treasury notes and bills on the secondary market...as opposed to holding our fixed income at Vanguard via funds.
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Kevin M
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Re: Treasury bonds with same YTM but differing coupon rates

Post by Kevin M »

jjj_22 wrote: Sat Jun 25, 2022 7:24 pm
grabiner wrote: Sat Jun 25, 2022 6:35 pm If you buy a bond at a discount, you amortize the discount for tax purposes. You increase the principal annually, and pay tax on that increased amount, rather than getting it as a capital gain at maturity.
If you buy through a brokerage does the end of year 1099 include the amortization for you in a way that’s easy to do your taxes? I have only ever used bond funds but I have started looking at individual treasuries to start saving up for a known expense coming in a couple years.
Accrued market discount is included in the interest shown on 1099-INT--at least it should be. There should be a supplemental section that shows how much of the interest is stated interest, and how much is accrued market discount.
If I make a calculation error, #Cruncher probably will let me know.
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Lecture
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Re: Treasury bonds with same YTM but differing coupon rates

Post by Lecture »

grabiner wrote: Sat Jun 25, 2022 6:35 pm Welcome to the forum!

The yield to maturity is computed from the current price, so your total return on the same dollar amount will be the same on two bonds with the same yield if you reinvest the coupons at that yield. It will be close to the same if rates change so that coupons are reinvested at a different rate from the current yield.

If you buy 9 bonds priced at 100, you have to spend $9000, and you will get $9000 at maturity, plus the full coupon payment. If you instead buy 10 bonds priced at 90, you also spend $9000, and you will get $10,000 at maturity, but you will receive about $1000 less in coupons. (The reason the coupon difference is not exactly $1000 is that coupons grow to more than their value if reinvested.)

There won't even be a significant tax difference. If you buy a bond at a discount, you amortize the discount for tax purposes. You increase the principal annually, and pay tax on that increased amount, rather than getting it as a capital gain at maturity.
Thank you for the welcome and the clear explanation! And the other replies as well. This is a great forum, I've learned so much already in a short time :).
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Re: Treasury bonds with same YTM but differing coupon rates

Post by JayB »

Lecture wrote: Fri Jun 24, 2022 12:08 pm Hello, I am thinking of a 5 yr Treasury bond for my tax-free retirement fund (SEP). On my self-directed brokerage site, there's a 5 yr Treasury priced at ~ 87.8, Yield to worst is 3.18%, coupon rate is 0.5%. Then there's another 5 yr Treasury priced higher at 97.6, yield to worst is 3.15%, coupon rate is much higher at 2.63%.
If I plan on holding the bond to full maturity, isn't the best option the lower priced bond, despite the lower coupon rate? Thanks in advance for any education on this!
If you choose the lower coupon rate, you're moving closer to simulating a zero coupon Treasury bond. If you want and/or need the semi-annual income that the purchase generates, then go for the higher coupon bond. If you don't really need or want the coupon payouts, then why not just purchase a zero coupon bond instead? Zero coupon bonds often have a higher Yield to Maturity, and they eliminate the uncertainty about what rate the coupon payments can be reinvested at. Whether you purchase coupon-paying or zero coupon bonds, you will be responsible for taxes each year if the bonds are in a taxable account.
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Re: Treasury bonds with same YTM but differing coupon rates

Post by #Cruncher »

grabiner wrote: Sat Jun 25, 2022 6:35 pmIf you buy 9 bonds priced at 100, you have to spend $9000, and you will get $9000 at maturity, plus the full coupon payment. If you instead buy 10 bonds priced at 90, you also spend $9000, and you will get $10,000 at maturity, but you will receive about $1000 less in coupons.
We can also model this as a savings account.
  1. Deposit $9,000 and withdraw all the interest each year. After 10 years will still have a balance of $9,000.
  2. Also deposit $9,000 but withdraw a smaller but constant amount each year so that after 10 years, the balance grows to $10,000.
We can use the Excel PMT function to determine what the annual withdrawal needs to be for the balance to grow to $10,000. Row 5 in the following table shows that, with an interest rate of 2.75%, the withdrawal would be $247.50 in case A (9000 X 2.75%) but only $159.26 in case B. These correspond to the coupons in grabiner's example.

Code: Select all

Row         Col A     Col B     Col C      Col D      Col E
  1         Yield     2.75%
  2         Years        10
  3       Deposit     9,000
  4      Grows to     9,000               10,000
  5      Withdraw    247.50               159.26   =PMT($B1,$B2,-$B3,B4,0) [formula in col B copied to col D]
  6          Year  Interest   Balance   Interest    Balance

Code: Select all

  7             0            9,000.00              9,000.00
  8             1    247.50  9,000.00     247.50   9,088.24
  9             2    247.50  9,000.00     249.93   9,178.91
 10             3    247.50  9,000.00     252.42   9,272.07
 11             4    247.50  9,000.00     254.98   9,367.79
 12             5    247.50  9,000.00     257.61   9,466.14
 13             6    247.50  9,000.00     260.32   9,567.20
 14             7    247.50  9,000.00     263.10   9,671.04
 15             8    247.50  9,000.00     265.95   9,777.73
 16             9    247.50  9,000.00     268.89   9,887.36
 17            10    247.50  9,000.00     271.90  10,000.00
 18  Sum interest  2,475.00             2,592.60
 19  Sum withdraw  2,475.00             1,592.60
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