What is capital gain and interest when bond is bought at premium vs discount?

[Hector]

If I buy US Treasury 2.625% 03/31/2025, 9128284F4 at premium by paying $104.83500 and hold to maturity, is $4.83500 capital loss?
If it appreciates and I sell it for more than $104.83500 before maturity, is the difference capital gain?
If it depreciates and I sell it for less than $104.83500 before maturity, is the difference capital loss?

Does it makes sense to buy mostly at premium in HSA in California due to
interest from Treasury is exempt from state income tax so no state income tax on interest from higher coupon treasury.
bond bought at premium tend to create capital loss which reduces taxable income at state level.

[troysapp]

If you purchase a taxable bond at a premium you can choose to amortize the premium over the life of the bond. This election will reduce your taxable income as well as reduce your basis in the bond. If you sell the bond before maturity, the gain/loss is determined by comparing the proceeds with the amortized basis. In most all cases amortization makes sense.

If a bond yields tax-exempt interest, you MUST amortize the premium.

Assuming by HSA you mean "Health Savings Account", I'm not sure why you'd want to purchase a muni bond in a tax-efficient account. It's likely you'd be better off with a higher yielding investment grade corporate bond portfolio in an HSA. As a side, with the exception of Treasuries, I'd also suggest broadly diversifying a portfolio of bonds. For many years I oversaw the accounting and tax work for a muni mutual fund. Trust me, individual muni bonds became hindered or defaulted quite regularly, mainly revenue bonds.

Assuming your a CA resident you have a bit more work to do than us WA residents in that you need to estimate your after tax yields using both federal and CA tax assumptions. You might find that even if you pay higher CA tax the reduction in fed taxes more than compensates. Also remember that unless you're subject to AMT you might also receive a federal deduction for CA taxes paid (though the amount of folks able to itemize has dropped significantly).

[Hector]

Assuming by HSA you mean "Health Savings Account", I'm not sure why you'd want to purchase a muni bond in a tax-efficient account. It's likely you'd be better off with a higher yielding investment grade corporate bond portfolio in an HSA. As a side, with the exception of Treasuries, I'd also suggest broadly diversifying a portfolio of bonds. For many years I oversaw the accounting and tax work for a muni mutual fund. Trust me, individual muni bonds became hindered or defaulted quite regularly, mainly revenue bonds.

Assuming your a CA resident you have a bit more work to do than us WA residents in that you need to estimate your after tax yields using both federal and CA tax assumptions. You might find that even if you pay higher CA tax the reduction in fed taxes more than compensates. Also remember that unless you're subject to AMT you might also receive a federal deduction for CA taxes paid (though the amount of folks able to itemize has dropped significantly).

Yes, I mean "Health Savings Account". California does not recognize HSA. So it makes sense to put Treasury in HSA in California since interest from Treasury is not taxed in California.

[Hector]

If you purchase a taxable bond at a premium you can choose to amortize the premium over the life of the bond. This election will reduce your taxable income as well as reduce your basis in the bond. If you sell the bond before maturity, the gain/loss is determined by comparing the proceeds with the amortized basis. In most all cases amortization makes sense.

If a bond yields tax-exempt interest, you MUST amortize the premium.

Do I have to amortize the premium for Treasurys?
In HSA in California, there is not state income tax on interest from Treasurys.
By not amortizing, probability of capital loss is higher which is tax efficient in HSA in California.

[acegolfer]

If you purchase a taxable bond at a premium you can choose to amortize the premium over the life of the bond. This election will reduce your taxable income as well as reduce your basis in the bond. If you sell the bond before maturity, the gain/loss is determined by comparing the proceeds with the amortized basis. In most all cases amortization makes sense.

If a bond yields tax-exempt interest, you MUST amortize the premium.

Do I have to amortize the premium for Treasurys?
In HSA in California, there is not state income tax on interest from Treasurys.
By not amortizing, probability of capital loss is higher which is tax efficient in HSA in California.

Amortize in this context means you are taking pro-rated capital loss each year. For more, https://www.investopedia.com/articles/t ... nd-tax.asp

[ofckrupke]

Does it makes sense to buy mostly at premium in HSA in California

Personally I think it makes more sense in a CA HSA to buy discount treasuries, as feasible.

My HSA custodian isn't going to do the annual accounting for amortization required for CA tax compliance because it isn't required for federal compliance because it's an HSA....which would leave the FTB task to me. It's just spreadsheet stuff, but in reporting it to FTB I'd be exposing myself to defending it in audit. But if I hold a treasury security acquired at discount to maturity, then I can wait til that year's return to roll up all the accreted discount for inclusion on schedule 540 CA [as an addition in cell 2C because HSAs are not CA exempt, and as a subtraction in 2B because treasury interest is CA-exempt] rather than calculating/reporting the adjustments annually.

To answer your followup question upthread: yes, you have to amortize premium on treasuries (and CA-exempt munis) for CA tax reporting because their interest is CA-exempt. But since the income is exempt, you get no corresponding benefit in the form of a tax adjustment to the coupon income.

When you buy the bond, and hold to maturity, you're going to get the YTM advertised in conjunction with the purchase, and reportable interest income is the only thing you're going to get out of it - less net reportable income than the coupons, but no bankable capital loss. Similar reasoning applies for dispositions short of maturity: sure you may have capital gain or loss, but there's going to be a carve-out/adjustment to that number because, OF the coupon payments received plus interest paid you by the buyer for the fraction of a period you held since the last coupon, some of it is interest net of adjustment and some of it is essentially return of premium capital. So it turns out there's no free lunch to be had here.

[Hector]

Thank you for responses.

Is this how the calculation works on bond bought at premium?
Lets say the I bought 200 quantity of bonds that I mentioned in OP on 8/8/2020 and sold it on 8/8/2020 at $104.00.

Code: Select all

Price	Transaction Date	Buy/Sell	Qty	Total		Accrued Interest	
$104.84	1/8/2020		Buy		200	-$20,967.00	$143.84 (Qty * Coupon rate * 100* (purchased date - last interest payment date) / 365)
$104.00	8/8/2020		Sell		200	$20,800.00	$186.99 (Qty * Coupon rate * 100* (Sell date - next interest payment date) / 365)
						

Code: Select all

$20,967.00	Purchase Price
$20,800.00	Sale Price
$167.00		Premium paid
$107.89		Amortizing amount = $967.00 * (Sold date - Purchased date) / (Maturity date - Purchased date)
$186.99		Accrued Interest at Sale. I report that as interest payment.
$20,613.01	Sale Amount = Sale Price - Accrued Interest
-$353.99	Capital Gains = Sale Amount - Purchase Price
$262.50		Interest received on 3/31/20. Coupon rate * Quantity * 100 / 2. I report that as interest payment.	

[ofckrupke]

Is this how the calculation works on bond bought at premium?

For acquisition and disposition you want to use the settlement date, which is normally the next business day. All the interest arithmetic is predicated on this. That is, if you buy a bond on Friday it settles on Monday, and the accrued interest you pay the seller is calculated using Monday. Same deal at disposition. [If you watch accrued interest #s for a particular bond you'll see that the number steps up three days' worth between Thu and Fri (in a week where neither Fri nor the following Mon is a holiday), not between Fri and Mon.]
But let's say your 8Jan2020 and 8Aug2020 dates are the settlement dates.
And let's use your #s for accrued interest - I'm not checking them. Note though, that 2020 is a leap year.

The quoted bond price by convention excludes accrued interest considerations; if the acquisition price is 104.84 then your premium cost for 200 would be $968.00, and the outlay, including accrued interest paid to the seller, would be $21111.84. If you paid $20967 including accrued interest then the acquisition price was not 104.84.
Same convention applies at disposition, obviously; if you sell at 104.00 then you receive $20800.00 plus the accrued interest.

You chose straight line amortization. 8Jan2020 and 31Aug2025 are 1909 days apart (at least, according to a 20 year old copy of excel that appears to account for leap days). If the premium at acquisition was 4.84 then the slope of the line is -4.84/1909 and the day rate is -0.002551.

You sell at settlement-date 8Aug2020 for 104.00, by which date the amortized basis has declined to 104.29662. At the end of the year you'll report a capital loss of 200*(104.29662 - 104.00) = $59.32 on schedule D; and coupon interest of $262.50, net accrued interest received of $43.15, and ABP of ($108.68) in the interest section of schedule B. The capital gain plus the amortization-adjustment to interest income = ($59.32) + ($108.68) = ($168.00), which equals the difference between your $20800 proceeds and $20968 cost (both net of accrued interest).

edited after correction of my own data entry errors.

[Hector]

Is this how the calculation works on bond bought at premium?

For acquisition and disposition you want to use the settlement date, which is normally the next business day. All the interest arithmetic is predicated on this. That is, if you buy a bond on Friday it settles on Monday, and the accrued interest you pay the seller is calculated using Monday. Same deal at disposition. [If you watch accrued interest #s for a particular bond you'll see that the number steps up three days' worth between Thu and Fri (in a week where neither Fri nor the following Mon is a holiday), not between Fri and Mon.]
But let's say your 8Jan2020 and 8Aug2020 dates are the settlement dates.
And let's use your #s for accrued interest - I'm not checking them. Note though, that 2020 is a leap year.

The quoted bond price by convention excludes accrued interest considerations; if the acquisition price is 104.84 then your premium cost for 200 would be $968.00, and the outlay, including accrued interest paid to the seller, would be $21111.84. If you paid $20967 including accrued interest then the acquisition price was not 104.84.
Same convention applies at disposition, obviously; if you sell at 104.00 then you receive $20800.00 plus the accrued interest.

You chose straight line amortization. 8Jan2020 and 31Aug2025 are 1909 days apart (at least, according to a 20 year old copy of excel that appears to account for leap days). If the premium at acquisition was 4.84 then the slope of the line is -4.84/1909 and the day rate is -0.002551.

You sell at settlement-date 8Aug2020 for 104.00, by which date the amortized basis has declined to 104.29662. At the end of the year you'll report a capital loss of 200*(104.29662 - 104.00) = $59.32 on schedule D; and coupon interest of $262.50, net accrued interest received of $43.15, and ABP of ($108.68) in the interest section of schedule B. The capital gain plus the amortization-adjustment to interest income = ($59.32) + ($108.68) = ($168.00), which equals the difference between your $20800 proceeds and $20968 cost (both net of accrued interest).

edited after correction of my own data entry errors.

How did you calculate accrued interest received of $43.15, and ABP of ($108.68) ?
What is ABP?

[ofckrupke]

[...]
But let's say your 8Jan2020 and 8Aug2020 dates are the settlement dates.
And let's use your #s for accrued interest - I'm not checking them. Note though, that 2020 is a leap year.
[...]

How did you calculate accrued interest received of $43.15, and ABP of ($108.68) ?
What is ABP?

accrued interest was from your numbers, $186.99 received at disposition less $143.84 paid at acquisition.

APB is shorthand for "adjustment to interest received, offsetting Amortization of Bond Premium".
That is, it's equal to the decline in capital basis over the number of days held. Here I've used the day count of the interest-bearing period.
So, 213/1909*968 =...108.01, not 108.68. Ponders. OK, found one more erroneous 4.87 in a cell that should have held 4.84.
Sorry about that (and thanks for calling me on it).
So, revise to $59.99 of capital loss, and ($108.01) of APB.

An argument can be made that the premium amortization should be taken over the capital holding period within the tax year being reported, which as mentioned in the other topic might be a different number of days (as would be the days to maturity at acquisition). I expect that the question is clarified/settled in an IRS publication; however, in point of fact my broker generates and reports APB annually on 1099-INT, and I've relied on that, checking only after the year of maturity that the sum of adjustments over the years added to the market premium originally paid. I did calculate via constant-rate method and was surprised that it was so close to the broker's presumably straight-line amortization.

[Hector]

[...]
But let's say your 8Jan2020 and 8Aug2020 dates are the settlement dates.
And let's use your #s for accrued interest - I'm not checking them. Note though, that 2020 is a leap year.
[...]

How did you calculate accrued interest received of $43.15, and ABP of ($108.68) ?
What is ABP?

accrued interest was from your numbers, $186.99 received at disposition less $143.84 paid at acquisition.

APB is shorthand for "adjustment to interest received, offsetting Amortization of Bond Premium".
That is, it's equal to the decline in capital basis over the number of days held. Here I've used the day count of the interest-bearing period.
So, 213/1909*968 =...108.01, not 108.68. Ponders. OK, found one more erroneous 4.87 in a cell that should have held 4.84.
Sorry about that (and thanks for calling me on it).
So, revise to $59.99 of capital loss, and ($108.01) of APB.

An argument can be made that the premium amortization should be taken over the capital holding period within the tax year being reported, which as mentioned in the other topic might be a different number of days (as would be the days to maturity at acquisition). I expect that the question is clarified/settled in an IRS publication; however, in point of fact my broker generates and reports APB annually on 1099-INT, and I've relied on that, checking only after the year of maturity that the sum of adjustments over the years added to the market premium originally paid. I did calculate via constant-rate method and was surprised that it was so close to the broker's presumably straight-line amortization.

Thank you!
To sum up, following needs to be reported on tax return:
1. Capital gain/loss

2. Interest
- Accrued Interest at sale
- Accrued Interest at purchase (negative number)
- APB
- Coupon interest

In case if it is held to maturity,
There won't be Capital gain/loss and Accrued Interest at sale.
APB and Coupon interest should be reported every year.
Accrued Interest at purchase (negative number) needs to reported only for the year it was purchased.

[ofckrupke]

Don't see anything obviously wrong with your summary.
Let me note an exception though: a bond that is taxable for all your taxing entities could have basis adjustment postponed until disposition and no adjustment of its coupon income in intervening years....but only if you've never elected previously to amortize bond premiums (or been required to as a practical matter because you had a bond whose interest was exempt for one of your taxing entities), or have requested and been granted permission by the IRS to revert to non-amortizing practice. Anyone who buys a premium treasury while resident in an income-taxing state should passively elect to amortize (if they haven't already in a previous year) by using broker-provided ABP info from the 1099-INT, because annual amortization will be required anyway for state reporting, and maintaining a single basis for both taxing entities, as feasible, is preferable.

edit: oh, here's another thing: if you buy a coupon bearing bond after its last coupon date of the year and hold it through the end of the year, then you are probably going to want to read up on whether to subtract the accrued interest you paid at acquisition in that year's return, vs. delaying its recognition until the subsequent year when the first coupon interest comes your way (or you receive greater accrued interest for a pre-coupon disposition). I took the instructions on accrued-interest-paid subtractions in the pertinent IRS publication as applicable bond by bond, so take the subtraction in the tax year for which I first receive interest on that bond purchase rather than recognizing it and netting against interest received from other debt instruments in the purchase year; but if you're like me you'll want to do your own literature search and decide for yourself.

[venkman]

If a bond yields tax-exempt interest, you MUST amortize the premium.

Do you know how this works with tax-exempt bond funds? If they hold premium bonds, the higher interest payments should ultimately be offset by a decline in NAV. But the fund shareholders don't have to amortize the drop in NAV, do they? I've wondered if this could be somewhat of a free lunch, where fund shareholders get more tax-free money up front, plus a long-term capital loss on the back end.

[Hector]

Personally I think it makes more sense in a CA HSA to buy discount treasuries, as feasible.

My HSA custodian isn't going to do the annual accounting for amortization required for CA tax compliance because it isn't required for federal compliance because it's an HSA....which would leave the FTB task to me. It's just spreadsheet stuff, but in reporting it to FTB I'd be exposing myself to defending it in audit. But if I hold a treasury security acquired at discount to maturity, then I can wait til that year's return to roll up all the accreted discount for inclusion on schedule 540 CA [as an addition in cell 2C because HSAs are not CA exempt, and as a subtraction in 2B because treasury interest is CA-exempt] rather than calculating/reporting the adjustments annually.

So if I have some bonds at discount and some at premium,
I have option to report only coupon interest for discount bonds every year. And report other interest and capital gain/loss (if I sell before maturity) for the year when bond matures/sold?
Calculation for everything is similar to premium bonds, correct?

[ofckrupke]

So if I have some bonds at discount and some at premium,
I have option to report only coupon interest for discount bonds every year. And report other interest and capital gain/loss (if I sell before maturity) for the year when bond matures/sold?

Right, at least for market discount; and actually if the discount is less than 1/4% times the number of years to maturity at acquisition then you don't have to even report it at disposition, and you can opt to report the difference between disposition and acquisition value entirely as a capital gain rather than 1) a combination of gain/loss measured from its rising basis path plus 2) adjustment to interest income equalling the rise in basis between acquisition and disposition. [This is known as a de minimis exception to the report-accretion-along-the-rising-basis-path-as-interest rule.]
Original issue discount accretion, if applicable, on issues longer than 52 weeks at issue, needs to be annually reported...again unless smaller than 1/4% times the number of years to maturity at original issue.

I think it's fairly standard broker/custodian policy that unless you demand otherwise they're going to treat your silence as a choice to delay recognition on discount and will not report accretion of market discount in 1099-INT until after disposition, and as a passive election to report amortization of premium annually (and therefore will report this). I went with the flow: delay on discount, report on premium. I did not have any de minimis exceptions in 2018 and didn't actually think about it at all when shopping in 2019.

Calculation for everything is similar to premium bonds, correct?

Discount, if accreted annually, must use a constant rate curve (compounded at least annually).

This reminds me: upthread I gave you a pass on the straight line method; but actually unless the bond was issued before 28 Sep 1985, you are supposed to use the constant-rate path method for premium amortization rather than a straight line. [The lower the yield, the smaller the premium, the shorter the term, the smaller the divergence between the two paths, not that it matters because you don't have a choice anymore really...but if enough of the factors and the holding size are small enough the two results might round to the same dollar. Probably not on your 2025 maturity holding though.]

You really should find independent, credible sources to confirm my representations. I wouldn't have treated someone doing his own editing as an authority when I was facing this stuff for the first time.

[Hector]

You really should find independent, credible sources to confirm my representations. I wouldn't have treated someone doing his own editing as an authority when I was facing this stuff for the first time.

I will do that.

Discount, if accreted annually, must use a constant rate curve (compounded at least annually).

This reminds me: upthread I gave you a pass on the straight line method; but actually unless the bond was issued before 28 Sep 1985, you are supposed to use the constant-rate path method for premium amortization rather than a straight line. [The lower the yield, the smaller the premium, the shorter the term, the smaller the divergence between the two paths, not that it matters because you don't have a choice anymore really...but if enough of the factors and the holding size are small enough the two results might round to the same dollar. Probably not on your 2025 maturity holding though.]

I was reading Publication 550 and this is the case. Thank you for pointing it out.

Following is from the "How To Figure Amortization" from Publication 550. Do you see anything wrong with it?
Bought 10 quantity of UNITED STATES TREAS NTS COUPON 2.00000% MATURITY DATE 02/15/2025 at 101.734375 on settlement date of 01-13-20. Interest paid to seller at purchase: $8.21.
Broker shows YIELD TO MATURITY as 1.643%.

Code: Select all

Date		Coupon 		Interest 	premium					Carrying value
		interest	based on	amortized
				YTM at
				purchase
1/13/2020	  -		-		-					$1,017.34(purchase price)
12/31/2020	 $ 20.00 	$16.17	 	-$ 4.38($ 20.00 - $16.17-$8.21)		$1,021.72(1,017.34 - -4.38)	$16.17 = $1,017.34 * 1.64% * (12-31-2020 - 1/13/2020) / 365
12/31/2021	 $ 20.00 	$16.79	 	$ 3.21 					$1,018.51			$16.79 = $1,021.72 * 1.64%
12/31/2022	 $ 20.00 	$16.73	 	$ 3.27 					$1,015.24	
12/31/2023	 $ 20.00 	$16.68	 	$ 3.32 					$1,011.92
12/31/2024	 $ 20.00 	$16.63	 	$ 3.37 					$1,008.55	
2/15/2025	 $ 10.00 	$2.09	 	$ 7.91 					$1,000.63

For reporting interest on tax return, report $20.00 - $8.21 as first year's interest. $20 for every year after that and $10 in the last year if held to maturity.

[Hector]

Right, at least for market discount; and actually if the discount is less than 1/4% times the number of years to maturity at acquisition then you don't have to even report it at disposition, and you can opt to report the difference between disposition and acquisition value entirely as a capital gain rather than 1) a combination of gain/loss measured from its rising basis path plus 2) adjustment to interest income equalling the rise in basis between acquisition and disposition. [This is known as a de minimis exception to the report-accretion-along-the-rising-basis-path-as-interest rule.]
Original issue discount accretion, if applicable, on issues longer than 52 weeks at issue, needs to be annually reported...again unless smaller than 1/4% times the number of years to maturity at original issue.

I think it's fairly standard broker/custodian policy that unless you demand otherwise they're going to treat your silence as a choice to delay recognition on discount and will not report accretion of market discount in 1099-INT until after disposition, and as a passive election to report amortization of premium annually (and therefore will report this). I went with the flow: delay on discount, report on premium. I did not have any de minimis exceptions in 2018 and didn't actually think about it at all when shopping in 2019.

Regarding de minimis exception, seems like one can report de minimis interest as capital gain, but one does not have to do it.
It makes sense to treat it as interest in HSA in California since capital gain is taxable and interest is not.

[ofckrupke]

Following is from the "How To Figure Amortization" from Publication 550. Do you see anything wrong with it?

Well here is how I would do it (differently).
For purpose of calculating the basis path, don't include the accrued interest paid in the basis. Don't include the coupons either. Just relax the face value plus premium down to par over the period to maturity at a constant rate.
So: calculate the notional internal rate of return for this declining-value asset using XIRR(), with a payment of 1017.34375 on 1/13/2020 and a return of 1000.00 on 2/15/2025.
This gives me a return rate of -0.336862% per year.
Then I find the value of the asset at the several Dec 31sts from 2020 to 2024, and finally the maturity date, using the Power() function using the fractional number of years (seems to work better when even the leap years are denominated as 365 days) in the interval as the exponent. That gives me 1014.03,1010.61,1007.21,1003.83,1000.43 for the EOY values of the wasting asset, and finally 1000.00. So the amounts for amortization adjustment are (3.31),(3.42),(3.40),(3.39),(3.39),(0.43). Up to rounding error that sums to (17.34).

So for 2020 "reporting" I'll list as separate adjustments the accrued interest paid and the fractional-year 2020 amortization, against the coupon interest. Subsequently, just the amortizations.

Of course neither of these will do anything for me on a treasury in an HSA in CA because I won't even be reporting interest income federally and although the account isn't exempt in CA, the interest is. So the record and the method are mainly of use if I sell the treasury note before maturity, in which case for that year I will amortize only the fraction of a year up to the sale settlement.

Sorry I didn't put this into easy to read code block.

[ofckrupke]

Regarding de minimis exception, seems like one can report de minimis interest as capital gain, but one does not have to do it.
It makes sense to treat it as interest in HSA in California since capital gain is taxable and interest is not.

+1

[FactualFran]

Following is from the "How To Figure Amortization" from Publication 550. Do you see anything wrong with it?
Bought 10 quantity of UNITED STATES TREAS NTS COUPON 2.00000% MATURITY DATE 02/15/2025 at 101.734375 on settlement date of 01-13-20. Interest paid to seller at purchase: $8.21.
Broker shows YIELD TO MATURITY as 1.643%.

Code: Select all

Date		Coupon 		Interest 	premium					Carrying value
		interest	based on	amortized
				YTM at
				purchase
1/13/2020	  -		-		-					$1,017.34(purchase price)
12/31/2020	 $ 20.00 	$16.17	 	-$ 4.38($ 20.00 - $16.17-$8.21)		$1,021.72(1,017.34 - -4.38)	$16.17 = $1,017.34 * 1.64% * (12-31-2020 - 1/13/2020) / 365
12/31/2021	 $ 20.00 	$16.79	 	$ 3.21 					$1,018.51			$16.79 = $1,021.72 * 1.64%
12/31/2022	 $ 20.00 	$16.73	 	$ 3.27 					$1,015.24	
12/31/2023	 $ 20.00 	$16.68	 	$ 3.32 					$1,011.92
12/31/2024	 $ 20.00 	$16.63	 	$ 3.37 					$1,008.55	
2/15/2025	 $ 10.00 	$2.09	 	$ 7.91 					$1,000.63

For reporting interest on tax return, report $20.00 - $8.21 as first year's interest. $20 for every year after that and $10 in the last year if held to maturity.

That example is not in the How To Figure Amortization section of the current HTML version of the Publication 550[/url]. Something that is there is:

Step 2: Determine the accrual periods. You can choose the accrual periods to use. They may be of any length and may vary in length over the term of the bond, but each accrual period can be no longer than 1 year, and each scheduled payment of principal or interest must occur either on the first or the final day of an accrual period. The computation is simplest if accrual periods are the same as the intervals between interest payment dates.

In the table you posted, it is not the case that each scheduled payment of principal or interest occurs either on the first or the final day of an accrual period.

For a covered security (and based on the settlement date the example is for a covered security), the brokerage should report to you (and the IRS) every year the dollar amount of the amortization.

The large difference between the amortization amount for the final full year ($3.37) and for the portion of the year of maturity ($7.91) does not look right. Ideally, the final "Carrying value" should be the par value ($1,000.00 in this case).

[ofckrupke]

Well here is how I would do it (differently).
For purpose of calculating the basis path, don't include the accrued interest paid in the basis. Don't include the coupons either. Just relax the face value plus premium down to par over the period to maturity at a constant rate.
So: calculate the notional internal rate of return for this declining-value asset using XIRR(), with a payment of 1017.34375 on 1/13/2020 and a return of 1000.00 on 2/15/2025.
This gives me a return rate of -0.336862% per year.
Then I find the value of the asset at the several Dec 31sts from 2020 to 2024, and finally the maturity date, using the Power() function using the fractional number of years (seems to work better when even the leap years are denominated as 365 days) in the interval as the exponent. That gives me 1014.03,1010.61,1007.21,1003.83,1000.43 for the EOY values of the wasting asset, and finally 1000.00. So the amounts for amortization adjustment are (3.31),(3.42),(3.40),(3.39),(3.39),(0.43). Up to rounding error that sums to (17.34).

So for 2020 "reporting" I'll list as separate adjustments the accrued interest paid and the fractional-year 2020 amortization, against the coupon interest. Subsequently, just the amortizations.

Of course neither of these will do anything for me on a treasury in an HSA in CA because I won't even be reporting interest income federally and although the account isn't exempt in CA, the interest is. So the record and the method are mainly of use if I sell the treasury note before maturity, in which case for that year I will amortize only the fraction of a year up to the sale settlement.

Sorry I didn't put this into easy to read code block.

However the method described above is plainly contrary to pub 550. It's probably a good thing I haven't bought any premium bonds in my HSA and have relied on broker numbers for taxable accounts.

FactualFran is right about your initial stab not looking right in particular because of the large amount for the fractional year in early 2025 though.

Below is my attempt to redeem myself. Note the order in which the cells are calculated does not proceed left to right.
The amount of interest at the specified YTM for the period/row is calculated first using power() and the difference in fractional years since the previous coupon date.
This is subtracted from the net coupon interest for the period to get the amortization for period. Once the amortization is known then the basis at date is just the basis at previous coupon date minus the amortization for the period.

Code: Select all

Date			Basis at date		Net coupon interest	Amortization	Interest at specified yield
1/13/2020		$1,017.34		during period		for period	for period
2/15/2020		$1,017.05		$1.79			0.29		1.50
8/15/2020		$1,015.33		$10.00			1.72		8.28
2/15/2021		$1,013.72		$10.00			1.61		8.39
8/15/2021		$1,011.97		$10.00			1.75		8.25
2/15/2022		$1,010.37		$10.00			1.61		8.39
8/15/2022		$1,008.62		$10.00			1.75		8.25
2/15/2023		$1,007.01		$10.00			1.61		8.39
8/15/2023		$1,005.27		$10.00			1.75		8.25
2/15/2024		$1,003.64		$10.00			1.63		8.37
8/15/2024		$1,001.91		$10.00			1.72		8.28
2/15/2025		$1,000.31		$10.00			1.61		8.39

Yes it should end up at $1000.00. But neither did I use XIRR() with all the coupon payments included to determine the YTM; instead I took the 1.643% as a given. [For me it works out to the penny if I use 1.637% btw.]
Note the fluctuations in interest at specified yield per period because the day counts are in the ratio 184:181 (184:182 in leap years)

[Hector]

Thank you both!
When I change dates for accrual periods in spreadsheet that I created, calculation looks like this:

Code: Select all

  
	 	Net		Interest
	 	coupon		based on
		interest	YTM at	 	premium		Carrying
Date		received	purchase	amortized	value
1/13/2020							$1,017.34
2/15/2020	 $ 1.79 	$1.51	 	$ 0.28 		$1,017.06
8/15/2020	 $ 10.00 	$8.31	 	$ 1.69 		$1,015.37
2/15/2021	 $ 10.00 	$8.41		$ 1.59 		$1,013.78
8/15/2021	 $ 10.00 	$8.26	 	$ 1.74 		$1,012.04
2/15/2022	 $ 10.00 	$8.38	 	$ 1.62 		$1,010.42
8/15/2022	 $ 10.00 	$8.23	 	$ 1.77 		$1,008.65
2/15/2023	 $ 10.00 	$8.35		$ 1.65 		$1,007.01
8/15/2023	 $ 10.00 	$8.20	 	$ 1.80 		$1,005.21
2/15/2024	 $ 10.00 	$8.30		$ 1.70 		$1,003.52
8/15/2024	 $ 10.00 	$8.20	 	$ 1.80 		$1,001.72
2/15/2025	 $ 10.00 	$8.30	 	$ 1.70 		$1,000.01

Interest based on YTM at purchase: previous carrying value * YTM * # of days since last date / 365(366 for leap year)
For 2020 reporting, I report $1.79 + $10.00 for net coupon interest and -$0.28+ -$1.69 for APB. That is interest in "Interest based on YTM at purchase" column.

[ofckrupke]

I think you have cracked it.
In doing so you have helped me realize that in my most recent calculation table above, using power() to get the specified yield per period was the wrong approach - that actually following what was written in Pub 550, as you did, was the way to go. My way overstated specified yield in period, so understated amortization, hence the basis did not fully relax to par.
Also in retrospect I think there's independent merit to my initial approach of deriving an effective constant rate of basis decline for the underlying asset and ignoring the coupons. Not sure I would want to try convincing an auditor that logical suitability is as good as dutifully adhering to a published recipe for calculation though.

[FactualFran]

When I did this type of calculation for non-covered fixed income securities that I bought at a premium, I calculated the accrual with each interest payment. With the example that was given, I would use a yield of 1.6433%, with an additional digit to what was given, in order for the basis at maturity to be the par value. Here is a table of the results:

Code: Select all

                      Accrual for  ABP for	
   Date       Basis      Period	     Year
2019-08-15
2020-01-13  1,017.34
2020-02-15  1,017.05     -0.29
2020-08-15  1,015.41     -1.64      -1.93
2021-02-15  1,013.75     -1.66
2021-08-15  1,012.08     -1.67      -3.33
2022-02-15  1,010.40     -1.68
2022-08-15  1,008.70     -1.70      -3.38
2023-02-15  1,006.99     -1.71
2023-08-15  1,005.26     -1.73      -3.44
2024-02-15  1,003.52     -1.74
2024-08-15  1,001.77     -1.75      -3.49
2025-02-15  1,000.00     -1.77      -1.77

Some comments:

• The basis on the settlement date is the price paid without the accrued interest.
• The accrual for the first period is very small because it is for about one month instead of the usual six months between interest payments.
• The accruals for other than the first period do not involve the number of days, they are (Yield*PeriodStartBasis-AnnualInterest)/2.
• The ABP for Year is the sum of the accruals during the year.
• The ABP for the final year is about half of that for the previous year because the final year will have only one interest payment instead of the usual two.

[Hector]

The accruals for other than the first period do not involve the number of days, they are (Yield*PeriodStartBasis-AnnualInterest)/2.

It makes sense.