buying an individual gilt question

Linton

There are 2 prices for gilts, "clean" and "dirty".  The published value is usually the clean price.   Dirty=clean+adjustment for interest due when a bond is bought between interest pay-outs.  Trades are actually carried out on the dirty price.

The standard measure of overall gilt return is given by the YTM (yield to maturity), otherwise known as "Yield".   You may find the current Yield in listings of bonds but you can calculate it from : https://dqydj.com/bond-yield-to-maturity-calculator/.  Note that the price used for the calculations is "clean".

YTM is ony relevent if you do hold to maturity.  If you sell before maturity the returns could be quite different.

aroominyork

MK62 said:

aroominyork said:

Thanks, EthicsGradient - though I've never used functions like XIRR (but given how simple it looks I will study it).

In response to my question "Does (1+145/365) represent full + part years until maturity?" the answer is Yes. So I have refined the equation to:

((100+(0.125*3))/95.87)) ^ (1/(([redemption date]-TODAY())/365))-1

Try

=((100+(0.0625*3))/95.87)^(1/(YEARFRAC(TODAY(),"31/01/24")))-1

PS, while you'll get 3 coupons, they'll each be only half the annual coupon rate (masonic did it the other way.....by halving the no. of coupons - same result though)

Thanks, I've corrected it to "coupon/2".

I'll take your word that your equation gives the same outcome.

So let's cut to the chase of what this tells us about the market's expectations of future interest rates, taking the price from yesterday's last trade on the LSE website and the calculated YTMs.

TN24. 31/1/24, 0.125%. YTM: 4.04%

TN25. 31/1/25, 0.25%. YTM: 4.60%

T26. 31/1/26, 0.125%. YTM: 4.43%

TN30. 22/10/30, 0.375%. YTM: 4.13%.

TR30. 7/12/30, 4.75%. YTM: 3.61%.

Comparing the two 2030 gilts, do those with higher coupons generally have a lower YTM?

Ciprico

What is the reason for the difference in yield between the two 2030 gilts.

Why haven't they self adjusted to parity by market forces...? 

aroominyork

A bit more on those two 2030 gilts:

The last trade for higher coupon one, TR30, shows on the LSE website as 105.00 on Thursday. YTM 3.61%

The lower coupon one is TG30 (not TN30 - apologies), with the last trade at 73.88 on Friday (the final trade on Thursday also shows as 73.88). YTM 4.23%.

masonic

aroominyork said:

A bit more on those two 2030 gilts:

The last trade for higher coupon one, TR30, shows on the LSE website as 105.00 on Thursday. YTM 3.61%

The lower coupon one is TG30 (not TN30 - apologies), with the last trade at 73.88 on Friday (the final trade on Thursday also shows as 73.88). YTM 4.23%.

The prospectus can be found here: https://www.dmo.gov.uk/media/1aehow1z/prosp260520a.pdf and https://www.dmo.gov.uk/media/5snbalfh/prosp220909b.pdf
There doesn't seem to be anything unusual in one vs the other. Clearly one is returning mostly taxable interest, while the other is returning mostly a tax exempt capital gain, but I wouldn't have expected that to make much difference to the YTM. There is a clear difference in trading volumes between the two.

EthicsGradient

The formula you're using will get increasingly inaccurate over long time periods for higher coupons, since it does not take into account the equivalent of compound interest - you get some of the interest payments earlier than others. The dqydj.com link above goes into more detail - a geometric series is involved.
The XIRR spreadsheet method does this for you; TG30 has a YTM of 4.28%, TR30 4.30%.

(That didn't take into account the 'clean'/'dirty' prices mentioned above. If I've understood that bit right, then, using the closing price from the LSE site, and adding 0.25% on for the buy/sell spread, which someone said was reasonable, then you get a YTM of 4.18% for TG30 (lower coupon), and 4.14% for TR30.)

aroominyork

masonic said:

aroominyork said:

A bit more on those two 2030 gilts:

The last trade for higher coupon one, TR30, shows on the LSE website as 105.00 on Thursday. YTM 3.61%

The lower coupon one is TG30 (not TN30 - apologies), with the last trade at 73.88 on Friday (the final trade on Thursday also shows as 73.88). YTM 4.23%.

The prospectus can be found here: https://www.dmo.gov.uk/media/1aehow1z/prosp260520a.pdf and https://www.dmo.gov.uk/media/5snbalfh/prosp220909b.pdf
There doesn't seem to be anything unusual in one vs the other. Clearly one is returning mostly taxable interest, while the other is returning mostly a tax exempt capital gain, but I wouldn't have expected that to make much difference to the YTM. There is a clear difference in trading volumes between the two.

If there was a difference you would expect the gilt with the tax-exempt gain to perform better.

EthicsGradient said:

The formula you're using will get increasingly inaccurate over long time periods for higher coupons, since it does not take into account the equivalent of compound interest - you get some of the interest payments earlier than others. The dqydj.com link above goes into more detail - a geometric series is involved.
The XIRR spreadsheet method does this for you; TG30 has a YTM of 4.28%, TR30 4.30%.

Clearly I am doing something wrong here, based on 100 units. What is it please (apart from not bothering to add the small amount of accrued interest to the purchase price)?

TG30	30/09/2022	-£   73.88		TR30	30/09/2022	-£ 105.00
	22/10/2022	£    0.38			07/12/2022	£    4.75
	22/04/2023	£    0.38			07/07/2023	£    4.75
	22/10/2023	£    0.38			07/12/2023	£    4.75
	22/04/2024	£    0.38			07/07/2024	£    4.75
	22/10/2024	£    0.38			07/12/2024	£    4.75
	22/04/2025	£    0.38			07/07/2025	£    4.75
	22/10/2025	£    0.38			07/12/2025	£    4.75
	22/04/2026	£    0.38			07/07/2026	£    4.75
	22/10/2026	£    0.38			07/12/2026	£    4.75
	22/04/2027	£    0.38			07/07/2027	£    4.75
	22/10/2027	£    0.38			07/12/2027	£    4.75
	22/04/2028	£    0.38			07/07/2028	£    4.75
	22/10/2028	£    0.38			07/12/2028	£    4.75
	22/04/2029	£    0.38			07/07/2029	£    4.75
	22/10/2029	£    0.38			07/12/2029	£    4.75
	22/04/2030	£    0.38			07/07/2030	£    4.75
	22/10/2030	£ 100.38			07/12/2030	£ 104.75
		4.79%				9.31%

Linton

aroominyork said:

masonic said:

aroominyork said:

A bit more on those two 2030 gilts:

The last trade for higher coupon one, TR30, shows on the LSE website as 105.00 on Thursday. YTM 3.61%

The lower coupon one is TG30 (not TN30 - apologies), with the last trade at 73.88 on Friday (the final trade on Thursday also shows as 73.88). YTM 4.23%.

The prospectus can be found here: https://www.dmo.gov.uk/media/1aehow1z/prosp260520a.pdf and https://www.dmo.gov.uk/media/5snbalfh/prosp220909b.pdf
There doesn't seem to be anything unusual in one vs the other. Clearly one is returning mostly taxable interest, while the other is returning mostly a tax exempt capital gain, but I wouldn't have expected that to make much difference to the YTM. There is a clear difference in trading volumes between the two.

If there was a difference you would expect the gilt with the tax-exempt gain to perform better.

EthicsGradient said:

The formula you're using will get increasingly inaccurate over long time periods for higher coupons, since it does not take into account the equivalent of compound interest - you get some of the interest payments earlier than others. The dqydj.com link above goes into more detail - a geometric series is involved.
The XIRR spreadsheet method does this for you; TG30 has a YTM of 4.28%, TR30 4.30%.

Clearly I am doing something wrong here, based on 100 units. What is it please (apart from not bothering to add the small amount of accrued interest to the purchase price)?

TG30	30/09/2022	-£   73.88		TR30	30/09/2022	-£ 105.00
	22/10/2022	£    0.38			07/12/2022	£    4.75
	22/04/2023	£    0.38			07/07/2023	£    4.75
	22/10/2023	£    0.38			07/12/2023	£    4.75
	22/04/2024	£    0.38			07/07/2024	£    4.75
	22/10/2024	£    0.38			07/12/2024	£    4.75
	22/04/2025	£    0.38			07/07/2025	£    4.75
	22/10/2025	£    0.38			07/12/2025	£    4.75
	22/04/2026	£    0.38			07/07/2026	£    4.75
	22/10/2026	£    0.38			07/12/2026	£    4.75
	22/04/2027	£    0.38			07/07/2027	£    4.75
	22/10/2027	£    0.38			07/12/2027	£    4.75
	22/04/2028	£    0.38			07/07/2028	£    4.75
	22/10/2028	£    0.38			07/12/2028	£    4.75
	22/04/2029	£    0.38			07/07/2029	£    4.75
	22/10/2029	£    0.38			07/12/2029	£    4.75
	22/04/2030	£    0.38			07/07/2030	£    4.75
	22/10/2030	£ 100.38			07/12/2030	£ 104.75
		4.79%				9.31%

You seem to be adding the annual interest twice a year.  Minor point the dates for T30 are not 6 months apart.

aroominyork

Linton said:

aroominyork said:

masonic said:

aroominyork said:

A bit more on those two 2030 gilts:

The last trade for higher coupon one, TR30, shows on the LSE website as 105.00 on Thursday. YTM 3.61%

The lower coupon one is TG30 (not TN30 - apologies), with the last trade at 73.88 on Friday (the final trade on Thursday also shows as 73.88). YTM 4.23%.

The prospectus can be found here: https://www.dmo.gov.uk/media/1aehow1z/prosp260520a.pdf and https://www.dmo.gov.uk/media/5snbalfh/prosp220909b.pdf
There doesn't seem to be anything unusual in one vs the other. Clearly one is returning mostly taxable interest, while the other is returning mostly a tax exempt capital gain, but I wouldn't have expected that to make much difference to the YTM. There is a clear difference in trading volumes between the two.

If there was a difference you would expect the gilt with the tax-exempt gain to perform better.

EthicsGradient said:

The formula you're using will get increasingly inaccurate over long time periods for higher coupons, since it does not take into account the equivalent of compound interest - you get some of the interest payments earlier than others. The dqydj.com link above goes into more detail - a geometric series is involved.
The XIRR spreadsheet method does this for you; TG30 has a YTM of 4.28%, TR30 4.30%.

Clearly I am doing something wrong here, based on 100 units. What is it please (apart from not bothering to add the small amount of accrued interest to the purchase price)?

TG30	30/09/2022	-£   73.88		TR30	30/09/2022	-£ 105.00
	22/10/2022	£    0.38			07/12/2022	£    4.75
	22/04/2023	£    0.38			07/07/2023	£    4.75
	22/10/2023	£    0.38			07/12/2023	£    4.75
	22/04/2024	£    0.38			07/07/2024	£    4.75
	22/10/2024	£    0.38			07/12/2024	£    4.75
	22/04/2025	£    0.38			07/07/2025	£    4.75
	22/10/2025	£    0.38			07/12/2025	£    4.75
	22/04/2026	£    0.38			07/07/2026	£    4.75
	22/10/2026	£    0.38			07/12/2026	£    4.75
	22/04/2027	£    0.38			07/07/2027	£    4.75
	22/10/2027	£    0.38			07/12/2027	£    4.75
	22/04/2028	£    0.38			07/07/2028	£    4.75
	22/10/2028	£    0.38			07/12/2028	£    4.75
	22/04/2029	£    0.38			07/07/2029	£    4.75
	22/10/2029	£    0.38			07/12/2029	£    4.75
	22/04/2030	£    0.38			07/07/2030	£    4.75
	22/10/2030	£ 100.38			07/12/2030	£ 104.75
		4.79%				9.31%

You seem to be adding the annual interest twice a year.  Minor point the dates for T30 are not 6 months apart.

Not the first time I've done that. Thanks, Linton.

TG30	30/09/2022	-£   73.88		TR30	30/09/2022	-£ 105.00
	22/10/2022	£    0.19			07/12/2022	£    2.38
	22/04/2023	£    0.19			07/07/2023	£    2.38
	22/10/2023	£    0.19			07/12/2023	£    2.38
	22/04/2024	£    0.19			07/07/2024	£    2.38
	22/10/2024	£    0.19			07/12/2024	£    2.38
	22/04/2025	£    0.19			07/07/2025	£    2.38
	22/10/2025	£    0.19			07/12/2025	£    2.38
	22/04/2026	£    0.19			07/07/2026	£    2.38
	22/10/2026	£    0.19			07/12/2026	£    2.38
	22/04/2027	£    0.19			07/07/2027	£    2.38
	22/10/2027	£    0.19			07/12/2027	£    2.38
	22/04/2028	£    0.19			07/07/2028	£    2.38
	22/10/2028	£    0.19			07/12/2028	£    2.38
	22/04/2029	£    0.19			07/07/2029	£    2.38
	22/10/2029	£    0.19			07/12/2029	£    2.38
	22/04/2030	£    0.19			07/07/2030	£    2.38
	22/10/2030	£ 100.19			07/12/2030	£ 102.38
		4.30%				4.27%

Is there a shortcut for "add six months to previous date"?

EthicsGradient

The "shortcut" I used was "date above +182" or +183" (eg '=B2+182' in cell B3), and then find where to put in an extra 1 for any leap years. Make a couple of "B2+182" and "B3+183", then you can copy that and paste them in every 2 cells down. There probably is a proper formula, but I'm not good enough at spreadsheets to know it.