UK gilt calculations

saajan_12

nonolerigolo said:

I am calculating the redemption rate annually for the gilt TG31 - 31/07/31 coupon 0.25%. 

Yield Gimp website gives a redemption of 4.20%. Current price is £76.96.

My calculation is: 100 (par value) -76.96 ‎ = 23.04 - thats £23.04 gain per bond, not a % of your initial investment. 

23.04\6.75 (year to maturity) =3.41 

3.41 + 0.35 coupons= 3.76% - where did the 0.35 come from? Do you mean 0.25? 

So approximately 0.36% difference. 

Where does the difference come from?

Thank you 

You're calculating the £ you make per £100 bond.  But you suddenly introduce a % symbol, but remember what it's a % of? Your original investment was only £76.96. 

You're also dividing the return over a 6.75 year period, but here not all the money is kept invested over 6.75 years. In fact you get £2.20 of the money at various points before the maturity, which can be re-invested to get a higher return in the same period. 

SnowMan

EthicsGradient said:

Odd thing about the YIELD function on LibreOffice: I'd think that, if the coupon is zero, then the frequency of payment shouldn't make a difference.
But
=YIELD("04/11/2024","31/07/2031",0,76.96,100,2,1) gives me 3.924%, while
=YIELD("04/11/2024","31/07/2031",0,76.96,100,1,1) gives me 3.962%.
Why?

To sort of answer my own question: half of 3.924 is 1.962; 1.01962 squared is 1.3962. So it's as if the function is giving the answer to "what gross rate, paid twice yearly, gives the same amount?", rather than "what AER...".

And if you do the YIELD calculation 
=YIELD("04/11/2024","31/07/2031",0.0025,76.96,100,1,1)
you get 4.255% - or 4.26%, to the 2 decimal places used until now.

I think you have correctly answered your own question. If you look at the official document it does appear (I don't have the energy to properly check) that the convention is to quote the gross rate payable half yearly if the coupon frequency is twice a year, and the gross rate payable yearly if the coupon frequency is once a year (i.e 'AER' in that case), and gross rate payable quarterly if the coupon frequency is payable quarterly etc

https://www.dmo.gov.uk/media/1sljygul/yldeqns.pdf

Seems silly to me, but that's the convention. I think 4.26%pa is the most relevant answer because that's equivalent to the AER on a savings account, and AERs makes for easy comparison between accounts/gilts paying interest at different frequencies. But the convention is you quote the gross rate payable half yearly for half-yearly paying gilts.

OldScientist

SnowMan said:

EthicsGradient said:

Odd thing about the YIELD function on LibreOffice: I'd think that, if the coupon is zero, then the frequency of payment shouldn't make a difference.
But
=YIELD("04/11/2024","31/07/2031",0,76.96,100,2,1) gives me 3.924%, while
=YIELD("04/11/2024","31/07/2031",0,76.96,100,1,1) gives me 3.962%.
Why?

To sort of answer my own question: half of 3.924 is 1.962; 1.01962 squared is 1.3962. So it's as if the function is giving the answer to "what gross rate, paid twice yearly, gives the same amount?", rather than "what AER...".

And if you do the YIELD calculation 
=YIELD("04/11/2024","31/07/2031",0.0025,76.96,100,1,1)
you get 4.255% - or 4.26%, to the 2 decimal places used until now.

I think you have correctly answered your own question. If you look at the official document it does appear (I don't have the energy to properly check) that the convention is to quote the gross rate payable half yearly if the coupon frequency is twice a year, and the gross rate payable yearly if the coupon frequency is once a year (i.e 'AER' in that case), and gross rate payable quarterly if the coupon frequency is payable quarterly etc

https://www.dmo.gov.uk/media/1sljygul/yldeqns.pdf

Seems silly to me, but that's the convention. I think 4.26%pa is the most relevant answer because that's equivalent to the AER on a savings account, and AERs makes for easy comparison between accounts/gilts paying interest at different frequencies. But the convention is you quote the gross rate payable half yearly for half-yearly paying gilts.

That is my understanding on the difference between annual and semi-annual coupons too. With the demise of consols, at least 3-monthly coupons no longer exist (in the UK at least).

I think yields are quoted, rather than returns or AER because bonds were held to provide an income rather than as a source of returns. I also note that for a bond bought at par, the yield (i.e., income) is independent of future changes in price (i.e., yield). However, total returns and realised yields for a bond not bought at par are dependent on future changes in price, so these are projections only.