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Yield to maturity calculation
Saltyrob
Posted: 10 October 2022 07:47:33(UTC)
#1

Joined: 10/11/2012(UTC)
Posts: 167

Hi Folks,

Would be grateful if you could confirm how you calculate yield to maturity on a UK gilt. Early days but looking at future possibly of one year gilt to park some money . Sorry if its a bit basic but prefer to dot the is and cross the t's and check its right. when it comes to my hard earned

Many thanks

SR
Tony Peterson
Posted: 10 October 2022 08:01:24(UTC)
#2

Joined: 10/08/2009(UTC)
Posts: 2,178

Are you talking index-linked or non index-linked?

The "dirty price" you pay and the "clean price" that is quoted makes for a complicated problem for would-be index linked gilt buyers.

Saltyrob
Posted: 10 October 2022 08:14:29(UTC)
#3

Joined: 10/11/2012(UTC)
Posts: 167

Hi Tony,

Non index linked bond. Just to confirm looking at 6-12 month to maturity.
paul armstrong
Posted: 10 October 2022 08:28:49(UTC)
#4

Joined: 14/03/2010(UTC)
Posts: 1,366

Did this years ago so from memory...
Its an Internal Rate of Return calculation. Excel has an inbuilt function no doubt.
Need to discount all future cash flows by a discount rate which equates those to the current price, ie present value.
So using clean price take each coupon payment and discount by number of years away, then take par value and discount back from maturity. Need to do it by trial and error, ie assume i=0.02 then if calculated pv is higher than current price try a higher discount.

https://www.journalofacc...xcel.html#:~:text=Excel's%20IRR%20function%20calculates%20the,rate%20of%20return%20of%2012.22%25.
Saltyrob
Posted: 10 October 2022 08:46:46(UTC)
#5

Joined: 10/11/2012(UTC)
Posts: 167

Would be grateful if a hypothetical worked example could be shown. Should have listened more in maths .

Many thanks

SR
Tony Peterson
Posted: 10 October 2022 09:23:25(UTC)
#6

Joined: 10/08/2009(UTC)
Posts: 2,178

You need to know the cost to you of each £100 of stock including dealing charges. Let's call this C.

If you hold for more than six months but less than a year you will get, at maturity, N days away, a return ( of the £100 nominal plus the annual coupon. Let's call the money repaid R.

Divide R by C. to get a proportionate gain - call this G. - you have made (G-1) times 100%.as a percentage gain (if it comes out negative you've made a loss)

To calculate this as an annualised yield raise G to the power of (365/N). Your percentage annualised yield is this answer, take away 1, and multiply by 100%.

Now let's look for the real yield allowing for inflation. I reckon you reasonably expect 10% inflation to continue.

The real return is almost guaranteed to be negative. Which is why I wouldn't be very interested at present in short dated gilts.
Saltyrob
Posted: 10 October 2022 09:28:45(UTC)
#7

Joined: 10/11/2012(UTC)
Posts: 167

Cheers Tony , owe you a pint

SR
paul armstrong
Posted: 11 October 2022 10:25:53(UTC)
#8

Joined: 14/03/2010(UTC)
Posts: 1,366

I'll see if my memory holds.
You have, or can buy, gilts at a price X for each £100 par value.
You get a coupon B every 6 months. Can't be bothered working in 6 months if long dated so do it by year and so you get twice B lets call it C per year.
You will also get €100 back on maturity.
Lets say maturity is N years in the future.
So, assuming the alphabet doesn't run out of letters,
You need to find the value r, the rate of return, where

X = 100/(1+r)^N +C/(1+r)^N+ C/(1+r)^(N-1) +C/(1+r)^(N-2) ....and so on back to a year from now.

So return at par plus coupon in final year (but you may get only a half the annual coupon depending when it matures) plus coupon in next to last year plus....

Of course this doesn't exactly match niceties of dirty price when you buy or 6 monthly increments but should be close enough I would think.

Or

https://support.microsof...8-495b-b290-3ad0c163c1bc
Tony Peterson
Posted: 11 October 2022 12:03:51(UTC)
#9

Joined: 10/08/2009(UTC)
Posts: 2,178

Paul


Saltyrob was asking only about a "one year gilt" held to maturity.

And as far as I know, "dirty" and "clean" prices only apply to index linkers. You do of course, as I remember it from last century, pay up front as part of your buying cost any accrued interest towards the next coupon.

But, at a time of rising interest rates ordinary gilts are not on my buying list. There may come a time, though...





1 user thanked Tony Peterson for this post.
paul armstrong on 11/10/2022(UTC)
paul armstrong
Posted: 11 October 2022 12:20:33(UTC)
#10

Joined: 14/03/2010(UTC)
Posts: 1,366

I bought some more of the Royal London global short duration Il fund today. Robert Armstrong in the FT in his Unhedged column ( recommended) was wondering what was going on with IL gilts as the yield jumped. Having no clear idea of my own I thought why not...

For ordinary bonds and gilts, dirty price includes the entitlement earned towards the next coupon. For IL gilts dirty also includes the inflation uplift

https://www.google.com/u...w3HiRTCN33hNlSFGT4AvFGH

Sorry, hadn't spotted the one year interest thing. Why would you go through the telephone hassle and expense to buy a gilt maturing in one year rather than a short or ultrashort fund ??.
3 users thanked paul armstrong for this post.
Tony Peterson on 11/10/2022(UTC), Saltyrob on 11/10/2022(UTC), Tim D on 11/10/2022(UTC)
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