Bond fund yields

masonic

MK62 said:

masonic said:

aroominyork said:

masonic said:

aroominyork said:

masonic said:

aroominyork said:

Second, to what degree is there a correlation between a gilt fund and a nominal gilt with a similar duration (or is it the maturity of the fund I should be looking at?)?

As Beddie suggests, it is the YTM that you'd expect to line up with a gilt. So take TR33, with a current YTM of 4.4%. This is roughly what you'd expect this fund to return if it wound down its portfolio from here. If it buys additional gilts as others mature, as surely it will, then the actual return will depend on the YTM of those too.

Many thanks for this. To compare a gilt fund with a nominal gilt is it important to choose a nominal gilt with a similar yield? For example, if looking at a very long duration gilt fund yielding around 4%, TR60 and TR63 both have 4% coupons and yield 4.84%; TG61, coupon 0.5%, yields 4.46%. Would it be important to choose TR60/TR63 to give similar duration and hence similar responses to interest rate changes?

It is not as important to match the yield as to match the duration. There will be some effect from the more favourable tax treatment of low coupon gilts, but you should be able to see from the tables that it doesn't make much difference, especially out at longer durations. But the longer the duration the more different the "average" composition of the fund will be to today's composition over that duration period.

But doesn't a higher coupon equate to a shorter duration? Surely with a zero-coupon bond, the bond's time to maturity is equal to its duration. When a coupon is added, the duration is less than time to maturity, and the larger the coupon the shorter the duration. (For my purposes it will make little difference which I choose but it is good to grasp the theory.)

Edit: though it's an interesting question how much yield difference is down to duration and how much to tax treatment. TY25 3.5% with 334 days to maturity yields 4.589%. T26 0.125% with 434 days to maturity yields 3.99%. That's a material difference in yield.

The coupon is a function of the interest rate landscape when the gilt was issued. The price and YTM normalises to the current yield curve, which may vary in shape depending on the economic conditions of the day. Things like tax treatment will distort things a bit, but the effect usually isn't large.

Hmmm.......depends on the investor. This website shows the YTM and the effective YTM for a 40% taxpayer.....https://www.yieldgimp.com/gilt-yields

From there you can see that while the YTM for TY25 3.5% is 4.57%, it's YTM for a 40% taxpayer is 3.16%.
Conversely it shows that the YTM for T26 0.125% is 3.96%, while the YTM for a 40% taxpayer is 3.91%.
This is due to the tax treatment of gilt coupons vs capital gain.......low coupon gilts are more desirable for those who must pay HR tax on their gilt returns.......of course, this consideration doesn't apply if investing in an ISA or pension.

The site also shows the equivalent rate a HR taxpaying investor would need to get on a cash deposit account to equal the net yield from a gilt.....not hard to see why investing in gilts is popular with some HR taxpayers, and why low coupon gilts are more popular with such investors.

I'm referring to gross rates of return. I don't dispute that certain investors will prefer low coupon for tax reasons. What I am saying is that this doesn't significantly distort the market, so a low coupon 10 year gilt doesn't have a significantly lower YTM before tax than a corresponding 10 year high coupon gilt. For an example, see T31 vs TG31 - a difference of 0.03%.

Differences tend to be greater at the short end of the yield curve, and that is probably related to how close these securities trade to par. Recently this has also been the most mobile and attractive part of the curve.

masonic

Just for fun, I grabbed the data from YieldGimp and generated this scatter plot of (gross) YTM vs maturity using time to maturity or duration (normalised to a time-based figure from the Mod.Duration (+0.1%) figure):

To me it doesn't look like there is a better curve using interest rate sensitivity and YTM as compared with time to maturity.

OldScientist

masonic said:

MK62 said:

masonic said:

aroominyork said:

masonic said:

aroominyork said:

masonic said:

aroominyork said:

Second, to what degree is there a correlation between a gilt fund and a nominal gilt with a similar duration (or is it the maturity of the fund I should be looking at?)?

As Beddie suggests, it is the YTM that you'd expect to line up with a gilt. So take TR33, with a current YTM of 4.4%. This is roughly what you'd expect this fund to return if it wound down its portfolio from here. If it buys additional gilts as others mature, as surely it will, then the actual return will depend on the YTM of those too.

Many thanks for this. To compare a gilt fund with a nominal gilt is it important to choose a nominal gilt with a similar yield? For example, if looking at a very long duration gilt fund yielding around 4%, TR60 and TR63 both have 4% coupons and yield 4.84%; TG61, coupon 0.5%, yields 4.46%. Would it be important to choose TR60/TR63 to give similar duration and hence similar responses to interest rate changes?

It is not as important to match the yield as to match the duration. There will be some effect from the more favourable tax treatment of low coupon gilts, but you should be able to see from the tables that it doesn't make much difference, especially out at longer durations. But the longer the duration the more different the "average" composition of the fund will be to today's composition over that duration period.

But doesn't a higher coupon equate to a shorter duration? Surely with a zero-coupon bond, the bond's time to maturity is equal to its duration. When a coupon is added, the duration is less than time to maturity, and the larger the coupon the shorter the duration. (For my purposes it will make little difference which I choose but it is good to grasp the theory.)

Edit: though it's an interesting question how much yield difference is down to duration and how much to tax treatment. TY25 3.5% with 334 days to maturity yields 4.589%. T26 0.125% with 434 days to maturity yields 3.99%. That's a material difference in yield.

The coupon is a function of the interest rate landscape when the gilt was issued. The price and YTM normalises to the current yield curve, which may vary in shape depending on the economic conditions of the day. Things like tax treatment will distort things a bit, but the effect usually isn't large.

Hmmm.......depends on the investor. This website shows the YTM and the effective YTM for a 40% taxpayer.....https://www.yieldgimp.com/gilt-yields

From there you can see that while the YTM for TY25 3.5% is 4.57%, it's YTM for a 40% taxpayer is 3.16%.
Conversely it shows that the YTM for T26 0.125% is 3.96%, while the YTM for a 40% taxpayer is 3.91%.
This is due to the tax treatment of gilt coupons vs capital gain.......low coupon gilts are more desirable for those who must pay HR tax on their gilt returns.......of course, this consideration doesn't apply if investing in an ISA or pension.

The site also shows the equivalent rate a HR taxpaying investor would need to get on a cash deposit account to equal the net yield from a gilt.....not hard to see why investing in gilts is popular with some HR taxpayers, and why low coupon gilts are more popular with such investors.

I'm referring to gross rates of return. I don't dispute that certain investors will prefer low coupon for tax reasons. What I am saying is that this doesn't significantly distort the market, so a low coupon 10 year gilt doesn't have a significantly lower YTM before tax than a corresponding 10 year high coupon gilt. For an example, see T31 vs TG31 - a difference of 0.03%.

Differences tend to be greater at the short end of the yield curve, and that is probably related to how close these securities trade to par. Recently this has also been the most mobile and attractive part of the curve.

Possibly of historical interest, I just happened to be looking at gilt yields in 1982 (my retirement is just fun, fun, fun!) and the difference in yields with coupon was marked then. For example, at the end of January 1982, around 4.5 years maturity, a 3% coupon gilt had a yield of 11.1%, while a 12% coupon gilt had a yield of 15.2% (there are other examples all along the yield curve). The government was even issuing 3% coupon bonds (despite the prevailing par yields of around 14 to 15%) in order to reduce interest repayments (although tax receipts would also have been reduced).  Income tax rate was somewhat higher (30% in 82/83) and, AFAIK, basic tax was removed from coupons at source.

I'm no expert, but commercial buyers (with insurance companies and pensions presumably being the largest holders) pay corporation tax on total returns not sure about pensions), while overseas investors do not pay UK tax on gilts, so that may explain why coupons are currently not having much effect on prices now.

incus432

Mikeeee_2 said:

 You can currently buy a 4.25% Gilt at a dirty price (more below if interested) of £98.32 at the time of writing. This means that you will receive 4.25% of the par value, so £4.25 for every gilt you buy at £98.32, which is a yield on your investment of 4.32% - higher than the stated 4.25% as the price is below par. The gilt matures in December 2049 so if you hold until redemption you will receive that coupon every year plus the shortfall of £1.68 between the dirty price you paid and the par value when the gilt matures. This effectively gives you a risk-free return of 4.38%.

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This was posted on another thread some time back and I'm wondering if someone can explain how you get from the £4.25 coupon plus the £1.68 price shortfall (=£5.93) to the 'effective return' of 4.38%? 

Just when I think Ive got my head round gilts I see something like this that throws me.

SnowMan

incus432 said:

Mikeeee_2 said:

 You can currently buy a 4.25% Gilt at a dirty price (more below if interested) of £98.32 at the time of writing. This means that you will receive 4.25% of the par value, so £4.25 for every gilt you buy at £98.32, which is a yield on your investment of 4.32% - higher than the stated 4.25% as the price is below par. The gilt matures in December 2049 so if you hold until redemption you will receive that coupon every year plus the shortfall of £1.68 between the dirty price you paid and the par value when the gilt matures. This effectively gives you a risk-free return of 4.38%.

--------

This was posted on another thread some time back and I'm wondering if someone can explain how you get from the £4.25 coupon plus the £1.68 price shortfall (=£5.93) to the 'effective return' of 4.38%? 

Just when I think Ive got my head round gilts I see something like this that throws me.

Firstly we should work with clean prices, so exclude the accrued interest in the price and exclude the accrued interest from the next half-yearly interest payment (coupon).

The clean price for T49 is currently 90.98 and the gross redemption yield is 4.88%pa (payable half yearly) which is equivalent to 4.94%pa (payable yearly)                          

The return from the coupons is 4.25% x 100/90.98 = 4.67%pa (payable half yearly) because the annual coupons are 4.25% of the £100 nominal which is more than 4.25% of the (less than £100) price.

Or expressed as an annual equivalent paid yearly rather than half yearly that's 4.73%pa (=(1+0.0467/2)^2)-1)

So the annual equivalent return from the price being below par is 0.21%pa (=4.94% - 4.73%)                           

The element of the gross redemption yield coming from the price being below par can't be independently calculated because it interacts with the return from the coupons. So you have to work out the gross redemption yield based on equating all the cashflows to an internal rate of return that balances everything, and then subtract the coupon element from that.   

You might erroneously think you can calculate the return from the price being below par independently to the return from the coupons. The extra redemption payment from getting 100 by paying 90.98 is 9.02 (= 100 - 90.98). And so you might think this return element might be 0.38%pa (as 90.98 x 1.0038^25 = 100). But it is actually 0.21%pa as above. What this 0.38%pa calculation misses is that the clean price has to reflect that in an environment where you can achieve 4.94%pa, interest payments of just 4.73%pa and return of capital at the end is a loss and that loss reduces the return from the coupons.

In summary it's easy to understand that if the gilt is priced at par (100) the gross redemption yield will be exactly equal to the coupon (allowing for frequency of payments). 

And it's relatively easy to understand that if the gilt is priced below par then the gross redemption yield will be more than the coupon. And that if the gilt is priced above par then the gross redemption yield will be less than the coupon. But to actually understand the scale of that difference is not easy without looking at the cashflows on an overall basis.                      

incus432

SnowMan said:

Firstly we should work with clean prices, so exclude the accrued interest in the price and exclude the accrued interest from the next half-yearly interest payment (coupon).

The clean price for T49 is currently 90.98 and the gross redemption yield is 4.88%pa (payable half yearly) which is equivalent to 4.94%pa (payable yearly)                          

The return from the coupons is 4.25% x 100/90.98 = 4.67%pa (payable half yearly) because the annual coupons are 4.25% of the £100 nominal which is more than 4.25% of the (less than £100) price.

Or expressed as an annual equivalent paid yearly rather than half yearly that's 4.73%pa (=(1+0.0467/2)^2)-1)

So the annual equivalent return from the price being below par is 0.21%pa (=4.94% - 4.73%)                           

The element of the gross redemption yield coming from the price being below par can't be independently calculated because it interacts with the return from the coupons. So you have to work out the gross redemption yield based on equating all the cashflows to an internal rate of return that balances everything, and then subtract the coupon element from that.   

You might erroneously think you can calculate the return from the price being below par independently to the return from the coupons. The extra redemption payment from getting 100 by paying 90.98 is 9.02 (= 100 - 90.98). And so you might think this return element might be 0.38%pa (as 90.98 x 1.0038^25 = 100). But it is actually 0.21%pa as above. What this 0.38%pa calculation misses is that the clean price has to reflect that in an environment where you can achieve 4.94%pa, interest payments of just 4.73%pa and return of capital at the end is a loss and that loss reduces the return from the coupons.

In summary it's easy to understand that if the gilt is priced at par (100) the gross redemption yield will be exactly equal to the coupon (allowing for frequency of payments). 

And it's relatively easy to understand that if the gilt is priced below par then the gross redemption yield will be more than the coupon. And that if the gilt is priced above par then the gross redemption yield will be less than the coupon. But to actually understand the scale of that difference is not easy without looking at the cashflows on an overall basis.                      

That error is exactly what I did. Thanks very much for going through that.

Is it any wonder that so many consider gilts as arcane and confusing? 

So when I look at the Yieldgimp table, the Gross Redemption Yield figure (in this example 4.88%)is the one to look at, and should take into account all these factors?

OldScientist

Just to add to the neat answer that  @SnowMan gave.

I note that the gross redemption yield in the yieldgimp table is good enough, but also that yield is not equal to return.

To take TY25 as an example (since the calculations are much shorter than for T49) and using some of the tools in excel (the clean price for TY25 is that on 22 November 2024, I've estimated the dirty price at 99.41 which agrees with the yieldgimp table).



Not surprisingly, the yield is the same (4.54%) as given on the yieldgimp table.
The XIRR calculation gives an internal rate of return very slightly higher at 4.595%.

The total return with reinvestment of coupons is unknown at the the time of purchase since the prices at which coupons will be reinvested is unknown. The following example shows the return assuming the coupon in April 2025 is reinvested at a clean price of 99.5 (for simplicity, I'm ignoring ex-coupon dates).



In this case, the annualised return lies between the yield and the IRR calculated above.

While the reinvestment price in April 2025 might be fairly accurately guessed for TY25, it is impossible to predict what the coupon reinvestment prices for T49 will be over the next 25 years.

In fact, the only certain things with gilts is the coupon rate and the value at maturity (even the yield to maturity for a non-par or non-zero coupon gilt is dependent on intervening yields and prices).

incus432

But if you dont plan to reinvest the coupons the calculation is much simpler no?

OldScientist

incus432 said:

But if you dont plan to reinvest the coupons the calculation is much simpler no?

Yes, if you are not reinvesting the coupons you know the cash flow exactly.

If you buy £90.98 worth of T49 (using Friday's clean price) you will receive £2.125 every six months and, at maturity you will receive £100 plus the final coupon of £2.125. Calculating the IRR is then relatively trivial in a spreadsheet.