The bond/gilt market

OldScientist

Mikeeee_2 said:

Bobziz said:

Very useful, thank you @Mikeeee_2 Could you explain the 14.96% calculation please.

It's quite a complex formula but the Modified Duration (which is the % above) is derived from the Macaulay Duration:

Usefully, the duration function (in most/all spreadsheet packages) can be used to calculate the Macualay duration - the modified duration is then a (relatively) trivial calculation. I aldo note that for back of the envelope calculations, the modified duration is close enough to the Macualay duration except when the YTM is high.

While I agree that care must be taken in chasing coupons (particularly since, when held outside of a tax sheltered environment, they attract tax), they do have the effect of reducing the Macaulay duration (and hence modified duration). In other words, a zero coupon gilt will have a higher volatility with changes in interest rates than one with a non-zero coupon. For example, the following graph shows the modified duration as a function of YTM for a bond with a maturity of 20 years and with semi-annual coupons of 0%, 1%, 2%, 3%, 4%, and 5%.

 

For a YTM of 4%, the modified duration ranges from about 19% for a 0% coupon to about 13% for a 5% coupon.

Of course, if you are holding the gilt to maturity then the volatility is not a significant concern, but might be disturbing for anyone holding a gilt ladder.

In passing., I note that this graph also illustrates why bond prices reacted with such volatility to changes in yields over the last couple of years. Firstly, the starting YTM were low (~1.5%) and secondly, since gilts are usually issued with positive coupons close to the prevailing yield many gilts issued in the last decade or so, have had relatively small coupons.

OldScientist

sevenhills said:

Short duration gilts are 5-7 years or less, like holding a 5 year fix in a savings account, you cannot sell early?

Are the dealing charges similar to buying shares, a £1,000 holding for example or are bonds just for the big money people?

Yes, for short durations, a good initial comparison is between the gilt yield and the interest rate on a fixed rate savings account with several caveats.
1) there is a difference in liquidity since fixed rate savings cannot be redeemed early (except, I think, of ISA type) whereas the gilts can be sold at any time (but possibly at a loss).
2) Outside of tax-sheltered platforms, interest and coupons potentially attract tax. For gilts bought below par (i.e., the price is less than 100) the capital gains are tax free.
3) There is no equivalent index linked savings account (unless NS&I bring them back).

I'm not familiar with buying bonds on other platforms, but iweb charge £5 per transaction for gilts (i.e., the same as for any other transaction).

OldScientist

'Risk' is a term rather widely used in finance and can mean different things in different contexts

'Risk-free return' is based on return of nominal capital solely because for most of history index linked bonds were not available (i.e., prior to the 1980s in the UK). In the US, it is often considered to be the yield associated with the 10 year note (i.e., a US treasury with a maturity of 10 years) or 3 month Treasury Bills. In the UK, the SONIA appears to be considered by the BoE to be the risk free rate (see https://www.bankofengland.co.uk/markets/transition-to-sterling-risk-free-rates-from-libor ).

Inflation risk is an additional risk that ought to be considered in retirement planning (amongst other things). No financial instruments are immune to the risks of inflation (e.g., as an extreme example, in 1920s Germany, inflation completely outstripped returns from the German stock market).

zagfles

Notepad_Phil said:

ChesterDog said:

Mikeeee_2 said:

Johnjdc said:

zagfles said:

Johnjdc said:

Mikeee is correct. The risk free rate is the risk free rate, that's what it's called and it just means the nominal return you can get without risking your nominal capital.

The fact that the real terms return might be lower, or even negative, is something to consider when investing, but doesn't affect the definition of the terms.

Now it's just semantics. On that definition you can get "risk free" 27% pa return on Turkish govt bonds

I am intrigued by how you would propose to settle a disagreement about the meaning of a word or phrase without engaging in semantics, the study of the meaning of words and phrases.

There are much bigger things in the world to worry about. It actually makes me sad that I spent quite a lot of time putting this guide together and all people are interested in is the definition of a commonly used phrase.

That just shows what a great job you did.

I'm a bit baffled about the argument, too. Risk-free in this context is universally taken to mean the nominal value of capital is assured.

You may know that, I may know that, but I'm not sure that every visitor to this site would know exactly what is meant by 'risk free' in that context and why they are not necessarily risk free. So the additional explanatory text is certainly welcomed by me.

Indeed - this "universally taken" definition is clearly looking at the specific risk of ending up with less £ than you started with, rather than the more useful broader risk of ending up with less spending power than you started with. 

From the POV of an investor investing for his/her future, rather than a technical term used in the finance industry, unless your investment is going to be used to pay for something which you know won't increase in price (for example paying off a mortgage etc), it is misleading to refer to anything as "risk free" unless there's no risk of its spending power going down.

noclaf

Thanks to OP for this thread, will be bookmarked!

 Bonds are an area I have started to read up on but need to do lot more to grasp the fundamentals
.
Any thoughts/comments on the use of Bond ETFS? As to the 'why'...due to capped ETF charges on one of my investment platforms. 

zagfles

OldScientist said:

Mikeeee_2 said:

Bobziz said:

Very useful, thank you @Mikeeee_2 Could you explain the 14.96% calculation please.

It's quite a complex formula but the Modified Duration (which is the % above) is derived from the Macaulay Duration:

Usefully, the duration function (in most/all spreadsheet packages) can be used to calculate the Macualay duration - the modified duration is then a (relatively) trivial calculation. I aldo note that for back of the envelope calculations, the modified duration is close enough to the Macualay duration except when the YTM is high.

While I agree that care must be taken in chasing coupons (particularly since, when held outside of a tax sheltered environment, they attract tax), they do have the effect of reducing the Macaulay duration (and hence modified duration). In other words, a zero coupon gilt will have a higher volatility with changes in interest rates than one with a non-zero coupon. For example, the following graph shows the modified duration as a function of YTM for a bond with a maturity of 20 years and with semi-annual coupons of 0%, 1%, 2%, 3%, 4%, and 5%.

 

For a YTM of 4%, the modified duration ranges from about 19% for a 0% coupon to about 13% for a 5% coupon.

Of course, if you are holding the gilt to maturity then the volatility is not a significant concern, but might be disturbing for anyone holding a gilt ladder.

In passing., I note that this graph also illustrates why bond prices reacted with such volatility to changes in yields over the last couple of years. Firstly, the starting YTM were low (~1.5%) and secondly, since gilts are usually issued with positive coupons close to the prevailing yield many gilts issued in the last decade or so, have had relatively small coupons.

It's interesting that the implication of this, if I've understood correctly, is that interest rate changes now are assumed to affect the expected interest rate decades down the line. It's clear why gilts will go up/down with interest rates, what I don't really get is why long dated gilts are so much more volatile than mid dated gilts. Say a 15 year gilt compared to a 50 year one. This seems to assume that any interest change now is going to affect interest rates in 15+ years time.

boingy

Mikeeee_2 said:

Johnjdc said:

zagfles said:

Johnjdc said:

Mikeee is correct. The risk free rate is the risk free rate, that's what it's called and it just means the nominal return you can get without risking your nominal capital.

The fact that the real terms return might be lower, or even negative, is something to consider when investing, but doesn't affect the definition of the terms.

Now it's just semantics. On that definition you can get "risk free" 27% pa return on Turkish govt bonds

I am intrigued by how you would propose to settle a disagreement about the meaning of a word or phrase without engaging in semantics, the study of the meaning of words and phrases.

There are much bigger things in the world to worry about. It actually makes me sad that I spent quite a lot of time putting this guide together and all people are interested in is the definition of a commonly used phrase.

I think the vast majority of people will appreciate the guide rather than feel the need to endless bicker about stuff. So thank you for posting it. It would be useful if the Mods could remove all those bickering posts to leave a cleaner thread to make it more useful for future visitors.

Mikeeee_2

zagfles said:

OldScientist said:

Mikeeee_2 said:

Bobziz said:

Very useful, thank you @Mikeeee_2 Could you explain the 14.96% calculation please.

It's quite a complex formula but the Modified Duration (which is the % above) is derived from the Macaulay Duration:

Usefully, the duration function (in most/all spreadsheet packages) can be used to calculate the Macualay duration - the modified duration is then a (relatively) trivial calculation. I aldo note that for back of the envelope calculations, the modified duration is close enough to the Macualay duration except when the YTM is high.

While I agree that care must be taken in chasing coupons (particularly since, when held outside of a tax sheltered environment, they attract tax), they do have the effect of reducing the Macaulay duration (and hence modified duration). In other words, a zero coupon gilt will have a higher volatility with changes in interest rates than one with a non-zero coupon. For example, the following graph shows the modified duration as a function of YTM for a bond with a maturity of 20 years and with semi-annual coupons of 0%, 1%, 2%, 3%, 4%, and 5%.

 

For a YTM of 4%, the modified duration ranges from about 19% for a 0% coupon to about 13% for a 5% coupon.

Of course, if you are holding the gilt to maturity then the volatility is not a significant concern, but might be disturbing for anyone holding a gilt ladder.

In passing., I note that this graph also illustrates why bond prices reacted with such volatility to changes in yields over the last couple of years. Firstly, the starting YTM were low (~1.5%) and secondly, since gilts are usually issued with positive coupons close to the prevailing yield many gilts issued in the last decade or so, have had relatively small coupons.

It's interesting that the implication of this, if I've understood correctly, is that interest rate changes now are assumed to affect the expected interest rate decades down the line. It's clear why gilts will go up/down with interest rates, what I don't really get is why long dated gilts are so much more volatile than mid dated gilts. Say a 15 year gilt compared to a 50 year one. This seems to assume that any interest change now is going to affect interest rates in 15+ years time.

Gilts are linked to the base rate. So a low yielding longer dated gilt will always have to move more than anything else. As well as an overview, that's mainly the point of the OP. There are big opportunities here if you are sure the BoEs next move is to reduce rates rather than raise.

zagfles

Mikeeee_2 said:

zagfles said:

OldScientist said:

Mikeeee_2 said:

Bobziz said:

Very useful, thank you @Mikeeee_2 Could you explain the 14.96% calculation please.

It's quite a complex formula but the Modified Duration (which is the % above) is derived from the Macaulay Duration:

Usefully, the duration function (in most/all spreadsheet packages) can be used to calculate the Macualay duration - the modified duration is then a (relatively) trivial calculation. I aldo note that for back of the envelope calculations, the modified duration is close enough to the Macualay duration except when the YTM is high.

While I agree that care must be taken in chasing coupons (particularly since, when held outside of a tax sheltered environment, they attract tax), they do have the effect of reducing the Macaulay duration (and hence modified duration). In other words, a zero coupon gilt will have a higher volatility with changes in interest rates than one with a non-zero coupon. For example, the following graph shows the modified duration as a function of YTM for a bond with a maturity of 20 years and with semi-annual coupons of 0%, 1%, 2%, 3%, 4%, and 5%.

 

For a YTM of 4%, the modified duration ranges from about 19% for a 0% coupon to about 13% for a 5% coupon.

Of course, if you are holding the gilt to maturity then the volatility is not a significant concern, but might be disturbing for anyone holding a gilt ladder.

In passing., I note that this graph also illustrates why bond prices reacted with such volatility to changes in yields over the last couple of years. Firstly, the starting YTM were low (~1.5%) and secondly, since gilts are usually issued with positive coupons close to the prevailing yield many gilts issued in the last decade or so, have had relatively small coupons.

It's interesting that the implication of this, if I've understood correctly, is that interest rate changes now are assumed to affect the expected interest rate decades down the line. It's clear why gilts will go up/down with interest rates, what I don't really get is why long dated gilts are so much more volatile than mid dated gilts. Say a 15 year gilt compared to a 50 year one. This seems to assume that any interest change now is going to affect interest rates in 15+ years time.

Gilts are linked to the base rate. So a low yielding longer dated gilt will always have to move more than anything else. As well as an overview, that's mainly the point of the OP. There are big opportunities here if you are sure the BoEs next move is to reduce rates rather than raise.

Do you mean the YTM is linked to the base rate, that's the issue. As an example, say the base rate/market expected "risk free return" (BoE definition not mine) is 4%.

You have a 15 year gilt and 50 year gilt, both with coupons of 4%, and therefore both trading at par, £100. 

Then some market turbulence occurs, and the BoE need to raise base rates, say to 6% over a year or two.

Clearly both gilts will drop in price. But it makes no sense that the 50 year drops by more, unless the market expectation is that the turbulence is going to have a long term effect and as a result interest rates will be higher than originally expected in 15 years time.

If the expectation is that the turbulence is short term and interest rates will return to "normal", ie back to 4% within 15 years, then the market expectation should be that the 50 year gilt will be trading at £100 in 15 years time, ie exactly the same as the known redemption price of the 15 year gilt. In that scenario it makes no sense that the 50 year gilt is more affected than the 15 year one.

OldScientist

zagfles said:

OldScientist said:

Mikeeee_2 said:

Bobziz said:

Very useful, thank you @Mikeeee_2 Could you explain the 14.96% calculation please.

It's quite a complex formula but the Modified Duration (which is the % above) is derived from the Macaulay Duration:

Usefully, the duration function (in most/all spreadsheet packages) can be used to calculate the Macualay duration - the modified duration is then a (relatively) trivial calculation. I aldo note that for back of the envelope calculations, the modified duration is close enough to the Macualay duration except when the YTM is high.

While I agree that care must be taken in chasing coupons (particularly since, when held outside of a tax sheltered environment, they attract tax), they do have the effect of reducing the Macaulay duration (and hence modified duration). In other words, a zero coupon gilt will have a higher volatility with changes in interest rates than one with a non-zero coupon. For example, the following graph shows the modified duration as a function of YTM for a bond with a maturity of 20 years and with semi-annual coupons of 0%, 1%, 2%, 3%, 4%, and 5%.

 

For a YTM of 4%, the modified duration ranges from about 19% for a 0% coupon to about 13% for a 5% coupon.

Of course, if you are holding the gilt to maturity then the volatility is not a significant concern, but might be disturbing for anyone holding a gilt ladder.

In passing., I note that this graph also illustrates why bond prices reacted with such volatility to changes in yields over the last couple of years. Firstly, the starting YTM were low (~1.5%) and secondly, since gilts are usually issued with positive coupons close to the prevailing yield many gilts issued in the last decade or so, have had relatively small coupons.

It's interesting that the implication of this, if I've understood correctly, is that interest rate changes now are assumed to affect the expected interest rate decades down the line. It's clear why gilts will go up/down with interest rates, what I don't really get is why long dated gilts are so much more volatile than mid dated gilts. Say a 15 year gilt compared to a 50 year one. This seems to assume that any interest change now is going to affect interest rates in 15+ years time.

Probably easiest to illustrate this an example. Imagine we have two zero coupon bonds (this just makes the maths a bit easier) one with 15 years to maturity and the other with 50 years. The price, P is then given by 100/(1+y)^n where y is the yield expressed as a fraction and n is the number of years to maturity. Assuming that both bonds have the same yield of 3% (i.e., the yield curve is flat) then

For the 15 year bond, the price is 100/(1+0.03)^15=64.186 (the modified duration is 14.6)

For the 50 year bond, the price would be 100/(1+0.03)^50=22.811 (the modified duration is 48.5)

You can start with the current price and check whether the final price is 100. So, for the 15 year bond final price=64.186*(1+0.03)^15=100.

Now let us assume that the yield increases to 5% (again, for the purposes of this example, the yield is the same for both bonds).

For the 15 year bond the price is now P=100/(1+0.05)^15=48.102

While for the 50 year bond the price falls to 100/(1+0.05)^50=8.720

The price of the 15 year bond has fallen by about 25%, while that of the 50 year bond has fallen by 60% - i.e. the volatility of the longer bond is greater. This happens because of the power term in the equation - the effect of the yield change is played out over a much longer time for the longer maturity bond. I also note that this example illustrates the approximate nature of the rule of thumb associated with modified duration - it is only accurate for small changes in yields (but is otherwise is good enough).