Yield margins on corporate v govt bonds

[novagirl]

I read in one of the past paper solutions, that if all yields remain constant over a period, corporates are likely to ouperform government bonds in terms of income performance. And that if yield margins narrow, corporates will outperform government bonds in terms of capital performance.

I understand that corporate bonds are less marketable and less secure than government bonds and are thus expected to have higher yields, but I'm not clear on what the above statements mean when refering to income performance and capital performance.

Could anyone shed some light on this?

 

[Anna Bishop]

Helloooo

The first key concept to get is that the price and the GRY on any fixed-interest bond move in opposite directions.

Eg consider a zero coupon bond

P = 100 / (1 + i) ^ n

P is the price, i is the GRY.

Someone paying 85 for this bond would lock into a GRY of 5.6% (if n = 3).

If the next day, the price rises to 87, a new investor would lock into a GRY of 4.8% (if n = 3).

So price up = GRY down and vice versa.

Now onto your query. If the yield margin of corporates over gilts narrows, then equivalently this means that the price of a corporate bond will have risen by more than on the gilt. This is because price and yield move in the opposite direction, which I have illustrated above.

So a narrowing of the yield margin means that corporates will outperform gilts in terms of capital gains.

Now lets look at income. Consider both a gilt and a corporate bond paying a coupon of 8% pa annually in arrears and redeemable at par both with a 10-year term. We would expect the corporate bond to have the higher GRY and the lower price (as it is riskier). Say the corporate has a GRY of 8% and the gilt has a GRY of 7%. The respective prices are 100 for the corporate and 107.02 for the gilt.

The income yield on the gilt is 8 / 107.02 = 7.48%.
The income yield on the corporate is 8/100 = 8%.

So the corporate is outperforming the gilt in income terms.

 

[PittaPan]

bond yields

Hi Anna /anyone else who can answer,

My questions are not directly related to the original question but still concerning the same topic (bond yields).

(1) Why are the market values of long-dated stocks more volatile than short-term ones? Is it simply because in the former case the term is longer, hence more potential for uncertain events to operate and affect the price? Along the same vein, why are long-dated stocks less liquid than short-dated ones?

(2) Why do index-linked govt bonds have a higher discounted mean term than conventional ones?

(3) Can index-linked govt bonds also be irredeemable? (ActEd tutorial notes for Day 2, p16 seem to suggest not).

Thanks....

 

[pig]

(1) Why are the market values of long-dated stocks more volatile than short-term ones? Is it simply because in the former case the term is longer, hence more potential for uncertain events to operate and affect the price? Along the same vein, why are long-dated stocks less liquid than short-dated ones?

I think it's because -

If the bond is long-dated, the value (or present value) of the bond will be more affected by the discount rate used. A small change in required yield would means a larger changes in prices.

Another possibility is that there may be higher supply and demand for shorter term bonds making the shorter term bond more marketable and hence the price more stable?

(2) Why do index-linked govt bonds have a higher discounted mean term than conventional ones?

For two govt bonds with same present value (and hence price), one index-linked and one conventional, the index linked one would have lower initial coupon payment compare with the conventional, which will have flat coupon payment over the term of the bond. Therefore it just takes longer to repay the 'price' of the bond for the index linked bond because it's coupon values are smaller for the early years.

(3) Can index-linked govt bonds also be irredeemable? (ActEd tutorial notes for Day 2, p16 seem to suggest not).

No idea...

 

[PittaPan]

For two govt bonds with same present value (and hence price), one index-linked and one conventional, the index linked one would have lower initial coupon payment compare with the conventional, which will have flat coupon payment over the term of the bond. Therefore it just takes longer to repay the 'price' of the bond for the index linked bond because it's coupon values are smaller for the early years.

Thanks pig. For the discounted mean term question, I can see why the coupon payment for index-linked bonds are initially lower than those for paid on conventional bonds. But wouldn't the same reasoning (inflation) imply that later on in the term the coupon payments on index-linked bonds would rise above those of the conventional bond, so that on average it all balances out (to give same discounted mean term)?

 

[didster]

PittaPan

Yes the coupon payments at later dates for an index linked bond should be greater than the initial payments on the index linked bond. In addition if all goes according to assumptions (inflation etc) the coupon on the index linded bonds should exceed the payments on a similar comventional bond.

This means the the discounted mean term (DMT) on an index linked bond is higher than the DMT on a conventional bond (with same term and price) and here's why.

You can think of DMT as an average of the payment times weighted by the PV of each payment. So if you compare two bonds with the same timing of payments, then the one with higher weights for larger times will have a higher DMT. Bigger weights means that value has a bigger influence.

As the coupons from the Index linked bond are bigger in the later period then this "pulls" the DMT towards a larger value.

When you compare like with like(ie same price, payment timing, etc), index linked bonds has a higher DMT than conventional because the inital payments are lower than conventional (and don't count as much) and the later payments are higher (and count for more)

 

[pig]

Thanks pig. For the discounted mean term question, I can see why the coupon payment for index-linked bonds are initially lower than those for paid on conventional bonds. But wouldn't the same reasoning (inflation) imply that later on in the term the coupon payments on index-linked bonds would rise above those of the conventional bond, so that on average it all balances out (to give same discounted mean term)?

sorry didn't read your question properly (should remember not to do that in an exam!)

My answer is similar to the one above, but seeing that I've typed it up I'll put it here anyway

I think the answer is

Discounted mean term = sum(from 1 to t) (PV of coupon(i)t(i)) / Price of the bond

where t(i() = remaining term to maturity date.

Assume the interest rate used is exactly the same.

Therefore, if there's a conventional bond than PV of coupon will decrease as t reduces. but more weight are put towards the early duration i.e. when t is large.

For index linked bond PV of coupon will decrease in a lesser rate as t reduces because of the index linked property - coupon value increases yearly.

Therefore the discount mean term is higher for index linked bond as more weight are put towards the early coupon payment and less weight towards the later coupon payment.

 

[PittaPan]

thanks

Thanks for your explanations pig and didster. Crystal clear now.