Why is Maturity effect not likely to hold for a low-coupon bond trading at a discount to par?
Maturity effect = longer bond has higher duration.
As the discount to par increases (price of the bond is falling), the YTM increases. As YTM increases, the discount rate increases by definition.
A low coupon bond would usually have a large proportion of its duration allocated to the principal payment, but if we increase the discount rate, the weight of the principal in the duration calculation decreases.
I would modify your statement to say the likelihood of the maturity effect holding for a low coupon bond trading at discount to par will decrease as the discount increases. So a 5% 2020 bond trading at 80 will less likely be affected by maturity effect than the same bond trading at 99.
Hope that helps?
yea it does… thanks…
can you please elaborate the explanation for the same, that is why there is an exception to the maturity effect for Lower - coupon bonds ?
Understand how maturity effect is derived
Basically, the maturity effect is saying, LM should have a larger duration.
And it makes sense (generally) because. duration is the time-weighted sum of CF’s PV, so the higher a single PMT’s PV, the more strength it has to drag duration towards it.
Now looking at a bullet bond, because face value is way higher than its coupons. The final pmt of par should have more weight in deciding how much duration is. And Since the final pmt of par is paid at the end, the longer the maturity of a bullet bond, the higher the duration it should have.
But why doesn’t this rule apply to a low coupon LM bond?
Because it is the PV of CF that decides how much weight it has, you need to not only consider
- how large the undiscounted CF is, but also
- how much is the CF discounted
The problem with LM low coupon bond is that the final payment of par (which should have held most of the weight in all CF’s PV) is discounted so deeply that it does not have the power to drag duration towards it anymore. On the other hand, first few CF has the same PV as before, but they have more weight comparing to the PV of final par pmt (comparing to before). Overall, the CF at the end loses their weight while CF at the beginning increases their weight, causing the duration be smaller.
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really makes sense!