Relationship between Coupon Rate and Interest Rate Risk

[e2lcfa]

Study Session 15 – Reading 61 says:
“a zero-coupon bond has more interest rate risk than a coupon bond of the same maturity”. I have also read that a lower coupon is less interest rate risk than a higher coupon bond. Can someone explain to me what the logic behind this is? Thanks.
Also, page 34 of Reading 61 in Schweser says investment grade bonds are are below BBB. Maybe this has already been pointed out, but igrade bonds are below BBB- not BBB.

 

[billy22g]

A zero coupon bond has more interest rate risk because as the bond moves closer to maturity from inception, the duration becomes longer than that of a coupon bond (same maturity) with some of the repayment already having been received. The coupon bond has progressively greater re-investment risk that replaces the interest rate risk as the coupon payments are made.

 

[gauri]

e2lcfa Wrote:
——————————————————-
> Study Session 15 – Reading 61 says:
>
> “a zero-coupon bond has more interest rate risk
> than a coupon bond of the same maturity”. I have
> also read that a lower coupon is less interest
> rate risk than a higher coupon bond. Can someone
> explain to me what the logic behind this is?
> Thanks.
where did you read a lower coupon => less interest rate risk?
this is wrong, the lower the coupon rate the greater the interest rate risk! Once you get that clear, you will get an answer to your question urself.

 

[imranmir1]

BTW, what is the “yield” on the yield curve? It is the annuallised interest rate, right?

 

[imranmir1]

well, for the benefit of all, heres how you get the Yeild on the Yield curve:
The Treasury uses complex mathematical modeling to calculate the specific yields based on arithmetic averages of the trading prices for the most recently issued securities. Based on the precise values the Treasury calculates and reports on a daily basis, it’s easy to visualize the current yield curve or even draw its basic shape on your own.
source: http://www.pathtoinvesting.org/invchoices/bonds/yieldcrv/ic_yieldcrv_021...

 

[billy22g]

gauri Wrote:
——————————————————-
> e2lcfa Wrote:
> ————————————————–
> —–
> > Study Session 15 – Reading 61 says:
> >
> > “a zero-coupon bond has more interest rate risk
> > than a coupon bond of the same maturity”. I
> have
> > also read that a lower coupon is less interest
> > rate risk than a higher coupon bond. Can
> someone
> > explain to me what the logic behind this is?
> > Thanks.
>
>
> where did you read a lower coupon => less interest
> rate risk?
> this is wrong, the lower the coupon rate the
> greater the interest rate risk! Once you get that
> clear, you will get an answer to your question
> urself.
Why is this? I get that lower coupon = more interest rate risk, but I don’t understand why. Shouldn’t the same percentage change in yields give a proportional change in price?

 

[sbmarti2]

Think of it this way. if your coupon is 2%, than a 1% change is 1/2= 50% overall change.
If you have a 10% coupon, then a 1% change is 1/10= 10% overall change.
Obviously the prices of the bonds won’t change by 10 and 50%, but you see the general idea. A 1% change in yield is proportionately larger at 2% than 10%, so the larger coupon bond’s price can absorb a 1% rate change much easier than the 2% bond.

 

[nalzaki]

i havent reached fixed income yet but wat i do remember from a class in university… zero coupon bonds have the highest interest rate risk. compared to a coupon bond with the same maturity, zero coupon bond will have the higher duration ( which equals the bonds maturity, but decreases as the bond gets closer to its maturity i.e. 5 yr zero coupon would have a duration=5). higher duration means any fluctuations in interest rates would impact prices more (upward or downward) the formula proves that higher coupons will result in lower durations and vice versa. again i still havent gone over fixed income, so i could be wrong, can anyone confirm?!

 

[sbmarti2]

nalzaki Wrote:
——————————————————-
> i havent reached fixed income yet but wat i do
> remember from a class in university… zero coupon
> bonds have the highest interest rate risk.
> compared to a coupon bond with the same maturity,
> zero coupon bond will have the higher duration (
> which equals the bonds maturity, but decreases as
> the bond gets closer to its maturity i.e. 5 yr
> zero coupon would have a duration=5). higher
> duration means any fluctuations in interest rates
> would impact prices more (upward or downward) the
> formula proves that higher coupons will result in
> lower durations and vice versa. again i still
> havent gone over fixed income, so i could be
> wrong, can anyone confirm?!
you are correct.

 

[e2lcfa]

Thanks all!
Billy22g – thanks much for your explanation. Sbmarti2 – your explanation was really helpful too!
I meant to say “lower coupon = more interest rate risk”, didn’t understand why, but I think I am beginning to get the concept now.